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Title: On the Philosophy of Discovery, Chapters Historical and Critical

Author: William Whewell

Release date: March 25, 2016 [eBook #51555]

Language: English

Credits: Produced by Sonya Schermann, Les Galloway and the Online
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Produced by Sonya Schermann, Les Galloway and the Online
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                                ON THE

                              PHILOSOPHY

                                  OF

                              DISCOVERY.




                              Cambridge:

                      PRINTED BY C. J. CLAY, M.A.

                       AT THE UNIVERSITY PRESS.




                                ON THE

                       PHILOSOPHY OF DISCOVERY,

                   CHAPTERS HISTORICAL AND CRITICAL;

                                  BY

                         WILLIAM WHEWELL, D.D.

               MASTER OF TRINITY COLLEGE, CAMBRIDGE, AND
           CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE.

             INCLUDING THE COMPLETION OF THE THIRD EDITION
             OF THE PHILOSOPHY OF THE INDUCTIVE SCIENCES.

                            [Illustration: Hand passing torch to hand]

                 ΛΑΜΠΑΔΙΑ ΕΧΟΝΤΕΣ ΔΙΑΔΩΣΟΥΣΙΝ ΑΛΛΗΛΟΙΣ

                                LONDON:

                 JOHN W. PARKER AND SON, WEST STRAND.

                                 1860.




The following are the latest editions of the series of works which has
been published connected with the present subject:

  _History of the Inductive Sciences_, 3 Vols. 1857.
  _History of Scientific Ideas_, 2 Vols. 1858.
  _Novum Organon Renovatum_, 1 Vol. 1858.
  _On the Philosophy of Discovery_, 1 Vol. 1860.

To the _History of the Inductive Sciences_ are appended two Indexes (in
Vol. 1.), an Index of Proper Names, and an Index of Technical Terms.
These Indexes, and the Tables of Contents of the other works, will
enable the reader to refer to any person or event included in this
series.




PREFACE


The two works which I entitled _The History of the Inductive Sciences_,
and _The Philosophy of the Inductive Sciences_, were intended to
present to the reader a view of the steps by which those portions of
human knowledge which are held to be most certain and stable have
been acquired, and of the philosophical principles which are involved
in those steps. Each of these steps was a scientific _Discovery_, in
which a _new_ conception was applied in order to bind together observed
facts. And though the conjunction of the observed facts was in each
case an example of logical _Induction_, it was not the inductive
process merely, but the _novelty_ of the result in each case which gave
its peculiar character to the History; and the Philosophy at which
I aimed was not the Philosophy of Induction, but the _Philosophy of
Discovery_. In the present edition I have described this as my object
in my Title.

A great part of the present volume consists of chapters which composed
the twelfth Book of the Philosophy in former editions, which Book was
then described as a 'Review of Opinions on the nature of Knowledge
and the Method of seeking it.' I have added to this part several new
chapters, on Plato, Aristotle, the Arabian Philosophers, Francis Bacon,
Mr. Mill, Mr. Mansel, the late Sir William Hamilton, and the German
philosophers Kant, Fichte, Schelling and Hegel. I might, if time had
allowed, have added a new chapter on Roger Bacon, founded on his _Opus
Minus_ and other works, recently published for the first time under the
direction of the Master of the Rolls; a valuable contribution to the
history of philosophy. But the review of this work would not materially
alter the estimate of Roger Bacon which I had derived from the _Opus
Majus_.

But besides these historical and critical surveys of the philosophy of
others, I have ventured to introduce some new views of my own; namely,
views which bear upon the philosophy of religion. I have done so under
the conviction that no philosophy of the universe can satisfy the minds
of thoughtful men which does not deal with such questions as inevitably
force themselves on our notice, respecting the Author and the Object
of the universe; and also under the conviction that every philosophy
of the universe which has any consistency must suggest answers, at
least conjectural, to such questions. No _Cosmos_ is complete from
which the question of Deity is excluded; and all Cosmology has a side
turned towards Theology. Though I am aware therefore how easy it is, on
this subject, to give offence and to incur obloquy, I have not thought
it right to abstain from following out my philosophical principles
to their results in this department of speculation. The results do
not differ materially from those at which many pious and thoughtful
speculators have arrived in previous ages of the world; though they
have here, as seems to me, something of novelty in their connection
with the philosophy of science. But this point I willingly leave to the
calm decision of competent judges.

I have added in an Appendix various Essays, previously published at
different times, which may serve perhaps to illustrate some points of
the history and philosophy of science.

  TRINITY LODGE,

  _February 8, 1856_.




                                  ON

                     THE PHILOSOPHY OF DISCOVERY.




CONTENTS.

 The chapters marked thus * appear now for the first time.

 The chapters marked thus † have appeared in other works.


  CHAP. I. INTRODUCTION.

  CHAP. II. PLATO.

  CHAP. III. * ADDITIONAL REMARKS ON PLATO.
            1. The Doctrine of Ideas.
            2. The Doctrine of the One and Many.
            3. The notion of the nature and aim of Science.
            4. The Survey of existing Sciences.
            5. The Constitution of the human Mind.

  CHAP. IV. ARISTOTLE.

  CHAP. V. * ADDITIONAL REMARKS ON ARISTOTLE.
            1. Induction.
            2. Invention.
            3. The One in the Many.
            4. The "Five Words."
            5. Aristotle's contribution to the Physical Sciences.
            6. Aristotle's Astronomy.
            7. Aristotle on Classification.
            8. F. Bacon on Aristotle.
            9. Discovery of Causes.
           10. Plato and Aristotle.
           11. Aristotle against Plato's _Ideas_.

  CHAP. VI. THE LATER GREEKS.

  CHAP. VII. THE ROMANS.

  CHAP. VIII. * ARABIAN PHILOSOPHERS.

  CHAP. IX. THE SCHOOLMEN OF THE MIDDLE AGES.

  CHAP. X. THE INNOVATORS OF THE MIDDLE AGES.
             Raymond Lully.

  CHAP. XI. THE INNOVATORS OF THE MIDDLE AGES--_continued_.
             Roger Bacon.

  CHAP. XII. THE REVIVAL OF PLATONISM.
             1. Causes of Delay in the Advance of Knowledge.
             2. Causes of Progress.
             3. Hermolaus Barbarus, &c.
             4. Nicolaus Cusanus.
             5. Manilius Ficinus.
             6. Francis Patricius.
             7. Picus, Agrippa, &c.
             8. Paracelsus, Fludd, &c.

  CHAP. XIII. THE THEORETICAL REFORMERS OF SCIENCE.
             1. Bernardinus Telesius.
             2. Thomas Campanella.
             3. Andrew Cæsalpinus.
             4. Giordano Bruno.
             5. Peter Ramus.
             6. The Reformers in General.
             7. Melancthon.

  CHAP. XIV. THE PRACTICAL REFORMERS OF SCIENCE.
             1. Character of the Practical Reformers.
             2. Leonardo da Vinci.
             3. Copernicus.
             4. Fabricius.
             5. Maurolycus.
             6. Benedetti.
             7. Gilbert.
             8. Galileo.
             9. Kepler.
            10. Tycho.

  CHAP. XV. FRANCIS BACON.
             1. (I.) General Remarks.
             2. Common estimate of him.
             3. We consider only Physical Science.
             4. He is placed at the head of the change:
             5. (II.) _He proclaims a New Era_;
             6. (III.) _By a Change of Method_;
             7. Including successive Steps;
             8. Gradually ascending.
             9. (IV.) _He contrasts the Old and the New Method._
            10. (V.) _Has he neglected Ideas?_
            11. No.
            12. Examples of Ideas treated by him.
            13. He has failed in applying his Method;
            14. (VI.) _To the Cause of Heat._
            15. He seeks Causes before Laws.
            16. (VII.) _His Technical Form worthless._
            17. He is confused by words.
            18. His "Instances."
            19. Contain some good Suggestions.
            20. (VIII.) _His "Idols."_
            21. (IX.) _His view of Utility._
            22. (X.) _His Hopefulness._
            23. (XI.) _His Piety._

  CHAP. XVI. * ADDITIONAL REMARKS ON FRANCIS BACON.
             1. Mr. Ellis's views.
             2. Mr. Spedding's views.

  CHAP. XVII. FROM BACON TO NEWTON.
             1. Harvey.
             2. Descartes.
             3. Gassendi.
             4. Actual Progress in Science.
             5. Otto Guericke, &c.
             6. Hooke.
             7. Royal Society.
             8. Bacon's _New Atalantis_.
             9. Cowley.
            10. Barrow.

  CHAP. XVIII. NEWTON.
             1. Animating effect of his Discoveries.
             2. They confirm Bacon's views.
             3. Newton shuns Hypotheses.
             4. His views of Inductive Philosophy.
             5. His "Rules of Philosophizing."
             6. _The First Rule._
             7. What is a "True Cause"?
             8. _Such_ as are real?
             9. Or _those_ which are proved?
            10. Use of the Rule.
            11. Rule otherwise expressed.
            12. _The Second Rule._
            13. What are Events "of the same kind"?
            14. _The Third Rule_:
            15. Not safe.
            16. _The Fourth Rule._
            17. Occult Qualities.
            18. Ridiculed.
            19. Distinction of Laws and Causes.

  CHAP. XIX. LOCKE AND HIS FRENCH FOLLOWERS.
             1. Cause of Locke's popularity.
             2. Sensational School.
             3. His inconsistencies.
             4. Condillac, &c.
             5. Importance of Language.
             6. Ground of this.
             7. The Encyclopedists.
             8. Helvetius.
             9. Value of Arts.
            10. Tendency to Reaction.

  CHAP. XX. THE REACTION AGAINST THE SENSATIONAL SCHOOL.
             1. "Nisi intellectus ipse."
             2. Price's "Review."
             3. Stewart defends Price.
             4. Archbishop Whately.
             5. Laromiguière.
             6. M. Cousin.
             7. M. Ampère.
             8. His Classification of Sciences.
             9. Kant's Reform of Philosophy.
            10. Its Effect in Germany.

  CHAP. XXI. FURTHER ADVANCE OF THE SENSATIONAL SCHOOL.
                M. Auguste Comte.
             1. M. Comte on three States of Science.
             2. M. Comte rejects the Search of Causes.
             3. Causes in Physics.
             4. Causes in other Sciences.
             5. M. Comte's Practical Philosophy.
             6. M. Comte on Hypotheses.
             7. M. Comte's Classification of Sciences.

  CHAP. XXII. † MR. MILL'S LOGIC.
             (I.) What is Induction? §§ 1-14.
            (II.) Induction or Description, §§ 15-23.
           (III.) In Discovery a new Conception is introduced, §§ 24-37.
            (IV.) Mr. Mill's Four Methods of Inquiry, §§ 38-40.
             (V.) His Examples, §§ 41-48.
            (VI.) Mr. Mill against Hypotheses, §§ 49, 50.
           (VII.) Against prediction of Facts, §§ 51-53.
          (VIII.) Newton's Vera Causa, §§ 54, 55.
            (IX.) Successive Generalizations, §§ 56-62.
             (X.) Mr. Mill's Hope from Deductions, §§ 63-67.
            (XI.) Fundamental opposition of our Doctrines, §§ 68-71.
           (XII.) Absurdities in Mr. Mill's Logic, §§ 72-74.

  CHAP. XXIII. * POLITICAL ECONOMY AS AN INDUCTIVE SCIENCE.
             1. Moral Sciences.
             2. Political Economy.
             3. Wages, Profits, and Rents.
             4. Premature Generalizations.
             5. Correction of these by Induction--Rent.
             6.     "      Wages.
             7.     "      Population.

  CHAP. XXIV. † MODERN GERMAN PHILOSOPHY.
            (I.) Science is the Idealization of Facts, §§ 1-8.
           (II.) Successive German Philosophies.
                 Kant, Fichte, Schelling, Hegel, §§ 9-16.

  CHAP. XXV. † THE FUNDAMENTAL ANTITHESIS AS IT EXISTS IN THE MORAL WORLD.
                 Moral Progress is the Realization of Ideas.

  CHAP. XXVI. * OF THE "PHILOSOPHY OF THE INFINITE."
                 God is Eternal.

  CHAP. XXVII. * SIR WILLIAM HAMILTON ON INERTIA AND WEIGHT.
             1. Primary and Secondary Qualities.
             2. Meaning of the Distinction.
             3. Sir W. Hamilton adds "Secundo-Primary."
             4. Inertia.
             5. Sir W. Hamilton's arguments and reply.
             6. Gravity.
                Sir W. Hamilton's arguments and reply.

  CHAP. XXVIII. † INFLUENCE OF GERMAN SYSTEMS OF PHILOSOPHY IN BRITAIN.
             1. Stewart on Kant.
             2. Mr. G. H. Lewes on Kant.
           4-6. Mr. Mansel on Kant.
                His objection to our Fundamental Ideas, and Reply.
          7-10. New Axioms are possible.
         11-13. Mr. Mansel's Kantianism.
         14-16. Axioms are not from experience.

  CHAP. XXIX. * NECESSARY TRUTH IS PROGRESSIVE.
             Objections considered.

  CHAP. XXX. * THE THEOLOGICAL BEARING OF THE PHILOSOPHY OF DISCOVERY.
           1-4. How can necessary truths be actual?
          5, 6. Small extent of necessary truth.
             7. How did things come to be as they are?
             8. View of the Theist.
          9-12. Is this Platonism?
            13. Idea of Time.
        14, 15. Ideas of Force and Matter.
            16. Creation of Matter.
            17. Platonic Ideas.
         18-21. Idea of Kind.
            22. Idea of Substance.
            23. Idea of Final Cause.
        24, 25. Human immeasurably inferior to Divine.
            26. Science advances towards the Divine Ideas.
            27. Recapitulation.

  CHAP. XXXI. * MAN'S KNOWLEDGE OF GOD.
          1, 2. Opinions.
             3. From Nature we learn something of God.
           4-6. Though but little.
          7, 8. From ourselves we learn something concerning God.
          9-11. Objections answered.
            12. Creation.
            13. End of the World.
            14. Moral and Theological views enter.

  CHAP. XXXII. * ANALOGIES OF PHYSICAL AND RELIGIOUS PHILOSOPHY.
          1, 2. Idealization of Facts and Realization of Ideas;
          3, 4. Both imperfect.
          5, 6. Divine Ideas perfect.
           7-9. Realization of Divine Love.
         10-13. Realization of Divine Justice.
            14. Analogy of Physical and Moral Philosophy.
        15, 16. Supernatural Beginning, Middle, and End indicated.
            17. Suggestion of a Future State.
         18-20. Confirmation from the Intellect of Man.
            21. From the Moral Nature of Man.


  APPENDIX.

                                                   PAGE

  APPEND. A. OF THE PLATONIC THEORY OF IDEAS        403
          B. ON PLATO'S SURVEY OF THE SCIENCES      417
         BB. ON PLATO'S NOTION OF DIALECTIC         429
          C. OF THE INTELLECTUAL POWERS ACCORDING
                 TO PLATO                           440
          D. CRITICISM OF ARISTOTLE'S ACCOUNT OF
                 INDUCTION                          449
          E. ON THE FUNDAMENTAL ANTITHESIS OF
                 PHILOSOPHY                         462
          F. REMARKS ON A REVIEW OF THE PHILOSOPHY
                 OF THE INDUCTIVE SCIENCES          482
          G. ON THE TRANSFORMATION OF HYPOTHESES
                 IN THE HISTORY OF SCIENCE          492
          H. ON HEGEL'S CRITICISM OF NEWTON'S
                 PRINCIPIA                          504
               Appendix to the Memoir on Hegel's Criticism
                 of Newton's Principia              513
          K. DEMONSTRATION THAT ALL MATTER IS
                 HEAVY                              522




                                ON THE
                              PHILOSOPHY
                                  OF
                              DISCOVERY.


    Wär' nicht das Auge sonnenhaft
    Wie könnten wir das Licht erblicken?
    Lebt' nicht in uns des Gottes eigne Kraft
    Wie könnte uns das Göttliche entzücken?
                                       GOETHE.

    Were nothing sunlike in the Eye
    How could we Light itself descry?
    Were nothing godlike in the Mind
    How could we God in Nature find?


CHAPTER I.

INTRODUCTION.


By the examination of the elements of human thought in which I have
been engaged, and by a consideration of the history of the most clear
and certain parts of our knowledge, I have been led to doctrines
respecting the progress of that exact and systematic knowledge which
we call Science; and these doctrines I have endeavoured to lay before
the reader in the History of the Sciences and of Scientific Ideas. The
questions on which I have thus ventured to pronounce have had a strong
interest for man from the earliest period of his intellectual progress,
and have been the subjects of lively discussion and bold speculation in
every age. I conceive that in the doctrines to which these researches
have conducted us, we have a far better hope that we possess a body of
permanent truths than the earlier essays on the same subjects could
furnish. For we have not taken our examples of knowledge at hazard,
as earlier speculators did, and were almost compelled to do; but have
drawn our materials from the vast store of unquestioned truths which
modern science offers to us: and we have formed our judgment concerning
the nature and progress of knowledge by considering what such science
is, and how it has reached its present condition. But though we have
thus pursued our speculations concerning knowledge with advantages
which earlier writers did not possess, it is still both interesting
and instructive for us to regard the opinions upon this subject which
have been delivered by the philosophers of past times. It is especially
interesting to see some of the truths which we have endeavoured to
expound, gradually dawning in men's minds, and assuming the clear
and permanent form in which we can now contemplate them. I shall
therefore, in the ensuing chapters, pass in review many of the opinions
of the writers of various ages concerning the mode by which man best
acquires the truest knowledge; and I shall endeavour, as we proceed,
to appreciate the real value of such judgments, and their place in the
progress of sound philosophy.

In this estimate of the opinions of others, I shall be guided by
those general doctrines which I have, as I trust, established in the
histories already published. And without attempting here to give any
summary of these doctrines, I may remark that there are two main
principles by which speculations on such subjects in all ages are
connected and related to each other; namely, the opposition of _Ideas_
and _Sensations_, and the distinction of _practical_ and _speculative_
knowledge. The opposition of Ideas and Sensations is exhibited to us
in the antithesis of Theory and Fact, which are necessarily considered
as distinct and of opposite natures, and yet necessarily identical,
and constituting Science by their identity. In like manner, although
practical knowledge is in substance identical with speculative, (for
all knowledge is speculation,) there is a distinction between the two
in their history, and in the subjects by which they are exemplified,
which distinction is quite essential in judging of the philosophical
views of the ancients. The alternatives of identity and diversity,
in these two antitheses,--the successive separation, opposition, and
reunion of principles which thus arise,--have produced, (as they may
easily be imagined capable of doing,) a long and varied series of
systems concerning the nature of knowledge; among which we shall have
to guide our course by the aid of the views already presented.

I am far from undertaking, or wishing, to review the whole series of
opinions which thus come under our notice; and I do not even attempt to
examine all the principal authors who have written on such subjects. I
merely wish to select some of the most considerable forms which, such
opinions have assumed, and to point out in some measure the progress
of truth from age to age. In doing this, I can only endeavour to seize
some of the most prominent features of each time and of each step, and
I must pass rapidly from classical antiquity to those which we have
called the dark ages, and from them to modern times. At each of these
periods the modifications of opinion, and the speculations with which
they were connected, formed a vast and tangled maze, the byways of
which our plan does not allow us to enter. We shall esteem ourselves
but too fortunate, if we can discover the single track by which ancient
led to modern philosophy.

I must also repeat that my survey of philosophical writers is here
confined to this one point,--their opinions on the nature of knowledge
and the method of science. I with some effort avoid entering upon other
parts of the philosophy of those authors of whom I speak; I knowingly
pass by those portions of their speculations which are in many cases
the most interesting and celebrated;--their opinions concerning the
human soul, the Divine Governor of the world, the foundations or
leading doctrines of politics, religion, and general philosophy. I
am desirous that my reader should bear this in mind, since he must
otherwise be offended with the scanty and partial view which I give in
this place of the philosophers whom I enumerate.




CHAPTER II.

PLATO.


There would be small advantage in beginning our examination earlier
than the period of the Socratic School at Athens; for although the
spirit of inquiry on such subjects had awakened in Greece at an earlier
period, and although the peculiar aptitude of the Grecian mind for
such researches had shown itself repeatedly in subtle distinctions
and acute reasonings, all the positive results of these early efforts
were contained in a more definite form in the reasonings of the
Platonic age. Before that time, the Greeks did not possess plain and
familiar examples of exact knowledge, such as the truths of Arithmetic,
Geometry, Astronomy and Optics became in the school of Plato; nor
were the antitheses of which we spoke above, so distinctly and fully
unfolded as we find them in Plato's works.

The question which hinges upon one of these antitheses, occupies
a prominent place in several of the Platonic dialogues; namely,
whether our knowledge be obtained by means of Sensation or of Ideas.
One of the doctrines which Plato most earnestly inculcated upon his
countrymen was, that we do not _know_ concerning sensible objects, but
concerning ideas. The first attempts of the Greeks at metaphysical
analysis had given rise to a school which maintained that material
objects are the only realities. In opposition to this, arose another
school, which taught that material objects have no permanent reality,
but are ever waxing and waning, constantly changing their substance.
"And hence," as Aristotle says[1], "arose the doctrine of ideas which
the Platonists held. For they assented to the opinion of Heraclitus,
that all sensible objects are in a constant state of flux. So that if
there is to be any knowledge and science, it must be concerning some
permanent natures, different from the sensible natures of objects;
for there can be no permanent science respecting that which is
perpetually changing. It happened that Socrates turned his speculations
to the moral virtues, and was the first philosopher who endeavoured
to give universal definitions of such matters. He wished to reason
systematically, and therefore he tried to establish definitions, for
definitions are the basis of systematic reasoning. There are two things
which may justly be looked upon as steps in philosophy due to Socrates;
inductive reasonings, and universal definitions;--both of them steps
which belong to the foundations of science. Socrates, however, did not
make universals, or definitions separable from the objects; but his
followers separated them, and these essences they termed _Ideas_." And
the same account is given by other writers[2]. "Some existences are
sensible, some intelligible: and according to Plato, if we wish to
understand the principles of things, we must first separate the _ideas_
from the _things_, such as the ideas of Similarity, Unity, Number,
Magnitude, Position, Motion: second, that we must assume an absolute
Fair, Good, Just, and the like: third, that we must consider the ideas
of relation, as Knowledge, Power: recollecting that the Things which
we perceive have this or that appellation applied to them because
they partake of this or that Idea; those things being _just_ which
participate in the idea of The Just, those being _beautiful_, which
contain the idea of The Beautiful." And many of the arguments by which
this doctrine was maintained are to be found in the Platonic dialogues.
Thus the opinion that true knowledge consists in sensation, which had
been asserted by Protagoras and others, is refuted in the _Theætetus_:
and, we may add, so victoriously refuted, that the arguments there
put forth have ever since exercised a strong influence upon the
speculative world. It may be remarked that in the minds of Plato and
of those who have since pursued the same paths of speculation, the
interest of such discussions as those we are now referring to, was by
no means limited to their bearing upon mere theory; but was closely
connected with those great questions of morals which have always a
practical import. Those who asserted that the only foundation of
knowledge was sensation, asserted also that the only foundation of
virtue was the desire of pleasure. And in Plato, the metaphysical
part of the disquisitions concerning knowledge in general, though
independent in its principles, always seems to be subordinate in its
purpose to the questions concerning the knowledge of our duty.

Since Plato thus looked upon the Ideas which were involved in each
department of knowledge as forming its only essential part, it was
natural that he should look upon the study of Ideas as the true mode
of pursuing knowledge. This he himself describes in the _Philebus_[3].
"The best way of arriving at truth is not very difficult to point out,
but most hard to pursue. All the arts which have ever been discovered,
were revealed in this manner. It is a gift of the gods to man, which,
as I conceive, they sent down by some Prometheus, as by Prometheus
they gave us the light of fire; and the ancients, more clear-sighted
than we, and less removed from the gods, handed down this traditionary
doctrine: that whatever is said to be, comes of One and of Many, and
comprehends in itself the Finite and the Infinite in coalition
(being One Kind, and consisting of Infinite Individuals). And this
being the state of things, we must, in each case, endeavour to seize
the One Idea (the idea of the Kind) as the chief point; for we shall
find that it is there. And when we have seized this one thing, we may
then consider how it comprehends in itself two, or three, or any other
number; and, again, examine each of these ramifications separately;
till at last we perceive, not only that One is at the same time One
and Many, but also _how many_. And when we have thus filled up the
interval between the Infinite and the One, we may consider that we
have done with each one. The gods then, as I have said, taught us by
tradition thus to contemplate, and to learn, and to teach one another.
But the philosophers of the present day seize upon the One, at hazard,
too soon or too late, and then immediately snatch at the Infinite; but
the intermediate steps escape them, in which resides the distinction
between a truly logical and a mere disputatious discussion."

It would seem that what the author here describes as the most perfect
form of exposition, is that which refers each object to its place in
a classification containing a complete series of subordinations, and
which gives a definition of each class. We have repeatedly remarked
that, in sciences of classification, each new definition which gives a
tenable and distinct separation of classes is an important advance in
our knowledge; but that such definitions are rather the last than the
first step in each advance. In the progress of real knowledge, these
definitions are always the results of a laborious study of individual
cases, and are never arrived at by a pure effort of thought, which is
what Plato appears to have imagined as the true mode of philosophizing.
And still less do the advances of other sciences consist in seizing
at once upon the highest generality, and filling in afterwards all
the intermediate steps between that and the special instances. On the
contrary, as we have seen, the ascents from particular to general are
all successive; and each step of this ascent requires time, and labour,
and a patient examination of actual facts and objects.

It would, of course, be absurd to blame Plato for having inadequate
views of the nature of progressive knowledge, at the time when
knowledge could hardly be said to have begun its progress. But we
already find in his speculations, as appears in the passages just
quoted from his writings, several points brought into view which will
require our continued attention as we proceed. In overlooking the
necessity of a gradual and successive advance from the less general to
the more general truths, Plato shared in a dimness of vision[4] which
prevailed among philosophers to the time of Francis Bacon. In thinking
too slightly of the study of actual nature, he manifested a bias from
which the human intellect freed itself in the vigorous struggles which
terminated the dark ages. In pointing out that all knowledge implies
a unity of what we observe as manifold, which unity is given by the
mind, Plato taught a lesson which has of late been too obscurely
acknowledged, the recoil by which men repaired their long neglect of
facts having carried them for a while so far as to think that facts
were the whole of our knowledge. And in analysing this principle of
Unity, by which we thus connect sensible things, into various Ideas,
such as Number, Magnitude, Position, Motion, he made a highly important
step, which it has been the business of philosophers in succeeding
times to complete and to follow out.

But the efficacy of Plato's speculations in their bearing upon physical
science, and upon theory in general, was much weakened by the confusion
of practical with theoretical knowledge, which arose from the ethical
propensities of the Socratic school. In the Platonic Dialogues, Art and
Science are constantly spoken of indiscriminately. The skill possessed
by the Painter, the Architect, the Shoemaker, is considered as a just
example of human science, no less than the knowledge which the geometer
or the astronomer possesses of the theoretical truths with which he
is conversant. Not only so; but traditionary and mythological tales,
mystical imaginations and fantastical etymologies, are mixed up, as
no less choice ingredients, with the most acute logical analyses, and
the most exact conduct of metaphysical controversies. There is no
distinction made between the knowledge possessed by the theoretical
psychologist and the physician, the philosophical teacher of morals
and the legislator or the administrator of law. This, indeed, is the
less to be wondered at, since even in our own time the same confusion
is very commonly made by persons not otherwise ignorant or uncultured.

On the other hand, we may remark finally, that Plato's admiration of
Ideas was not a barren imagination, even so far as regarded physical
science. For, as we have seen[5], he had a very important share in
the introduction of the theory of epicycles, having been the first to
propose to astronomers in a distinct form, the problem of which that
theory was the solution; namely, "to explain the celestial phenomena
by the combination of equable circular motions." This demand of an
ideal hypothesis which should exactly express the phenomena (as well
as they could then be observed), and from which, by the interposition
of suitable steps, all special cases might be deduced, falls in well
with those views respecting the proper mode of seeking knowledge
which we have quoted from the _Philebus_. And the Idea which could
thus represent and replace all the particular Facts, being not only
sought but found, we may readily suppose that the philosopher was, by
this event, strongly confirmed in his persuasion that such an Idea
was indeed what the inquirer ought to seek. In this conviction all
his genuine followers up to modern times have participated; and thus,
though they have avoided the error of those who hold that facts alone
are valuable as the elements of our knowledge, they have frequently run
into the opposite error of too much despising and neglecting facts, and
of thinking that the business of the inquirer after truth was only a
profound and constant contemplation of the conceptions of his own mind.
But of this hereafter.

FOOTNOTES:

[Footnote 1: _Metaph._ xii. 4.]

[Footnote 2: Diog. Laert. _Vit. Plat._]

[Footnote 3: T. ii. p. 16, c, d. ed. Bekker, t. v. p. 437.]

[Footnote 4: See the remarks on this phrase in the next chapter.]

[Footnote 5: _Hist. Ind. Sc._ b. iii. c. ii.]




CHAPTER III.

ADDITIONAL REMARKS ON PLATO.


The leading points in Plato's writings which bear upon the philosophy
of discovery are these:

  1. The Doctrine of Ideas.
  2. The Doctrine of the One and the Many.
  3. The notion of the nature and aim of Science.
  4. The survey of existing Sciences.

1. The Doctrine of Ideas is an attempt to solve a problem which in all
ages forces itself upon the notice of thoughtful men; namely, How can
certain and permanent knowledge be possible for man, since all his
knowledge must be derived from transient and fluctuating sensations?
And the answer given by this doctrine is, that certain and permanent
knowledge is _not_ derived from _Sensations_, but from _Ideas_. There
are in the mind certain elements of knowledge which are not derived
from sensation, and are only imperfectly exemplified in sensible
objects; and when we reason concerning sensible things so as to obtain
real knowledge, we do so by considering such things as partaking of
the qualities of the Ideas concerning which there can be truth. The
sciences of Geometry and Arithmetic show that there _are_ truths which
man can know; and the Doctrine of Ideas explains how this is possible.

So far the Doctrine of Ideas answers its primary purpose, and is a
reply (by no means the least intelligible and satisfactory reply) to
a question still agitated among philosophers: What is the ground of
geometrical (and other necessary) truth?

But Plato seems, in many of his writings, to extend this doctrine much
further; and to assume, not only Ideas of Space and its properties,
from which geometrical truths are derived; but of Relations, as the
Relations of Like and Unlike, Greater and Less; and of mere material
objects, as Tables and Chairs. Now to assume Ideas of such things as
these solves no difficulty and is supported by no argument. In this
respect the Ideal theory is of no value in Science.

It is curious that we have a very acute refutation of the Ideal theory
in this sense, not only in Aristotle, the open opponent of Plato on
this subject, but in the Platonic writings themselves: namely, in the
Dialogue entitled _Parmenides_; which, on this and on other accounts, I
consider to be the work not of Plato, but of an opponent of Plato[6].


2. I have spoken, in the preceding chapter, of Plato's doctrine that
truth is to be obtained by discerning the One in the Many. This
expression is used, it would seem, in a somewhat large and fluctuating
way, to mean several things; as for instance, finding the one _kind_ in
many _individuals_ (for instance, the one idea of dog in many dogs);
or the one _law_ in many _phenomena_ (for instance, the eccentrics and
epicycles in many planets). In any interpretation, it is too loose and
indefinite a rule to be of much value in the formation of sciences,
though it has been recently again propounded as important in modern
times.


3. I have said, in the preceding chapter, that Plato, though he saw
that scientific truths of great generality might be obtained and
were to be arrived at by philosophers, overlooked the necessity of a
_gradual_ and _successive_ advance from the less general to the more
general; and I have described this as a 'dimness of vision.' I must now
acknowledge that this is not a very appropriate phrase; for not only
no acuteness of vision could have enabled Plato to see that gradual
generalization in science of which, as yet, no example had appeared;
but it was very fortunate for the progress of truth, at that time, that
Plato had imagined to himself the object of science to be general
and sublime truths which prove themselves to be true by the light of
their own generality and symmetry. It is worth while to illustrate this
notice of Plato by some references to his writings.

In the Sixth Book of the _Republic_, Plato treats of the then existing
sciences as the instruments of a philosophical education. Among the
most conspicuous of these is astronomy. He there ridicules the notion
that astronomy is a sublime science because it makes men look _upward_.
He asserts that the really sublime science is that which makes men look
at the _realities_, which are suggested by the appearances seen in the
heavens: namely, the spheres which revolve and carry the luminaries
in their revolutions. Now it was no doubt the determined search for
such "realities" as these which gave birth to the Greek _Astronomy_,
that first and critical step in the progress of science. Plato, by his
exhortations, if not by his suggestions, contributed effectually, as
I conceive, to this step in science. In the same manner he requires
a science of _Harmonics_ which shall be free from the defects and
inaccuracies which occur in actual instruments. This belief that the
universe was full of mathematical relations, and that these were the
true objects of scientific research, gave a vigour, largeness of mind,
and confidence to the Greek speculators which no more cautious view of
the problem of scientific discovery could have supplied. It was well
that this advanced guard in the army of discoverers was filled with
indomitable courage, boundless hopes, and creative minds.

But we must not forget that this disposition to what Bacon calls
_anticipation_ was full of danger as well as of hope. It led Plato
into error, as it led Kepler afterwards, and many others in all ages
of scientific activity. It led Plato into error, for instance, when it
led him to assert (in the _Timæus_) that the four elements, Earth, Air,
Fire and Water, have, for the forms of their particles respectively,
the Cube, the Icosahedron, the Pyramid, and the Octahedron; and again,
when it led him to despise the practical controversies of the musicians
of his time; which controversies were, in fact, the proof of the
truth of the mathematical theory of Harmonics. And in like manner it
led Kepler into error when it led him to believe that he had found the
reason of the number, size and motion of the planetary orbits in the
application of the five regular solids to the frame of the universe[7].

How far the caution in forming hypotheses which Bacon's writings urge
upon us is more severe than suits the present prospects of science,
we may hereafter consider; but it is plainly very conceivable that
a boldness in the invention and application of hypotheses which was
propitious to science in its infancy, may be one of the greatest
dangers of its more mature period: and further, that the happy effect
of such a temper depended entirely upon the candour, skill and labour
with which the hypotheses were compared with the observed phenomena.


4. Plato has given a survey of the sciences of his time as Francis
Bacon has of _his_. Indeed Plato has given two such surveys: one,
in the _Republic_, in reviewing, as I have said, the elements of a
philosophical education; the other in the _Timæus_, as the portions
of a theological view of the universe--such as has been called a
_Theodicæa_, a justification of God. In the former passage of Plato,
the sciences enumerated are Arithmetic, Plane Geometry, Solid Geometry,
Astronomy and Harmonics[8]. In the _Timæus_ we have a further notice
of many other subjects, in a way which is intended, I conceive, to
include such knowledge as Plato had then arrived at on the various
parts of the universe. The subjects there referred to are, as I have
elsewhere stated[9], these: light and heat, water, ice, gold, gems,
rust and other natural objects:--odours, taste, hearing, lights,
colour, and the powers of sense in general:--the parts and organs of
the body, as the bones, the marrow, the brain, flesh, muscles, tendons,
ligaments and nerves; the skin, the hair, the nails; the veins and
arteries; respiration; generation; and in short, every obvious point
of physiology. But the opinions thus delivered in the _Timæus_ on the
latter subject have little to do with the progress of real knowledge.
The doctrines, on the other hand, which depend upon geometrical and
arithmetical relations are portions or preludes of the sciences which
the fulness of time brought forth.


5. I may, as further bearing upon the Platonic notion of science,
notice Plato's view of the constitution of the human mind. According
to him the Ideas which are the constituents of science form an
Intelligible World, while the visible and tangible things which we
perceive by our senses form the Visible World. In the visible world we
have shadows and reflections of actual objects, and by these shadows
and reflections we may judge of the objects, even when we cannot do
so directly; as when men in a dark cavern judge of external objects
by the shadows which they cast into the cavern. In like manner in the
Intelligible World there are conceptions which are the usual objects of
human thought, and about which we reason; but these are only shadows
and reflections of the Ideas which are the real sources of truth.
And the Reasoning Faculty, the Discursive Reason, the _Logos_, which
thus deals with conceptions, is subordinate to the Intuitive Faculty,
the Intuitive Reason, the _Nous_, which apprehends Ideas[10]. This
recognition of a Faculty in man which contemplates the foundations--the
_Fundamental Ideas_--of science, and by apprehending such Ideas, makes
science possible, is consentaneous to the philosophy which I have
all along presented, as the view taught us by a careful study of the
history and nature of science. That new Fundamental Ideas are unfolded,
and the Intuitive Faculty developed and enlarged by the progress of
science and by an intimate acquaintance with its reasonings, Plato
appears to have discerned in some measure, though dimly. And this is
the less wonderful, inasmuch as this gradual and successive extension
of the field of Intuitive Truth, in proportion as we become familiar
with a larger amount of derived truth, is even now accepted by few,
though proved by the reasonings of the greatest scientific discoverers
in every age.

The leading defect in Plato's view of the nature of real science is his
not seeing fully the extent to which experience and observation are the
basis of all our knowledge of the universe. He considers the luminaries
which appear in the heavens to be not the true objects of astronomy,
but only some imperfect adumbration of them;--mere diagrams which may
assist us in the study of a higher truth, as beautiful diagrams might
illustrate the truths of geometry, but would not prove them. This
notion of an astronomy which is an astronomy of Theories and not of
Facts, is not tenable, for Theories _are_ Facts. Theories and Facts
are equally _real_; true Theories are Facts, and Facts are familiar
Theories. But when Plato says that astronomy is a series of problems
suggested by visible things, he uses expressions quite conformable
to the true philosophy of science; and the like is true of all other
sciences.

FOOTNOTES:

[Footnote 6: This matter is further discussed in the Appendix, Essay A.]

[Footnote 7: These matters are further discussed in the Appendix, Essay
B.]

[Footnote 8: See Appendix, Essay B.]

[Footnote 9: _Hist. Ind. Sc._ b. ii. Additions to 3rd Ed.]

[Footnote 10: See these views further discussed in the Appendix, Essay
C.]




CHAPTER IV.

ARISTOTLE.


The views of Aristotle with regard to the foundations of human
knowledge are very different from those of his tutor Plato, and are
even by himself put in opposition to them. He dissents altogether
from the Platonic doctrine that Ideas are the true materials of our
knowledge; and after giving, respecting the origin of this doctrine,
the account which we quoted in the last chapter, he goes on to reason
against it. "Thus," he says[11], "they devised Ideas of all things
which are spoken of as universals: much as if any one having to count a
number of objects, should think that he could not do it while they were
few, and should expect to count them by making them more numerous. For
the kinds of things are almost more numerous than the special sensible
objects, by seeking the causes of which they were led to their Ideas."
He then goes on to urge several other reasons against the assumption of
Ideas and the use of them in philosophical researches.

Aristotle himself establishes his doctrines by trains of reasoning. But
reasoning must proceed from certain First Principles; and the question
then arises, Whence are these First Principles obtained? To this he
replies, that they are the result of _Experience_, and he even employs
the same technical expression by which we at this day describe the
process of collecting these principles from observed facts;--that they
are obtained by _Induction_. I have already quoted passages in which
this statement is made[12]. "The way of reasoning," he says[13], "is
the same in philosophy, and in any art or science: we must collect
the _facts_ (τὰ ὑπὰρχοντα), and the things to which the facts happen,
and must have as large a supply of these as possible, and then we must
examine them according to the terms of our syllogisms." ... "There are
peculiar principles in each science; and in each case these principles
must be obtained from _experience_. Thus astronomical observation
supplies the principles of astronomical science. For the phenomena
being rightly taken, the demonstrations of astronomy were discovered;
and the same is the case with any other Art or Science. So that if
the facts in each case be taken, it is our business to construct the
demonstrations. For if _in our natural history_ (κατὰ τὰν ἱστορί αν)
we have omitted none of the facts and properties which belong to the
subject, we shall learn what we can demonstrate and what we cannot."
And again[14], "It is manifest that if any sensation be wanting, there
must be some knowledge wanting, which we are thus prevented from
having. For we acquire knowledge either _by Induction_ (ἐπαγωγῆ) or
by Demonstration: and Demonstration is from universals, but Induction
from particulars. It is impossible to have universal theoretical
propositions except by Induction: and we cannot make inductions without
having sensation; for sensation has to do with particulars."

It is easy to show that Aristotle uses the term _Induction_, as we use
it, to express the process of collecting a general proposition from
particular cases in which it is exemplified. Thus in a passage which
we have already quoted[15], he says, "Induction, and Syllogism from
Induction, is when we attribute one extreme term to the middle by means
of the other." The import of this technical phraseology will further
appear by the example which he gives: "We find that several animals
which are deficient in bile are long-lived, as man, the horse, the
mule; hence we infer that _all_ animals which are deficient in bile are
long-lived."

We may observe, however, that both Aristotle's notion of induction,
and many other parts of his philosophy, are obscure and imperfect, in
consequence of his refusing to contemplate ideas as something distinct
from sensation. It thus happens that he always assumes the ideas
which enter into his proposition as _given_; and considers it as the
philosopher's business to determine whether such propositions are true
or not: whereas the most important feature in induction is, as we have
said, the _introduction_ of a new idea, and not its employment when
once introduced. That the mind in this manner gives unity to that which
is manifold,--that we are thus led to speculative principles which have
an evidence higher than any others,--and that a peculiar sagacity in
some men seizes upon the conceptions by which the facts may be bound
into true propositions,--are doctrines which form no essential part
of the philosophy of the Stagirite, although such views are sometimes
recognized, more or less clearly, in his expressions. Thus he says[16],
"There can be no knowledge when the sensation does not continue in
the mind. For this purpose, it is necessary both to perceive, and to
have some _unity_ in the mind (αἰσθανομένοις εχειν ἔν τι[17] ἐν τῇ
ψυχῇ); and many such perceptions having taken place, some difference
is then perceived: and from the remembrance of these arises Reason.
Thus from Sensation comes Memory, and from Memory of the same thing
often repeated comes Experience: for many acts of Memory make up one
Experience. And from Experience, or from any Universal Notion which
takes a permanent place in the mind,--from the _unity in the manifold_,
the same some one thing being found in many facts,--springs the first
principle of Art and of Science; of Art, if it be employed about
production; of Science, if about existence."

I will add to this, Aristotle's notice of _Sagacity_; since, although
little or no further reference is made to this quality in his
philosophy, the passage fixes our attention upon an important step in
the formation of knowledge. "Sagacity" (ἀγχίνοια), he says[18], "is a
hitting by guess (εὐστοχία τις) upon the middle term (the conception
common to two cases) in an inappreciable time. As for example, if any
one seeing that the bright side of the moon is always towards the sun,
suddenly perceives why this is; namely, because the moon shines by the
light of the sun:--or if he sees a person talking with a rich man, he
guesses that he is borrowing money;--or conjectures that two persons
are friends, because they are enemies of the same person."--To consider
only the first of these examples;--the conception here introduced,
that of a body shining by the light which another casts upon it, is
not contained in the observed facts, but introduced by the mind. It
is, in short, that conception which, in the act of induction, the mind
superadds to the phenomena as they are presented by the senses: and to
invent such appropriate conceptions, such "eustochies," is, indeed, the
precise office of inductive sagacity.

At the end of this work (the _Later Analytics_) Aristotle ascribes
our knowledge of principles to Intellect (νοῦς), or, as it appears
necessary to translate the word, _Intuition_[19]. "Since, of our
intellectual habits by which we aim at truth, some are always true, but
some admit of being false, as Opinion and Reasoning, but Science and
Intuition are always true; and since there is nothing which is more
certain than Science except Intuition; and since Principles are better
known to us than the Deductions from them; and since all Science is
connected by reasoning, we cannot have Science respecting Principles.
Considering this then, and that the beginning of Demonstration cannot
be Demonstration, nor the beginning of Science, Science; and since, as
we have said, there is no other kind of truth, Intuition must be the
beginning of Science."

What is here said, is, no doubt, in accordance with the doctrines which
we have endeavoured to establish respecting the nature of Science,
if by this _Intuition_ we understand that contemplation of certain
Fundamental Ideas, which is the basis of all rigorous knowledge. But
notwithstanding this apparent approximation, Aristotle was far from
having an habitual and practical possession of the principles which he
thus touches upon. He did not, in reality, construct his philosophy by
giving Unity to that which was manifold, or by seeking in Intuition
principles which might be the basis of Demonstration; nor did he
collect, in each subject, fundamental propositions by an induction
of particulars. He rather endeavoured to divide than to unite; he
employed himself, not in combining facts, but in analysing notions;
and the criterion to which he referred his analysis was, not the facts
of our experience, but our habits of language. Thus his opinions
rested, not upon sound inductions, gathered in each case from the
phenomena by means of appropriate Ideas; but upon the loose and vague
generalizations which are implied in the common use of speech.

Yet Aristotle was so far consistent with his own doctrine of the
derivation of knowledge from experience, that he made in almost
every province of human knowledge, a vast collection of such special
facts as the experience of his time supplied. These collections are
almost unrivalled, even to the present day, especially in Natural
History; in other departments, when to the facts we must add the right
Inductive Idea, in order to obtain truth, we find little of value
in the Aristotelic works. But in those parts which refer to Natural
History, we find not only an immense and varied collection of facts and
observations, but a sagacity and acuteness in classification which it
is impossible not to admire. This indeed appears to have been the most
eminent faculty in Aristotle's mind.

The influence of Aristotle in succeeding ages will come under our
notice shortly.


FOOTNOTES:

[Footnote 11: _Metaph._ xii. 4.]

[Footnote 12: _Hist. Ind. Sc._ b. i. c. iii. sect. 2.]

[Footnote 13: _Analyt. Prior._ i. 30.]

[Footnote 14: _Analyt. Post._ i. 18.]

[Footnote 15: _Analyt. Prior._ ii. 23, περὶ τῆς ἐπαγωγῆς.]

[Footnote 16: _Analyt. Post._ ii. 19.]

[Footnote 17: But the best reading seems to be not ἔν τι but ἔτι:
and the clause must be rendered "both to perceive and to retain the
perception in the mind." This correction does not disturb the general
sense of the passage, that the first principles of science are obtained
by finding the One in the Many.]

[Footnote 18: _Analyt. Post._ i. 34.]

[Footnote 19: _Ibid._ ii. 19.]




CHAPTER V.

ADDITIONAL REMARKS ON ARISTOTLE.


1. One of the most conspicuous points in Aristotle's doctrines as
bearing upon the philosophy of Science is his account of that mode of
attaining truth which is called _Induction_; for we are accustomed
to consider Induction as the process by which our Sciences have been
formed; and we call them collectively the _Inductive Sciences_.
Aristotle often speaks of Induction, as for instance, when he says that
Socrates introduced the frequent use of it. But the cardinal passage
on this subject is in his _Analytics_, in which he compares Syllogism
and Induction as two modes of drawing conclusions[20]. He there says
that all belief arises either from Syllogism or from Induction: and
adds that Induction is, when by means of one extreme term we infer
the other extreme to be true of the middle term. The example which
he gives is this: knowing that particular animals are long-lived, as
elephant, horse, mule; and finding that these animals agree in having
no gall-bladder; we infer, by _Induction_, that _all_ animals which
have no gall-bladder are long-lived. This may be done, he says, if the
middle and the second extreme are convertible: as the following formal
statement may show.

  Elephant, horse, mule, &c. are long-lived.
  Elephant, horse, mule, &c. are all gall-less.

If we might convert this proposition, and say

All gall-less animals are as elephant, horse, mule, &c.:

we might infer _syllogistically_ that

All gall-less animals are long-lived.

And though we cannot infer this syllogistically, we infer it by
Induction, when we have a sufficient amount of instances[21].

I have already elsewhere given this account of Induction, as a process
employed in the formation of our knowledge[22]. What I have now to
remark concerning Aristotle is, that it does not appear to have
occurred to him, that in establishing such a proposition as that which
he gives as his instance, the main difficulty is the _discovery_ of
a _middle term_ which will allow us to frame such a proposition as
we need. The zoologist who wanted to know what kind of animals are
long-lived, might guess long before he guessed that the absence of the
gall-bladder supplied the requisite middle term; (if the proposition
were true; which it is not.) And in like manner in other cases, it
is difficult to find a middle term, which enables us to collect a
proposition by Induction. And herein consists the imperfection of his
view of the subject; which considers the main point to be the proof
of the proposition when the conceptions are _given_, whereas the main
point really is, the _discovery_ of conceptions which will make a true
proposition possible.


2. Since the main characteristic of the steps which have occurred in
the formation of the physical sciences, is not merely that they are
propositions collected by Induction, but by the introduction of a _new_
conception; it has been suggested that it is not a characteristic
designation of these Sciences to call them _Inductive Sciences_. Almost
every discovery involves in it the introduction of a new conception,
as the element of a new proposition; and the novelty of the conception
is more characteristic of the stages of discovery than the inductive
application of it. Hence as bearing upon the Philosophy of Discovery,
the statements of Aristotle concerning Induction, though acute and
valuable, are not so valuable as they might seem. Even Francis Bacon,
it has been asserted, erred in the same way (and of course with less
excuse) in asserting Induction, of a certain kind, to be the great
instrument for the promotion of knowledge, and in overlooking the
necessity of the _Invention_ which gives Induction its value.


3. The invention or discovery of a conception by which many facts
of observation are conjoined so as to make them the materials of a
proposition, is called in Plato, as we have seen, _finding the One in
the Many_.

In the passage quoted from the _Later Analytics_, Aristotle uses the
same expression, and speaks very justly respecting the formation of
knowledge. Indeed the _Titles_ of the chapters of this and many parts
of Aristotle's works would lead us to expect just such a Philosophy
of Discovery as is the object of our study at present. Thus we have,
_Anal. Post._ B. II. chap. 13: "How we are to hunt (θηρεύειν) the
predications of a Definition." Chap. 14: "Precepts for the invention
of Problems and of a Middle Term:" and the like. But when we come to
read these chapters, they contain little that is of value, and resolve
themselves mostly into permutations of Aristotle's logical phraseology.


4. The part of the Aristotelian philosophy which has most permanently
retained its place in modern Sciences is a part of which a use has been
made quite different from that which was originally contemplated. The
"Five words" which are explained in the Introduction to Aristotle's
_Categories_: namely, the words _Genus_, _Species_, _Difference_,
_Property_, _Accident_, were introduced mainly that they might be used
in the propositions of which Syllogisms consist, and might thus be the
elements of reasoning. But it has so happened that these words are
rarely used in Sciences of Reasoning, but are abundantly and commonly
used in the Sciences of Classification, as I have explained in
speaking of the Classificatory Sciences[23].


5. Of Aristotle's actual contributions to the Physical Sciences I have
spoken in the History of those Sciences[24]. I have[25] stated that
he conceived the globular form of the earth so clearly and gave so
forcibly the arguments for that doctrine, that we may look upon him as
the most effective teacher of it. Also in the Appendix to that History,
published in the third edition, I have given Aristotle's account of the
Rainbow, as a further example of his industrious accumulation of facts,
and of his liability to error in his facts.


6. We do not find Aristotle so much impressed as we might have expected
by that great monument of Grecian ingenuity, the theory of epicycles
and excentrics which his predecessor Plato urged so strongly upon the
attention of his contemporaries. Aristotle proves, as I have said,
the globular form of the earth by good and sufficient arguments. He
also proves by arguments which seem to him quite conclusive[26], that
the earth is in the center of the universe, and immoveable. As to the
motions of the rest of the planets, he says little. The questions
of their order, and their distances, and the like, belong, he says,
to Astrology[27]. He remarks only that the revolution of the heaven
itself, the outermost revolution, is simple and the quickest of all:
that the revolutions of the others are slower, each moving in a
direction opposite to the heaven in its own circle: and that it is
reasonable that those which are nearest to the first revolution should
take the longest time in describing their own circle, and those that
are furthest off, the least time, and the intermediate ones in the
order of their distances, "as also the mathematicians show."

In the _Metaphysics_[28] he enumerates the circular movements which
had been introduced by the astronomers Eudoxus and Calippus for the
explanation of the phenomena presented by the sun, moon and planets.
These, he says, amount to fifty-five; and this, he says, must be the
number of essences and principles which exist in the universe.


7. In the Sciences of Classification, and especially in the
classification of animals, higher claims have been made for Aristotle,
which I have discussed in the History[29]. I have there attempted to
show that Aristotle's classification, inasmuch as it enumerates all
the parts of animals, may be said to contain the _materials_ of every
subsequent classification: but that it cannot be said to anticipate
any modern system, because the different grades of classification are
not made _subordinate_ to one another as a _system_ of classification
requires. I have the satisfaction of finding Mr. Owen agreeing with me
in these views[30].


8. Francis Bacon's criticism on Aristotle which I have quoted in the
Appendix to the History[31], is severe, and I think evidently the
result of prejudice. He disparages Aristotle in comparison with the
other philosophers of Greece. 'Their systems,' he says, 'had some
savour of experience, and nature, and bodily things; while the Physics
of Aristotle, in general, sound only of Logical Terms.

'Nor let anyone be moved by this: that in his books _Of Animals_,
and in his _Problems_, and in others of his tracts, there is often a
quoting of experiments. For he had made up his mind beforehand; and did
not consult experience in order to make right propositions and axioms,
but when he had settled his system to his will, he twisted experience
round and made her bend to his system.'

I do not think that this can be said with any truth. I know no
instances in which Aristotle has twisted experience round, and made
her bend to his system. In his _Problems_, he is so far from giving
dogmatical solutions of the questions proposed, that in most cases, he
propounds two or three solutions as mere suggestions and conjectures.
And both in his History of Animals, as I have said, and in others of
his works, the want of system gives them an incoherent and tumultuary
character, which even a false system would have advantageously removed;
for, as I have said elsewhere, it is easier to translate a false system
into a true one, than to introduce system into a mass of confusion.


9. It is curious that a fundamental error into which Aristotle fell in
his view of the conditions which determine the formation of Science
is very nearly the same as one of Francis Bacon's leading mistakes.
Aristotle says, that Science consists in knowing the _causes_ of
things, as Bacon aims at acquiring a knowledge of the _forms_ or
_essences_ of things and their qualities. But the history of all the
sciences teaches us that sciences do not begin with such knowledge, and
that in few cases only do they ever attain to it. Sciences begin by a
knowledge of the _laws_ of _phenomena_, and proceed by the discovery
of the scientific ideas by which the phenomena are colligated, as I
have shown in other works[32]. The discovery of causes is not beyond
the human powers, as some have taught. Those who thus speak disregard
the lessons taught by the history of Physical Astronomy, of Geology, of
Physical Optics, Thermotics and other sciences. But the discovery of
causes, and of the essential forms of qualities, is a triumph reserved
for the later stages of each Science, when the knowledge of the laws of
phenomena has already made great progress. It was not to be expected
that Aristotle would discern this truth, when, as yet, there was no
Science extant in which it had been exemplified. Yet in Astronomy, the
theory of epicycles and excentrics had immense value, and even has
still, as representing the laws of phenomena; while the attempt to find
in it, as Aristotle wished to do, the ultimate causes of the motions
of the universe, could only mislead. The Aristotelian maxim, which
sounds so plausible, and has been so generally accepted, that "to know
truly is to know the causes of things," is a bad guide in scientific
research. Instead of it we might substitute this: that "though we may
aspire to know at last _why_ things are, we must be content for a long
time with knowing _how_ they are."


10. Hence if we are asked whether Plato or Aristotle had the truer
views of the nature and property of Science, we must give the
preference to Plato; for though his notion of a real Intelligible
World, of which the Visible world was a fleeting and changeable shadow,
was extravagant, yet it led him to seek to determine the forms of the
Intelligible Things, which are really the laws of visible phenomena;
while Aristotle was led to pass lightly over such laws, because they
did not at once reveal the causes which produced the phenomena.


11. Aristotle, throughout his works, takes numerous occasions to
argue against Plato's doctrine of Ideas. Yet these Ideas, so far as
they were the Intelligible Forms of Visible Things, were really fit
objects of philosophical research; and the search after them had a
powerful influence in promoting the progress of Science. And we may
see in the effect of this search the answer to many of Aristotle's
strongest arguments. For instance, Aristotle says that Plato, by way of
explaining things, adds to them as many Ideas, and that this is just
as if a man having to reckon a large number, were to begin by adding
to it another large number. It is plain that to this we may reply,
that the adopting the Ideas of Cycles, along with the motions of the
Planets, does really explain the motions; and that the Cycles are not
simply added to the phenomena, but include and supersede the phenomena:
a finite number of Cycles include and represent an infinite number of
separate phenomena.

To Aristotle's argument that Ideas cannot be the Causes or Principles
of Things, we should reply, that though they cannot be this, they may
nevertheless be, and must be, the Conditions and Principles of our
Knowledge, which is what we want them to be.

I have given an account of the main features of Aristotle's philosophy,
so far as it concerns the Physical Sciences, in the History of the
Inductive Sciences, Book I.


FOOTNOTES:

[Footnote 20: _Analyt. Prior._ ii. 25.]

[Footnote 21: See on this subject Appendix, Essay D.]

[Footnote 22: See the chapter on Certain Characteristics of Scientific
Induction in the _Phil. Ind. Sc._ or in the _Nov. Org. Renov._]

[Footnote 23: _Phil. Ind. Sc._ b. viii. c. i. art. 11, or _Hist. Sc.
Id._ b. viii.]

[Footnote 24: B. i. c. xi. sect. 2.]

[Footnote 25: B. iii. c. i. sect. 9.]

[Footnote 26: _De Cælo_, ii. 13.]

[Footnote 27: _Ibid._ ii. 10.]

[Footnote 28: xii. 8.]

[Footnote 29: B. xvi. c. vi.]

[Footnote 30: _On the Classification of Mammalia, &c.: a Lecture
delivered at Cambridge_, May 10, 1859, p. 3.]

[Footnote 31: B. i. c. xi.]

[Footnote 32: _History of Scientific Ideas_, and _Novum Organum
Renovatum_.]




CHAPTER VI.

THE LATER GREEKS.


Thus while Plato was disposed to seek the essence of our knowledge
in Ideas alone, Aristotle, slighting this source of truth, looked to
Experience as the beginning of Science; and he attempted to obtain, by
division and deduction, all that Experience did not immediately supply.
And thus, with these two great names, began that struggle of opposite
opinions which has ever since that time agitated the speculative
world, as men have urged the claims of Ideas or of Experience to our
respect, and as alternately each of these elements of knowledge has
been elevated above its due place, while the other has been unduly
depressed. We shall see the successive turns of this balanced struggle
in the remaining portions of this review.

But we may observe that practically the influence of Plato predominated
rather than that of Aristotle, in the remaining part of the history
of ancient philosophy. It was, indeed, an habitual subject of dispute
among men of letters, whether the sources of true knowledge are
to be found in the Senses or in the Mind; the Epicureans taking
one side of this alternative, and the Academics another, while the
Stoics in a certain manner included both elements in their view. But
none of these sects showed their persuasion that the materials of
knowledge were to be found in the domain of Sense, by seeking them
there. No one appears to have thought of following the example of
Aristotle, and gathering together a store of observed facts. We may
except, perhaps, assertions belonging to some provinces of Natural
History, which were collected by various writers: but in these, the
mixed character of the statements, the want of discrimination in
the estimate of evidence, the credulity and love of the marvellous
which the authors for the most part displayed, showed that instead
of improving upon the example of Aristotle, they were wandering
further and further from the path of real knowledge. And while they
thus collected, with so little judgment, such statements as offered
themselves, it hardly appears to have occurred to any one to enlarge
the stores of observation by the aid of experiment; and to learn
what the laws of nature were, by trying what were their results in
particular cases. They used no instruments for obtaining an insight
into the constitution of the universe, except logical distinctions
and discussions; and proceeded as if the phenomena familiar to their
predecessors must contain all that was needed as a basis for natural
philosophy. By thus contenting themselves with the facts which the
earlier philosophers had contemplated, they were led also to confine
themselves to the ideas which those philosophers had put forth. For
all the most remarkable alternatives of hypothesis, so far as they
could be constructed with a slight and common knowledge of phenomena,
had been promulgated by the acute and profound thinkers who gave the
first impulse to philosophy: and it was not given to man to add much
to the original inventions of _their_ minds till he had undergone
anew a long discipline of observation, and of thought employed upon
observation. Thus the later authors of the Greek Schools became little
better than commentators on the earlier; and the commonplaces with
which the different schools carried on their debates,--the constantly
recurring argument, with its known attendant answer,--the distinctions
drawn finer and finer and leading to nothing,--render the speculations
of those times a _scholastic_ philosophy, in the same sense in which
we employ the term when we speak of the labours of the middle ages. It
will be understood that I now refer to that which is here my subject,
the opinions concerning our knowledge of nature, and the methods in
use for the purpose of obtaining such knowledge. Whether the moral
speculations of the ancient world were of the same stationary kind,
going their round in a limited circle, like their metaphysics and
physics, must be considered on some other occasion. [33] Mr. Grote,
in his very interesting discussion of Socrates's teaching, notices
also[34] the teaching of Hippocrates, which he conceives to have in
one respect the same tendency as the philosophy of Socrates; namely,
to turn away from the vague aggregate of doctrines and guesses which
constituted the Physical Philosophy of that time, and to pursue instead
a special and more practical course of inquiry: Hippocrates selecting
Medicine and Socrates selecting Ethics. By this limitation of their
subject, they avoided some of the errors of their predecessors. For,
as Mr. Grote has also remarked, "the earlier speculators, Anaxagoras,
Empedocles, Democritus, the Pythagoreans, all had still present to
their minds the vast and undivided problems which have been transmitted
down from the old poets; bending their minds to the invention of some
system which would explain them all at once, or assist the imagination
in conceiving both how the Kosmos first began and how it continued to
move on." There could be no better remedy for this ambitious error of
the human mind than to have a definite subject of study, such as the
diseases and the health of the human body. Accordingly, we see that the
study of medicine did draw its cultivators away from this ancient but
unprofitable field. Hippocrates[35] condemns those who, as Empedocles,
set themselves to make out what man was from the beginning, how he
began first to exist, and in what manner he was constructed. This is,
he says, no part of medicine. In like manner he blames and refutes
those who make some simple element, Hot, or Cold, or Moist, or Dry, the
cause of diseases, and give medical precepts professing to be founded
on this hypothesis.

These passages are marked by the prudence which practical study
suggests to a calm and clear-sighted man. They can hardly be said to
have opened the way to a Science of Medicine; for in the sense in which
we here use the word _Science_, namely, a collection of general truths
inferred from facts by successive discoverers, we have even yet no
Science of Medicine. The question with regard to the number and nature
of the Elements of which bodies are composed began to be agitated, as
we have seen, at a very early period of Greek philosophy, and continued
long to be regarded as a chief point of physiological doctrine. In
Galen's work we have a treatise entitled, _On the Elements according
to Hippocrates_; and the writer explains[36] that though Hippocrates
has not written any work with the title _On the Elements_, yet that
he has in his _Treatise on the Nature of Man_ shown his opinion on
that subject. That the doctrine of the Four Elements, Hot, Cold,
Moist, Dry, subsisted long in the schools, we have evidence in Galen.
He tells us[37] that when he was a student of nineteen years old a
teacher urged this lore upon him, and regarded him as very contentious
and perverse, because he offered objections to it. His account of the
Dialogue between him and the teacher is curious. But in Hippocrates the
doctrine of these four elements is replaced, in a great measure, by the
doctrine of the Four Humours of which the human body is constituted;
namely, Blood, Phlegm, Yellow Bile and Black Bile. Galen dwells with
emphasis upon Hippocrates's proof that there must be more than one such
element[38].

"What," he asks, "is the method of finding the Elements of bodies?
There can, in my opinion, be no other than that which was introduced by
Hippocrates; namely, we must inquire whether there be only one element,
everywhere the same in kind, or whether there are more than one,
various and unlike each other. And if the Element be not one only, but
several, various and dissimilar, we must inquire in the second place,
how many elements there are, and what, and of what kind they are, and
how related in their association.

"Now that the First Element is not one only of which both our bodies
and those of all other creatures were produced, Hippocrates shows
from these considerations. And it is better first to put down his own
expressions and then to expound them. 'I assert that if man consisted
of one element only he could not fall sick; for there would be nothing
which could derange his health, if he were all of one Element.'"

The doctrine of One Element did not prevail much after the time of
Hippocrates: the doctrine of Four Elements continued, as I have said,
long to hold possession of the Schools, but does not appear as an
important part of the doctrine of Hippocrates. The doctrine of the Four
Humours (Blood, Phlegm, Yellow Bile and Black Bile) is more peculiarly
his, and long retained its place as a principle of physiological
Science.

But we are here not so much concerned with his discoveries in medicine
as with his views respecting the method of acquiring sound knowledge,
and in this respect, as has been said, he recommends by his practice
a prudent limitation of the field of inquiry, a rejection of wide,
ambitious, general assertions, and a practical study of his proper
field.

In ascribing these merits to Hippocrates's medical speculations as
to the ethical speculations of his contemporary Socrates, we assign
considerable philosophical value to Hippocrates, no less than to
Socrates. These merits were at that time the great virtues of physical
as well as of ethical philosophy. But, as Mr. Grote well observes, the
community of character which then subsisted between the physical and
ethical speculations prevailing at that time, ceased to obtain in later
times. Indeed, it ceased to exist just at that time, in consequence of
the establishment of scientific astronomy by the exertions of Plato
and his contemporaries. From that time the Common Sense (as we call it)
of a man like Socrates, though it might be a good guide in ethics, was
not a good guide in physics. I have shown elsewhere[39] how the Common
Sense of Socrates was worthless in matters of astronomy. From that time
one of the great intellectual lessons was, that in order to understand
the external world, we must indeed observe carefully, but we must also
guess boldly. Discovery here required an inventive mind like Plato's
to deal with and arrange new and varied facts. But in ethics all the
facts were old and familiar, and the generalizations of language by
which they were grouped as Virtues and Vices, and the like, were common
and well-known words. Here was no room for invention; and thus in the
ethical speculations of Socrates or of any other moral teacher, we are
not to look for any contributions to the Philosophy of Discovery.

Nor do I find anything on this subject among later Greek writers,
beyond the commendation of such intellectual virtues as Hippocrates and
Galen, and other medical writers, schooled by the practice of their
art, enjoined and praised. But before we quit the ancients I will point
out some peculiarities which may be noticed in the Roman disciples of
the Greek philosophy.


FOOTNOTES:

[Footnote 33: The remainder of this chapter is new in the present
edition.]

[Footnote 34: _Hist. of Greece_, Part ii. chap. 68.]

[Footnote 35: _De Antiqua Medicina_, c. 20.]

[Footnote 36: Lib. i. c. 9.]

[Footnote 37: _De Elem._ i. 6.]

[Footnote 38: In former editions I have not done justice to this
passage.]

[Footnote 39: _Hist. Ind. Sc._ Addition to Introduction in Third
Edition.]




CHAPTER VII.

THE ROMANS.


The Romans had no philosophy but that which they borrowed from the
Greeks; and what they thus received, they hardly made entirely their
own. The vast and profound question of which we have been speaking,
the relation between Existence and our Knowledge of what exists, they
never appear to have fathomed, even so far as to discern how wide and
deep it is. In the development of the ideas by which nature is to be
understood, they went no further than their Greek masters had gone,
nor indeed was more to be looked for. And in the practical habit of
accumulating observed facts as materials for knowledge, they were much
less discriminating and more credulous than their Greek predecessors.
The descent from Aristotle to Pliny, in the judiciousness of the
authors and the value of their collections of facts, is immense.

Since the Romans were thus servile followers of their Greek teachers,
and little acquainted with any example of new truths collected from
the world around them, it was not to be expected that they could have
any just conception of that long and magnificent ascent from one set
of truths to others of higher order and wider compass, which the
history of science began to exhibit when the human mind recovered
its progressive habits. Yet some dim presentiment of the splendid
career thus destined for the intellect of man appears from time to
time to have arisen in their minds. Perhaps the circumstance which
most powerfully contributed to suggest this vision, was the vast
intellectual progress which they were themselves conscious of having
made, through the introduction of the Greek philosophy; and to this
may be added, perhaps, some other features of national character. Their
temper was too stubborn to acquiesce in the absolute authority of the
Greek philosophy, although their minds were not inventive enough to
establish a rival by its side. And the wonderful progress of their
political power had given them a hope in the progress of man which
the Greeks never possessed. The Roman, as he believed the fortune of
his State to be destined for eternity, believed also in the immortal
destiny and endless advance of that Intellectual Republic of which he
had been admitted a denizen.

It is easy to find examples of such feelings as I have endeavoured
to describe. The enthusiasm with which Lucretius and Virgil speak of
physical knowledge, manifestly arises in a great measure from the
delight which they had felt in becoming acquainted with the Greek
theories.

    Me vero primum dulces ante omnia Musæ
    Quarum sacra fero ingenti perculsus amore
    Accipiant, cœlique vias et sidera monstrent,
    Defectus Solis varios, Lunæque labores!...
    Felix qui potuit rerum cognoscere causas!

    Ye sacred Muses, with whose beauty fir'd,
    My soul is ravisht and my brain inspir'd:
    Whose Priest I am, whose holy fillets wear,
    Would you your Poet's first petition hear,
    Give me the ways of wand'ring stars to know,
    The depth of Heaven above and Earth below;
    Teach me the various labours of the Moon,
    And whence proceed th' eclipses of the Sun;
    Why flowing Tides prevail upon the main,
    And in what dark abyss they shrink again;
    What shakes the solid Earth; what cause delays
    The Summer Nights; and shortens Winter Days....
      Happy the man who, studying Nature's Laws,
    Through known effects can trace the secret cause!

Ovid[40] expresses a similar feeling.

    Felices animos quibus hæc cognoscere primis
      Inque domos superas scandere cura fuit!...
    Admovere oculis distantia sidera nostris
      Ætheraque ingenio supposuere suo.
    Sic petitur cœlum: non ut ferat Ossam Olympus
      Summaque Peliacus sidera tanget apex.

    Thrice happy souls! to whom 'twas given to rise
    To truths like these, and scale the spangled skies!
    Far distant stars to clearest view they brought,
    And girdled ether with their chain of thought.
    So heaven is reached:--not as of old they tried
    By mountains piled on mountains in their pride.


And from the whole tenour of these and similar passages, it is evident
that the intellectual pleasure which arises from our first introduction
to a beautiful physical theory had a main share in producing this
enthusiasm at the contemplation of the victories of science; although
undoubtedly the moral philosophy, which was never separated from the
natural philosophy, and the triumph over superstitious fears, which
a knowledge of nature was supposed to furnish, added warmth to the
feeling of exultation.

We may trace a similar impression in the ardent expressions which
Pliny[41] makes use of in speaking of the early astronomers, and which
we have quoted in the _History_. "Great men! elevated above the common
standard of human nature, by discovering the laws which celestial
occurrences obey, and by freeing the wretched mind of man from the
fears which eclipses inspired."

This exulting contemplation of what science had done, naturally led the
mind to an anticipation of further achievements still to be performed.
Expressions of this feeling occur in Seneca, and are of the most
remarkable kind, as the following example will show[42]:

"Why do we wonder that comets, so rare a phenomenon, have not yet had
their laws assigned?--that we should know so little of their beginning
and their end, when their recurrence is at wide intervals? It is not
yet fifteen hundred years since Greece,

  Stellis numeros et nomina fecit,

'reckoned the stars, and gave them names.' There are still many nations
which are acquainted with the heavens by sight only; which do not yet
know why the moon disappears, why she is eclipsed. It is but lately
that among us philosophy has reduced these matters to a certainty. The
day shall come when the course of time and the labour of a maturer age
shall bring to light what is yet concealed. One generation, even if it
devoted itself to the skies, is not enough for researches so extensive.
How then can it be so, when we divide this scanty allowance of years
into no equal shares between our studies and our vices? These things
then must be explained by a long succession of inquiries. We have but
just begun to know how arise the morning and evening appearances,
the stations, the progressions, and the retrogradations of the fixed
stars which put themselves in our way;--which appearing perpetually
in another and another place compel us to be curious. Some one will
hereafter demonstrate in what region the comets wander; why they move
so far asunder from the rest; of what size and nature they are. Let
us be content with what we have discovered: let posterity contribute
its share to truth." Again he adds[43] in the same strain: "Let us
not wonder that what lies so deep is brought out so slowly. How many
animals have become known for the first time in this age! And the
members of future generations shall know many of which we are ignorant.
Many things are reserved for ages to come, when our memory shall
have passed away. The world would be a small thing indeed, if it did
not contain matter of inquiry _for_ all the world. Eleusis reserves
something for the second visit of the worshipper. _So too Nature
does not at once disclose all_ HER _mysteries_. We think ourselves
initiated; we are but in the vestibule. The arcana are not thrown open
without distinction and without reserve. This age will see some things;
that which comes after us, others."

While we admire the happy coincidence of these conjectures with the
soundest views which the history of science teaches us, we must not
forget that they are merely conjectures, suggested by very vague
impressions, and associated with very scanty conceptions of the laws
of nature. Seneca's _Natural Questions_, from which the above extract
is taken, contains a series of dissertations on various subjects of
Natural Philosophy; as Meteors, Rainbows, Lightnings, Springs, Rivers,
Snow, Hail, Rain, Wind, Earthquakes and Comets. In the whole of these
dissertations, the statements are loose, and the explanations of little
or no value. Perhaps it may be worth our while to notice a case in
which he refers to an observation of his own, although his conclusion
from it be erroneous. He is arguing[44] against the opinion that
Springs arise from the water which falls in rain. "In the first place,"
he says, "I, a very diligent digger in my vineyard, affirm that no rain
is so heavy as to moisten the earth to the depth of more than ten feet.
All the moisture is consumed in this outer crust, and descends not to
the lower part." We have here something of the nature of an experiment;
and indeed, as we may readily conceive, the instinct which impels man
to seek truth by experiment can never be altogether extinguished.
Seneca's experiment was deprived of its value by the indistinctness of
his ideas, which led him to rest in the crude conception of the water
being "consumed" in the superficial crust of the earth.

It is unnecessary to pursue further the reasonings of the Romans on
such subjects, and we now proceed to the ages which succeeded the fall
of their empire.


FOOTNOTES:

[Footnote 40: Lib. i. _Fast._]

[Footnote 41: _Hist. Nat._ i. 75.]

[Footnote 42: _Quæst. Nat._ vii. 25.]

[Footnote 43: _Quæst. Nat._ vii. 30, 31.]

[Footnote 44: _Ibid._ iii. 7.]




CHAPTER VIII.

ARABIAN PHILOSOPHERS.


I have noticed certain additions to Physical Science made by the
Arabians; namely, in Astronomy[45]. The discovery of the motion of
the Sun's Apogee by Albategnius, and the discovery of the Moon's
_Variation_ by Aboul-Wefa; and in Optics[46] the assertion of Alhazen
that the angle of refraction is not proportional to the angle of
incidence, as Ptolemy had supposed: and certain steps in the philosophy
of vision. We must also suppose, as the Arabic word _alkali_ reminds
us, that the Arabians contributed to lay the foundations of chemistry.
The question which we have here to ask is, whether the Arabians made
any steps beyond their predecessors in the philosophy of discovery.
And to this question, I conceive the answer must be this: that among
them as among the Greeks, those who practically observed nature, and
especially those who made discoveries in Science, must have had a
practical acquaintance with some of the maxims which are exemplified
in the formation of Science. To discover that the Apogee of the Sun
was 17 degrees distant from the point where Ptolemy had placed it,
Albategnius made careful observations, and referred them to the theory
of the eccentric, so as to verify or correct that theory. And when, in
the eleventh century, Arzachel found the Apogee to be less advanced
than Albategnius had found it, he proceeded again to correct the
theory by introducing a new movement of the equinoctial points, which
was called the _Trepidation_. It appeared afterwards, however, that,
in doing this, he had had too much confidence in the observations of
his predecessors, and that no such movement as the Trepidation really
existed. In like manner to correct Ptolemy's law of refraction, Alhazen
had recourse to experiment: but he did not put his experiments in the
form of a Table, as Ptolemy had done. If he had done this, he might
possibly have discovered the law of sines, which Snell afterwards
discovered.

But though the Arabian philosophers thus, in some cases, observed
facts, and referred those facts to general mathematical laws, it does
not appear that they were led to put in any new or striking general
form such maxims as this: That the progress of Science consists in the
exact observation of facts and in colligating them by ideas. Those of
them who were dissatisfied with the existing philosophy as barren and
useless (for instance Algazel[47]), were led to point at the faults
and contradictions of that philosophy, but did not attempt, so far
as I know, to substitute for it anything better. If they rejected
Aristotle's _Organon_, they did not attempt to construct a new Organon
for themselves.

Indeed they do not appear even to have had sufficient confidence in the
real truth of the astronomical theories which they had adopted from the
Greeks, always to correct and extend those where their observations
showed that they required correction and extension. Sometimes they did
this, but not generally enough. When Arzachel found by observation
the Apogee of the Sun to be situated too far back, he ventured to
correct Ptolemy's statement of its motion. But when Aboul-Wefa had
really discovered the _Variation_ of the Moon's motion, he did not
express it by means of an epicycle. If he had done so, he would have
made it unnecessary for Tycho Brahe at a later period to make the same
discovery.

The moral of this incident is the same moral which we have perpetually
to note as taught us at every step by the history of Science:--namely,
the necessity of constant, careful and exact observation of Facts; and
the advantage of devising a Theory, (even if it have to be afterwards
rejected,) by which the Facts shall be bound together into a coherent
whole.

FOOTNOTES:

[Footnote 45: _Hist. Ind. Sc._ b. iii. c. iv. sect. 8.]

[Footnote 46: _Ibid._ b. ix. c. ii.]

[Footnote 47: See _Hist. Ind. Sc._ b. iv. c. i.]




CHAPTER IX.

THE SCHOOLMEN OF THE MIDDLE AGES.


In the _History of the Sciences_ I have devoted a Book to the state
of Science in the middle ages, and have endeavoured to analyse the
intellectual defects of that period. Among the characteristic features
of the human mind during those times, I have noticed Indistinctness of
Ideas, a Commentatorial Spirit, Mysticism, and Dogmatism. The account
there given of this portion of the history of man belongs, in reality,
rather to the History of Ideas than to the History of Progressive
Science. For, as we have there remarked, theoretical Science was,
during the period of which we speak, almost entirely stationary; and
the investigation of the causes of such a state of things may be
considered as a part of that review in which we are now engaged, of the
vicissitudes of man's acquaintance with the methods of discovery. But
when we offered to the world a history of science, to leave so large a
chasm unexplained, would have made the series of events seem defective
and broken; and the survey of the Middle Ages was therefore inserted.
I would beg to refer to that portion of the former work the reader who
wishes for information in addition to what is here given.

The Indistinctness of Ideas and the Commentatorial Disposition of those
ages have already been here brought under our notice. Viewed with
reference to the opposition between Experience and Ideas, on which
point, as we have said, the succession of opinions in a great measure
turns, it is clear that the commentatorial method belongs to the ideal
side of the question: for the commentator seeks for such knowledge
as he values, by analysing and illustrating what his author has said;
and, content with this material of speculation, does not desire to
add to it new stores of experience and observation. And with regard
to the two other features in the character which we gave to those
ages, we may observe that Dogmatism demands for philosophical theories
the submission of mind, due to those revealed religious doctrines
which are to guide our conduct and direct our hopes: while Mysticism
elevates ideas into realities, and offers them to us as the objects
of our religious regard. Thus the Mysticism of the middle ages and
their Dogmatism alike arose from not discriminating the offices of
theoretical and practical philosophy. Mysticism claimed for ideas the
dignity and reality of principles of moral action and religious hope:
Dogmatism imposed theoretical opinions respecting speculative points
with the imperative tone of rules of conduct and faith.

If, however, the opposite claims of theory and practice interfered
with the progress of science by the confusion they thus occasioned,
they did so far more by drawing men away altogether from mere physical
speculations. The Christian religion, with its precepts, its hopes, and
its promises, became the leading subject of men's thoughts; and the
great active truths thus revealed, and the duties thus enjoined, made
all inquiries of mere curiosity appear frivolous and unworthy of man.
The Fathers of the Church sometimes philosophized ill; but far more
commonly they were too intent upon the great lessons which they had to
teach, respecting man's situation in the eyes of his Heavenly Master,
to philosophize at all respecting things remote from the business of
life and of no importance in man's spiritual concerns.

Yet man has his intellectual as well as his spiritual wants. He has
faculties which demand systems and reasons, as well as precepts and
promises. The Christian doctor, who knew so much more than the heathen
philosopher respecting the Creator and Governor of the universe, was
not long content to know or to teach less, respecting the universe
itself. While it was still maintained that Theology was the only
really important study, Theology was so extended and so fashioned as to
include all other knowledge: and after no long time, the Fathers of the
Church themselves became the authors of systems of universal knowledge.

But when this happened, the commentatorial spirit was still in its
full vigour. The learned Christians could not, any more than the
later Greeks or the Romans, devise, by the mere force of their own
invention, new systems, full, comprehensive, and connected, like those
of the heroic age of philosophy. The same mental tendencies which led
men to look for speculative coherence and completeness in the view of
the universe, led them also to admire and dwell upon the splendid and
acute speculations of the Greeks. They were content to find, in those
immortal works, the answers to the questions which their curiosity
prompted; and to seek what further satisfaction they might require,
in analysing and unfolding the doctrines promulgated by those great
masters of knowledge. Thus the Christian doctors became, as to general
philosophy, commentators upon the ancient Greek teachers.

Among these, they selected Aristotle as their peculiar object of
admiration and study. The vast store, both of opinions and facts, which
his works contain, his acute distinctions, his cogent reasons in some
portions of his speculations, his symmetrical systems in almost all,
naturally commended him to the minds of subtle and curious men. We
may add that Plato, who taught men to contemplate Ideas separate from
Things, was not so well fitted for general acceptance as Aristotle, who
rejected this separation. For although the due apprehension of this
opposition of Ideas and Sensations is a necessary step in the progress
of true philosophy, it requires a clearer view and a more balanced mind
than the common herd of students possess; and Aristotle, who evaded the
necessary perplexities in which this antithesis involves us, appeared,
to the temper of those times, the easier and the plainer guide of the
two.

The Doctors of the middle ages having thus adopted Aristotle as
their master in philosophy, we shall not be surprised to find them
declaring, after him, that experience is the source of our knowledge
of the visible world. But though, like the Greeks, they thus talked of
experiment, like the Greeks, they showed little disposition to discover
the laws of nature by observation of facts. This barren and formal
recognition of experience or sensation as one source of knowledge,
not being illustrated by a practical study of nature, and by real
theoretical truths obtained by such a study, remained ever vague,
wavering, and empty. Such a mere acknowledgment cannot, in any times,
ancient or modern, be considered as indicating a just apprehension of
the true basis and nature of science.

In imperfectly perceiving how, and how far, experience is the source of
our knowledge of the external world, the teachers of the middle ages
were in the dark; but so, on this subject, have been almost all the
writers of all ages, with the exception of those who in recent times
have had their minds enlightened by contemplating philosophically the
modern progress of science. The opinions of the doctors of the middle
ages on such subjects generally had those of Aristotle for their basis;
but the subject was often still further analysed and systematized, with
an acute and methodical skill hardly inferior to that of Aristotle
himself.

The Stagirite, in the beginning of his _Physics_, had made the
following remarks. "In all bodies of doctrine which involve principles,
causes, or elements, Science and Knowledge arise from the knowledge
of these; (for we then consider ourselves to _know_ respecting any
subject, when we know its first cause, its first principles, its
ultimate elements.) It is evident, therefore, that in seeking a
knowledge of nature, we must first know what are its principles. But
the course of our knowledge is, from the things which are better known
and more manifest to us, to the things which are more certain and
evident in nature. For those things which are most evident in truth,
are not most evident to us. [And consequently we must advance from
things obscure in nature, but manifest to us, towards the things which
are really in nature more clear and certain.] The things which are
first obvious and apparent to us are complex; and from these we obtain,
by analysis, principles and elements. We must proceed from universals
to particulars. For the whole is better known to our senses than the
parts, and for the same reason, the universal better known than the
particular. And thus words signify things in a large and indiscriminate
way, which is afterwards analysed by definition; as we see that the
children at first call all men _father_, and all women _mother_, but
afterwards learn to distinguish."

There are various assertions contained in this extract which came to
be considered as standard maxims, and which occur constantly in the
writers of the middle ages. Such are, for instance, the maxim, "Verè
scire est per causas scire;" the remark, that compounds are known
to us before their parts, and the illustration from the expressions
used by children. Of the mode in which this subject was treated by
the schoolmen, we may judge by looking at passages of Thomas Aquinas
which treat of the subject of the human understanding. In the _Summa
Theologiæ_, the eighty-fifth Question is _On the manner and order of
understanding_, which subject he considers in eight Articles; and
these must, even now, be looked upon as exhibiting many of the most
important and interesting points of the subject. They are, _First_,
Whether our understanding understands by abstracting ideas (_species_)
from appearances; _Second_, Whether intelligible species abstracted
from appearances are related to our understanding as that _which_ we
understand, or that _by which_ we understand; _Third_, Whether our
understanding does naturally understand universals first; _Fourth_,
Whether our understanding can understand many things at once; _Fifth_,
Whether our understanding understands by compounding and dividing;
_Sixth_, Whether the understanding can err; _Seventh_, Whether one
person can understand the same thing better than another; _Eighth_,
Whether our understanding understands the indivisible sooner than
the divisible. And in the discussion of the last point, for example,
reference is made to the passage of Aristotle which we have already
quoted. "It may seem," he says, "that we understand the indivisible
before the divisible; for _the Philosopher_ says that we understand
and know by knowing principles and elements; but indivisibles are the
principles and elements of divisible things. But to this we may reply,
that in our receiving of science, principles and elements are not
always first; for sometimes from the sensible effects we go on to the
knowledge of intelligible principles and causes." We see that both the
objection and the answer are drawn from Aristotle.

We find the same close imitation of Aristotle in Albertus Magnus, who,
like Aquinas, flourished in the thirteenth century. Albertus, indeed,
wrote treatises corresponding to almost all those of the Stagirite, and
was called the _Ape of Aristotle_. In the beginning of his _Physics_,
he says, "Knowledge does not always begin from that which is first
according to the nature of things, but from that of which the knowledge
is easiest. For the human intellect, on account of its relation to the
senses (_propter reflexionem quam habet ad sensum_), collects science
from the senses; and thus it is easier for our knowledge to begin from
that which we can apprehend by sense, imagination, and intellect, than
from that which we apprehend by intellect alone." We see that he has
somewhat systematized what he has borrowed.

This disposition to dwell upon and systematize the leading doctrines
of metaphysics assumed a more definite and permanent shape in the
opposition of the Realists and Nominalists. The opposition involved
in this controversy is, in fact, that fundamental antithesis of Sense
and Ideas about which philosophy has always been engaged; and of
which we have marked the manifestation in Plato and Aristotle. The
question, What is the object of our thoughts when we reason concerning
the external world? must occur to all speculative minds: and the
difficulties of the answer are manifest. We must reply, either that our
own Ideas, or that Sensible Things, are the elements of our knowledge
of nature. And then the scruples again occur,--how we have any
_general_ knowledge if our thoughts are fixed on particular objects;
and, on the other hand,--how we can attain to any _true_ knowledge of
nature by contemplating ideas which are not identical with objects in
nature. The two opposite opinions maintained on this subject were, on
the one side,--that our general propositions refer to objects which
are _real_, though divested of the peculiarities of individuals; and,
on the other side,--that in such propositions, individuals are not
represented by any reality, but bound together by a _name_. These two
views were held by the Realists and Nominalists respectively: and thus
the Realist manifested the adherence to Ideas, and the Nominalist the
adherence to the impressions of Sense, which have always existed as
opposite yet correlative tendencies in man.

The Realists were the prevailing sect in the Scholastic times: for
example, both Thomas Aquinas and Duns Scotus, the _Angelical_ and the
_Subtle_ Doctor, held this opinion, although opposed to each other
in many of their leading doctrines on other subjects. And as the
Nominalist, fixing his attention upon sensible objects, is obliged to
consider what is the _principle of generalization_, in order that the
possibility of any general proposition may be conceivable; so on the
other hand, the Realist, beginning with the contemplation of universal
ideas, is compelled to ask what is the _principle of individuation_, in
order that he may comprehend the application of general propositions
in each particular instance. This inquiry concerning the principle of
individuation was accordingly a problem which occupied all the leading
minds among the Schoolmen[48]. It will be apparent from what has
been said, that it is only one of the many forms of the fundamental
antithesis of the Ideas and the Senses, which we have constantly before
us in this review.

The recognition of the derivation of our knowledge, in part at least,
from Experience, though always loose and incomplete, appears often
to be independent of the Peripatetic traditions. Thus Richard of St.
Victor, a writer of contemplative theology in the twelfth century,
says[49], that "there are three sources of knowledge, experience,
reason, faith. Some things we prove by experiment, others we collect
by reasoning, the certainty of others we hold by believing. And
with regard to temporal matters, we obtain our knowledge by actual
experience; the other guides belong to divine knowledge." Richard
also propounds a division of human knowledge which is clearly not
derived directly from the ancients, and which shows that considerable
attention must have been paid to such speculations. He begins by laying
down clearly and broadly the distinction, which, as we have seen, is
of primary importance, between _practice_ and _theory_. _Practice_,
he says, includes seven mechanical arts; those of the clothier, the
armourer, the navigator, the hunter, the physician, and the player.
_Theory_ is threefold, divine, natural, doctrinal; and is thus divided
into Theology, Physics, and Mathematics. _Mathematics_, he adds,
treats of the invisible _forms_ of visible things. We have seen that
by many profound thinkers this word _forms_ has been selected as best
fitted to describe those relations of things which are the subject of
mathematics. Again, Physics discovers causes from their effects and
effects from their causes. It would not be easy at the present day to
give a better account of the object of physical science. But Richard
of St. Victor makes this account still more remarkably judicious, by
the examples to which he alludes; which are earthquakes, the tides,
the virtues of plants, the instincts of animals, the classification of
minerals, plants and reptiles.

    Unde tremor terris, quâ vi maria alta tumescant,
    Herbarum vires, animos irasque ferarum,
    Omne genus fruticum, lapidum quoque, reptiliumque.

He further adds[50], "Physical science ascends from effects to
causes, and descends again from causes to effects." This declaration
Francis Bacon himself might have adopted. It is true, that Richard
would probably have been little able to produce any clear and
definite instances of knowledge, in which this ascent and descent
were exemplified; but still the statement, even considered as a
mere conjectural thought, contains a portion of that sagacity and
comprehensive power which we admire so much in Bacon.

Richard of St. Victor, who lived in the twelfth century, thus exhibits
more vigour and independence of speculative power than Thomas Aquinas,
Albertus Magnus, and Duns Scotus, in the thirteenth. In the interval,
about the end of the twelfth century, the writings of Aristotle had
become generally known in the West; and had been elevated into the
standard of philosophical doctrine, by the divines mentioned above, who
felt a reverent sympathy with the systematizing and subtle spirit of
the Stagirite as soon as it was made manifest to them. These doctors,
following the example of their great forerunner, reduced every part
of human knowledge to a systematic form; the systems which they thus
framed were presented to men's minds as the only true philosophy, and
dissent from them was no longer considered to be blameless. It was an
offence against religion as well as reason to reject the truth, and
the truth could be but one. In this manner arose that claim which the
Doctors of the Church put forth to control men's opinions upon all
subjects, and which we have spoken of in the _History of Science_ as
the Dogmatism of the Middle Ages. There is no difficulty in giving
examples of this characteristic. We may take for instance a Statute of
the University of Paris, occasioned by a Bull of Pope John XXI., in
which it is enacted, "that no Master or Bachelor of any faculty, shall
presume to read lectures upon any author in a private room, on account
of the many perils which may arise therefrom; but shall read in public
places, where all may resort, and may faithfully report what is there
taught; excepting only books of Grammar and Logic, in which there can
be no presumption." And certain errors of Brescian are condemned in a
Rescript[51] of the papal Legate Odo, with the following expressions:
"Whereas, as we have been informed, certain Logical professors
treating of Theology in their disputations, and Theologians treating
of Logic, contrary to the command of the law are not afraid to mix and
confound the lots of the Lord's heritage; we exhort and admonish your
University, all and singular, that they be content with the landmarks
of the Sciences and Faculties which our Fathers have fixed; and that
having due fear of the curse pronounced in the law against him who
removeth his neighbour's landmark, you hold such sober wisdom according
to the Apostles, that ye may by no means incur the blame of innovation
or presumption."

The account which, in the _History of Science_, I gave of Dogmatism as
a characteristic of the middle ages, has been indignantly rejected by
a very pleasing modern writer, who has, with great feeling and great
diligence, brought into view the merits and beauties of those times,
termed by him _Ages of Faith_. He urges[52] that religious authority
was never claimed for physical science: and he quotes from Thomas
Aquinas, a passage in which the author protests against the practice
of confounding opinions of philosophy with doctrines of faith. We
might quote in return the Rescript[53] of Stephen, bishop of Paris,
in which he declares that there can be but one truth, and rejects
the distinction of things being true according to philosophy and not
according to the Catholic faith; and it might be added, that among the
errors condemned in this document are some of Thomas Aquinas himself.
We might further observe, that if no physical doctrines were condemned
in the times of which we now speak, this was because, on such subjects,
no new opinions were promulgated, and not because opinion was free.
As soon as new opinions, even on physical subjects, attracted general
notice, they were prohibited by authority, as we see in the case of
Galileo[54].

But this disinclination to recognize philosophy as independent of
religion, and this disposition to find in new theories, even in
physical ones, something contrary to religion or scripture, are, it
would seem, very natural tendencies of theologians; and it would be
unjust to assert that these propensities were confined to the periods
when the authority of papal Rome was highest; or that the spirit which
has in a great degree controlled and removed such habits was introduced
by the Reformation of religion in the sixteenth century. We must trace
to other causes, the clear and general recognition of Philosophy,
as distinct from Theology, and independent of her authority. In
the earlier ages of the Church, indeed, this separation had been
acknowledged. St. Augustin says, "A Christian should beware how he
speaks on questions of natural philosophy, as if they were doctrines of
Holy Scripture; for an infidel who should hear him deliver absurdities
could not avoid laughing. Thus the Christian would be confused, and the
infidel but little edified; for the infidel would conclude that our
authors really entertained these extravagant opinions, and therefore
they would despise them, to their own eternal ruin. Therefore the
opinions of philosophers should never be proposed as dogmas of faith,
or rejected as contrary to faith, when it is not certain that they are
so." These words are quoted with approbation by Thomas Aquinas, and
it is said[55], are cited in the same manner in every encyclopedical
work of the middle ages. This warning of genuine wisdom was afterwards
rejected, as we have seen; and it is only in modern times that its
value has again been fully recognized. And this improvement we must
ascribe, mainly, to the progress of physical science. For a great body
of undeniable truths on physical subjects being accumulated, such as
had no reference to nor connexion with the truths of religion, and
yet such as possessed a strong interest for most men's minds, it was
impossible longer to deny that there were wide provinces of knowledge
which were not included in the dominions of Theology, and over which
she had no authority. In the fifteenth and sixteenth centuries, the
fundamental doctrines of mechanics, hydrostatics, optics, magnetics,
chemistry, were established and promulgated; and along with them,
a vast train of consequences, attractive to the mind by the ideal
relations which they exhibited, and striking to the senses by the power
which they gave man over nature. Here was a region in which philosophy
felt herself entitled and impelled to assert her independence. From
this region, there is a gradation of subjects in which philosophy
advances more and more towards the peculiar domain of religion;
and at some intermediate points there have been, and probably will
always be, conflicts respecting the boundary line of the two fields
of speculation. For the limit is vague and obscure, and appears to
fluctuate and shift with the progress of time and knowledge.

Our business at present is not with the whole extent and limits
of philosophy, but with the progress of physical science more
particularly, and the methods by which it may be attained: and we are
endeavouring to trace historically the views which have prevailed
respecting such methods, at various periods of man's intellectual
progress. Among the most conspicuous of the revolutions which opinions
on this subject have undergone, is the transition from an implicit
trust in the internal powers of man's mind to a professed dependence
upon external observation; and from an unbounded reverence for the
wisdom of the past, to a fervid expectation of change and improvement.
The origin and progress of this disposition of mind;--the introduction
of a state of things in which men not only obtained a body of
indestructible truths from experience, and increased it from generation
to generation, but professedly, and we may say, ostentatiously,
declared such to be the source of their knowledge, and such their
hopes of its destined career;--the rise, in short, of Experimental
Philosophy, not only as a habit, but as a Philosophy of Experience, is
what we must now endeavour to exhibit.


FOOTNOTES:

[Footnote 48: See the opinion of Aquinas, in Degerando, _Hist. Com. des
Syst._ iv. 499; of Duns Scotus, _ibid._ iv. 523.]

[Footnote 49: _Liber Excerptionum_, Lib. i. c. i.]

[Footnote 50: _Tr. Ex._ Lib. i. c. vii.]

[Footnote 51: Tenneman, viii. 461.]

[Footnote 52: _Mores Catholici, or Ages of Faith_, viii. p. 247.]

[Footnote 53: Tenneman, viii. 460.]

[Footnote 54: If there were any doubt on this subject, we might
refer to the writers who afterwards questioned the supremacy of
Aristotle, and who with one voice assert that an infallible authority
had been claimed for him. Thus Laurentius Valla: "Quo minus ferendi
sunt recentes Peripatetici, qui nullius sectæ hominibus interdicunt
libertate ab Aristotele dissentiendi, quasi sophos hic, non
philosophus." _Pref. in Dial._ (Tenneman, ix. 29.) So Ludovicus Vives:
"Sunt ex philosophis et ex theologis qui non solum quo Aristoteles
pervenit extremum esse aiunt naturæ, sed quâ pervenit eam rectissimam
esse omnium et certissimam in natura viam." (Tenneman, ix. 43.) We
might urge too, the evasions practised by philosophical Reformers,
through fear of the dogmatism to which they had to submit; for example,
the protestation of Telesius at the end of the Proem to his work, _De
Rerum Natura_: "Nec tamen, si quid eorum quæ nobis posita sunt, sacris
literis, Catholicæve ecclesiæ decretis non cohæreat, tenendum id, quin
penitus rejiciendum asseveramus contendimusque. Neque enim _humana_
modo _ratio_ quævis, sed _ipse_ etiam _sensus_ illis _posthabendus_, et
si illis non congruat, abnegandus omnino et ipse etiam est sensus."]

[Footnote 55: _Ages of Faith_, viii. 247: to the author of which I am
obliged for this quotation.]




CHAPTER X.

THE INNOVATORS OF THE MIDDLE AGES.


_Raymond Lully._

1. _General Remarks._--In the rise of Experimental Philosophy,
understanding the term in the way just now stated, two features have
already been alluded to: the disposition to cast off the prevalent
reverence for the opinions and methods of preceding teachers with an
eager expectation of some vast advantage to be derived from a change;
and the belief that this improvement must be sought by drawing our
knowledge from external observation rather than from mere intellectual
efforts;--_the Insurrection against Authority_, and _the Appeal to
Experience_. These two movements were closely connected; but they may
easily be distinguished, and in fact, persons were very prominent in
the former part of the task, who had no comprehension of the latter
principle, from which alone the change derives its value. There were
many Malcontents who had not the temper, talent or knowledge, which
fitted them to be Reformers.

The authority which was questioned, in the struggle of which we speak,
was that of the Scholastic System, the combination of Philosophy with
Theology; of which Aristotle, presented in the form and manner which
the Doctors of the Church had imposed upon him, is to be considered
the representative. When there was demanded of men a submission of
the mind, such as this system claimed, the natural love of freedom in
man's bosom, and the speculative tendencies of his intellect, rose in
rebellion, from time to time, against the ruling oppression. We find
in all periods of the scholastic ages examples of this disposition
of man to resist overstrained authority; the tendency being mostly,
however, combined with a want of solid thought, and showing itself
in extravagant pretensions and fantastical systems put forwards by
the insurgents. We have pointed out one such opponent[56] of the
established systems, even among the Arabian schoolmen, a more servile
race than ever the Europeans were. We may here notice more especially
an extraordinary character who appeared in the thirteenth century, and
who may be considered as belonging to the Prelude of the Reform in
Philosophy, although he had no share in the Reform itself.

2. _Raymond Lully._--Raymond Lully is perhaps traditionally best known
as an Alchemist, of which art he appears to have been a cultivator. But
this was only one of the many impulses of a spirit ardently thirsty
of knowledge and novelty. He had[57], in his youth, been a man of
pleasure, but was driven by a sudden shock of feeling to resolve on a
complete change of life. He plunged into solitude, endeavoured to still
the remorse of his conscience by prayer and penance, and soon had his
soul possessed by visions which he conceived were vouchsafed to him.
In the feeling of religious enthusiasm thus excited, he resolved to
devote his life to the diffusion of Christian truth among Heathens and
Mahomedans. For this purpose, at the age of thirty he betook himself
to the study of Grammar, and of the Arabic language. He breathed
earnest supplications for an illumination from above; and these were
answered by his receiving from heaven, as his admirers declare, his
_Ars Magna_ by which he was able without labour or effort to learn
and apply all knowledge. The real state of the case is, that he put
himself in opposition to the established systems, and propounded a New
Art, from which he promised the most wonderful results; but that his
Art really is merely a mode of combining ideal conceptions without any
reference to real sources of knowledge, or any possibility of real
advantage. In a Treatise addressed, in A.D. 1310, to King Philip of
France, entitled _Liber Lamentationis Duodecim Principiorum Philosophiæ
contra Averroistas_, Lully introduced Philosophy, accompanied by her
twelve Principles, (Matter, Form, Generation, &c.) uttering loud
complaints against the prevailing system of doctrine; and represents
her as presenting to the king a petition that she may be upheld and
restored by her favourite, the Author. His _Tabula Generalis ad omnes
Scientias applicabilis_ was begun the 15th September, 1292, in the
Harbour of Tunis, and finished in 1293, at Naples. In order to frame an
Art of thus tabulating all existing sciences, and indeed all possible
knowledge, he divides into various classes the conceptions with which
he has to deal. The first class contains nine _Absolute Conceptions_:
Goodness, Greatness, Duration, Power, Wisdom, Will, Virtue, Truth,
Majesty. The second class has nine _Relative Conceptions_: Difference,
Identity, Contrariety, Beginning, Middle, End, Majority, Equality,
Minority. The third class contains nine _Questions_: Whether? What?
Whence? Why? How great? How circumstanced? When? Where? and How?
The fourth class contains the nine _Most General Subjects_: God,
Angel, Heaven, Man, _Imaginativum_, _Sensitivum_, _Vegetativum_,
_Elementativum_, _Instrumentativum_. Then come nine _Prædicaments_,
nine _Moral Qualities_, and so on. These conceptions are arranged in
the compartments of certain concentric moveable circles, and give
various combinations by means of triangles and other figures, and thus
propositions are constructed.

It must be clear at once, that real knowledge, which is the union of
facts and ideas, can never result from this machinery for shifting
about, joining and disjoining, empty conceptions. This, and all similar
schemes, go upon the supposition that the logical combinations of
notions do of themselves compose knowledge; and that really existing
things may be arrived at by a successive system of derivation from
our most general ideas. It is imagined that by distributing the
nomenclature of abstract ideas according to the place which they can
hold in our propositions, and by combining them according to certain
conditions, we may obtain formulæ including all possible truths, and
thus fabricate a science in which all sciences are contained. We thus
obtain the means of talking and writing upon all subjects, without the
trouble of thinking: the revolutions of the emblematical figures are
substituted for the operations of the mind. Both exertion of thought,
and knowledge of facts, become superfluous. And this reflection, adds
an intelligent author[58], explains the enormous number of books which
Lully is said to have written; for he might have written those even
during his sleep, by the aid of a moving power which should keep his
machine in motion. Having once devised this invention for manufacturing
science, Lully varied it in a thousand ways, and followed it into
a variety of developments. Besides Synoptical Tables, he employs
Genealogical Trees, each of which he dignifies with the name of the
Tree of Science. The only requisite for the application of his System
was a certain agreement in the numbers of the classes into which
different subjects were distributed; and as this symmetry does not
really exist in the operations of our thoughts, some violence was done
to the natural distinction and subordination of conceptions, in order
to fit them for the use of the system.

Thus Lully, while he professed to teach an Art which was to shed new
light upon every part of science, was in fact employed in a pedantic
and trifling repetition of known truths or truisms; and while he
complained of the errors of existing methods, he proposed in their
place one which was far more empty, barren, and worthless, than the
customary processes of human thought. Yet his method is spoken of[59]
with some praise by Leibnitz, who indeed rather delighted in the
region of ideas and words, than in the world of realities. But Francis
Bacon speaks far otherwise and more justly on this subject[60]. "It is
not to be omitted that some men, swollen with emptiness rather than
knowledge, have laboured to produce a certain Method, not deserving
the name of a legitimate Method, since it is rather a method of
imposture: which yet is doubtless highly grateful to certain would-be
philosophers. This method scatters about certain little drops of
science in such a manner that a smatterer may make a perverse and
ostentatious use of them with a certain show of learning. Such was
the art of Lully, which consisted of nothing but a mass and heap of
the words of each science; with the intention that he who can readily
produce the words of any science shall be supposed to know the science
itself. Such collections are like a rag shop, where you find a patch of
everything, but nothing which is of any value."


FOOTNOTES:

[Footnote 56: Algazel. See _Hist. Ind. Sc._ b. iv. c. i.]

[Footnote 57: Tenneman, viii. 830.]

[Footnote 58: Degerando, iv. 535.]

[Footnote 59: Leibnitz's expressions are, (_Op._ t. vi. p. 16): "Quand
j'étais jeune, je prenois quelque a l'_Art_ de Lulle, mais je crus y
entrevoir bien des défectuosités, dont j'ai dit quelque chose dans un
petit Essai d'écolier intitulé _De Arte Combinatoria_, publié en 1666,
et qui a été réimprimé après malgré moi. Mais comme je ne méprise
rien facilement, excepté les arts divinatoires que ne sont que des
tromperies toutes pures, j'ai trouvé quelque chose d'estimable encore
dans l'_Art_ de Lulle."]

[Footnote 60: _Works_, vii. 296.]




CHAPTER XI.

THE INNOVATORS OF THE MIDDLE AGES--CONTINUED.


_Roger Bacon._

We now come to a philosopher of a very different character, who was
impelled to declare his dissent from the reigning philosophy by the
abundance of his knowledge, and by his clear apprehension of the mode
in which real knowledge had been acquired and must be increased.

Roger Bacon was born in 1214, near Ilchester, in Somersetshire, of
an old family. In his youth he was a student at Oxford, and made
extraordinary progress in all branches of learning. He then went to
the University of Paris, as was at that time the custom of learned
Englishmen, and there received the degree of Doctor of Theology. At
the persuasion of Robert Grostête, bishop of Lincoln, he entered the
brotherhood of Franciscans in Oxford, and gave himself up to study
with extraordinary fervour. He was termed by his brother monks _Doctor
Mirabilis_. We know from his own works, as well as from the traditions
concerning him, that he possessed an intimate acquaintance with all the
science of his time which could be acquired from books; and that he had
made many remarkable advances by means of his own experimental labours.
He was acquainted with Arabic, as well as with the other languages
common in his time. In the title of his works, we find the whole
range of science and philosophy, Mathematics and Mechanics, Optics,
Astronomy, Geography, Chronology, Chemistry, Magic, Music, Medicine,
Grammar, Logic, Metaphysics, Ethics, and Theology; and judging from
those which are published, these works are full of sound and exact
knowledge. He is, with good reason, supposed to have discovered, or to
have had some knowledge of, several of the most remarkable inventions
which were made generally known soon afterwards; as gunpowder, lenses,
burning specula, telescopes, clocks, the correction of the calendar,
and the explanation of the rainbow.

Thus possessing, in the acquirements and habits of his own mind,
abundant examples of the nature of knowledge and of the process of
invention, Roger Bacon felt also a deep interest in the growth and
progress of science, a spirit of inquiry respecting the causes which
produced or prevented its advance, and a fervent hope and trust in its
future destinies; and these feelings impelled him to speculate worthily
and wisely respecting a Reform of the Method of Philosophizing. The
manuscripts of his works have existed for nearly six hundred years in
many of the libraries of Europe, and especially in those of England;
and for a long period the very imperfect portions of them which were
generally known, left the character and attainments of the author
shrouded in a kind of mysterious obscurity. About a century ago,
however, his _Opus Majus_ was published[61] by Dr. S. Jebb, principally
from a manuscript in the Library of Trinity College, Dublin; and this
contained most or all of the separate works which were previously
known to the public, along with others still more peculiar and
characteristic. We are thus able to judge of Roger Bacon's knowledge
and of his views, and they are in every way well worthy our attention.

The _Opus Majus_ is addressed to Pope Clement the Fourth, whom Bacon
had known when he was legate in England as Cardinal-bishop of Sabina,
and who admired the talents of the monk, and pitied him for the
persecutions to which he was exposed. On his elevation to the papal
chair, this account of Bacon's labours and views was sent, at the
earnest request of the pontiff. Besides the _Opus Majus_, he wrote
two others, the _Opus Minus_ and _Opus Tertium_; which were also sent
to the pope, as the author says[62], "on account of the danger of
roads, and the possible loss of the work." These works still exist
unpublished, in the Cottonian and other libraries. The _Opus Majus_ is
a work equally wonderful with regard to its general scheme, and to the
special treatises with which the outlines of the plan are filled up.
The professed object of the work is to urge the necessity of a reform
in the mode of philosophizing, to set forth the reasons why knowledge
had not made a greater progress, to draw back attention to the sources
of knowledge which had been unwisely neglected, to discover other
sources which were yet almost untouched, and to animate men in the
undertaking, by a prospect of the vast advantages which it offered.
In the development of this plan, all the leading portions of science
are expounded in the most complete shape which they had at that time
assumed; and improvements of a very wide and striking kind are proposed
in some of the principal of these departments. Even if the work had had
no leading purpose, it would have been highly valuable as a treasure of
the most solid knowledge and soundest speculations of the time; even
if it had contained no such details, it would have been a work most
remarkable for its general views and scope. It may be considered as,
at the same time, the _Encyclopedia_ and the _Novum Organon_ of the
thirteenth century.

Since this work is thus so important in the history of Inductive
Philosophy I shall give, in a note, a view[63] of its divisions and
contents. But I must now endeavour to point out more especially the way
in which the various principles, which the reform of scientific method
involved, are here brought into view.

One of the first points to be noticed for this purpose, is the
resistance to authority; and at the stage of philosophical history
with which we here have to do, this means resistance to the authority
of Aristotle, as adopted and interpreted by the Doctors of the
Schools. Bacon's work[64] is divided into Six Parts; and of these
Parts, the First is, Of the four universal Causes of all Human
Ignorance. The causes thus enumerated[65] are:--the force of unworthy
authority;--traditionary habit;--the imperfection of the undisciplined
senses;--and the disposition to conceal our ignorance and to make an
ostentatious show of our knowledge. These influences involve every man,
occupy every condition. They prevent our obtaining the most useful and
large and fair doctrines of wisdom, the secret of all sciences and
arts. He then proceeds to argue, from the testimony of philosophers
themselves, that the authority of antiquity, and especially of
Aristotle, is not infallible. "We find[66] their books full of doubts,
obscurities, and perplexities. They scarce agree with each other in
one empty question or one worthless sophism, or one operation of
science, as one man agrees with another in the practical operations
of medicine, surgery, and the like arts of Secular men. Indeed," he
adds, "not only the philosophers, but the saints have fallen into
errors which they have afterwards retracted," and this he instances
in Augustin, Jerome, and others. He gives an admirable sketch[67] of
the progress of philosophy from the Ionic School to Aristotle; of whom
he speaks with great applause. "Yet," he adds[68], "those who came
after him corrected him in some things, and added many things to his
works, and shall go on adding to the end of the world." Aristotle, he
adds, is now called peculiarly[69] the Philosopher, "yet there was a
time when his philosophy was silent and unregarded, either on account
of the rarity of copies of his works, or their difficulty, or from
envy; till after the time of Mahomet, when Avicenna and Averroes, and
others, recalled this philosophy into the full light of exposition. And
although the Logic and some other works were translated by Boethius
from the Greek, yet the philosophy of Aristotle first received a quick
increase among the Latins at the time of Michael Scot; who, in the year
of our Lord 1230, appeared, bringing with him portions of the books of
Aristotle on Natural Philosophy and Mathematics. And yet a small part
only of the works of this author is translated, and a still smaller
part is in the hands of common students." He adds further[70] (in the
Third Part of the _Opus Majus_, which is a Dissertation on language),
that the translations which are current of these writings, are very
bad and imperfect. With these views, he is moved to express himself
somewhat impatiently[71] respecting these works: "If I had," he says,
"power over the works of Aristotle, I would have them all burnt; for
it is only a loss of time to study in them, and a cause of error, and
a multiplication of ignorance beyond expression." "The common herd of
students," he says, "with their heads, have no principle by which they
can be excited to any worthy employment; and hence they mope and make
asses of themselves over their bad translations, and lose their time,
and trouble, and money."

The remedies which he recommends for these evils, are, in the first
place, the study of that only perfect wisdom which is to be found in
the sacred Scripture[72], in the next place, the study of mathematics
and the use of experiment[73]. By the aid of these methods, Bacon
anticipates the most splendid progress for human knowledge. He takes up
the strain of hope and confidence which we have noticed as so peculiar
in the Roman writers; and quotes some of the passages of Seneca which
we adduced in illustration of this:--that the attempts in science were
at first rude and imperfect, and were afterwards improved;--that the
day will come, when what is still unknown shall be brought to light by
the progress of time and the labours of a longer period;--that one age
does not suffice for inquiries so wide and various;--that the people
of future times shall know many things unknown to us;--and that the
time shall arrive when posterity will wonder that we overlooked what
was so obvious. Bacon himself adds anticipations more peculiarly in
the spirit of his own time. "We have seen," he says, at the end of the
work, "how Aristotle, by the ways which wisdom teaches, could give to
Alexander the empire of the world. And this the Church ought to take
into consideration against the infidels and rebels, that there may be a
sparing of Christian blood, and especially on account of the troubles
that shall come to pass in the days of Antichrist; which by the grace
of God, it would be easy to obviate, if prelates and princes would
encourage study, and join in searching out the secrets of nature and
art."

It may not be improper to observe here that this belief in the
appointed progress of knowledge, is not combined with any overweening
belief in the unbounded and independent power of the human intellect.
On the contrary, one of the lessons which Bacon draws from the state
and prospects of knowledge, is the duty of faith and humility. "To
him," he says[74], "who denies the truth of the faith because he is
unable to understand it, I will propose in reply the course of nature,
and as we have seen it in examples." And after giving some instances,
he adds, "These, and the like, ought to move men and to excite them
to the reception of divine truths. For if, in the vilest objects of
creation, truths are found, before which the inward pride of man must
bow, and believe though it cannot understand, how much more should
man humble his mind before the glorious truths of God!" He had before
said[75]: "Man is incapable of perfect wisdom in this life; it is
hard for him to ascend towards perfection, easy to glide downwards
to falsehoods and vanities: let him then not boast of his wisdom, or
extol his knowledge. What he knows is little and worthless, in respect
of that which he believes without knowing; and still less, in respect
of that which he is ignorant of. He is mad who thinks highly of his
wisdom; he most mad, who exhibits it as something to be wondered at."
He adds, as another reason for humility, that he has proved by trial,
he could teach in one year, to a poor boy, the marrow of all that
the most diligent person could acquire in forty years' laborious and
expensive study.

To proceed somewhat more in detail with regard to Roger Bacon's views
of a Reform in Scientific Inquiry, we may observe that by making
Mathematics and Experiment the two great points of his recommendation,
he directed his improvement to the two essential parts of all
knowledge, Ideas and Facts, and thus took the course which the most
enlightened philosophy would have suggested. He did not urge the
prosecution of experiment, to the comparative neglect of the existing
mathematical sciences and conception; a fault which there is some
ground for ascribing to his great namesake and successor Francis
Bacon: still less did he content himself with a mere protest against
the authority of the schools, and a vague demand for change, which
was almost all that was done by those who put themselves forward as
reformers in the intermediate time. Roger Bacon holds his way steadily
between the two poles of human knowledge; which, as we have seen, it
is far from easy to do. "There are two modes of knowing," says he[76];
"by argument, and by experiment. Argument concludes a question; but
it does not make us feel certain, or acquiesce in the contemplation
of truth, except the truth be also found to be so by experience."
It is not easy to express more decidedly the clearly seen union of
exact conceptions with certain facts, which, as we have explained,
constitutes real knowledge.

One large division of the _Opus Majus_ is "On the Usefulness of
Mathematics," which is shown by a copious enumeration of existing
branches of knowledge, as Chronology, Geography, the Calendar and
(in a separate Part) Optics. There is a chapter[77], in which it is
proved by reason, that all science requires mathematics. And the
arguments which are used to establish this doctrine, show a most just
appreciation of the office of mathematics in science. They are such as
follows:--That other sciences use examples taken from mathematics as
the most evident:--That mathematical knowledge is, as it were, innate
in us, on which point he refers to the well-known dialogue of Plato,
as quoted by Cicero:--That this science, being the easiest, offers the
best introduction to the more difficult:--That in mathematics, things
as known to us are identical with things as known to nature:--That
we can here entirely avoid doubt and error, and obtain certainty and
truth:--That mathematics is prior to other sciences in nature, because
it takes cognizance of quantity, which is apprehended by intuition,
(_intuitu intellectus_). "Moreover," he adds[78], "there have been
found famous men, as Robert, bishop of Lincoln, and Brother Adam
Marshman (de Marisco), and many others, who by the power of mathematics
have been able to explain the causes of things; as may be seen in the
writings of these men, for instance, concerning the Rainbow and Comets,
and the generation of heat, and climates, and the celestial bodies."

But undoubtedly the most remarkable portion of the _Opus Majus_ is the
Sixth and last Part, which is entitled "De Scientia experimentali."
It is indeed an extraordinary circumstance to find a writer of the
thirteenth century, not only recognizing experiment as one source
of knowledge, but urging its claims as something far more important
than men had yet been aware of, exemplifying its value by striking
and just examples, and speaking of its authority with a dignity of
diction which sounds like a foremurmur of the Baconian sentences
uttered nearly four hundred years later. Yet this is the character of
what we here find[79]. "Experimental science, the sole mistress of
speculative sciences, has three great Prerogatives among other parts
of knowledge: First she tests by experiment the noblest conclusions of
all other sciences: Next she discovers respecting the notions which
other sciences deal with, magnificent truths to which these sciences of
themselves can by no means attain: her Third dignity is, that she by
her own power and without respect of other sciences, investigates the
secret of nature."

The examples which Bacon gives of these "Prerogatives" are very
curious, exhibiting, among some error and credulity, sound and clear
views. His leading example of the First Prerogative, is the Rainbow,
of which the cause, as given by Aristotle, is tested by reference to
experiment with a skill which is, even to us now, truly admirable.
The examples of the Second Prerogative are three:--_first_, the art
of making an artificial sphere which shall move with the heavens by
natural influences, which Bacon trusts may be done, though astronomy
herself cannot do it--"et tunc," he says, "thesaurum unius regis
valeret hoc instrumentum;"--_secondly_, the art of prolonging life,
which experiment may teach, though medicine has no means of securing
it except by regimen[80];--_thirdly_, the art of making gold finer
than fine gold, which goes beyond the power of alchemy. The Third
Prerogative of experimental science, arts independent of the received
sciences, is exemplified in many curious examples, many of them
whimsical traditions. Thus it is said that the character of a people
may be altered by altering the air[81]. Alexander, it seems, applied
to Aristotle to know whether he should exterminate certain nations
which he had discovered, as being irreclaimably barbarous; to which
the philosopher replied, "If you can alter their air, permit them to
live, if not, put them to death." In this part, we find the suggestion
that the fire-works made by children, of saltpetre, might lead to the
invention of a formidable military weapon.

It could not be expected that Roger Bacon, at a time when experimental
science hardly existed, could give any _precepts_ for the discovery
of truth by experiment. But nothing can be a better _example_ of the
method of such investigation, than his inquiry concerning the cause of
the Rainbow. Neither Aristotle, nor Avicenna, nor Seneca, he says, have
given us any clear knowledge of this matter, but experimental science
can do so. Let the experimenter (_experimentator_) consider the cases
in which he finds the same colours, as the hexagonal crystals from
Ireland and India; by looking into these he will see colours like those
of the rainbow. Many think that this arises from some special virtue of
these stones and their hexagonal figure; let therefore the experimenter
go on, and he will find the same in other transparent stones, in dark
ones as well as in light-coloured. He will find the same effect also
in other forms than the hexagon, if they be furrowed in the surface,
as the Irish crystals are. Let him consider too, that he sees the same
colours in the drops which are dashed from oars in the sunshine;--and
in the spray thrown by a millwheel;--and in the dew-drops which lie on
the grass in a meadow on a summer-morning;--and if a man takes water
in his mouth and projects it on one side into a sunbeam;--and if in an
oil-lamp hanging in the air, the rays fall in certain positions upon
the surface of the oil;--and in many other ways, are colours produced.
We have here a collection of instances, which are almost all examples
of the same kind as the phenomenon under consideration; and by the help
of a principle collected by induction from these facts, the colours of
the rainbow were afterwards really explained.

With regard to the form and other circumstances of the bow he is still
more precise. He bids us measure the height of the bow and of the sun,
to show that the center of the bow is exactly opposite to the sun.
He explains the circular form of the bow,--its being independent of
the form of the cloud, its moving when we move, its flying when we
follow,--by its consisting of the reflections from a vast number of
minute drops. He does not, indeed, trace the course of the rays through
the drop, or account for the precise magnitude which the bow assumes;
but he approaches to the verge of this part of the explanation; and
must be considered as having given a most happy example of experimental
inquiry into nature, at a time when such examples were exceedingly
scanty. In this respect, he was more fortunate than Francis Bacon, as
we shall hereafter see.

We know but little of the biography of Roger Bacon, but we have every
reason to believe that his influence upon his age was not great.
He was suspected of magic, and is said to have been put into close
confinement in consequence of this charge. In his work he speaks
of Astrology as a science well worth cultivating. "But," says he,
"Theologians and Decretists, not being learned in such matters and
seeing that evil as well as good may be done, neglect and abhor such
things, and reckon them among Magic Arts." We have already seen, that
at the very time when Bacon was thus raising his voice against the
habit of blindly following authority, and seeking for all science
in Aristotle, Thomas Aquinas was employed in fashioning Aristotle's
tenets into that fixed form in which they became the great impediment
to the progress of knowledge. It would seem, indeed, that something
of a struggle between the progressive and stationary powers of the
human mind was going on at this time. Bacon himself says[82], "Never
was there so great an appearance of wisdom, nor so much exercise of
study in so many Faculties, in so many regions, as for this last forty
years. Doctors are dispersed everywhere, in every castle, in every
burgh, and especially by the students of two Orders, (he means the
Franciscans and Dominicans, who were almost the only religious orders
that distinguished themselves by an application to study[83],) which
has not happened except for about forty years. And yet there was never
so much ignorance, so much error." And in the part of his work which
refers to Mathematics, he says of that study[84], that it is the door
and the key of the sciences; and that the neglect of it for thirty or
forty years has entirely ruined the studies of the Latins. According to
these statements, some change, disastrous to the fortunes of science,
must have taken place about 1230, soon after the foundation of the
Dominican and Franciscan Orders[85]. Nor can we doubt that the adoption
of the Aristotelian philosophy by these two Orders, in the form in
which the Angelical Doctor had systematized it, was one of the events
which most tended to defer, for three centuries, the reform which Roger
Bacon urged as a matter of crying necessity in his own time.


FOOTNOTES:

[Footnote 61: _Fratris Rogeri Bacon, Ordinis Minorum_, Opus Majus, _ad
Clementem Quartum, Pontificem Romanum, ex MS. Codice Dubliniensi cum
aliis quibusdam collato, nunc primum edidit_ S. Jebb, M.D. Londini,
1733.]

[Footnote 62: _Opus Majus_, Præf.]

[Footnote 63: Contents of Roger Bacon's _Opus Majus_.

Part I. On the four causes of human ignorance:--Authority, Custom,
Popular Opinion, and the Pride of supposed Knowledge.

Part II. On the source of perfect wisdom in the Sacred Scripture.

Part III. On the Usefulness of Grammar.

Part IV. On the Usefulness of Mathematics.

(1) The necessity of Mathematics in Human Things (published separately
as the _Specula Mathematica_).

(2) The necessity of Mathematics in Divine Things.--1°. This study
has occupied holy men: 2°. Geography: 3°. Chronology: 4°. Cycles;
the Golden Number, &c.: 5°. Natural Phenomena, as the Rainbow: 6°.
Arithmetic: 7°. Music.

(3) The necessity of Mathematics in Ecclesiastical Things.--1°. The
Certification of Faith: 2°. The Correction of the Calendar.

(4) The necessity of Mathematics in the State.--1°. Of Climates: 2°.
Hydrography: 3°. Geography: 4°. Astrology.

Part V. On Perspective (published separately as _Perspectiva_).

(1) The organs of vision.

(2) Vision in straight lines.

(3) Vision reflected and refracted.

(4) De multiplicatione specierum (on the propagation of the impressions
of light, heat, &c.)

Part VI. On Experimental Science.]

[Footnote 64: _Op. Maj._ p. 1.]

[Footnote 65: _Ibid._ p. 2.]

[Footnote 66: _Ibid._ p. 10.]

[Footnote 67: I will give a specimen. _Opus Majus_, c. viii. p. 35:
"These two kinds of philosophers, the Ionic and Italic, ramified
through many sects and various successors, till they came to the
doctrine of Aristotle, who corrected and changed the propositions
of all his predecessors, and attempted to perfect philosophy. In
the [Italic] succession, Pythagoras, Archytas Tarentinus and Timæus
are most prominently mentioned. But the principal philosophers, as
Socrates, Plato, and Aristotle, did not descend from this line, but
were Ionics and true Greeks, of whom the first was Thales Milesius....
Socrates, according to Augustine in his 8th book, is related to have
been a disciple of Archelaus. This Socrates is called the father of the
great philosophers, since he was the master of Plato and Aristotle,
from whom all the sects of philosophers descended.... Plato, first
learning what Socrates and Greece could teach, made a laborious voyage
to Egypt, to Archytas of Tarentum and Timæus, as says Jerome to
Paulinus. And this Plato is, according to holy men, preferred to all
philosophers, because he has written many excellent things concerning
God, and morality, and a future life, which agree with the divine
wisdom of God. And Aristotle was born before the death of Socrates,
since he was his hearer for three years, as we read in the life of
Aristotle.... This Aristotle, being made the master of Alexander the
Great, sent two thousand men into all regions of the earth, to search
out the nature of things, as Pliny relates in the 8th book of his
_Naturalia_, and composed a thousand books, as we read in his life."]

[Footnote 68: _Ibid._ p. 36.]

[Footnote 69: _Autonomaticè._]

[Footnote 70: _Op. Maj._ p. 46.]

[Footnote 71: See _Pref._ to Jebb's edition. The passages, there
quoted, however, are not extracts from the _Opus Majus_, but
(apparently) from the _Opus Minus_ (_MS. Cott._ Tib. c. 5.) "Si haberem
potestatem supra libros Aristotelis, ego facerem omnes cremari; quia
non est nisi temporis amissio studere in illis, et causa erroris, et
multiplicatio ignorantiæ ultra id quod valeat explicari.... Vulgus
studentum cum capitibus suis non habet unde excitetur ad aliquid
dignum, et ideo languet et _asininat_ circa male translata, et tempus
et studium amittit in omnibus et expensas."]

[Footnote 72: Part ii.]

[Footnote 73: Parts iv. v. and vi.]

[Footnote 74: _Op. Maj._ p. 476.]

[Footnote 75: _Op. Maj._ p. 15.]

[Footnote 76: _Ibid._ p. 445, see also p. 448. "Scientiæ aliæ sciunt
sua principia invenire per experimenta, sed conclusiones per argumenta
facta ex principiis inventis. Si vero debeant habere experientiam
conclusionum suarum particularem et completam, tunc oportet quod
habeant per adjutorium istius scientiæ nobilis (experimentalis)."]

[Footnote 77: _Op. Maj._ p. 60.]

[Footnote 78: _Ibid._ p. 64.]

[Footnote 79: "Veritates magnificas in terminis aliarum scientiarum in
quas per nullam viam possunt illæ scientiæ, hæc sola scientiarum domina
speculativarum, potest dare." _Op. Maj._ p. 465.]

[Footnote 80: One of the ingredients of a preparation here mentioned,
is the flesh of a dragon, which it appears is used as food by the
Ethiopians. The mode of preparing this food cannot fail to amuse the
reader. "Where there are good flying dragons, by the art which they
possess, they draw them out of their dens, and have bridles and saddles
in readiness, and they ride upon them, and make them bound about in the
air in a violent manner, that the hardness and toughness of the flesh
may be reduced, as boars are hunted and bulls are baited before they
are killed for eating." _Op. Maj._ p. 470.]

[Footnote 81: _Op. Maj._ p. 473.]

[Footnote 82: Quoted by Jebb, _Pref._ to _Op. Maj._]

[Footnote 83: Mosheim, _Hist._ iii. 161.]

[Footnote 84: _Op. Maj._ p. 57.]

[Footnote 85: Mosheim, iii. 161.]




CHAPTER XII.

THE REVIVAL OF PLATONISM.


1. _Causes of Delay in the Advance of Knowledge._--In the insight
possessed by learned men into the method by which truth was to be
discovered, the fourteenth and fifteenth centuries went backwards,
rather than forwards, from the point which had been reached in the
thirteenth. Roger Bacon had urged them to have recourse to experiment;
but they returned with additional and exclusive zeal to the more
favourite employment of reasoning upon their own conceptions. He had
called upon them to look at the world without; but their eyes forthwith
turned back upon the world within. In the constant oscillation of the
human mind between Ideas and Facts, after having for a moment touched
the latter, it seemed to swing back more impetuously to the former.
Not only was the philosophy of Aristotle firmly established for a
considerable period, but when men began to question its authority, they
attempted to set up in its place a philosophy still more purely ideal,
that of Plato. It was not till the actual progress of experimental
knowledge for some centuries had given it a vast accumulation of force,
that it was able to break its way fully into the circle of speculative
science. The new Platonist schoolmen had to run their course, the
practical discoverers had to prove their merit by their works, the
Italian innovators had to utter their aspirations for a change, before
the second Bacon could truly declare that the time for a fundamental
reform was at length arrived.

It cannot but seem strange, to any one who attempts to trace the
general outline of the intellectual progress of man, and who considers
him as under the guidance of a Providential sway, that he should
thus be permitted to wander so long in a wilderness of intellectual
darkness; and even to turn back, by a perverse caprice as it might
seem, when on the very border of the brighter and better land which was
his destined inheritance. We do not attempt to solve this difficulty:
but such a course of things naturally suggests the thought, that a
progress in physical science is not the main object of man's career,
in the eyes of the Power who directs the fortunes of our race. We
can easily conceive that it may have been necessary to man's general
welfare that he should continue to turn his eyes inwards upon his own
heart and faculties, till Law and Duty, Religion and Government, Faith
and Hope, had been fully incorporated with all the past acquisitions of
human intellect; rather than that he should have rushed on into a train
of discoveries tending to chain him to the objects and operations of
the material world. The systematic Law[86] and philosophical Theology
which acquired their ascendancy in men's minds at the time of which
we speak, kept them engaged in a region of speculations which perhaps
prepared the way for a profounder and wider civilization, for a more
elevated and spiritual character, than might have been possible without
such a preparation. The great Italian poet of the fourteenth century
speaks with strong admiration of the founders of the system which
prevailed in his time. Thomas, Albert, Gratian, Peter Lombard, occupy
distinguished places in the Paradise. The first, who is the poet's
instructor, says,--

      Io fui degli agni della santa greggia
    Che Domenico mena per cammino
    U' ben s'impingua se non si vaneggia.
      Questo che m'è a destra piu vicino
    Frate e maestro fummi; ed esso Alberto
    E di Cologna, ed io Tomas d'Aquino....
      Quell' altro fiammeggiar esce del riso
      De Grazian, che l'uno et l'altro foro
        Ajutò si che piace in Paradiso.

      I, then, was of the lambs that Dominic
    Leads, for his saintly flock, along the way
    Where well they thrive not swoln with vanity.
    He nearest on my right-hand brother was
    And master to me; Albert of Cologne
    Is this; and of Aquinum Thomas, I....
    That next resplendence issues from the smile
    Of Gratian, who to either forum lent
    Such help as favour wins in Paradise.

It appears probable that neither poetry, nor painting, nor the other
arts which require for their perfection a lofty and spiritualized
imagination, would have appeared in the noble and beautiful forms which
they assumed in the fourteenth and fifteenth century, if men of genius
had, at the beginning of that period, made it their main business
to discover the laws of nature, and to reduce them to a rigorous
scientific form. Yet who can doubt that the absence of these touching
and impressive works would have left one of the best and purest parts
of man's nature without its due nutriment and development? It may
perhaps be a necessary condition in the progress of man, that the Arts
which aim at beauty should reach their excellence before the Sciences
which seek speculative truth; and if this be so, we inherit, from the
middle ages, treasures which may well reconcile us to the delay which
took place in their cultivation of experimental science.

However this may be, it is our business at present to trace the
circumstances of this very lingering advance. We have already noticed
the contest of the Nominalists and Realists, which was one form,
though, with regard to scientific methods, an unprofitable one, of
the antithesis of Ideas and Things. Though, therefore, this struggle
continued, we need not dwell upon it. The Nominalists denied the real
existence of Ideas, which doctrine was to a great extent implied
in the prevailing systems; but the controversy in which they thus
engaged, did not lead them to seek for knowledge in a new field and
by new methods. The arguments which Occam the Nominalist opposes to
those of Duns Scotus the Realist, are marked with the stamp of the
same system, and consist only in permutations and combinations of the
same elementary conceptions. It was not till the impulse of external
circumstances was added to the discontent, which the more stirring
intellects felt towards the barren dogmatism of their age, that the
activity of the human mind was again called into full play, and a new
career of progression entered upon, till then undreamt of, except by a
few prophetic spirits.


2. _Causes of Progress._--These circumstances were principally the
revival of Greek and Roman literature, the invention of Printing, the
Protestant Reformation, and a great number of curious discoveries and
inventions in the arts, which were soon succeeded by important steps
in speculative physical science. Connected with the first of these
events, was the rise of a party of learned men who expressed their
dissatisfaction with the Aristotelian philosophy, as it was then
taught, and manifested a strong preference for the views of Plato. It
is by no means suitable to our plan to give a detailed account of this
new Platonic school; but we may notice a few of the writers who belong
to it, so far at least as to indicate its influence upon the Methods of
pursuing science.

In the fourteenth century[87], the frequent intercourse of the most
cultivated persons of the Eastern and Western Empire, the increased
study of the Greek language in Italy, the intellectual activity of the
Italian States, the discovery of manuscripts of the classical authors,
were circumstances which excited or nourished a new and zealous study
of the works of Greek and Roman genius. The genuine writings of the
ancients, when presented in their native life and beauty, instead of
being seen only in those lifeless fragments and dull transformations
which the scholastic system had exhibited, excited an intense
enthusiasm. Europe, at that period, might be represented by Plato's
beautiful allegory, of a man who, after being long kept in a dark
cavern, in which his knowledge of the external world is gathered from
the images which stream through the chinks of his prison, is at last
led forth into the full blaze of day. It was inevitable that such a
change should animate men's efforts and enlarge their faculties. Greek
literature became more and more known, especially by the influence of
learned men who came from Constantinople into Italy: these teachers,
though they honoured Aristotle, reverenced Plato no less, and had never
been accustomed to follow with servile submission of thought either
these or any other leaders. The effect of such influences soon reveals
itself in the works of that period. Dante has woven into his _Divina
Commedia_ some of the ideas of Platonism. Petrarch, who had formed his
mind by the study of Cicero, and had thus been inspired with a profound
admiration for the literature of Greece, learnt Greek from Barlaam, a
monk who came as ambassador from the Emperor of the East to the Pope,
in 1339. With this instructor, the poet read the works of Plato; struck
by their beauty, he contributed, by his writings and his conversation,
to awake in others an admiration and love for that philosopher, which
soon became strongly and extensively prevalent among the learned in
Italy.


3. _Hermolaus Barbarus, &c._--Along with the feeling there prevailed
also, among those who had learnt to relish the genuine beauties of
the Greek and Latin writers, a strong disgust for the barbarisms in
which the scholastic philosophy was clothed. Hermolaus Barbarus[88],
who was born in 1454, at Venice, and had formed his taste by the
study of classical literature, translated, among other learned works,
Themistius's paraphrastic expositions of the Physics of Aristotle;
with the view of trying whether the Aristotelian Natural Philosophy
could not be presented in good Latin, which the scholastic teachers
denied. In his Preface he expresses great indignation against those
philosophers who have written and disputed on philosophical subjects
in barbarous Latin, and in an uncultured style, so that all refined
minds are repelled from these studies by weariness and disgust. They
have, he says, by this barbarism, endeavoured to secure to themselves,
in their own province, a supremacy without rivals or opponents. Hence
they maintain that mathematics, philosophy, jurisprudence, cannot
be expounded in correct Latin;--that between these sciences and the
genuine Latin language there is a great gulf, as between things that
cannot be brought together: and on this ground they blame those who
combine the study of philology and eloquence with that of science.
This opinion, adds Hermolaus, perverts and ruins our studies; and is
highly prejudicial and unworthy in respect to the state. Hermolaus
awoke in others, as for instance, in John Picus of Mirandula, the same
dislike to the reigning school philosophy. As an opponent of the same
kind, we may add Marius Nizolius of Bersallo, a scholar who carried
his admiration of Cicero to an exaggerated extent, and who was led,
by a controversy with the defenders of the scholastic philosophy,
to publish (1553) a work _On the True Principles and True Method of
Philosophizing_. In the title of this work, he professes to give "the
true principles of almost all arts and sciences, refuting and rejecting
almost all the false principles of the Logicians and Metaphysicians."
But although, in the work, he attacks the scholastic philosophy, he
does little or nothing to justify the large pretensions of his title;
and he excited, it is said, little notice. It is therefore curious that
Leibnitz should have thought it worth his while to re-edit this work,
which he did in 1670, adding remarks of his own.


4. _Nicolaus Cusanus._--Without dwelling upon this opposition to the
scholastic system on the ground of taste, I shall notice somewhat
further those writers who put forwards Platonic views, as fitted to
complete or to replace the doctrines of Aristotle. Among these, I may
place Nicolaus Cusanus, (so called from Cus, a village on the Moselle,
where he was born in 1401;) who was afterwards raised to the dignity
of cardinal. We might, indeed, at first be tempted to include Cusanus
among those persons who were led to reject the old philosophy by being
themselves agents in the progressive movement of physical science.
For he published, before Copernicus, and independently of him, the
doctrine that the earth is in motion[89]. But it should be recollected
that in order to see the possibility of this doctrine, and its claims
to acceptance, no new reference to observation was requisite. The
Heliocentric System was merely a new mode of representing to the mind
facts, with which all astronomers had long been familiar. The system
might very easily have been embraced and inculcated by Plato himself;
as indeed it is said to have been actually taught by Pythagoras. The
mere adoption of the Heliocentric view, therefore, without attempting
to realize the system in detail, as Copernicus did, cannot entitle a
writer of the fifteenth century to be looked upon as one of the authors
of the discoveries of that period; and we must consider Cusanus as a
speculative anti-Aristotelian, rather than as a practical reformer.

The title of Cusanus's book, _De Doctâ Ignorantiâ_, shows how far
he was from agreeing with those who conceived that, in the works
of Aristotle, they had a full and complete system of all human
knowledge. At the outset of this book[90], he says, after pointing
out some difficulties in the received philosophy, "If, therefore,
the case be so, (as even the very profound Aristotle, in his _First
Philosophy_, affirms,) that in things most manifest by nature, there
is a difficulty, no less than for an owl to look at the sun; since
the appetite of knowledge is not implanted in us in vain, we ought
to desire to know that we are ignorant. If we can fully attain to
this, we shall arrive at _Instructed Ignorance_." How far he was from
placing the source of knowledge in experience, as opposed to ideas,
we may see in the following passage[91] from another work of his,
_On Conjectures_. "Conjectures must proceed from our mind, as the
real world proceeds from the infinite Divine Reason. For since the
human mind, the lofty likeness of God, participates, as it may, in
the fruitfulness of the creative nature, it doth from itself, as the
image of the Omnipotent Form, bring forth reasonable thoughts which
have a similitude to real existences. Thus the Human Mind exists as a
conjectural form of the world, as the Divine Mind is its real form." We
have here the Platonic or ideal side of knowledge put prominently and
exclusively forwards.


5. _Marsilius Ficinus, &c._--A person who had much more influence
on the diffusion of Platonism was Marsilius Ficinus, a physician
of Florence. In that city there prevailed, at the time of which we
speak, the greatest enthusiasm for Plato. George Gemistius Pletho,
when in attendance upon the Council of Florence, had imparted to
many persons the doctrines of the Greek philosopher; and, among
others, had infused a lively interest on this subject into the elder
Cosmo, the head of the family of the Medici. Cosmo formed the plan
of founding a Platonic academy. Ficinus[92], well instructed in the
works of Plato, Plotinus, Proclus, and other Platonists, was selected
to further this object, and was employed in translating the works of
these authors into Latin. It is not to our present purpose to consider
the doctrines of this school, except so far as they bear upon the
nature and methods of knowledge; and therefore I must pass by, as I
have in other instances done, the greater part of their speculations,
which related to the nature of God, the immortality of the soul, the
principles of Goodness and Beauty, and other points of the same order.
The object of these and other Platonists of this school, however, was
not to expel the authority of Aristotle by that of Plato. Many of
them had come to the conviction that the highest ends of philosophy
were to be reached only by bringing into accordance the doctrines
of Plato and of Aristotle. Of this opinion was John Picus, Count of
Mirandula and Concordia; and under this persuasion he employed the
whole of his life in labouring upon a work, _De Concordiâ Platonis et
Aristotelis_, which was not completed at the time of his death, in
1494; and has never been published. But about a century later, another
writer of the same school, Francis Patricius[93], pointing out the
discrepancies between the two Greek teachers, urged the propriety of
deposing Aristotle from the supremacy he had so long enjoyed. "Now all
these doctrines, and others not a few," he says[94], "since they are
Platonic doctrines, philosophically most true, and consonant with the
Catholic faith, whilst the Aristotelian tenets are contrary to the
faith, and philosophically false, who will not, both as a Christian and
a Philosopher, prefer Plato to Aristotle? And why should not hereafter,
in all the colleges and monasteries of Europe, the reading and study
of Plato be introduced? Why should not the philosophy of Aristotle be
forthwith exiled from such places? Why must men continue to drink the
mortal poison of impiety from that source?" with much more in the same
strain.

The Platonic school, of which we have spoken, had, however, reached
its highest point of prosperity before this time, and was already
declining. About 1500, the Platonists appeared to triumph over the
Peripatetics[95]; but the death of their great patron, Cardinal
Bessarion, about this time, and we may add, the hollowness of their
system in many points, and its want of fitness for the wants and
expectations of the age, turned men's thoughts partly back to the
established Aristotelian doctrines, and partly forwards to schemes of
bolder and fresher promise.


6. _Francis Patricius._--Patricius, of whom we have just spoken, was
one of those who had arrived at the conviction that the formation of
a new philosophy, and not merely the restoration of an old one, was
needed. In 1593, appeared his _Nova de Universis Philosophia_; and
the mode in which it begins[96] can hardly fail to remind us of the
expressions which Francis Bacon soon afterwards used in the opening of
a work of the same nature. "Francis Patricius, being about to found
anew the true philosophy of the universe, dared to begin by announcing
the following indisputable principles." Here, however, the resemblance
between Patricius and true inductive philosophers ends. His principles
are barren _à priori_ axioms; and his system has one main element,
_Light_, (_Lux_, or _Lumen_,) to which all operations of nature are
referred. In general cultivation, and practical knowledge of nature,
he was distinguished among his contemporaries. In various passages of
his works he relates[97] observations which he had made in the course
of his travels, in Cyprus, Corfu, Spain, the mountains of the Modenese,
and Dalmatia, which was his own country; his observations relate to
light, the saltness of the sea, its flux and reflux, and other points
of astronomy, meteorology, and natural history. He speaks of the sex of
plants[98]; rejects judicial astrology; and notices the astronomical
systems of Copernicus, Tycho, Fracastoro, and Torre. But the mode in
which he speaks of experiments proves, what indeed is evident from the
general scheme of his system, that he had no due appreciation of the
place which observation must hold in real and natural philosophy.


7. _Picus, Agrippa, &c._--It had been seen in the later philosophical
history of Greece, how readily the ideas of the Platonic school lead
on to a system of unfathomable and unbounded mysticism. John Picus,
of Mirandula[99], added to the study of Plato and the Neoplatonists,
a mass of allegorical interpretations of the Scriptures, and the
dreams of the Cabbala, a Jewish system[100], which pretends to explain
how all things are an emanation of the Deity. To this his nephew,
Francis Picus, added a reference to inward illumination[101], by which
knowledge is obtained, independently of the progress of reasoning.
John Reuchlin, or Capnio, born 1455; John Baptist Helmont, born 1577;
Francis Mercurius Helmont, born 1618, and others, succeeded John Picus
in his admiration of the Cabbala: while others, as Jacob Bœhmen,
rested upon internal revelations like Francis Picus. And thus we have
a series of mystical writers, continued into modern times, who may
be considered as the successors of the Platonic school; and who all
exhibit views altogether erroneous with regard to the nature and origin
of knowledge. Among the various dreams of this school are certain wide
and loose analogies of terrestrial and spiritual things. Thus in the
writings of Cornelius Agrippa (who was born 1487, at Cologne) we have
such systems as the following[102]:--"Since there is a threefold world,
elemental, celestial, and intellectual, and each lower one is governed
by that above it, and receives the influence of its powers: so that
the very Archetype and Supreme Author transfuses the virtues of his
omnipotence into us through angels, heavens, stars, elements, animals,
plants, stones,--into us, I say, for whose service he has framed and
created all these things;--the Magi do not think it irrational that
we should be able to ascend by the same degrees, the same worlds, to
this Archetype of the world, the Author and First Cause of all, of whom
all things are, and from whom they proceed; and should not only avail
ourselves of those powers which exist in the nobler works of creation,
but also should be able to attract other powers, and add them to these."

Agrippa's work, _De Vanitate Scientiarum_, may be said rather to
have a skeptical and cynical, than a Platonic, character. It is a
declamation[103], in a melancholy mood, against the condition of the
sciences in his time. His indignation at the worldly success of men
whom he considered inferior to himself, had, he says, metamorphosed him
into a dog, as the poets relate of Hecuba of Troy, so that his impulse
was to snarl and bark. His professed purpose, however, was to expose
the dogmatism, the servility, the self-conceit, and the neglect of
religious truth which prevailed in the reigning Schools of philosophy.
His views of the nature of science, and the modes of improving its
cultivation, are too imperfect and vague to allow us to rank him among
the reformers of science.


8. _Paracelsus, Fludd, &c._--The celebrated Paracelsus[104] put himself
forwards as a reformer in philosophy, and obtained no small number of
adherents. He was, in most respects, a shallow and impudent pretender;
and had small knowledge of the literature or science of his time:
but by the tone of his speaking and writing he manifestly belongs
to the mystical school of which we are now speaking. Perhaps by the
boldness with which he proposed new systems, and by connecting these
with the practical doctrines of medicine, he contributed something to
the introduction of a new philosophy. We have seen in the History of
Chemistry that he was the author of the system of Three Principles,
(salt, sulphur, and mercury,) which replaced the ancient doctrine of
Four Elements, and prepared the way for a true science of chemistry.
But the salt, sulphur, and mercury of Paracelsus were not, he tells his
disciples, the visible bodies which we call by those names, but certain
invisible, astral, or sidereal elements. The astral salt is the basis
of the solidity and incombustible parts in bodies; the astral sulphur
is the source of combustion and vegetation; the astral mercury is the
origin of fluidity and volatility. And again, these three elements are
analogous to the three elements of man,--Body, Spirit, and Soul.

A writer of our own country, belonging to this mystical school, is
Robert Fludd, or De Fluctibus, who was born in 1571, in Kent, and
after pursuing his studies at Oxford, travelled for several years.
Of all the Theosophists and Mystics, he is by much the most learned;
and was engaged in various controversies with Mersenne, Gassendi,
Kepler, and others. He thus brings us in contact with the next class
of philosophers whom we have to consider, the practical reformers
of philosophy;--those who furthered the cause of science by making,
promulgating, or defending the great discoveries which now began
to occupy men. He adopted the principle, which we have noticed
elsewhere[105], of the analogy of the Macrocosm and Microcosm, the
world of nature and the world of man. His system contains such a
mixture and confusion of physical and metaphysical doctrines as might
be expected from his ground-plan, and from his school. Indeed his
object, the general object of mystical speculators, is to identify
physical with spiritual truths. Yet the influence of the practical
experimental philosophy which was now gaining ground in the world may
be traced in him. Thus he refers to experiments on distillation to
prove the existence and relation of the regions of water, air, and
fire, and of the spirits which correspond to them; and is conceived, by
some persons[106], to have anticipated Torricelli in the invention of
the Barometer.

We need no further follow the speculations of this school. We see
already abundant reason why the reform of the methods of pursuing
science could not proceed from the Platonists. Instead of seeking
knowledge by experiment, they immersed themselves deeper than even the
Aristotelians had done in traditionary lore, or turned their eyes
inwards in search of an internal illumination. Some attempts were made
to remedy the defects of philosophy by a recourse to the doctrines
of other sects of antiquity, when men began to feel more distinctly
the need of a more connected and solid knowledge of nature than the
established system gave them. Among these attempts were those of
Berigard[107], Magernus, and especially Gassendi, to bring into repute
the philosophy of the Ionian school, of Democritus and of Epicurus. But
these endeavours were posterior in time to the new impulse given to
knowledge by Copernicus, Kepler, and Galileo, and were influenced by
views arising out of the success of these discoveries, and they must,
therefore, be considered hereafter. In the mean time, some independent
efforts (arising from speculative rather than practical reformers)
were made to cast off the yoke of the Aristotelian dogmatism, and to
apprehend the true form of that new philosophy which the most active
and hopeful minds saw to be needed; and we must give some account of
these attempts, before we can commit ourselves to the full stream of
progressive philosophy.


FOOTNOTES:

[Footnote 86: Gratian published the _Decretals_ in the twelfth century;
and the Canon and Civil Law became a regular study in the universities
soon afterwards.]

[Footnote 87: Tenneman, ix. 4.]

[Footnote 88: Tenneman, ix. 25.]

[Footnote 89: "Jam nobis manifestum est terram istam in veritate
moveri," &c.--_De Doctâ Ignorantiâ_, lib. ii. c. xii.]

[Footnote 90: _De Doct. Ignor._ lib. i. c. i.]

[Footnote 91: _De Conjecturis_, lib. i. c. iii. iv.]

[Footnote 92: Born in 1433.]

[Footnote 93: Born 1529, died 1597.]

[Footnote 94: _Aristoteles Exotericus_, p. 50.]

[Footnote 95: Tiraboschi, t. vii. pt. ii. p. 411.]

[Footnote 96: "Franciscus Patricius, novam veram integram de universis
conditurus philosophiam, sequentia uti verissima prænuntiare est
ausus. Prænunciata ordine persecutus, divinis oraculis, geometricis
rationibus, clarissimisque experimentis comprobavit.

  Ante primum nihil,
  Post primum omnia,
  A principio omnia," &c.

His other works are _Panaugia_, _Pancosmia_, _Dissertations
Peripateticæ_.]

[Footnote 97: Tiraboschi, t. vii. pt. ii. p. 411.]

[Footnote 98: _Dissert. Perip._ t. ii. lib. v. sub fin.]

[Footnote 99: Tenneman, ix. 148.]

[Footnote 100: Tenneman, ix. 167.]

[Footnote 101: _Ibid._ 158.]

[Footnote 102: Agrippa, _De Occult. Phil._ lib. i. c. l.]

[Footnote 103: Written in 1526.]

[Footnote 104: Philip Aurelius Theophrastus Bombastus von Hohenheim,
also called Paracelsus Eremita, born at Einsiedlen in Switzerland, in
1493.]

[Footnote 105: _Hist. Sc. Id._ b. ix. c. 2. sect. 1. The Mystical
School of Biology.]

[Footnote 106: Tenneman, ix. 221.]

[Footnote 107: Tenneman, ix. 265.]




CHAPTER XIII.

THE THEORETICAL REFORMERS OF SCIENCE.


We have already seen that Patricius, about the middle of the sixteenth
century, announced his purpose of founding anew the whole fabric
of philosophy; but that, in executing this plan, he ran into wide
and baseless hypotheses, suggested by _à priori_ conceptions rather
than by external observation; and that he was further misled by
fanciful analogies resembling those which the Platonic mystics loved
to contemplate. The same time, and the period which followed it,
produced several other essays which were of the same nature, with the
exception of their being free from the peculiar tendencies of the
Platonic school: and these insurrections against the authority of
the established dogmas, although they did not directly substitute a
better positive system in the place of that which they assailed, shook
the authority of the Aristotelian system, and led to its overthrow;
which took place as soon as these theoretical reformers were aided by
practical reformers.


1. _Bernardinus Telesius._--Italy, always, in modern times, fertile in
the beginnings of new systems, was the soil on which these innovators
arose. The earliest and most conspicuous of them is Bernardinus
Telesius, who was born in 1508, at Cosenza, in the kingdom of Naples.
His studies, carried on with great zeal and ability, first at Milan
and then at Rome, made him well acquainted with the knowledge of
his times; but his own reflections convinced him that the basis of
science, as then received, was altogether erroneous; and led him to
attempt a reform, with which view, in 1565, he published, at Rome,
his work[108], "_Bernardinus Telesius, of Cosenza, on the Nature of
Things, according to principles of his own_." In the preface of this
work he gives a short account[109] of the train of reflection by which
he was led to put himself in opposition to the Aristotelian philosophy.
This kind of autobiography occurs not unfrequently in the writings of
theoretical reformers; and shows how livelily they felt the novelty of
their undertaking. After the storm and sack of Rome in 1527, Telesius
retired to Padua, as a peaceful seat of the muses; and there studied
philosophy and mathematics, with great zeal, under the direction of
Jerome Amalthæus and Frederic Delphinus. In these studies he made great
progress; and the knowledge which he thus acquired threw a new light
upon his view of the Aristotelian philosophy. He undertook a closer
examination of the Physical Doctrines of Aristotle; and as the result
of this, he was astonished how it could have been possible that so
many excellent men, so many nations, and even almost the whole human
race, should, for so long a time, have allowed themselves to be carried
away by a blind reverence for a teacher, who had committed errors so
numerous and grave as he perceived to exist in "the philosopher." Along
with this view of the insufficiency of the Aristotelian philosophy,
arose, at an early period, the thought of erecting a better system in
its place. With this purpose he left Padua, when he had received the
degree of Doctor, and went to Rome, where he was encouraged in his
design by the approval and friendly exhortations of distinguished men
of letters, amongst whom were Ubaldino Bandinelli and Giovanni della
Casa. From Rome he went to his native place, when the incidents and
occupations of a married life for a while interrupted his philosophical
project. But after his wife was dead, and his eldest son grown to
manhood, he resumed with ardour the scheme of his youth; again studied
the works of Aristotle and other philosophers, and composed and
published the first two books of his treatise. The opening to this
work sufficiently exhibits the spirit in which it was conceived. Its
object is stated in the title to be to show, that "the construction
of the world, the magnitude and nature of the bodies contained in
it, are not to be investigated by reasoning, which was done by the
ancients, but are to be apprehended by the senses, and collected from
the things themselves." And the Proem is in the same strain. "They who
before us have inquired concerning the construction of this world and
of the things which it contains, seem indeed to have prosecuted their
examination with protracted vigils and great labour, but _never to have
looked at it_." And thus, he observes, they found nothing but error.
This he ascribes to their presumption. "For, as it were, attempting
to rival God in wisdom, and venturing to seek for the principles and
causes of the world by the light of their own reason, and thinking they
had found what they had only invented, they made an arbitrary world of
their own." "_We_ then," he adds, "not relying on ourselves, and of a
duller intellect than they, propose to ourselves to turn our regards to
the world itself and its parts."

The execution of the work, however, by no means corresponds to the
announcement. The doctrines of Aristotle are indeed attacked; and the
objections to these, and to other received opinions, form a large
part of the work. But these objections are supported by _à priori_
reasoning, and not by experiments. And thus, rejecting the Aristotelian
physics, he proposes a system at least equally baseless; although, no
doubt, grateful to the author from its sweeping and apparently simple
character. He assumes three principles, Heat, Cold, and Matter: Heat
is the principle of motion, Cold of immobility, and Matter is the
corporeal substratum, in which these incorporeal and active principles
produce their effects. It is easy to imagine that, by combining and
separating these abstractions in various ways, a sort of account of
many natural phenomena may be given; but it is impossible to ascribe
any real value to such a system. The merit of Telesius must be
considered to consist in his rejection of the Aristotelian errors,
in his perception of the necessity of a reform in the method of
philosophizing, and in his persuasion that this reform must be founded
on experiments rather than on reasoning. When he said[110], "We propose
to ourselves to turn our eyes to the world itself, and its parts, their
passions, actions, operations, and species," his view of the course to
be followed was right; but his purpose remained but ill fulfilled, by
the arbitrary edifice of abstract conceptions which his system exhibits.

Francis Bacon, who, about half a century later, treated the subject
of a reform of philosophy in a far more penetrating and masterly
manner, has given us his judgment of Telesius. In his view, he takes
Telesius as the restorer of the Atomic philosophy, which Democritus
and Parmenides taught among the ancients; and according to his
custom, he presents an image of this philosophy in an adaptation of
a portion of ancient mythology[111]. The Celestial Cupid, who with
Cœlus, was the parent of the Gods and of the Universe, is exhibited
as a representation of matter and its properties, according to the
Democritean philosophy. "Concerning Telesius," says Bacon, "we think
well, and acknowledge him as a lover of truth, a useful contributor to
science, an amender of some tenets, the first of recent men. But we
have to do with him as the restorer of the philosophy of Parmenides,
to whom much reverence is due." With regard to this philosophy,
he pronounces a judgment which very truly expresses the cause of
its rashness and emptiness. "It is," he says, "such a system[112]
as naturally proceeds from the intellect, abandoned to its own
impulse, and not rising from experience to theory continuously and
successively." Accordingly, he says that, "Telesius, although learned
in the Peripatetic philosophy (if that were anything), which indeed, he
has turned against the teachers of it, is hindered by his affirmations,
and is more successful in destroying than in building."

The work of Telesius excited no small notice, and was placed in the
_Index Expurgatorius_. It made many disciples, a consequence probably
due to its spirit of system-making, no less than to its promise of
reform, or its acuteness of argument; for till trial and reflection
have taught man modesty and moderation, he can never be content to
receive knowledge in the small successive instalments in which nature
gives it forth to him. It is the makers of large systems, arranged with
an _appearance_ of completeness and symmetry, who, principally, give
rise to Schools of philosophy.


2. (_Thomas Campanella_).--Accordingly, Telesius may be looked upon as
the founder of a School. His most distinguished successor was Thomas
Campanella, who was born in 1568, at Stilo, in Calabria. He showed
great talents at an early age, prosecuting his studies at Cosenza,
the birth-place of the great opponent of Aristotle and reformer of
philosophy. He, too, has given us an account[113] of the course of
thought by which he was led to become an innovator. "Being afraid
that not genuine truth, but falsehood in the place of truth, was the
tenant of the Peripatetic School, I examined all the Greek, Latin,
and Arabic commentators of Aristotle, and hesitated more and more, as
I sought to learn whether what they have said were also to be read
in the world itself, which I had been taught by learned men was the
living book of God. And as my doctors could not satisfy my scruples,
I resolved to read all the books of Plato, Pliny, Galen, the Stoics,
and the Democriteans, and especially those of Telesius; and to compare
them with that _first and original writing, the world_; that thus from
the primary autograph, I might learn if the copies contained anything
false." Campanella probably refers here to an expression of Plato,
who says, "the world is God's epistle to mankind." And this image, of
the natural world as an original manuscript, while human systems of
philosophy are but copies, and may be false ones, became a favourite
thought of the reformers, and appears repeatedly in their writings from
this time. "When I held my public disputation at Cosenza," Campanella
proceeds, "and still more, when I conversed privately with the brethren
of the monastery, I found little satisfaction in their answers; but
Telesius delighted me, on account of his freedom in philosophizing,
and because he rested upon the nature of things, and not upon the
assertions of men."

With these views and feelings, it is not wonderful that Campanella,
at the early age of twenty-two (1590,) published a work remarkable
for the bold promise of its title: "_Thomas Campanella's Philosophy
demonstrated to the senses, against those who have philosophized in an
arbitrary and dogmatical manner, not taking nature for their guide; in
which the errors of Aristotle and his followers are refuted from their
own assertions and the laws of nature: and all the imaginations feigned
in the place of nature by the Peripatetics are altogether rejected;
with a true defence of Bernardin Telesius of Cosenza, the greatest
of philosophers; confirmed by the opinions of the ancients, here
elucidated and defended, especially those of the Platonists_."

This work was written in answer to a book published against Telesius
by a Neapolitan professor named Marta; and it was the boast of the
young author that he had only employed eleven months in the composition
of his defence, while his adversary had been engaged eleven years
in preparing his attack. Campanella found a favourable reception in
the house of the Marchese Lavelli, and there employed himself in the
composition of an additional work, entitled _On the Sense of Things
and Magic_, and in other literary labours. These, however, are full
of the indications of an enthusiastic temper, inclined to mystical
devotion, and of opinions bearing the cast of pantheism. For instance,
the title of the book last quoted sets forth as demonstrated in the
course of the work, that "the world is the living and intelligent
statue of God; and that all its parts, and particles of parts, are
endowed some with a clearer, some with a more obscure sense, such
as suffices for the preservation of each and of the whole." Besides
these opinions, which could not fail to make him obnoxious to the
religious authorities, Campanella[114] engaged in schemes of political
revolution, which involved him in danger and calamity. He took part
in a conspiracy, of which the object was to cast off the tyranny of
Spain, and to make Calabria a republic. This design was discovered; and
Campanella, along with others, was thrown into prison and subjected to
torture. He was kept in confinement twenty-seven years; and at last
obtained his liberation by the interposition of Pope Urban VIII. He
was, however, still in danger from the Neapolitan Inquisition; and
escaped in disguise to Paris, where he received a pension from the
king, and lived in intercourse with the most eminent men of letters. He
died there in 1639.

Campanella was a contemporary of Francis Bacon, whom we must consider
as belonging to an epoch to which the Calabrian school of innovators
was only a prelude. I shall not therefore further follow the connexion
of writers of this order. Tobias Adami, a Saxon writer, an admirer
of Campanella's works, employed himself, about 1620, in adapting
them to the German public, and in recommending them strongly to
German philosophers. Descartes, and even Bacon, may be considered as
successors of Campanella; for they too were theoretical reformers; but
they enjoyed the advantage of the light which had, in the mean time,
been thrown upon the philosophy of science, by the great practical
advances of Kepler, Galileo, and others. To these practical reformers
we must soon turn our attention: but we may first notice one or two
additional circumstances belonging to our present subject.

Campanella remarks that both the Peripatetics and the Platonists
conducted the learner to knowledge by a long and circuitous path, which
he wished to shorten by setting out from the sense. Without speaking
of the methods which he proposed, we may notice one maxim[115] of
considerable value which he propounds, and to which we have already
been led. "We begin to reason from sensible objects, and definition
is the end and epilogue of science. It is not the beginning of our
knowing, but only of our teaching."


3. (_Andrew Cæsalpinus._)--The same maxim had already been announced
by Cæsalpinus, a contemporary of Telesius; (he was born at Arezzo in
1520, and died at Rome in 1603). Cæsalpinus is a great name in science,
though professedly an Aristotelian. It has been seen in the _History
of Science_[116], that he formed the first great epoch of the science
of botany by his systematic arrangement of plants, and that in this
task he had no successor for nearly a century. He also approached near
to the great discovery of the circulation of the blood[117]. He takes
a view of science which includes the remark that we have just quoted
from Campanella: "We reach perfect knowledge by three steps: Induction,
Division, Definition. By Induction, we collect likeness and agreement
from observation; by Division, we collect unlikeness and disagreement;
by Definition, we learn the proper substance of each object. Induction
makes universals from particulars, and offers to the mind all
intelligible matter; Division discovers the difference of universals,
and leads to species; Definition resolves species into their principles
and elements[118]." Without asserting this to be rigorously correct, it
is incomparably more true and philosophical than the opposite view,
which represents definition as the beginning of our knowledge; and
the establishment of such a doctrine is a material step in inductive
philosophy[119].


4. (_Giordano Bruno._)--Among the Italian innovators of this time
we must notice the unfortunate Giordano Bruno, who was born at Nola
about 1550 and burnt at Rome in 1600. He is, however, a reformer of a
different school from Campanella; for he derives his philosophy from
Ideas and not from Observation. He represents himself as the author of
a new doctrine, which he terms the _Nolan Philosophy_. He was a zealous
promulgator and defender of the Copernican system of the universe, as
we have noticed in the _History of Science_[120]. Campanella also wrote
in defence of that system.

It is worthy of remark that a thought which is often quoted from
Francis Bacon, occurs in Bruno's _Cena di Cenere_, published in
1584; I mean, the notion that the later times are more aged than
the earlier. In the course of the dialogue, the Pedant, who is one
of the interlocutors, says, "In antiquity is wisdom;" to which the
Philosophical Character replies, "If you knew what you were talking
about, you would see that your principle leads to the opposite result
of that which you wish to infer;--I mean, that _we_ are older, and have
lived longer, than our predecessors." He then proceeds to apply this,
by tracing the course of astronomy through the earlier astronomers up
to Copernicus.


5. (_Peter Ramus._)--I will notice one other reformer of this period,
who attacked the Aristotelian system on another side, on which it
was considered to be most impregnable. This was Peter Ramus,(born in
Picardy in 1515,) who ventured to denounce the _Logic_ of Aristotle as
unphilosophical and useless. After showing an extraordinary aptitude
for the acquirement of knowledge in his youth, when he proceeded to
the degree of Master of Arts, he astonished his examiners by choosing
for the subject of the requisite disputation the thesis[121], "that
what Aristotle has said is all wrong." This position, so startling in
1535, he defended for the whole day, without being defeated. This was,
however, only a formal academical exercise, which did not necessarily
imply any permanent conviction of the opinion thus expressed. But his
mind was really labouring to detect and remedy the errors which he
thus proclaimed. From him, as from the other reformers of this time,
we have an account of this mental struggle[122]. He says, in a work on
this subject, "I will candidly and simply explain how I was delivered
from the darkness of Aristotle. When, according to the laws of our
university, I had spent three years and a half in the Aristotelian
philosophy, and was now invested with the philosophical laurel as a
Master of Arts, I took an account of the time which I had consumed
in this study, and considered on what subjects I should employ this
logical art of Aristotle, which I had learnt with so much labour and
noise, I found it made me not more versed in history or antiquities,
more eloquent in discourse, more ready in verse, more wise in any
subject. Alas for me! how was I overpowered, how deeply did I groan,
how did I deplore my lot and my nature, how did I deem myself to be
by some unhappy and dismal fate and frame of mind abhorrent from the
Muses, when I found that I was one who, after all my pains, could
reap no benefit from that wisdom of which I heard so much, as being
contained in the Logic of Aristotle." He then relates that he was
led to the study of the Dialogues of Plato, and was delighted with
the kind of analysis of the subjects discussed which Socrates is
there represented as executing. "Well," he adds, "I began thus to
reflect within myself--(I should have thought it impious to say it to
another)--What, I pray you, prevents me from _socratizing_; and from
asking, without regard to Aristotle's authority, whether Aristotle's
Logic be true and correct? It may be that that philosopher leads
us wrong; and if so, no wonder that I cannot find in his books the
treasure which is not there. What if his dogmas be mere figments? Do
I not tease and torment myself in vain, trying to get a harvest from
a barren soil?" He convinced himself that the Aristotelian logic was
worthless: and constructed a new system of Logic, founded mainly on the
Platonic process of exhausting a subject by analytical classification
of its parts. Both works, his _Animadversions on Aristotle_, and his
_Logic_, appeared in 1543. The learned world was startled and shocked
to find a young man, on his first entrance into life, condemning
as faulty, fallacious, and useless, that part of Aristotle's works
which had always hitherto been held as a masterpiece of philosophical
acuteness, and as the Organon of scientific reasoning. And in truth, it
must be granted that Ramus does not appear to have understood the real
nature and object of Aristotle's Logic; while his own system could not
supply the place of the old one, and was not of much real value. This
dissent from the established doctrines was, however, not only condemned
but punished. The printing and selling of his books was forbidden
through France; and Ramus was stigmatized by a sentence[123] which
declared him rash, arrogant, impudent, and ignorant, and prohibited
from teaching logic and philosophy. He was, however, afterwards
restored to the office of professor: and though much attacked,
persisted in his plan of reforming, not only Logic but Physics and
Metaphysics. He made his position still more dangerous by adopting the
reformed religion; and during the unhappy civil wars of France, he was
deprived of his professorship, driven from Paris, and had his library
plundered. He endeavoured, but in vain, to engage a German professor,
Schegk, to undertake the reform of the Aristotelian Physics; a portion
of knowledge in which he felt himself not to be strong. Unhappily for
himself, he afterwards returned to Paris, where he perished in the
massacre of St. Bartholomew in 1572.

Ramus's main objection to the Aristotelian Logic is, that it is not
the image of the natural process of thought; an objection which shows
little philosophical insight; for the course by which we obtain
knowledge may well differ from the order in which our knowledge,
when obtained, is exhibited. We have already seen that Ramus's
contemporaries, Cæsalpinus and Campanella, had a wiser view; placing
definition as the last step in knowing, but the first in teaching.
But the effect which Ramus produced was by no means slight. He aided
powerfully in turning the minds of men to question the authority of
Aristotle on all points; and had many followers, especially among the
Protestants. Among the rest, Milton, our great poet, published "Artis
Logicæ plenior Institutio _ad Petri Rami methodum concinnata_;" but
this work, appearing in 1672, belongs to a succeeding period.


6. (_The Reformers in general_).--It is impossible not to be struck
with the series of misfortunes which assailed the reformers of
philosophy of the period we have had to review. Roger Bacon was
repeatedly condemned and imprisoned; and, not to speak of others who
suffered under the imputation of magical arts, Telesius is said[124] to
have been driven from Naples to his native city by calumny and envy;
Cæsalpinus was accused of atheism[125]; Campanella was imprisoned for
twenty-seven years and tortured; Giordano Bruno was burnt at Rome as
a heretic; Ramus was persecuted during his life, and finally murdered
by his personal enemy Jacques Charpentier, in a massacre of which the
plea was religion. It is true, that for the most part these misfortunes
were not principally due to the attempts at philosophical reform, but
were connected rather with politics or religion. But we cannot doubt
that the spirit which led men to assail the received philosophy, might
readily incline them to reject some tenets of the established religion;
since the boundary line of these subjects is difficult to draw. And as
we have seen, there was in most of the persons of whom we have spoken,
not only a well-founded persuasion of the defects of existing systems,
but an eager spirit of change, and a sanguine anticipation of some
wide and lofty philosophy, which was soon to elevate the minds and
conditions of men. The most unfortunate were, for the most part, the
least temperate and judicious reformers. Patricius, who, as we have
seen, declared himself against the Aristotelian philosophy, lived and
died at Rome in peace and honour[126].


7. (_Melancthon._)--It is not easy to point out with precision the
connexion between the efforts at a Reform in Philosophy, and the great
Reformation of Religion in the sixteenth century. The disposition to
assert (practically at least) a freedom of thinking, and to reject the
corruptions which tradition had introduced and authority maintained,
naturally extended its influence from one subject to another; and
especially in subjects so nearly connected as theology and philosophy.
The Protestants, however, did not reject the Aristotelian system;
they only reformed it, by going back to the original works of the
author, and by reducing it to a conformity with Scripture. In this
reform, Melancthon was the chief author, and wrote works on Logic,
Physics, Morals, and Metaphysics, which were used among Protestants.
On the subject of the origin of our knowledge, his views contained
a very philosophical improvement of the Aristotelian doctrines. He
recognized the importance of Ideas, as well as of Experience. "We could
not," he says[127], "proceed to reason at all, except there were by
nature innate in man certain fixed points, that is, principles of
science;--as Number, the recognition of Order and Proportion, logical,
geometrical, physical and moral Principles. Physical principles are
such as these,--everything which exists proceeds from a cause,--a body
cannot be in two places at once,--time is a continued series of things
or of motions,--and the like." It is not difficult to see that such
Principles partake of the nature of the Fundamental Ideas which we have
attempted to arrange and enumerate in a previous part of this work.

Before we proceed to the next chapter, which treats of the Practical
Reformers of Scientific Method, let us for an instant look at the
strong persuasion implied in the titles of the works of this period,
that the time of a philosophical revolution was at hand. Telesius
published _De Rerum Natura juxta propria principia_; Francis Helmont,
_Philosophia vulgaris refutata_; Patricius, _Nova de Universis
Philosophia_; Campanella, _Philosophia sensibus demonstrata, adversus
errores Aristotelis_; Bruno professed himself the author of a _Nolan
Philosophy_; and Ramus of a _New Logic_. The age announced itself
pregnant; and the eyes of all who took an interest in the intellectual
fortunes of the race, were looking eagerly for the expected offspring.


FOOTNOTES:

[Footnote 108: Bernardini Telesii Consentini _De Rerum Natura juxta
propria Principia_.]

[Footnote 109: I take this account from Tenneman: this Proem was
omitted in subsequent editions of Telesius, and is not in the one which
I have consulted. Tenneman, _Gesch. d. Phil._ ix. 280.]

[Footnote 110: Proem.]

[Footnote 111: "De Principiis atque Originibus secundum fabulas
Cupidinis et Cœli: sive Parmenidis et Telesii et præcipuè Democriti
Philosophia tractata in Fabula de Cupidine."]

[Footnote 112: "Talia sunt qualia possunt esse ea quæ ab intellectu
sibi permisso, nec ab experimentis continenter et gradatim sublevato,
profecta videntur."]

[Footnote 113: Thom. Campanella _de Libris propriis_, as quoted in
Tenneman, ix. 291.]

[Footnote 114: _Economisti Italiani_, t. i. p. xxxiii.]

[Footnote 115: Tenneman, ix. 305.]

[Footnote 116: _Hist. Ind. Sc._ b. xvi. c. iii. sect. 2.]

[Footnote 117: _Ibid._ b. xvii. c. ii. sect. 1.]

[Footnote 118: _Quæst. Peripat._ i. 1.]

[Footnote 119: Tenneman, ix. 108.]

[Footnote 120: _Hist. Ind. Sc._ b. v. c. iii. sect. 2.]

[Footnote 121: Tenneman, ix. 420. "Quæcunque ab Aristotele dicta essent
commenticia esse." Freigius, _Vita Petri Rami_, p. 10.]

[Footnote 122: Rami, _Animadv. Aristot._ i. iv.]

[Footnote 123: See _Hist. Ind. Sc._ b. iv. c. iv. sect. 4.]

[Footnote 124: Tenneman, ix. 230.]

[Footnote 125: _Ibid._ 108.]

[Footnote 126: Tenneman, ix. 246.]

[Footnote 127: Melancthon, _De Anima_, p. 207, quoted in Tenneman, ix.
121.]




CHAPTER XIV.

THE PRACTICAL REFORMERS OF SCIENCE.


1. _Character of the Practical Reformers._--We now come to a class
of speculators who had perhaps a greater share in bringing about the
change from stationary to progressive knowledge, than those writers who
so loudly announced the revolution. The mode in which the philosophers
of whom we now speak produced their impressions on men's minds, was
very different from the procedure of the theoretical reformers. What
these talked of, they did; what these promised, they performed. While
the theorists concerning knowledge proclaimed that great advances
were to be made, the practical discoverers went steadily forwards.
While one class spoke of a complete Reform of scientific Methods, the
other, boasting little, and often thinking little of Method, proved
the novelty of their instrument by obtaining new results. While the
metaphysicians were exhorting men to consult experience and the senses,
the physicists were examining nature by such means with unparalleled
success. And while the former, even when they did for a moment refer
to facts, soon rushed back into their own region of ideas, and tried
at once to seize the widest generalizations, the latter, fastening
their attention upon the phenomena, and trying to reduce them to
laws, were carried forwards by steps measured and gradual, such as no
conjectural view of scientific method had suggested; but leading to
truths as profound and comprehensive as any which conjecture had dared
to anticipate. The theoretical reformers were bold, self-confident,
hasty, contemptuous of antiquity, ambitious of ruling all future
speculations, as they whom they sought to depose had ruled the past.
The practical reformers were cautious, modest, slow, despising no
knowledge, whether borrowed from tradition or observation, confident in
the ultimate triumph of science, but impressed with the conviction that
each single person could contribute a little only to its progress. Yet
though thus working rather than speculating,--dealing with particulars
more than with generals,--employed mainly in adding to knowledge, and
not in defining what knowledge is, or how additions are to be made
to it,--these men, thoughtful, curious, and of comprehensive minds,
were constantly led to important views on the nature and methods of
science. And these views, thus suggested by reflections on their own
mental activity, were gradually incorporated with the more abstract
doctrines of the metaphysicians, and had a most important influence
in establishing an improved philosophy of science. The indications of
such views we must now endeavour to collect from the writings of the
discoverers of the times preceding the seventeenth century.

Some of the earliest of these indications are to be found in those who
dealt with Art rather than with Science. I have already endeavoured
to show that the advance of the arts which give us a command over the
powers of nature, is generally prior to the formation of exact and
speculative knowledge concerning those powers. But Art, which is thus
the predecessor of Science, is, among nations of acute and active
intellects, usually its parent. There operates, in such a case, a
speculative spirit, leading men to seek for the reasons of that which
they find themselves able to do. How slowly, and with what repeated
deviations men follow this leading, when under the influence of a
partial and dogmatical philosophy, the late birth and slow growth of
sound physical theory shows. But at the period of which we now speak,
we find men, at length, proceeding in obedience to the impulse which
thus drives them from practice to theory;--from an acquaintance with
phenomena to a free and intelligent inquiry concerning their causes.


2. _Leonardo da Vinci._--I have already noted, in the History of
Science, that the Indistinctness of Ideas, which was long one main
impediment to the progress of science in the middle ages, was first
remedied among architects and engineers. These men, so far at least as
mechanical ideas were concerned, were compelled by their employments
to judge rightly of the relations and properties of the materials with
which they had to deal; and would have been chastised by the failure
of their works, if they had violated the laws of mechanical truth. It
was not wonderful, therefore, that these laws became known to _them_
first. We have seen, in the _History_, that Leonardo da Vinci, the
celebrated painter, who was also an engineer, is the first writer in
whom we find the true view of the laws of equilibrium of the lever in
the most general case. This artist, a man of a lively and discursive
mind, is led to make some remarks[128] on the formation of our
knowledge, which may show the opinions on that subject that already
offered themselves at the beginning of the sixteenth century[129]. He
expresses himself as follows:--"Theory is the general, Experiments are
the soldiers. The interpreter of the artifices of nature is Experience:
she is never deceived. Our judgment sometimes is deceived, because it
expects effects which Experience refuses to allow." And again, "We
must consult Experience, and vary the circumstances till we have drawn
from them general rules; for it is she who furnishes true rules. But
of what use, you ask, are these rules; I reply, that they direct us in
the researches of nature and the operations of art. They prevent our
imposing upon ourselves and others by promising ourselves results which
we cannot obtain.

"In the study of the sciences which depend on mathematics, those who do
not consult nature but authors, are not the children of nature, they
are only her grandchildren. She is the true teacher of men of genius.
But see the absurdity of men! They turn up their noses at a man who
prefers to learn from nature herself rather than from authors who are
only her clerks."

In another place, in reference to a particular case, he says, "Nature
begins from the Reason and ends in Experience; but for all that, we
must take the opposite course; begin from the Experiment and try to
discover the Reason."

Leonardo was born forty-six years before Telesius; yet we have here
an estimate of the value of experience far more just and substantial
than the Calabrian school ever reached. The expressions contained in
the above extracts, are well worthy our notice;--that experience is
never deceived;--that we must vary our experiments, and draw from them
general rules;--that nature is the original source of knowledge, and
books only a derivative substitute;--with a lively image of the sons
and grandsons of nature. Some of these assertions have been deemed,
and not without reason, very similar to those made by Bacon a century
later. Yet it is probable that the import of such expressions, in
Leonardo's mind, was less clear and definite than that which they
acquired by the progress of sound philosophy. When he says that theory
is the general and experiments the soldiers, he probably meant that
theory directs men what experiments to make; and had not in his mind
the notion of a theoretical Idea ordering and brigading the Facts. When
he says that Experience is the interpreter of Nature, we may recollect,
that in a more correct use of this image, Experience and Nature are the
writing, and the Intellect of man the interpreter. We may add, that
the clear apprehension of the importance of Experience led, in this as
in other cases, to an unjust depreciation of the value of what science
owed to books. Leonardo would have made little progress, if he had
attempted to master a complex science, astronomy for instance, by means
of observation alone, without the aid of books.

But in spite of such criticism, Leonardo's maxims show extraordinary
sagacity and insight; and they appear to us the more remarkable, when
we see how rare such views are for a century after his time.


3. _Copernicus._--For we by no means find, even in those practical
discoverers to whom, in reality, the revolution in science, and
consequently in the philosophy of science, was due, this prompt and
vigorous recognition of the supreme authority of observation as a
ground of belief; this bold estimate of the probable worthlessness
of traditional knowledge; and this plain assertion of the reality of
theory founded upon experience. Among such discoverers, Copernicus must
ever hold a most distinguished place. The heliocentric theory of the
universe, established by him with vast labour and deep knowledge, was,
for the succeeding century, the field of discipline and exertion of all
the most active speculative minds. Men, during that time, proved their
freedom of thought, their hopeful spirit, and their comprehensive view,
by adopting, inculcating, and following out the philosophy which this
theory suggested. But in the first promulgation of the theory, in the
works of Copernicus himself, we find a far more cautious and reserved
temper. He does not, indeed, give up the reality of his theory, but
he expresses himself so as to avoid shocking those who might (as some
afterwards did) think it safe to speak of it as an _hypothesis_ rather
than a truth. In his preface addressed to the Pope[130], after speaking
of the difficulties in the old and received doctrines, by which he
was led to his own theory, he says, "Hence I began to think of the
mobility of the earth; and although the opinion seemed absurd, yet
because I knew that to others before me this liberty had been conceded,
of imagining any kinds of circles in order to explain the phenomena
of the stars, I thought it would also be readily granted me, that I
might try whether, by supposing the earth to be in motion, I might
not arrive at a better explanation than theirs, of the revolutions of
the celestial orbs." Nor does he anywhere assert that the seeming
absurdity had become a certain truth, or betray any feeling of triumph
over the mistaken belief of his predecessors. And, as I have elsewhere
shown, his disciples[131] indignantly and justly defended him from the
charge of disrespect towards Ptolemy and other ancient astronomers. Yet
Copernicus is far from compromising the value or evidence of the great
truths which he introduced to general acceptance; and from sinking in
his exposition of his discoveries below the temper which had led to
them. His quotation from Ptolemy, that "He who is to follow philosophy
must be a freeman in mind," is a grand and noble maxim, which it well
became him to utter.


4. _Fabricius._--In another of the great discoverers of this period,
though employed on a very different subject, we discern much of the
same temper. Fabricius of Acquapendente[132], the tutor and forerunner
of our Harvey, and one of that illustrious series of Paduan professors
who were the fathers of anatomy[133], exhibits something of the same
respect for antiquity, in the midst of his original speculations.
Thus in a dissertation[134] _On the Action of the Joints_, he quotes
Aristotle's Mechanical Problems to prove that in all animal motion
there must be some quiescent fulcrum; and finds merit even in
Aristotle's ignorance. "Aristotle," he says[135], "did not know that
motion was produced by the muscle; and after staggering about from one
supposition to another, at last is compelled by the facts themselves
to recur to an innate spirit, which, he conceives, is contrasted, and
which pulls and pushes. And here we cannot help admiring the genius of
Aristotle, who, though ignorant of the muscle, invents something which
produces nearly the same effect as the muscle, namely, contraction and
pulling." He then, with great acuteness, points out the distinction
between Aristotle's opinions, thus favourably interpreted, and those of
Galen. In all this, we see something of the wish to find all truths in
the writings of the ancients, but nothing which materially interferes
with freedom of inquiry. The anatomists have in all ages and countries
been practically employed in seeking knowledge from observation. Facts
have ever been to them a subject of careful and profitable study; while
the ideas which enter into the wider truths of the science, are, as we
have seen, even still involved in obscurity, doubt, and contest.


5. _Maurolycus._--Francis Maurolycus of Messana, whose mathematical
works were published in 1575, was one of the great improvers of the
science of optics in his time. In his Preface to his Treatise on
the Spheres, he speaks of previous writers on the same subject; and
observes that as they have not superseded one another, they have not
rendered it unfit for any one to treat the subject afresh. "Yet," he
says, "it is impossible to amend the errors of all who have preceded
us. This would be a task too hard for Atlas, although he supports the
heavens. Even Copernicus is tolerated, who makes the sun to be fixed,
and the earth to move round it in a circle, and who is more worthy
of a whip or a scourge than of a refutation." The mathematicians and
astronomers of that time were not the persons most sensible of the
progress of physical knowledge; for the basis of their science, and
a great part of its substance, were contained in the writings of the
ancients; and till the time of Kepler, Ptolemy's work was, very justly,
looked upon as including all that was essential in the science.


6. _Benedetti._--But the writers on Mechanics were naturally led to
present themselves as innovators and experimenters; for all that the
ancients had taught concerning the doctrine of motion was erroneous;
while those who sought their knowledge from experiment, were constantly
led to new truths. John Baptist Benedetti, a Venetian nobleman, in
1599, published his _Speculationum Liber_, containing, among other
matter, a treatise on Mechanics, in which several of the Aristotelian
errors were refuted. In the Preface to this Treatise, he says, "Many
authors have written much, and with great ability, on Mechanics; but
since nature is constantly bringing to light something either new,
or before unnoticed, I too wished to put forth a few things hitherto
unattempted, or not sufficiently explained." In the doctrine of motion
he distinctly and at some length condemns and argues against all the
Aristotelian doctrines concerning motion, weight, and many other
fundamental principles of physics. Benedetti is also an adherent of
the Copernican doctrine. He states[136] the enormous velocity which
the heavenly bodies must have, if the earth be the centre of their
motions; and adds, "which difficulty does not occur according to the
beautiful theory of the Samian Aristarchus, expounded in a divine
manner by Nicolas Copernicus; against which the reasons alleged by
Aristotle are of no weight." Benedetti throughout shows no want of the
courage or ability which were needed in order to rise in opposition
against the dogmas of the Peripatetics. He does not, however, refer to
experiment in a very direct manner; indeed most of the facts on which
the elementary truths of mechanics rest, were known and admitted by the
Aristotelians; and therefore could not be adduced as novelties. On the
contrary, he begins with _à priori_ maxims, which experience would not
have confirmed. "Since," he says[137], "we have undertaken the task
of proving that Aristotle is wrong in his opinions concerning motion,
there are certain absolute truths, the objects of the intellect known
of themselves, which we must lay down in the first place." And then, as
an example of these truths, he states this: "Any two bodies of equal
size and figure, but of different materials, will have their natural
velocities in the same proportion as their weights;" where by their
natural velocities, he means the velocities with which they naturally
fall downwards.


7. _Gilbert._--The greatest of these practical reformers of science
is our countryman, William Gilbert; if, indeed, in virtue of the
clear views of the prospects which were then opening to science,
and of the methods by which her future progress was to be secured,
while he exemplified those views by physical discoveries, he does not
rather deserve the still higher praise of being at the same time a
theoretical and a practical reformer. Gilbert's physical researches
and speculations were employed principally upon subjects on which the
ancients had known little or nothing; and on which therefore it could
not be doubtful whether tradition or observation was the source of
knowledge. Such was magnetism; for the ancients were barely acquainted
with the attractive property of the magnet. Its polarity, including
repulsion as well as attraction, its direction towards the north,
its limited variation from this direction, its declination from the
horizontal position, were all modern discoveries. Gilbert's work[138]
on the magnet and on the magnetism of the earth, appeared in 1600;
and in this, he repeatedly maintains the superiority of experimental
knowledge over the physical philosophy of the ancients. His preface
opens thus: "Since in making discoveries and searching out the hidden
causes of things, stronger reasons are obtained from trustworthy
experiments and demonstrable arguments, than from probable conjectures
and the dogmas of those who philosophize in the usual manner," he has,
he says, "endeavoured to proceed from common magnetical experiments to
the inward constitution of the earth." As I have stated in the History
of Magnetism[139], Gilbert's work contains all the fundamental facts
of that science, so fully stated, that we have, at this day, little to
add to them. He is not, however, by the advance which he thus made,
led to depreciate the ancients, but only to claim for himself the same
liberty of philosophizing which they had enjoyed[140]. "To those
ancient and first parents of philosophy, Aristotle, Theophrastus,
Ptolemy, Hippocrates, Galen, be all due honour; from them it was that
the stream of wisdom has been derived down to posterity. But our age
has discovered and brought to light many things which they, if they
were yet alive, would gladly embrace. Wherefore we also shall not
hesitate to expound, by probable hypotheses, those things which by long
experience we have ascertained."

In this work the author not only adopts the Copernican doctrine of the
earth's motion, but speaks[141] of the contrary supposition as utterly
absurd, founding his argument mainly on the vast velocities which such
a supposition requires us to ascribe to the celestial bodies. Dr.
Gilbert was physician to Queen Elizabeth and to James the First, and
died in 1603. Some time after his death the executors of his brother
published another work of his, _De Mundo nostro Sublunari Philosophia
Nova_, in which similar views are still more comprehensively presented.
In this he says, "The two lords of philosophy, Aristotle and Galen,
are held in worship like gods, and rule the schools;--the former by
some destiny obtained a sway and influence among philosophers, like
that of his pupil Alexander among the kings of the earth;--Galen, with
like success, holds his triumph among the physicians of Europe." This
comparison of Aristotle to Alexander was also taken hold of by Bacon.
Nor is Gilbert an unworthy precursor of Bacon in the view he gives of
the History of Science, which occupies the first three chapters of his
Philosophy. He traces this history from "the simplicity and ignorance
of the ancients," through "the fabrication of the fable of the four
elements," to Aristotle and Galen. He mentions with due disapproval the
host of commentators which succeeded, the alchemists, the "shipwreck
of science in the deluge of the Goths," and the revival of letters
and genius in the time of "our grandfathers." "This later age," he
says, "has exploded the Barbarians, and restored the Greeks and Latins
to their pristine grace and honour. It remains, that if they have
written aught in error, this should be remedied by better and more
productive processes (_frugiferis_ institutis), not to be contemned
for their novelty; (for nothing which is true is really new, but is
perfect from eternity, though to weak man it may be unknown;) and that
thus Philosophy may bear her fruit." The reader of Bacon will not fail
to recognize, in these references to "fruit-bearing" knowledge, a
similarity of expression with the _Novum Organon_.

Bacon does not appear to me to have done justice to his contemporary.
He nowhere recognizes in the labours of Gilbert a community of
purpose and spirit with his own. On the other hand, he casts upon
him a reflection which he by no means deserves. In the _Advancement
of Learning_[142], he says, "Another error is, that men have used to
infect their meditations, opinions, and doctrines, with some conceits
which they have most admired, or some sciences to which they have
most applied; and given all things else a tincture according to
them, utterly untrue and improper.... So have the alchemists made a
philosophy out of a few experiments of the furnace; and Gilbertus,
our countryman, hath made a philosophy out of the observations of a
loadstone," (in the Latin, philosophiam etiam e magnete elicuit).
And in the same manner he mentions him in the _Novum Organon_[143],
as affording an example of an empirical kind of philosophy, which
appears to those daily conversant with the experiments, probable, but
to other persons incredible and empty. But instead of blaming Gilbert
for disturbing and narrowing science by a too constant reference to
magnetical rules, we might rather censure Bacon, for not seeing how
important in all natural philosophy are those laws of attraction
and repulsion of which magnetical phenomena are the most obvious
illustration. We may find ground for such a judgment in another passage
in which Bacon speaks of Gilbert. In the Second Book[144] of the _Novum
Organon_, having classified motions, he gives, as one kind, what he
calls, in his figurative language, _motion for gain_, or _motion of
need_, by which a body shuns heterogeneous, and seeks cognate bodies.
And he adds, "The Electrical operation, concerning which Gilbert and
others since him have made up such a wonderful story, is nothing less
than the appetite of a body, which, excited by friction, does not well
tolerate the air, and prefers another tangible body if it be found
near." Bacon's notion of an appetite in the body is certainly much
less philosophical than Gilbert's, who speaks of light bodies as drawn
towards amber by certain material radii[145]; and we might perhaps
venture to say that Bacon here manifests a want of clear mechanical
ideas. Bacon, too, showed his inferior aptitude for physical research
in rejecting the Copernican doctrine which Gilbert adopted. In the
_Advancement of Learning_[146], suggesting a history of the opinions
of philosophers, he says that he would have inserted in it even recent
theories, as those of Paracelsus; of Telesius, who restored the
philosophy of Parmenides; or Patricius, who resublimed the fumes of
Platonism; or Gilbert, who brought back the dogmas of Philolaus. But
Bacon quotes[147] with pleasure Gilbert's ridicule of the Peripatetics'
definition of heat. They had said, that heat is that which separates
heterogeneous and unites homogeneous matter; which, said Gilbert, is
as if any one were to define _man_ as that which sows wheat and plants
vines.

Galileo, another of Gilbert's distinguished contemporaries, had a
higher opinion of him. He says[148], "I extremely admire and envy this
author. I think him worthy of the greatest praise for the many new and
true observations which he has made, to the disgrace of so many vain
and fabling authors; who write, not from their own knowledge only,
but repeat everything they hear from the foolish and vulgar, without
attempting to satisfy themselves of the same by experience; perhaps
that they may not diminish the size of their books."


8. _Galileo._--Galileo was content with the active and successful
practice of experimental inquiry; and did not demand that such
researches should be made expressly subservient to that wider and
more ambitious philosophy, on which the author of the _Novum Organon_
employed his powers. But still it now becomes our business to trace
those portions of Galileo's views which have reference to the theory,
as well as the practice, of scientific investigation. On this subject,
Galileo did not think more profoundly, perhaps, than several of his
contemporaries; but in the liveliness of expression and illustration
with which he recommended his opinions on such topics, he was
unrivalled. Writing in the language of the people, in the attractive
form of dialogue, with clearness, grace, and wit, he did far more than
any of his predecessors had done to render the new methods, results,
and prospects of science familiar to a wide circle of readers, first
in Italy, and soon, all over Europe. The principal points inculcated
by him were already becoming familiar to men of active and inquiring
minds; such as,--that knowledge was to be sought from observation, and
not from books;--that it was absurd to adhere to, and debate about,
the physical tenets of Aristotle and the rest of the ancients. On
persons who followed this latter course, Galileo fixed the epithet of
Paper Philosophers[149]; because, as he wrote in a letter to Kepler,
this sort of men fancied that philosophy was to be studied like the
_Æneid_ or _Odyssey_, and that the true reading of nature was to be
detected by the collation of texts. Nothing so much shook the authority
of the received system of Physics as the experimental discoveries,
directly contradicting it, which Galileo made. By experiment, as I
have elsewhere stated[150], he disproved the Aristotelian doctrine that
bodies fall quickly or slowly in proportion to their weight. And when
he had invented the telescope, a number of new discoveries of the most
striking kind (the inequalities of the moon's surface, the spots in
the sun, the moon-like phases of Venus, the satellites of Jupiter, the
ring of Saturn,) showed, by the evidence of the eyes, how inadequate
were the conceptions, and how erroneous the doctrines of the ancients,
respecting the constitution of the universe. How severe the blow was to
the disciples of the ancient schools, we may judge by the extraordinary
forms of defence in which they tried to intrench themselves. They would
not look through Galileo's glasses; they maintained that what was seen
was an illusion of witchcraft; and they tried, as Galileo says[151],
with logical arguments, as if with magical incantations, to charm the
new planets out of the sky. No one could be better fitted than Galileo
for such a warfare. His great knowledge, clear intellect, gaiety, and
light irony, (with the advantage of being in the right,) enabled him to
play with his adversaries as he pleased. Thus when an Aristotelian[152]
rejected the discovery of the irregularities in the moon's surface,
because, according to the ancient doctrine, her form was a perfect
sphere, and held that the apparent cavities were filled with an
invisible crystal substance, Galileo replied, that he had no objection
to assent to this, but that then he should require his adversary in
return to believe that there were on the same surface invisible crystal
mountains ten times as high as those visible ones which he had actually
observed and measured.

We find in Galileo many thoughts which have since become established
maxims of modern philosophy. "Philosophy," he says[153], "is written
in that great book, I mean the Universe, which is constantly open
before our eyes; but it cannot be understood, unless we first know the
language and learn the characters in which it is written." With this
thought he combines some other lively images. One of his interlocutors
says concerning another, "Sarsi perhaps thinks that philosophy is
a book made up of the fancies of men, like the _Iliad_ or _Orlando
Furioso_, in which the matter of least importance is, that what is
written be true." And again, with regard to the system of authority, he
says, "I think I discover in him a firm belief that, in philosophizing,
it is necessary to lean upon the opinion of some celebrated author;
as if our mind must necessarily remain unfruitful and barren till it
be married to another man's reason."--"No," he says, "the case is not
so.--When we have the decrees of Nature, authority goes for nothing;
reason is absolute[154]."

In the course of Galileo's controversies, questions of the logic of
science came under discussion. Vincenzio di Grazia objected to a proof
from induction which Galileo adduced, because _all_ the particulars
were not enumerated; to which the latter justly replies[155], that
if induction were required to pass through all the cases, it would
be either useless or impossible;--impossible when the cases are
innumerable; useless when they have each already been verified, since
then the general proposition adds nothing to our knowledge.

One of the most novel of the characters which Science assumes in
Galileo's hands is, that she becomes cautious. She not only proceeds
leaning upon Experience, but she is content to proceed a little way
at a time. She already begins to perceive that she must rise to the
heights of knowledge by many small and separate steps. The philosopher
is desirous to know much, but resigned to be ignorant for a time of
that which cannot yet be known. Thus when Galileo discovered the true
law of the motion of a falling body[156], that the velocity increases
proportionally to the time from the beginning of the fall, he did
not insist upon immediately assigning the cause of this law. "The
cause of the acceleration of the motions of falling bodies is not,"
he says, "a necessary part of the investigation." Yet the conception
of this acceleration, as the result of the continued action of the
force of gravity upon the falling body, could hardly fail to suggest
itself to one who had formed the idea of force. In like manner, the
truth that the velocities, acquired by bodies falling down planes of
equal heights, are all equal, was known to Galileo and his disciples,
long before he accounted for it[157], by the principle, apparently
so obvious, that the momentum generated is as the moving force which
generates it. He was not tempted to rush at once, from an experimental
truth to a universal system. Science had learnt that she must move step
by step; and the gravity of her pace already indicated her approaching
maturity and her consciousness of the long path which lay before her.

But besides the genuine philosophical prudence which thus withheld
Galileo from leaping hastily from one inference to another, he had
perhaps a preponderating inclination towards facts; and did not feel,
so much as some other persons of his time, the need of reducing them to
ideas. He could bear to contemplate laws of motion without being urged
by an uncontrollable desire to refer them to conceptions of force.


9. _Kepler._--In this respect his friend Kepler differed from him;
for Kepler was restless and unsatisfied till he had reduced facts to
laws, and laws to causes; and never acquiesced in ignorance, though
he tested with the most rigorous scrutiny that which presented itself
in the shape of knowledge to fill the void. It may be seen in the
History of Astronomy[158] with what perseverance, energy, and fertility
of invention, Kepler pursued his labours, (enlivened and relieved by
the most curious freaks of fancy,) with a view of discovering the
rules which regulate the motions of the planet Mars. He represents
this employment under the image of a warfare; and describes[159] his
object to be "to triumph over Mars, and to prepare for him, as for one
altogether vanquished, tabular prisons and equated eccentric fetters;"
and when, "the enemy, left at home a despised captive, had burst all
the chains of the equations, and broken forth of the prisons of the
tables;"--when "it was buzzed here and there that the victory is vain,
and that the war is raging anew as violently as before;"--that is, when
the rules which he had proposed did not coincide with the facts;--he
by no means desisted from his attempts, but "suddenly sent into the
field a reserve of new physical reasonings on the rout and dispersion
of the veterans," that is, tried new suppositions suggested by such
views as he then entertained of the celestial motions. His efforts
to obtain the formal laws of the planetary motions resulted in some
of the most important discoveries ever made in astronomy; and if his
physical reasonings were for the time fruitless, this arose only from
the want of that discipline in mechanical ideas which the minds of
mathematicians had still to undergo; for the great discoveries of
Newton in the next generation showed that, in reality, the next step
of the advance was in this direction. Among all Kepler's fantastical
expressions, the fundamental thoughts were sound and true; namely,
that it was his business, as a physical investigator, to discover a
mathematical rule which governed and included all the special facts;
and that the rules of the motions of the planets must conform to some
conception of causation.

The same characteristics,--the conviction of rule and cause,
perseverance in seeking these, inventiveness in devising hypotheses,
love of truth in trying and rejecting them, and a lively Fancy playing
with the Reason without interrupting her,--appear also in his work
on Optics; in which he tried to discover the exact law of optical
refraction[160]. In this undertaking he did not succeed entirely;
nor does he profess to have done so. He ends his numerous attempts by
saying, "Now, reader, you and I have been detained sufficiently long
while I have been attempting to _collect into one fagot_ the measures
of different refractions."

In this and in other expressions, we see how clearly he apprehended
that _colligation of facts_ which is the main business of the practical
discoverer. And by his peculiar endowments and habits, Kepler exhibits
an essential portion of this process, which hardly appears at all in
Galileo. In order to bind together facts, theory is requisite as well
as observation,--the cord as well as the fagots. And the true theory
is often, if not always, obtained by trying several and selecting the
right. Now of this portion of the discoverer's exertions, Kepler is
a most conspicuous example. His fertility in devising suppositions,
his undaunted industry in calculating the results of them, his entire
honesty and candour in resigning them if these results disagreed with
the facts, are a very instructive spectacle; and are fortunately
exhibited to us in the most lively manner in his own garrulous
narratives. Galileo urged men by precept as well as example to begin
their philosophy from observation; Kepler taught them by his practice
that they must proceed from observation by means of hypotheses. The
one insisted upon facts; the other dealt no less copiously with ideas.
In the practical, as in the speculative portion of our history, this
antithesis shows itself; although in the practical part we cannot have
the two elements separated, as in the speculative we sometimes have.

In the _History of Science_[161], I have devoted several pages to the
intellectual character of Kepler, inasmuch as his habit of devising so
great a multitude of hypotheses, so fancifully expressed, had led some
writers to look upon him as an inquirer who transgressed the most fixed
rules of philosophical inquiry. This opinion has arisen, I conceive,
among those who have forgotten the necessity of Ideas as well as Facts
for all theory; or who have overlooked the impossibility of selecting
and explicating our ideas without a good deal of spontaneous play of
the mind. It must, however, always be recollected that Kepler's genius
and fancy derived all their scientific value from his genuine and
unmingled love of truth. These qualities appeared, not only in the
judgment he passed upon hypotheses, but also in matters which more
immediately concerned his reputation. Thus when Galileo's discovery of
the telescope disproved several opinions which Kepler had published
and strenuously maintained, he did not hesitate a moment to retract
his assertions and range himself by the side of Galileo, whom he
vigorously supported in his warfare against those who were incapable of
thus cheerfully acknowledging the triumph of new facts over their old
theories.


10. _Tycho._--There remains one eminent astronomer, the friend and
fellow-labourer of Kepler, whom we must not separate from him as one
of the practical reformers of science. I speak of Tycho Brahe, who is,
I think, not justly appreciated by the literary world in general, in
consequence of his having made a retrograde step in that portion of
astronomical theory which is most familiar to the popular mind. Though
he adopted the Copernican view of the motion of the planets about the
sun, he refused to acknowledge the annual and diurnal motion of the
earth. But notwithstanding this mistake, into which he was led by his
interpretation of Scripture rather than of nature, Tycho must ever be
one of the greatest names in astronomy. In the philosophy of science
also, the influence of what he did is far from inconsiderable; and
especially its value in bringing into notice these two points:--that
not only are observations the beginning of science, but that the
progress of science may often depend upon the observer's pursuing his
task regularly and carefully for a long time, and with well devised
instruments; and again, that observed facts offer a _succession_ of
laws which we discover as our observations become better, and as our
theories are better adapted to the observations. With regard to the
former point, Tycho's observatory was far superior to all that had
preceded it[162], not only in the optical, but in the mechanical
arrangements; a matter of almost equal consequence. And hence it was
that his observations inspired in Kepler that confidence which led him
to all his labours and all his discoveries. "Since," he says[163], "the
divine goodness has given us in Tycho Brahe an exact observer, from
whose observations this error of eight minutes in the calculations of
the Ptolemaic hypothesis is detected, let us acknowledge and make use
of this gift of God: and since this error cannot be neglected, these
eight minutes alone have prepared the way for an entire reform of
Astronomy, and are to be the main subject of this work."

With regard to Tycho's discoveries respecting the moon, it is to be
recollected that besides the first inequality of the moon's motion,
(the _equation of the centre_, arising from the elliptical form of her
orbit,) Ptolemy had discovered a second inequality, the _evection_,
which, as we have observed in the History of this subject[164], might
have naturally suggested the suspicion that there were still other
inequalities. In the middle ages, however, such suggestions, implying
a constant progress in science, were little attended to; and, we have
seen, that when an Arabian astronomer[165] had really discovered
another inequality of the moon, it was soon forgotten, because it had
no place in the established systems. Tycho not only rediscovered the
lunar inequality, (the _variation_,) thus once before won and lost, but
also two other inequalities; namely[166], the _change of inclination_
of the moon's orbit as the line of nodes moves round, and an inequality
in the motion of the line of nodes. Thus, as I have elsewhere said,
it appeared that the discovery of a rule is a step to the discovery
of deviations from that rule, which require to be expressed in other
rules. It became manifest to astronomers, and through them to all
philosophers, that in the application of theory to observation, we
find, not only the stated phenomena, for which the theory does account,
but also _residual phenomena_, which are unaccounted for, and remain
over and above the calculation. And it was seen further, that these
residual phenomena might be, altogether or in part, exhausted by new
theories.

These were valuable lessons; and the more valuable inasmuch as men
were now trying to lay down maxims and methods for the conduct of
science. A revolution was not only at hand, but had really taken place,
in the great body of real cultivators of science. The occasion now
required that this revolution should be formally recognized;--that
the new intellectual power should be clothed with the forms of
government;--that the new philosophical republic should be acknowledged
as a sister state by the ancient dynasties of Aristotle and Plato.
There was needed some great Theoretical Reformer, to speak in the name
of the Experimental Philosophy; to lay before the world a declaration
of its rights and a scheme of its laws. And thus our eyes are turned to
Francis Bacon, and others who like him attempted this great office. We
quit those august and venerable names of discoverers, whose appearance
was the prelude and announcement of the new state of things then
opening; and in doing so, we may apply to them the language which Bacon
applies to himself[167]:--

  Χαίρετε Κήρυκες Διὸ ς ἄγγελοι ἠδὲ καὶ ἀνδρῶν.

  Hail, Heralds, Messengers of Gods and Men!


FOOTNOTES:

[Footnote 128: His works have never been published, and exist in
manuscript in the library of the Institute at Paris. Some extracts were
published by Venturi, _Essai sur les Ouvrages de Leonard da Vinci_.
Paris, 1797.]

[Footnote 129: Leonardo died in 1520, at the age of 78.]

[Footnote 130: Paul III. in 1543.]

[Footnote 131: _Hist. Ind. Sc._ b. v. c. ii.]

[Footnote 132: Born 1537, died 1619.]

[Footnote 133: _Hist. Ind. Sc._ b. xvii. c. ii. sect. 1.]

[Footnote 134: Fabricius, _De Motu Locali_, p. 182.]

[Footnote 135: p. 199.]

[Footnote 136: _Speculationum Liber_, p. 195.]

[Footnote 137: _Ibid._ p. 169.]

[Footnote 138: Gulielmi Gilberti, _Colcestriensis, Medici Londinensis,
De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure,
Physiologia Nova, plurimis et Argumentis et Experimentis demonstrata_.]

[Footnote 139: _Hist. Ind. Sc._ b. xii. c. i.]

[Footnote 140: Pref.]

[Footnote 141: _De Magnete_, lib. vi. c. 3, 4.]

[Footnote 142: _Nov. Org._ b. i.]

[Footnote 143: B. i. Aph. 64.]

[Footnote 144: Vol. ix. 185.]

[Footnote 145: _De Magnete_, p. 60.]

[Footnote 146: B. iii. c. 4.]

[Footnote 147: _Nov. Org._ b. ii. Aph. 48.]

[Footnote 148: Drinkwater's _Life of Galileo_, p. 18.]

[Footnote 149: _Life of Galileo_, p. 9.]

[Footnote 150: _Hist. Ind. Sc._ b. vi. c. ii. sect. 5.]

[Footnote 151: _Life of Galileo_, p. 29.]

[Footnote 152: _Ibid._ p. 33.]

[Footnote 153: _Il Saggiatore_, ii. 247.]

[Footnote 154: _Il Saggiatore_, ii. 200.]

[Footnote 155: _Ibid._ i. 501.]

[Footnote 156: _Hist. Ind. Sc._ b. vi. c. ii. sect. 2.]

[Footnote 157: _Hist. Ind. Sc._ b. vi. c. ii. sect. 4.]

[Footnote 158: _Ibid._ b. v. c. iv. sect. 1.]

[Footnote 159: _De Stell. Mart._ p. iv. c. 51 (1609); Drinkwater's
_Kepler_, p. 33.]

[Footnote 160: Published 1604. _Hist. Ind. Sc._ b. ix. c. ii.]

[Footnote 161: _Hist. Ind. Sc._ b. v. c. iv. sect. 1.]

[Footnote 162: _Hist. Ind. Sc._ b. vii. c. vi. sect 1.]

[Footnote 163: _De Stell. Mart._ p. 11. c. 19.]

[Footnote 164: _Hist. Ind. Sc._ b. ii. c. iv. sect. 6.]

[Footnote 165: _Ibid._ sect. 8.]

[Footnote 166: Montucla, i. 566.]

[Footnote 167: _De Augm._ lib. iv. c. 1.]




CHAPTER XV.

FRANCIS BACON.


(I.) 1. _General Remarks._--It is a matter of some difficulty to speak
of the character and merits of this illustrious man, as regards his
place in that philosophical history with which we are here engaged.
If we were to content ourselves with estimating him according to the
office which, as we have just seen, he claims for himself[168], as
merely the harbinger and announcer of a sounder method of scientific
inquiry than that which was recognized before him, the task would
be comparatively easy. For we might select from his writings those
passages in which he has delivered opinions and pointed out processes,
then novel and strange, but since confirmed by the experience of
actual discoverers, and by the judgments of the wisest of succeeding
philosophers; and we might pass by, without disrespect, but without
notice, maxims and proposals which have not been found available for
use;--views so indistinct and vague, that we are even yet unable to
pronounce upon their justice;--and boundless anticipations, dictated
by the sanguine hopes of a noble and comprehensive intellect. But
if we thus reduce the philosophy of Bacon to that portion which the
subsequent progress of science has rigorously verified, we shall
have to pass over many of those declarations which have excited
most notice in his writings, and shall lose sight of many of those
striking thoughts which his admirers most love to dwell upon. For he
is usually spoken of, at least in this country, as a teacher who
not only commenced, but in a great measure completed, the Philosophy
of Induction. He is considered, not only as having asserted some
general principles, but laid down the special rules of scientific
investigation; as not only one of the Founders, but the supreme
Legislator of the modern Republic of Science; not only the Hercules who
slew the monsters that obstructed the earlier traveller, but the Solon
who established a constitution fitted for all future time.


2. Nor is it our purpose to deny that of such praise he deserves
a share which, considering the period at which he lived, is truly
astonishing. But it is necessary for us in this place to discriminate
and select that portion of his system which, bearing upon _physical_
science, has since been confirmed by the actual history of science.
Many of Bacon's most impressive and captivating passages contemplate
the extension of the new methods of discovering truth to intellectual,
to moral, to political, as well as to physical science. And how far,
and how, the advantages of the inductive method may be secured for
those important branches of speculation, it will at some future time
be a highly interesting task to examine. But our plan requires us at
present to omit the consideration of these; for our purpose is to learn
what the genuine course of the formation of science is, by tracing it
in those portions of human knowledge, which, by the confession of all,
are most exact, most certain, most complete. Hence we must here deny
ourselves the dignity and interest which float about all speculations
in which the great moral and political concerns of men are involved.
It cannot be doubted that the commanding position which Bacon occupies
in men's estimation arises from his proclaiming a reform in philosophy
of so comprehensive a nature;--a reform which was to infuse a new
spirit into every part of knowledge. Physical Science has tranquilly
and noiselessly adopted many of his suggestions; which were, indeed,
her own natural impulses, not borrowed from him; and she is too deeply
and satisfactorily absorbed in contemplating her results, to talk much
about the methods of obtaining them which she has thus instinctively
pursued. But the philosophy which deals with mind, with manners,
with morals, with polity, is conscious still of much obscurity and
perplexity; and would gladly borrow aid from a system in which aid
is so confidently promised. The aphorisms and phrases of the _Novum
Organon_ are far more frequently quoted by metaphysical, ethical, and
even theological writers, than they are by the authors of works on
physics.


3. Again, even as regards physics, Bacon's fame rests upon something
besides the novelty of the maxims which he promulgated. That a
revolution in the method of scientific research was going on, all
the greatest physical investigators of the sixteenth century were
fully aware, as we have shown in the last chapter. But their writings
conveyed this conviction to the public at large somewhat slowly. Men of
letters, men of the world, men of rank, did not become familiar with
the abstruse works in which these views were published; and above all,
they did not, by such occasional glimpses as they took of the state of
physical science, become aware of the magnitude and consequences of
this change. But Bacon's lofty eloquence, wide learning, comprehensive
views, bold pictures of the coming state of things, were fitted to
make men turn a far more general and earnest gaze upon the passing
change. When a man of his acquirements, of his talents, of his rank and
position, of his gravity and caution, poured forth the strongest and
loftiest expressions and images which his mind could supply, in order
to depict the "Great Instauration" which he announced;--in order to
contrast the weakness, the blindness, the ignorance, the wretchedness,
under which men had laboured while they followed the long beaten track,
with the light, the power, the privileges, which they were to find in
the paths to which he pointed;--it was impossible that readers of all
classes should not have their attention arrested, their minds stirred,
their hopes warmed; and should not listen with wonder and with pleasure
to the strains of prophetic eloquence in which so great a subject
was presented. And when it was found that the prophecy was verified;
when it appeared that an immense change in the methods of scientific
research really _had_ occurred;--that vast additions to man's knowledge
and power had been acquired, in modes like those which had been spoken
of;--that further advances might be constantly looked for;--and that a
progress, seemingly boundless, was going on in the direction in which
the seer had thus pointed;--it was natural that men should hail him as
the leader of the revolution; that they should identify him with the
event which he was the first to announce; that they should look upon
him as the author of that which he had, as they perceived, so soon and
so thoroughly comprehended.


4. For we must remark, that although (as we have seen) he was not the
only, nor the earliest writer, who declared that the time was come
for such a change, he not only proclaimed it more emphatically, but
understood it, in its general character, much more exactly, than any
of his contemporaries. Among the maxims, suggestions and anticipations
which he threw out, there were many of which the wisdom and the novelty
were alike striking to his immediate successors;--there are many
which even now, from time to time, we find fresh reason to admire,
for their acuteness and justice. Bacon stands far above the herd of
loose and visionary speculators who, before and about his time, spoke
of the establishment of new philosophies. If we must select some one
philosopher as the Hero of the revolution in scientific method, beyond
all doubt Francis Bacon must occupy the place of honour.

We shall, however, no longer dwell upon these general considerations,
but shall proceed to notice some of the more peculiar and
characteristic features of Bacon's philosophy; and especially those
views, which, occurring for the first time in his writings, have been
fully illustrated and confirmed by the subsequent progress of science,
and have become a portion of the permanent philosophy of our times.


(II.) 5. _A New Era announced._--The first great feature which
strikes us in Bacon's philosophical views is that which we have
already noticed;--his confident and emphatic announcement of a _New
Era_ in the progress of science, compared with which the advances of
former times were poor and trifling. This was with Bacon no loose and
shallow opinion, taken up on light grounds and involving only vague,
general notions. He had satisfied himself of the justice of such a
view by a laborious course of research and reflection. In 1605, at the
age of forty-four, he published his Treatise of the _Advancement of
Learning_, in which he takes a comprehensive and spirited survey of
the condition of all branches of knowledge which had been cultivated
up to that time. This work was composed with a view to that reform
of the existing philosophy which Bacon always had before his eyes;
and in the Latin edition of his works, forms the First Part of the
_Instauratio Magna_. In the Second Part of the Instauratio, the _Novum
Organon_, published in 1620, he more explicitly and confidently states
his expectations on this subject. He points out how slightly and
feebly the examination of nature had been pursued up to his time, and
with what scanty fruit. He notes the indications of this in the very
limited knowledge of the Greeks who had till then been the teachers
of Europe, in the complaints of authors concerning the subtilty and
obscurity of the secrets of nature, in the dissensions of sects, in
the absence of useful inventions resulting from theory, in the fixed
form which the sciences had retained for two thousand years. Nor, he
adds[169], is this wonderful; for how little of his thought and labour
has man bestowed upon science! Out of twenty-five centuries scarce six
have been favourable to the progress of knowledge. And even in those
favoured times, natural philosophy received the smallest share of man's
attention; while the portion so given was marred by controversy and
dogmatism; and even those who have bestowed a little thought upon
this philosophy, have never made it their main study, but have used it
as a passage or drawbridge to serve other objects. And thus, he says,
the great Mother of the Sciences is thrust down with indignity to the
offices of a handmaid; is made to minister to the labours of medicine
or mathematics, or to give the first preparatory tinge to the immature
minds of youth. For these and similar considerations of the errors of
past time, he draws hope for the future, employing the same argument
which Demosthenes uses to the Athenians: "That which is worst in the
events of the past, is the best as a ground of trust in the future.
For if you had done all that became you, and still had been in this
condition, your case might be desperate; but since your failure is the
result of your own mistakes, there is good hope that, correcting the
error of your course, you may reach a prosperity yet unknown to you."


(III.) 6. _A change of existing Method._--All Bacon's hope of
improvement indeed was placed in an entire _change of the Method_ by
which science was pursued; and the boldness, and at the same time (the
then existing state of science being considered), the definiteness of
his views of the change that was requisite, are truly remarkable.

That all knowledge must begin with observation, is one great principle
of Bacon's philosophy; but I hardly think it necessary to notice the
inculcation of this maxim as one of his main services to the cause of
sound knowledge, since it had, as we have seen, been fully insisted
upon by others before him, and was growing rapidly into general
acceptance without his aid. But if he was not the first to tell men
that they must collect their knowledge from observation, he had no
rival in his peculiar office of teaching them _how_ science must thus
be gathered from experience.

It appears to me that by far the most extraordinary parts of Bacon's
works are those in which, with extreme earnestness and clearness, he
insists upon a _graduated and successive induction_, as opposed to a
hasty transit from special facts to the highest generalizations. The
nineteenth Axiom of the First Book of the _Novum Organon_ contains a
view of the nature of true science most exact and profound, and, so
far as I am aware, at the time perfectly new. "There are two ways, and
can only be two, of seeking and finding truth. The one, from sense and
particulars, takes a flight to the most general axioms, and from those
principles and their truth, settled once for all, invents and judges of
intermediate axioms. The other method collects axioms from sense and
particulars, ascending _continuously and by degrees_, so that in the
end it arrives at the most general axioms; this latter way is the true
one, but hitherto untried."

It is to be remarked, that in this passage Bacon employs the term
_axioms_ to express any propositions collected from facts by induction,
and thus fitted to become the starting-point of deductive reasonings.
How far propositions so obtained may approach to the character of
axioms in the more rigorous sense of the term, we have already in some
measure examined; but that question does not here immediately concern
us. The truly remarkable circumstance is to find this recommendation
of a continuous advance from observation, by limited steps, through
successive gradations of generality, given at a time when speculative
men in general had only just begun to perceive that they must begin
their course from experience in some way or other. How exactly this
description represents the general structure of the soundest and
most comprehensive physical theories, all persons who have studied
the progress of science up to modern times can bear testimony; but
perhaps this structure of science cannot in any other way be made so
apparent as by those Tables of successive generalizations in which we
have exhibited the history and constitution of some of the principal
physical sciences, in the Chapter of a preceding work which treats of
the Logic of Induction. And the view which Bacon thus took of the true
progress of science was not only new, but, so far as I am aware, has
never been adequately illustrated up to the present day.


7. It is true, as I observed in the last chapter, that Galileo had been
led to see the necessity, not only of proceeding from experience in the
pursuit of knowledge, but of proceeding cautiously and gradually; and
he had exemplified this rule more than once, when, having made one step
in discovery, he held back his foot, for a time, from the next step,
however tempting. But Galileo had not reached this wide and commanding
view of the successive subordination of many steps, all leading up at
last to some wide and simple general truth. In catching sight of this
principle, and in ascribing to it its due importance, Bacon's sagacity,
so far as I am aware, wrought unassisted and unrivalled.


8. Nor is there any wavering or vagueness in Bacon's assertion of this
important truth. He repeats it over and over again; illustrates it by
a great number of the most lively metaphors and emphatic expressions.
Thus he speaks of the successive _floors_ (_tabulata_) of induction;
and speaks of each science as a _pyramid_[170] which has observation
and experience for its basis. No images can better exhibit the relation
of general and particular truths, as our own Inductive Tables may serve
to show.


(IV.) 9. _Comparison of the New and Old Method._ Again; not less
remarkable is his contrasting this true Method of Science (while it was
almost, as he says, yet untried) with the ancient and _vicious Method_,
which began, indeed, with facts of observation, but rushed at once
and with no gradations, to the most general principles. For this was
the course which had been actually followed by all those speculative
reformers who had talked so loudly of the necessity of beginning our
philosophy from experience. All these men, if they attempted to frame
physical doctrines at all, had caught up a few facts of observation,
and had erected a universal theory upon the suggestions which these
offered. This process of illicit generalization, or, as Bacon terms
it, Anticipation of Nature (_anticipatio naturæ_), in opposition to
the Interpretation of Nature, he depicts with singular acuteness, in
its character and causes. "These two ways," he says[171], "both begin
from sense and particulars; but their discrepancy is immense. The one
merely skims over experience and particulars in a cursory transit; the
other deals with them in a due and orderly manner. The one, at its very
outset, frames certain general abstract principles, but useless; the
other gradually rises to those principles which have a real existence
in nature."

"The former path," he adds[172], "that of illicit and hasty
generalization, is one which the intellect follows when abandoned to
its own impulse; and this it does from the requisitions of logic. For
the mind has a yearning which makes it dart forth to generalities, that
it may have something to rest in; and after a little dallying with
experience, becomes weary of it; and all these evils are augmented by
logic, which requires these generalities to make a show with in its
disputations."

"In a sober, patient, grave intellect," he further adds, "the mind, by
its own impulse, (and more especially if it be not impelled by the sway
of established opinions) attempts in some measure that other and true
way, of gradual generalization; but this it does with small profit;
for the intellect, except it be regulated and aided, is a faculty of
unequal operation, and altogether unapt to master the obscurity of
things."

The profound and searching wisdom of these remarks appears more
and more, as we apply them to the various attempts which men have
made to obtain knowledge; when they begin with the contemplation of
a few facts, and pursue their speculations, as upon most subjects
they have hitherto generally done; for almost all such attempts have
led immediately to some process of illicit generalization, which
introduces an interminable course of controversy. In the physical
sciences, however, we have the further inestimable advantage of seeing
the other side of the contrast exemplified: for many of them, as our
inductive Tables show us, have gone on according to the most rigorous
conditions of gradual and successive generalization; and in consequence
of this circumstance in their constitution, possess, in each part of
their structure, a solid truth, which is always ready to stand the
severest tests of reasoning and experiment.

We see how justly and clearly Bacon judged concerning the mode in which
facts are to be employed in the construction of science. This, indeed,
has ever been deemed his great merit: insomuch that many persons appear
to apprehend the main substance of his doctrine to reside in the maxim
that facts of observation, and such facts alone, are the essential
elements of all true science.


(V.) 10. _Ideas are necessary._--Yet we have endeavoured to establish
the doctrine that facts are but one of two ingredients of knowledge
both equally necessary;--that _Ideas_ are no less indispensable than
facts themselves; and that except these be duly unfolded and applied,
facts are collected in vain. Has Bacon then neglected this great
portion of his subject? Has he been led by some partiality of view, or
some peculiarity of circumstances, to leave this curious and essential
element of science in its pristine obscurity? Was he unaware of its
interest and importance?

We may reply that Bacon's philosophy, in its effect upon his readers
in general, does _not_ give due weight or due attention to the ideal
element of our knowledge. He is considered as peculiarly and eminently
the asserter of the value of experiment and observation. He is always
understood to belong to the experiential, as opposed to the ideal
school. He is held up in contrast to Plato and others who love to dwell
upon that part of knowledge which has its origin in the intellect of
man.


11. Nor can it be denied that Bacon has, in the finished part of his
_Novum Organon_, put prominently forwards the necessary dependence of
all our knowledge upon Experience, and said little of its dependence,
equally necessary, upon the Conceptions which the intellect itself
supplies. It will appear, however, on a close examination, that he
was by no means insensible or careless of this internal element of
all connected speculation. He held the balance, with no partial or
feeble hand, between phenomena and ideas. He urged the Colligation of
Facts, but he was not the less aware of the value of the Explication of
Conceptions.


12. This appears plainly from some remarkable Aphorisms in the _Novum
Organon_. Thus, in noticing the causes of the little progress then
made by science[173], he states this:--"In the current Notions, all is
unsound, whether they be logical or physical. _Substance_, _quality_,
_action_, _passion_, even _being_, are not good Conceptions; still less
are _heavy_, _light_, _dense_, _rare_, _moist_, _dry_, _generation_,
_corruption_, _attraction_, _repulsion_, _element_, _matter_, _form_,
and others of that kind; all are fantastical and ill-defined." And in
his attempt to exemplify his own system, he hesitates[174] in accepting
or rejecting the notions of _elementary_, _celestial_, _rare_, as
belonging to fire, since, as he says, they are vague and ill-defined
notions (_notiones vagæ nec bene terminatæ_). In that part of his work
which appears to be completed, there is not, so far as I have noticed,
any attempt to fix and define any notions thus complained of as loose
and obscure. But yet such an undertaking appears to have formed part
of his plan; and in the _Abecedarium Naturæ_[175], which consists of
the heads of various portions of his great scheme, marked by letters
of the alphabet, we find the titles of a series of dissertations "On
the Conditions of Being," which must have had for their object the
elucidation of divers Notions essential to science, and which would
have been contributions to the Explication of Conceptions, such as
we have attempted in a former part of this work. Thus some of the
subjects of these dissertations are;--Of Much and Little;--Of Durable
and Transitory;--Of Natural and Monstrous;--Of Natural and Artificial.
When the philosopher of induction came to discuss these, considered as
_conditions of existence_, he could not do otherwise than develope,
limit, methodize, and define the Ideas involved in these Notions,
so as to make them consistent with themselves, and a fit basis of
demonstrative reasoning. His task would have been of the same nature
as ours has been, in that part of this work which treats of the
Fundamental Ideas of the various classes of sciences.


13. Thus Bacon, in his speculative philosophy, took firmly hold of
both the handles of science; and if he had completed his scheme, would
probably have given due attention to Ideas, no less than to Facts, as
an element of our knowledge; while in his view of the general method
of ascending from facts to principles, he displayed a sagacity truly
wonderful. But we cannot be surprised, that in attempting to exemplify
the method which he recommended, he should have failed. For the method
could be exemplified only by some important discovery in physical
science; and great discoveries, even with the most perfect methods, do
not come at command. Moreover, although the general structure of his
scheme was correct, the precise import of some of its details could
hardly be understood, till the actual progress of science had made men
somewhat familiar with the kind of steps which it included.


(VI.) 14. _Bacon's Example._--Accordingly, Bacon's _Inquisition into
the Nature of Heat_, which is given in the Second Book of the _Novum
Organon_ as an example of the mode of interrogating Nature, cannot be
looked upon otherwise than as a complete failure. This will be evident
if we consider that, although the exact nature of heat is still an
obscure and controverted matter, the science of Heat now consists of
many important truths; and that to none of these truths is there any
approximation in Bacon's essay. From his process he arrives at this,
as the "forma or true definition" of heat;--"that it is an expansive,
restrained motion, modified in certain ways, and exerted in the
smaller particles of the body." But the steps by which the science of
Heat really advanced were (as may be seen in the history[176] of the
subject) these;--The discovery of a _measure_ of heat or temperature
(the thermometer); the establishment of the _laws_ of conduction
and radiation; of the _laws_ of specific heat, latent heat, and the
like. Such steps have led to Ampère's _hypothesis_[177], that heat
consists in the vibrations of an imponderable fluid; and to Laplace's
_hypothesis_, that temperature consists in the internal radiation of
such a fluid. These hypotheses cannot yet be said to be even probable;
but at least they are so modified as to include some of the preceding
laws which are firmly established; whereas Bacon's hypothetical motion
includes no laws of phenomena, explains no process, and is indeed
itself an example of illicit generalization.


15. One main ground of Bacon's ill fortune in this undertaking appears
to be, that he was not aware of an important maxim of inductive
science, that we must first obtain the _measure_ and ascertain the
_laws_ of phenomena, before we endeavour to discover their _causes_.
The whole history of thermotics up to the present time has been
occupied with the _former_ step, and the task is not yet completed:
it is no wonder, therefore, that Bacon failed entirely, when he so
prematurely attempted the _second_. His sagacity had taught him that
the progress of science must be gradual; but it had not led him to
judge adequately how gradual it must be, nor of what different kinds
of inquiries, taken in due order, it must needs consist, in order to
obtain success.

Another mistake, which could not fail to render it unlikely that Bacon
should really exemplify his precepts by any actual advance in science,
was, that he did not justly appreciate the sagacity, the inventive
genius, which all discovery requires. He conceived that he could
supersede the necessity of such peculiar endowments. "Our method of
discovery in science," he says[178], "is of such a nature, that there
is not much left to acuteness and strength of genius, but all degrees
of genius and intellect are brought nearly to the same level." And he
illustrates this by comparing his method to a pair of compasses, by
means of which a person with no manual skill may draw a perfect circle.
In the same spirit he speaks of proceeding by _due rejections_; and
appears to imagine that when we have obtained a collection of facts, if
we go on successively rejecting what is false, we shall at last find
that we have, left in our hands, that scientific truth which we seek.
I need not observe how far this view is removed from the real state of
the case. The necessity of a _conception_ which must be furnished by
the mind in order to bind together the facts, could hardly have escaped
the eye of Bacon, if he had cultivated more carefully the ideal side
of his own philosophy. And any attempts which he could have made to
construct such conceptions by mere rule and method, must have ended
in convincing him that nothing but a peculiar inventive talent could
supply that which was thus not contained in the facts, and yet was
needed for the discovery.


(VII.) 16. _His Failure._--Since Bacon, with all his acuteness, had not
divined circumstances so important in the formation of science, it is
not wonderful that his attempt to reduce this process to a _Technical
Form_ is of little value. In the first place, he says[179], we must
prepare a natural and experimental history, good and sufficient; in the
next place, the instances thus collected are to be arranged in Tables
in some orderly way; and then we must apply a legitimate and true
induction. And in his example[180], he first collects a great number
of cases in which heat appears under various circumstances, which he
calls "a Muster of Instances before the intellect," (_comparentia
instantiarum ad intellectum_,) or a _Table of the Presence_ of the
thing sought. He then adds a _Table of its Absence_ in proximate cases,
containing instances where heat does not appear; then a _Table of
Degrees_, in which it appears with greater or less intensity. He then
adds[181], that we must try to exclude several obvious suppositions,
which he does by reference to some of the instances he has collected;
and this step he calls the _Exclusive_, or the _Rejection of Natures_.
He then observes, (and justly,) that whereas truth emerges more easily
from error than from confusion, we may, after this preparation, _give
play to the intellect_, (fiat permissio intellectus,) and make an
attempt at induction, liable afterwards to be corrected; and by this
step, which he terms his _First Vindemiation_, or _Inchoate Induction_,
he is led to the proposition concerning heat, which we have stated
above.


17. In all the details of his example he is unfortunate. By proposing
to himself to examine at once into the _nature_ of heat, instead
of the laws of special classes of phenomena, he makes, as we have
said, a fundamental mistake; which is the less surprising since he
had before him so few examples of the right course in the previous
history of science. But further, his collection of instances is very
loosely brought together; for he includes in his list the _hot_ taste
of aromatic plants, the _caustic_ effects of acids, and many other
facts which cannot be ascribed to heat without a studious laxity in
the use of the word. And when he comes to that point where he permits
his intellect its range, the conception of _motion_ upon which it at
once fastens, appears to be selected with little choice or skill, the
suggestion being taken from flame[182], boiling liquids, a blown fire,
and some other cases. If from such examples we could imagine heat
to be motion, we ought at least to have some gradation to cases of
heat where no motion is visible, as in a red-hot iron. It would seem
that, after a large collection of instances had been looked at, the
intellect, even in its first attempts, ought not to have dwelt upon
such an hypothesis as this.


18. After these steps, Bacon speaks of several classes of instances
which, singling them out of the general and indiscriminate collection
of facts, he terms _Instances with Prerogative_: and these he points
out as peculiar aids and guides to the intellect in its task. These
Instances with Prerogative have generally been much dwelt upon by those
who have commented on the _Novum Organon_. Yet, in reality, such a
classification, as has been observed by one of the ablest writers of
the present day[183], is of little service in the task of induction.
For the instances are, for the most part, classed, not according to
the ideas which they involve, or to any obvious circumstance in the
facts of which they consist, but according to the extent or manner of
their influence upon the inquiry in which they are employed. Thus we
have Solitary Instances, Migrating Instances, Ostensive Instances,
Clandestine Instances, so termed according to the degree in which
they exhibit, or seem to exhibit, the property whose nature we would
examine. We have Guide-Post Instances, (_Instantiæ Crucis_,) Instances
of the Parted Road, of the Doorway, of the Lamp, according to the
guidance they supply to our advance. Such a classification is much of
the same nature as if, having to teach the art of building, we were to
describe tools with reference to the amount and place of the work which
they must do, instead of pointing out their construction and use:--as
if we were to inform the pupil that we must have tools for lifting a
stone up, tools for moving it sideways, tools for laying it square,
tools for cementing it firmly. Such an enumeration of ends would convey
little instruction as to the means. Moreover, many of Bacon's classes
of instances are vitiated by the assumption that the "form," that is,
the general law and cause of the property which is the subject of
investigation, is to be looked for directly in the instances; which, as
we have seen in his inquiry concerning heat, is a fundamental error.


19. Yet his phraseology in some cases, as in the _instantia crucis_,
serves well to mark the place which certain experiments hold in our
reasonings: and many of the special examples which he gives are full
of acuteness and sagacity. Thus he suggests swinging a pendulum in a
mine, in order to determine whether the attraction of the earth arises
from the attraction of its parts; and observing the tide at the same
moment in different parts of the world, in order to ascertain whether
the motion of the water is expansive or progressive; with other
ingenious proposals. These marks of genius may serve to counterbalance
the unfavourable judgment of Bacon's aptitude for physical science
which we are sometimes tempted to form, in consequence of his false
views on other points; as his rejection of the Copernican system, and
his undervaluing Gilbert's magnetical speculations. Most of these
errors arose from a too ambitious habit of intellect, which would not
be contented with any except very wide and general truths; and from an
indistinctness of mechanical, and perhaps, in general, of mathematical
ideas:--defects which Bacon's own philosophy was directed to remedy,
and which, in the progress of time, it has remedied in others.


(VIII.) 20. _His Idols._--Having thus freely given our judgment
concerning the most exact and definite portion of Bacon's precepts,
it cannot be necessary for us to discuss at any length the value
of those more vague and general _Warnings_ against prejudice and
partiality, against intellectual indolence and presumption, with which
his works abound. His advice and exhortations of this kind are always
expressed with energy and point, often clothed in the happiest forms
of imagery; and hence it has come to pass, that such passages are
perhaps more familiar to the general reader than any other part of
his writings. Nor are Bacon's counsels without their importance, when
we have to do with those subjects in which prejudice and partiality
exercise their peculiar sway. Questions of politics and morals,
of manners, taste, or history, cannot be subjected to a scheme of
rigorous induction; and though on such matters we venture to assert
general principles, these are commonly obtained with some degree of
insecurity, and depend upon special habits of thought, not upon mere
logical connexion. Here, therefore, the intellect may be perverted,
by mixing, with the pure reason, our gregarious affections, or our
individual propensities; the false suggestions involved in language,
or the imposing delusions of received theories. In these dim and
complex labyrinths of human thought, _the Idol of the Tribe_, or _of
the Den_, _of the Forum_, or _of the Theatre_, may occupy men's minds
with delusive shapes, and may obscure or pervert their vision of truth.
But in that Natural Philosophy with which we are here concerned, there
is little opportunity for such influences. As far as a physical theory
is completed through all the steps of a just induction, there is a
clear daylight diffused over it which leaves no lurking-place for
prejudice. Each part can be examined separately and repeatedly; and
the theory is not to be deemed perfect till it will bear the scrutiny
of all sound minds alike. Although, therefore, Bacon, by warning men
against the idols of fallacious images above spoken of, may have
guarded them from dangerous error, his precepts have little to do with
Natural Philosophy: and we cannot agree with him when he says[184],
that the doctrine concerning these idols bears the same relation to
the interpretation of nature as the doctrine concerning sophistical
paralogisms bears to common logic.


(IX.) 21. _His Aim, Utility._--There is one very prominent feature in
Bacon's speculations which we must not omit to notice; it is a leading
and constant object with him to apply his knowledge to _Use_. The
insight which he obtains into nature, he would employ in commanding
nature for the service of man. He wishes to have not only principles
but works. The phrase which best describes the aim of his philosophy is
his own[185], "Ascendendo ad _axiomata_, descendendo ad _opera_." This
disposition appears in the first aphorism of the _Novum Organon_, and
runs through the work. "Man, the _minister_ and interpreter of nature,
_does_ and understands, so far as he has, in fact or in thought,
observed the course of nature; and he cannot know or _do_ more than
this." It is not necessary for us to dwell much upon this turn of mind;
for the whole of our present inquiry goes upon the supposition that an
acquaintance with the laws of nature is worth our having for its own
sake. It may be universally true, that Knowledge is Power; but we have
to do with it not as Power, but as Knowledge. It is the formation of
Science, not of Art, with which we are here concerned. It may give a
peculiar interest to the history of science, to show how it constantly
tends to provide better and better for the wants and comforts of the
body; but _that_ is not the interest which engages us in our present
inquiry into the nature and course of philosophy. The consideration
of the means which promote man's material well-being often appears to
be invested with a kind of dignity, by the discovery of general laws
which it involves; and the satisfaction which rises in our minds at
the contemplation of such cases, men sometimes ascribe, with a false
ingenuity, to the love of mere bodily enjoyment. But it is never
difficult to see that this baser and coarser element is not the real
source of our admiration. Those who hold that it is the main business
of science to construct instruments for the uses of life, appear
sometimes to be willing to accept the consequence which follows from
such a doctrine, that the first shoemaker was a philosopher worthy of
the highest admiration[186]. But those who maintain such paradoxes,
often, by a happy inconsistency, make it their own aim, not to devise
some improved covering for the feet, but to delight the mind with acute
speculations, exhibited in all the graces of wit and fancy.

It has been said[187] that the key of the Baconian doctrine consists in
two words, Utility and Progress. With regard to the latter point, we
have already seen that the hope and prospect of a boundless progress in
human knowledge had sprung up in men's minds, even in the early times
of imperial Rome; and were most emphatically expressed by that very
Seneca who disdained to reckon the worth of knowledge by its value in
food and clothing. And when we say that Utility was the great business
of Bacon's philosophy, we forget one-half of his characteristic phrase:
"Ascendendo ad aximomata," no less than "descendendo ad opera," was,
he repeatedly declared, the scheme of his path. He constantly spoke,
we are told by his secretary[188], of two kinds of experiments,
_experimenta fructifera_, and _experimenta lucifera_.

Again; when we are told by modern writers that Bacon merely recommended
such induction as all men instinctively practise, we ought to recollect
his own earnest and incessant declarations to the contrary. The
induction hitherto practised is, he says, of no use for obtaining solid
science. There are two ways[189], "hæc via in usu est," "altera vera,
sed intentata." Men have constantly been employed in _anticipation_;
in illicit induction. The intellect left to itself rushes on in this
road[190]; the conclusions so obtained are persuasive[191]; far more
persuasive than inductions made with due caution[192]. But still this
method must be rejected if we would obtain true knowledge. We shall
then at length have ground of good hope for science when we proceed
in another manner[193]. We must rise, not by a leap, but by small
steps, by successive advances, by a gradation of ascents, trying our
facts, and clearing our notions at every interval. The scheme of true
philosophy, according to Bacon, is not obvious and simple, but long and
technical, requiring constant care and self-denial to follow it. And we
have seen that, in this opinion, his judgment is confirmed by the past
history and present condition of science.

Again; it is by no means a just view of Bacon's character to place
him in contrast to Plato. Plato's philosophy was the philosophy of
Ideas; but it was not left for Bacon to set up the philosophy of
Facts in opposition to that of Ideas. That had been done fully by the
speculative reformers of the sixteenth century. Bacon had the merit of
showing that Facts and Ideas must be combined; and not only so, but of
divining many of the special rules and forms of this combination, when
as yet there were no examples of them, with a sagacity hitherto quite
unparalleled.


(X.) 22. _His Perseverance._--With Bacon's unhappy political life we
have here nothing to do. But we cannot but notice with pleasure how
faithfully, how perseveringly, how energetically he discharged his
great philosophical office of a Reformer of Methods. He had conceived
the purpose of making this his object at an early period. When
meditating the continuation of his _Novum Organon_, and speaking of
his reasons for trusting that his work will reach some completeness
of effect, he says[194], "I am by two arguments thus persuaded.
First, I think thus from the zeal and constancy of my mind, which has
not waxed old in this design, nor, after so many years, grown cold
and indifferent; I remember that about forty years ago I composed
a juvenile work about these things, which with great contrivance
and a pompous title I called _temporis partum maximum_, or the most
considerable birth of time; Next, that on account of its usefulness,
it may hope the Divine blessing." In stating the grounds of hope for
future progress in the sciences, he says[195]: "Some hope may, we
conceive, be ministered to men by our own example: and this we say, not
for the sake of boasting, but because it is useful to be said. If any
despond, let them look at me, a man among all others of my age most
occupied with civil affairs, nor of very sound health, (which brings a
great loss of time;) also in this attempt the first explorer, following
the footsteps of no man, nor communicating on these subjects with any
mortal; yet, having steadily entered upon the true road and made my
mind submit to things themselves, one who has, in this undertaking,
made, (as we think,) some progress." He then proceeds to speak of what
may be done by the combined and more prosperous labours of others,
in that strain of noble hope and confidence, which rises again and
again, like a chorus, at intervals in every part of his writings. In
the _Advancement of Learning_ he had said, "I could not be true and
constant to the argument I handle, if I were not willing to go beyond
others, but yet not more willing than to have others go beyond me
again." In the Preface to the _Instauratio Magna_, he had placed among
his postulates those expressions which have more than once warmed the
breast of a philosophical reformer[196]. "Concerning ourselves we
speak not; but as touching the matter which we have in hand, this we
ask;--that men be of good hope, neither feign and imagine to themselves
this our Reform as something of infinite dimension and beyond the grasp
of mortal man, when in truth it is the end and true limit of infinite
error; and is by no means unmindful of the condition of mortality and
humanity, not confiding that such a thing can be carried to its perfect
close in the space of a single age, but assigning it as a task to a
succession of generations." In a later portion of the _Instauratio_ he
says: "We bear the strongest love to the _human republic_ our common
country; and we by no means abandon the hope that there will arise and
come forth some man among posterity, who will be able to receive and
digest all that is best in what we deliver; and whose care it will be
to cultivate and perfect such things. Therefore, by the blessing of the
Deity, to tend to this object, to open up the fountains, to discover
the useful, to gather guidance for the way, shall be our task; and from
this we shall never, while we remain in life, desist."


(XI.) 23. _His Piety._--We may add, that the spirit of piety as well as
of hope which is seen in this passage, appears to have been habitual
to Bacon at all periods of his life. We find in his works several
drafts of portions of his great scheme, and several of them begin with
a prayer. One of these entitled, in the edition of his works, "The
Student's Prayer," appears to me to belong probably to his early youth.
Another, entitled "The Writer's Prayer," is inserted at the end of
the Preface of the _Instauratio_, as it was finally published. I will
conclude my notice of this wonderful man by inserting here these two
prayers.

"To God the Father, God the Word, God the Spirit, we pour forth most
humble and hearty supplications; that he, remembering the calamities
of mankind, and the pilgrimage of this our life, in which we wear out
days few and evil, would please to open to us new refreshments out of
the fountains of his goodness for the alleviating of our miseries.
This also we humbly and earnestly beg, that human things may not
prejudice such as are divine; neither that, from the unlocking of the
gates of sense, and the kindling of a greater natural light, anything
of incredulity, or intellectual night, may arise in our minds towards
divine mysteries. But rather, that by our mind thoroughly cleansed and
purged from fancy and vanities, and yet subject and perfectly given up
to the Divine oracles, there may be given unto faith the things that
are faith's."

"Thou, O Father, who gavest the visible light as the first-born of
thy creatures, and didst pour into man the intellectual light as the
top and consummation of thy workmanship, be pleased to protect and
govern this work, which coming from thy goodness, returneth to thy
glory. Thou, after thou hadst reviewed the works which thy hands had
made, beheldest that everything was very good, and thou didst rest
with complacency in them. But man, reflecting on the works which he
had made, saw that all was vanity and vexation of spirit, and could by
no means acquiesce in them. Wherefore, if we labour in thy works with
the sweat of our brows, thou wilt make us partakers of thy vision and
thy Sabbath. We humbly beg that this mind may be steadfastly in us;
and that thou, by our hands, and also by the hands of others on whom
thou shalt bestow the same spirit, wilt please to convey a largess
of new alms to thy family of mankind. These things we commend to thy
everlasting love, by our Jesus, thy Christ, God with us. Amen."


FOOTNOTES:

[Footnote 168: And in other passages: thus, "Ego enim buccinator tantum
pugnam non ineo." _Nov. Org._ lib. iv. c. i.]

[Footnote 169: Lib. 1. Aphor. 78 _et seq._]

[Footnote 170: _Aug. Sc._ Lib. iii. c. 4. p. 194. So in other places,
as _Nov. Org._ i. Aph. 104. "De scientiis tum demum bene sperandum est
quando per scalam veram et per gradus continuos, et non intermissos aut
hiulcos a particularibus ascendetur ad axiomata minora, et deinde ad
media, alia aliis superiora, et postremo demum ad generalissima."]

[Footnote 171: _Nov. Org._ 1. Aph. 22.]

[Footnote 172: _Ib._ Aph. 20.]

[Footnote 173: 1 Ax. 15.]

[Footnote 174: _Nov. Org._ lib. ii. Aph. 19.]

[Footnote 175: _Inst. Mag._ par. iii. (vol. viii. p. 244).]

[Footnote 176: _Hist. Ind. Sc._ b. x. c. i.]

[Footnote 177: _Ib._ c. iv.]

[Footnote 178: _Nov. Org._ lib. i. Aph. 61.]

[Footnote 179: _Nov. Org._ lib. ii. Aph. 10.]

[Footnote 180: Aph. 11.]

[Footnote 181: Aph. 15, p. 105.]

[Footnote 182: Page 110.]

[Footnote 183: Herschel, _On the Study of Nat. Phil._ Art. 192.]

[Footnote 184: _Nov. Org._ lib. i. Aph. 40.]

[Footnote 185: _Nov. Org._ lib. i. Ax. 103.]

[Footnote 186: _Edinb. Rev._ No. cxxxii. p. 65.]

[Footnote 187: _Ib._]

[Footnote 188: Pref. to the _Nat. Hist._ i. 243.]

[Footnote 189: _Nov. Org._ lib. i. Aph. 19.]

[Footnote 190: _Ibid._ lib. i. Aph. 20.]

[Footnote 191: Aph. 27.]

[Footnote 192: _Ib._ 28.]

[Footnote 193: Aph. 104. So Aph. 105. "In constituendo axiomate forma
_inductionis_ alia quam adhuc in usu fuit excogitanda est," &c.]

[Footnote 194: _Ep. ad P. Fulgentium._ _Op._ x. 330.]

[Footnote 195: _Nov. Org._ i. Aph. 113.]

[Footnote 196: See the motto to Kant's _Kritik der Reinen Vernunft_.]




CHAPTER XVI.

ADDITIONAL REMARKS ON FRANCIS BACON.


Francis Bacon and his works have recently been discussed and examined
by various writers in France and Germany as well as England[197]. Not
to mention smaller essays, M. Bouillet has published a valuable edition
of his philosophical works; Count Joseph de Maistre wrote a severe
critique of his philosophy, which has been published since the death of
the author; M. Charles Remusat has written a lucid and discriminating
Essay on the subject; and in England we have had a new edition of the
works published, with a careful and thoughtful examination of the
philosophy which they contain, written by one of the editors: a person
especially fitted for such an examination by an acute intellect, great
acquaintance with philosophical literature, and a wide knowledge of
modern science. Robert Leslie Ellis, the editor of whom I speak, died
during the publication of the edition, and before he had done full
justice to his powers; but he had already written various dissertations
on Bacon's philosophy, which accompany the different Treatises in the
new edition.

Mr. Ellis has given a more precise view than any of his predecessors
had done of the nature of Bacon's induction and of his philosophy of
discovery. Bacon's object was to discover the 'natures' or essences
of things, in order that he might reproduce these natures or essences
at will; he conceived that these natures were limited in number, and
manifested in various combinations in the bodies which exist in the
universe; so that by accumulating observations of them in a multitude
of cases, we may learn by induction in what they do and in what
they do not consist; the _Induction_ which is to be used for this
purpose consists in a great measure of _excluding_ the cases which
do not exhibit the 'nature' in question; and by such exclusion, duly
repeated, we have at last left in our hands the elements of which the
proposed nature consists. And the knowledge which is thus obtained may
be applied to reproduce the things so analysed. As exhibiting this
view clearly we may take a passage in the _Sylva Sylvarum_: "Gold has
these natures: greatness of weight, closeness of parts, fixation,
pliantness or softness, immunity from rust, colour or tincture of
yellow. Therefore the sure way, though most about, to make gold, is to
know the causes of the several natures before rehearsed, and the axioms
concerning the same. For if a man can make a metal, that hath all these
properties, let men dispute whether it be gold or no." He means that
however they dispute, it is gold for all practical purposes.

For such an Induction as this, Bacon claims the merit both of
being certain, and of being nearly independent of the ingenuity of
the inquirer. It is a method which enables all men to make exact
discoveries, as a pair of compasses enables all men to draw an exact
circle.

Now it is necessary for us, who are exploring the progress of the true
philosophy of discovery, to say plainly that this part of Bacon's
speculation is erroneous and valueless. No scientific discovery ever
has been made in this way. Men have not obtained truths concerning
the natural world by seeking for the natures of things, and by
extracting them from phenomena by rejecting the cases in which they
were not. On the contrary, they have begun by ascertaining the _laws
of the phenomena_; and have then gone on, not by a mechanical method
which levels all intellect, but by special efforts of the brightest
intellects to catch hold of the ideas by which these laws of phenomena
might be interpreted and expressed in more general terms. These two
steps, the finding the laws of phenomena, and finding the conceptions
by which those laws can be expressed, are really the course of
discovery, as the history of science exhibits it to us.

Bacon, therefore, according to the view now presented, was wrong both
as to his object and as to his method. He was wrong in taking for his
object the essences of things,--the causes of abstract properties:
for these man cannot, or can very rarely discover; and all Bacon's
ingenuity in enumerating and classifying these essences and abstract
properties has led, and could lead, to no result. The vast results
of modern science have been obtained, not by seeking and finding the
essences of things, but by exploring the laws of phenomena and the
causes of those laws.

And Bacon's method, as well as his object, is vitiated by a pervading
error:--the error of supposing that to be done by method which must
be done by mind;--that to be done by rule which must be done by a
flight beyond rule;--that to be mainly negative which is eminently
positive;--that to depend on other men which must depend on the
discoverer himself;--that to be mere prose which must have a dash of
poetry;--that to be a work of mere labour which must be also a work of
genius.

Mr. Ellis has seen very clearly and explained very candidly that this
method thus recommended by Bacon has not led to discovery. "It is," he
says, "neither to the technical part of his method nor to the details
of his view of the nature and progress of science, that his great fame
is justly owing. His merits are of another kind. They belong to the
spirit rather than to the positive precepts of his philosophy."

As the reader of the last chapter will see, this amounts to much the
same as the account which I had given of the positive results of
Bacon's method, and the real value of that portion of his philosophy
which he himself valued most. But still there remain, as I have also
noted, portions of Bacon's speculations which have a great and enduring
value, namely, his doctrine that Science is the Interpretation of
Nature, his distinction of this Interpretation of Nature from the
vicious and premature Anticipation of Nature which had generally
prevailed till then; and the recommendation of a graduated and
successive induction by which alone the highest and most general
truths were to be reached. These are points which he urges with great
clearness and with great earnestness; and these are important points in
the true philosophy of discovery.

I may add that Mr. Ellis agrees with me in noting the invention of
the conception by which the laws of phenomena are interpreted as
something additional to _Induction_, both in the common and in the
Baconian sense of the word. He says (General Preface, Art. 9), "In
all cases this process [scientific discovery] involves an element to
which nothing corresponds in the Tables of Comparence and Exclusion;
namely the application to the facts of a _principle_ of arrangement,
an _idea_, existing in the mind of the discoverer antecedently to the
act of induction." It may be said that this principle or idea is aimed
at in the Baconian analysis. "And this is in one sense true: but it
must be added, that this _analysis_, if it be thought right to call it
so, is of the essence of the discovery which results from it. To take
for granted that it has been already effected is simply a _petitio
principii_. In most cases the mere act of induction follows as a matter
of course as soon as the _appropriate idea_ has been introduced." And
as an example he takes Kepler's invention of the ellipse, as the idea
by which Mars's motions could be reduced to law; making the same use of
this example which we have repeatedly made of it.

Mr. Ellis may at first sight appear to express himself more favourably
than I have done, with regard to the value of Bacon's _Inquisitio in
Naturam Calidi_ in the Second Book of the _Novum Organon_. He says of
one part of it[198]: "Bacon here anticipates not merely the essential
character of the most recent theory of heat, but also the kind of
evidence by which it has been established.... The merit of having
perceived the true significance of the production of heat by friction
belongs of right to Bacon."

But notwithstanding this, Mr. Ellis's general judgment on this specimen
of Bacon's application of his own method does not differ essentially
from mine. He examines the _Inquisitio_ at some length, and finally
says: "If it were affirmed that Bacon, after having had a glimpse of
the truth suggested by some obvious phenomena, had then recourse, as he
himself expresses it, to certain 'differentiæ inanes' in order to save
the phenomena, I think it would be hard to dispute the truth of the
censure."


Another of the Editors of this edition (Mr. Spedding) fixes his
attention upon another of the features of the method of discovery
proposed by Bacon, and is disposed to think that the proposed method
has never yet had justice done it, because it has not been tried in the
way and on the scale that Bacon proposes[199]. Bacon recommended that
a great collection of facts should be at once made and accumulated,
regarding every branch of human knowledge; and conceived that, when
this had been done by common observers, philosophers might extract
scientific truths from this mass of facts by the application of a right
method. This separation of the offices of the observer and discoverer,
Mr. Spedding thinks is shown to be possible by such practical examples
as meteorological observations, made by ordinary observers, and
reduced to tables and laws by a central calculator; by hydrographical
observations made by ships provided with proper instructions, and
reduced to general laws by the man of science in his study; by
magnetical observations made by many persons in every part of the
world, and reduced into subservience to theory by mathematicians at
home.

And to this our reply will be, in the terms which the history of
all the Sciences has taught us, that such methods of procedure as
this do not belong to the _Epoch of Discovery_, but to the Period of
_verification_ and _application_ of the discovery which follows. When a
theory has been established in its general form, our knowledge of the
distribution of its phenomena in time and space can be much promoted
by ordinary observers scattered over the earth, and succeeding each
other in time, provided they are furnished with instruments and methods
of observation, duly constructed on the principles of science; but
such observers cannot in any degree supersede the discoverer who is
first to establish the theory, and to introduce into the facts a new
principle of order. When the laws of nature have been caught sight
of, much may be done, even by ordinary observers, in verifying and
exactly determining them; but when a real discovery is to be made,
this separation of the observer and the theorist is not possible. In
those cases, the questioning temper, the busy suggestive mind, is
needed at every step, to direct the operating hand or the open gaze.
No possible accumulation of facts about mixture and heat, collected in
the way of blind trial, could have led to the doctrines of chemistry,
or crystallography, or the atomic theory, or voltaic and chemical
and magnetic polarity, or physiology, or any other science. Indeed
not only is an existing theory requisite to supply the observer with
instruments and methods, but without theory he cannot even describe his
observations. He says that he mixes an acid and an alkali; but what
is an acid? What is an alkali? How does he know them? He classifies
crystals according to their forms: but till he has learnt what is
distinctive in the form of a crystal, he cannot distinguish a cube
from a square prism, even if he had a goniometer and could use it. And
the like impossibility hangs over all the other subjects. To report
facts for scientific purposes without some aid from theory, is not only
useless, but impossible.

When Mr. Spedding says, "I could wish that men of science would apply
themselves earnestly to the solution of this practical problem:
What measures are to be taken in order that the greatest variety of
judicious observations of nature all over the world may be carried on
in concert upon a common plan and brought to a common centre:"--he is
urging upon men of science to do what they have always done, so far
as they have had any power, and in proportion as the state of science
rendered such a procedure possible and profitable to science. In
Astronomy, it has been done from the times of the Greeks and even of
the Chaldeans, having been begun _as soon as_ the heavens were reduced
to law at all. In meteorology, it has been done extensively, though to
little purpose, because the weather has _not yet_ been reduced to rule.
Men of science have shown how barometers, thermometers, hygrometers,
and the like, may be constructed; and these may be now read by any one
as easily as a clock; but of ten thousand meteorological registers
thus kept by ordinary observers, what good has come to science?
Again: The laws of the tides have been in a great measure determined
by observations in all parts of the globe, _because_ theory pointed
out what was to be observed. In like manner the facts of terrestrial
magnetism were ascertained with tolerable completeness by extended
observations, _then_, and then only, when a most recondite and profound
branch of mathematics had pointed out what was to be observed, and most
ingenious instruments had been devised by men of science for observing.
And even with these, it requires an education to use the instruments.
But in many cases no education in the use of instruments devised by
others can supersede the necessity of a theoretical and suggestive
spirit in the inquirer himself. He must devise his own instruments
and his own methods, if he is to make any discovery. What chemist, or
inquirer about polarities, or about optical laws yet undiscovered, can
make any progress by using another man's experiments and observations?
He must invent at every step of his observation; and the observer and
theorist can no more be dissevered, than the body and soul of the
inquirer.

That persons of moderate philosophical powers may, when duly
educated, make observations which may be used by greater discoverers
than themselves, is true. We have examples of such a subordination
of scientific offices in astronomy, in geology, and in many other
departments. But still, as I have said, a very considerable degree of
scientific education is needed even for the subordinate labourers in
science; and the more considerable in proportion as science advances
further and further; since every advance implies a knowledge of what
has already been done, and requires a new precision or generality in
the new points of inquiry.


FOOTNOTES:

[Footnote 197: _Œuvres Philosophiques de Bacon, &c._ par M. N.
Bouillet, 3 Tomes.

_Examen de la Philosophie de Bacon_ (_Œuvres Posthumes_ du Comte J. de
Maistre).

_Bacon, sa Vie, son Temps, sa Philosophie_, par Charles de Remusat.

_Histoire de la Vie et des Ouvrages de François Bacon_, par J. B. de
Vaugelles.

_Franz Baco von Verulam_, von Kuno Fischer.

_The Works of Francis Bacon_, collected and edited by James Spedding,
Robert Leslie Ellis, and Douglas Denon Heath.]

[Footnote 198: Note to Aph. xviii.]

[Footnote 199: Pref. to the _Parasceue_, Vol. i. p. 382.]




CHAPTER XVII.

FROM BACON TO NEWTON.


1. _Harvey._--We have already seen that Bacon was by no means the
first mover or principal author of the revolution in the method of
philosophizing which took place in his time; but only the writer who
proclaimed in the most impressive and comprehensive manner, the scheme,
the profit, the dignity, and the prospects of the new philosophy.
Those, therefore, who after him, took up the same views are not to be
considered as his successors, but as his fellow-labourers; and the
line of historical succession of opinions must be pursued without
special reference to any one leading character, as the principal figure
of the epoch. I resume this line, by noticing a contemporary and
fellow-countryman of Bacon, Harvey, the discoverer of the circulation
of the blood. This discovery was not published and generally accepted
till near the end of Bacon's life; but the anatomist's reflections
on the method of pursuing science, though strongly marked with the
character of the revolution that was taking place, belong to a very
different school from the Chancellor's. Harvey was a pupil of Fabricius
of Acquapendente, whom we noticed among the practical reformers of the
sixteenth century. He entertained, like his master, a strong reverence
for the great names which had ruled in philosophy up to that time,
Aristotle and Galen; and was disposed rather to recommend his own
method by exhibiting it as the true interpretation of ancient wisdom,
than to boast of its novelty. It is true, that he assigns, as his
reason for publishing some of his researches[200], "that by revealing
the method I use in searching into things, I might propose to studious
men, a new and (if I mistake not) a surer path to the attainment of
knowledge[201];" but he soon proceeds to fortify himself with the
authority of Aristotle. In doing this, however, he has the very great
merit of giving a living and practical character to truths which exist
in the Aristotelian works, but which had hitherto been barren and empty
professions. We have seen that Aristotle had asserted the importance
of experience as one root of knowledge; and in this had been followed
by the schoolmen of the middle ages: but this assertion came with very
different force and effect from a man, the whole of whose life had been
spent in obtaining, by means of experience, knowledge which no man had
possessed before. In Harvey's general reflections, the necessity of
both the elements of knowledge, sensations and ideas, experience and
reason, is fully brought into view, and rightly connected with the
metaphysics of Aristotle. He puts the antithesis of these two elements
with great clearness. "Universals are chiefly known to us, for science
is begot by reasoning from universals to particulars; yet that very
comprehension of universals in the understanding springs from the
perception of singulars in our sense." Again, he quotes Aristotle's
apparently opposite assertions:--that made in his _Physics_[202],
"that we must advance from things which are first known to us, though
confusedly, to things more distinctly intelligible in themselves;
from the whole to the part; from the universal to the particular;"
and that made in the _Analytics_[203]; that "Singulars are more known
to us and do first exist according to sense: for nothing is in the
understanding which was not before in the sense." Both, he says, are
true, though at first they seem to clash: for "though in knowledge
we begin with sense, sensation itself is a universal thing." This he
further illustrates; and quotes Seneca, who says, that "Art itself is
nothing but the _reason_ of the work, implanted in the Artist's mind:"
and adds, "the same way by which we gain an Art, by the very same way
we attain any kind of science or knowledge whatever; for as Art is
a habit whose object is something to be done, so Science is a habit
whose object is something to be known; and as the former proceedeth
from the imitation of examples, so this latter, from the knowledge of
things natural. The source of both is from sense and experience; since
[but?] it is impossible that Art should be rightly purchased by the one
or Science by the other without a direction from ideas." Without here
dwelling on the relation of Art and Science, (very justly stated by
Harvey, except that ideas exist in a very different form in the mind
of the Artist and the Scientist) it will be seen that this doctrine,
of science springing from experience with a direction from ideas, is
exactly that which we have repeatedly urged, as the true view of the
subject. From this view, Harvey proceeds to infer the importance of a
reference to sense in his own subject, not only for first discovering,
but for receiving knowledge: "Without experience, not other men's but
our own, no man is a proper disciple of any part of natural knowledge;
without experimental skill in anatomy, he will no better apprehend
what I shall deliver concerning generation, than a man born blind can
judge of the nature and difference of colours, or one born deaf, of
sounds." "If we do otherwise, we may get a humid and floating opinion,
but never a solid and infallible knowledge: as is happenable to those
who see foreign countries only in maps, and the bowels of men falsely
described in anatomical tables. And hence it comes about, that in this
rank age, we have many sophisters and bookwrights, but few wise men
and philosophers." He had before declared "how unsafe and degenerate a
thing it is, to be tutored by other men's commentaries, without making
trial of the things themselves; especially since Nature's book is so
open and legible." We are here reminded of Galileo's condemnation
of the "paper philosophers." The train of thought thus expressed by
the practical discoverers, spread rapidly with the spread of the
new knowledge that had suggested it, and soon became general and
unquestioned.


2. _Descartes._--Such opinions are now among the most familiar and
popular of those which are current among writers and speakers; but
we should err much if we were to imagine that after they were once
propounded they were never resisted or contradicted. Indeed, even in
our own time, not only are such maxims very often practically neglected
or forgotten, but the opposite opinions, and views of science quite
inconsistent with those we have been explaining, are often promulgated
and widely accepted. The philosophy of pure ideas has its commonplaces,
as well as the philosophy of experience. And at the time of which
we speak, the former philosophy, no less than the latter, had its
great asserter and expounder; a man in his own time more admired than
Bacon, regarded with more deference by a large body of disciples all
over Europe, and more powerful in stirring up men's minds to a new
activity of inquiry. I speak of Descartes, whose labours, considered
as a philosophical system, were an endeavour to revive the method
of obtaining knowledge by reasoning from our own ideas only, and to
erect it in opposition to the method of observation and experiment.
The Cartesian philosophy contained an attempt at a counter-revolution.
Thus in this author's _Principia Philosophiæ_[204], he says that "he
will give a short account of the principal phenomena of the world,
not that he may use them as reasons to prove anything; for," adds he,
"we desire to deduce effects from causes, not causes from effects;
but only in order that out of the innumerable effects which we learn
to be capable of resulting from the same causes, we may determine our
mind to consider some rather than others." He had before said, "The
principles which we have obtained [by pure _à priori_ reasoning] are so
vast and so fruitful, that many more consequences follow from them than
we see contained in this visible world, and even many more than our
mind can ever take a full survey of." And he professes to apply this
method in detail. Thus in attempting to state the three fundamental
laws of motion, he employs only _à priori_ reasonings, and is in fact
led into error in the third law which he thus obtains[205]. And in
his _Dioptrics_[206] he pretends to deduce the laws of reflection
and refraction of light from certain comparisons (which are, in
truth, arbitrary,) in which the radiation of light is represented
by the motion of a ball impinging upon the reflecting or refracting
body. It might be represented as a curious instance of the caprice
of fortune, which appears in scientific as in other history, that
Kepler, professing to derive all his knowledge from experience, and
exerting himself with the greatest energy and perseverance, failed in
detecting the law of refraction; while Descartes, who professed to be
able to despise experiment, obtained the true law of sines. But as we
have stated in the _History_[207], Descartes appears to have learnt
this law from Snell's papers. And whether this be so or not, it is
certain that notwithstanding the profession of independence which his
philosophy made, it was in reality constantly guided and instructed by
experience. Thus in explaining the Rainbow (in which his portion of
the discovery merits great praise) he speaks[208] of taking a globe
of glass, allowing the sun to shine on one side of it, and noting the
colours produced by rays after two refractions and one reflection.
And in many other instances, indeed in all that relates to physics,
the reasonings and explanations of Descartes and his followers were,
consciously or unconsciously, directed by the known facts, which they
had observed themselves or learnt from others.

But since Descartes thus, speculatively at least, set himself in
opposition to the great reform of scientific method which was going
on in his time, how, it may be asked, did he acquire so strong an
influence over the most active minds of his time? How is it that he
became the founder of a large and distinguished school of philosophers?
How is it that he not only was mainly instrumental in deposing
Aristotle from his intellectual throne, but for a time appeared to have
established himself with almost equal powers, and to have rendered the
Cartesian school as firm a body as the Peripatetic had been?

The causes to be assigned for this remarkable result are, I conceive,
the following. In the first place, the physicists of the Cartesian
school did, as I have just stated, found their philosophy upon
experiment, and did not practically, or indeed, most of them,
theoretically, assent to their master's boast of showing what the
phenomena _must be_, instead of looking to see what they _are_. And
as Descartes had really incorporated in his philosophy all the chief
physical discoveries of his own and preceding times, and had delivered,
in a more general and systematic shape than any one before him, the
principles which he thus established, the physical philosophy of his
school was in reality far the best then current; and was an immense
improvement upon the Aristotelian doctrines, which had not yet been
displaced as a system. Another circumstance which gained him much
favour, was the bold and ostentatious manner in which he professed
to begin his philosophy by liberating himself from all preconceived
prejudice. The first sentence of his philosophy contains this
celebrated declaration: "Since," he says, "we begin life as infants,
and have contracted various judgments concerning sensible things before
we possess the entire use of our reason, we are turned aside from the
knowledge of truth by many prejudices: from which it does not appear
that we can be any otherwise delivered, than if once in our life we
make it our business to doubt of everything in which we discern the
smallest suspicion of uncertainty." In the face of this sweeping
rejection or unhesitating scrutiny of all preconceived opinions,
the power of the ancient authorities and masters in philosophy must
obviously shrink away; and thus Descartes came to be considered as
the great hero of the overthrow of the Aristotelian dogmatism. But
in addition to these causes, and perhaps more powerful than all in
procuring the assent of men to his doctrines, came the deductive and
systematic character of his philosophy. For although all knowledge of
the external world is in reality only to be obtained from observation,
by inductive steps,--minute, perhaps, and slow, and many, as Galileo
and Bacon had already taught;--the human mind conforms to these
conditions reluctantly and unsteadily, and is ever ready to rush to
general principles, and then to employ itself in deducing conclusions
from these by synthetical reasonings; a task grateful, from the
distinctness and certainty of the result, and the accompanying feeling
of our own sufficiency. Hence men readily overlooked the precarious
character of Descartes' fundamental assumptions, in their admiration
of the skill with which a varied and complex Universe was evolved out
of them. And the complete and systematic character of this philosophy
attracted men no less than its logical connexion. I may quote here
what a philosopher[209] of our own time has said of another writer:
"He owed his influence to various causes; at the head of which may be
placed that genius for system which, though it cramps the growth of
knowledge, perhaps finally atones for that mischief by the zeal and
activity which it rouses among followers and opponents, who discover
truth by accident when in pursuit of weapons for their warfare. A
system which attempts a task so hard as that of subjecting vast
provinces of human knowledge to one or two principles, if it presents
some striking instances of conformity to superficial appearances, is
sure to delight the framer; and for a time to subdue and captivate the
student too entirely for sober reflection and rigorous examination. In
the first instance consistency passes for truth. When principles in
some instances have proved sufficient to give an unexpected explanation
of facts, the delighted reader is content to accept as true all other
deductions from the principles. Specious premises being assumed to be
true, nothing more can be required than logical inference. Mathematical
forms pass current as the equivalent of mathematical certainty. The
unwary admirer is satisfied with the completeness and symmetry of the
plan of his house, unmindful of the need of examining the firmness of
the foundation and the soundness of the materials. The system-maker,
like the conqueror, long dazzles and overawes the world; but when their
sway is past, the vulgar herd, unable to measure their astonishing
faculties, take revenge by trampling on fallen greatness." Bacon
showed his wisdom in his reflections on this subject, when he said
that "Method, carrying a show of total and perfect knowledge, hath a
tendency to generate acquiescence."

The main value of Descartes' physical doctrines consisted in their
being arrived at in a way inconsistent with his own professed method,
namely, by a reference to observation. But though he did in reality
begin from facts, his system was nevertheless a glaring example
of that error which Bacon had called _Anticipation_; that illicit
generalization which leaps at once from special facts to principles
of the widest and remotest kind; such, for instance, as the Cartesian
doctrine, that the world is an absolute _plenum_, every part being
full of matter of some kind, and that all natural effects depend on
the laws of motion. Against this fault, to which the human mind is
so prone, Bacon had lifted his warning voice in vain, so far as the
Cartesians were concerned; as indeed, to this day, one theorist after
another pursues his course, and turns a deaf ear to the Verulamian
injunctions; perhaps even complacently boasts that he founds his theory
upon observation; and forgets that there are, as the aphorism of the
_Novum Organon_ declares, two ways by which this may be done;--the one
hitherto in use and suggested by our common tendencies, but barren and
worthless; the other almost untried, to be pursued only with effort and
self-denial, but alone capable of producing true knowledge.


3. _Gassendi._--Thus the lessons which Bacon taught were far from being
generally accepted and applied at first. The amount of the influence of
these two men, Bacon and Descartes, upon their age, has often been a
subject of discussion. The fortunes of the Cartesian school have been
in some measure traced in the History of Science. But I may mention the
notice taken of these two philosophers by Gassendi, a contemporary and
countryman of Descartes. Gassendi, as I have elsewhere stated[210],
was associated with Descartes in public opinion, as an opponent of the
Aristotelian dogmatism; but was not in fact a follower or profound
admirer of that writer. In a Treatise on Logic, Gassendi gives an
account of the Logic of various sects and authors; treating, in order,
of the Logic of Zeno (the Eleatic), of Euclid (the Megarean), of
Plato, of Aristotle, of the Stoics, of Epicurus, of Lullius, of Ramus;
and to these he adds the Logic of Verulam, and the Logic of Cartesius.
"We must not," he says, "on account of the celebrity it has obtained,
pass over the Organon or Logic of Francis Bacon Lord Verulam, High
Chancellor of England, whose noble purpose in our time it has been, to
make an Instauration of the Sciences." He then gives a brief account
of the _Novum Organon_, noticing the principal features in its rules,
and especially the distinction between the vulgar induction which leaps
at once from particular experiments to the more general axioms, and
the chastised and gradual induction, which the author of the _Organon_
recommends. In his account of the Cartesian Logic, he justly observes,
that "He too imitated Verulam in this, that being about to build up a
new philosophy from the foundation, he wished in the first place to lay
aside all prejudice: and having then found some solid principle, to
make that the groundwork of his whole structure. But he proceeds by a
very different path from that which Verulam follows; for while Verulam
seeks aid from things, to perfect the cogitation of the intellect,
Cartesius conceives, that when we have laid aside all knowledge of
things, there is, in our thoughts alone, such a resource, that the
intellect may by its own power arrive at a perfect knowledge of all,
even the most abstruse things."

The writings of Descartes have been most admired, and his method
most commended, by those authors who have employed themselves upon
metaphysical rather than physical subjects of inquiry. Perhaps we might
say that, in reference to such subjects, this method is not so vicious
as at first, when contrasted with the Baconian induction, it seems to
be: for it might be urged that the _thoughts_ from which Descartes
begins his reasonings are, in reality, _experiments_ of the kind which
the subject requires us to consider: each such thought is a fact in
the intellectual world; and of such facts, the metaphysician seeks to
discover the laws. I shall not here examine the validity of this plea;
but shall turn to the consideration of the actual progress of physical
science, and its effect on men's minds.


4. _Actual progress in Science._--The practical discoverers were indeed
very active and very successful during the seventeenth century, which
opened with Bacon's survey and exhortations. The laws of nature, of
which men had begun to obtain a glimpse in the preceding century, were
investigated with zeal and sagacity, and the consequence was that the
foundations of most of the modern physical sciences were laid. That
mode of research by experiment and observation, which had, a little
time ago, been a strange, and to many, an unwelcome innovation, was now
become the habitual course of philosophers. The revolution from the
philosophy of tradition to the philosophy of experience was completed.
The great discoveries of Kepler belonged to the preceding century.
They are not, I believe, noticed, either by Bacon or by Descartes; but
they gave a strong impulse to astronomical and mechanical speculators,
by showing the necessity of a sound science of motion. Such a science
Galileo had already begun to construct. At the time of which I speak,
his disciples[211] were still labouring at this task, and at other
problems which rapidly suggested themselves. They had already convinced
themselves that air had weight; in 1643 Torricelli proved this
practically by the invention of the Barometer; in 1647 Pascal proved
it still further by sending the Barometer to the top of a mountain.
Pascal and Boyle brought into clear view the fundamental laws of fluid
equilibrium; Boyle and Mariotte determined the law of the compression
of air as regulated by its elasticity. Otto Guericke invented the
air-pump, and by his "Madgeburg Experiments" on a vacuum, illustrated
still further the effects of the air. Guericke pursued what Gilbert
had begun, the observation of electrical phenomena; and these two
physicists made an important step, by detecting repulsion as well as
attraction in these phenomena. Gilbert had already laid the foundations
of the science of Magnetism. The law of refraction, at which Kepler
had laboured in vain, was, as we have seen, discovered by Snell (about
1621), and published by Descartes. Mersenne had discovered some of
the more important parts of the theory of Harmonics. In sciences of
a different kind, the same movement was visible. Chemical doctrines
tended to assume a proper degree of generality, when Sylvius in 1679
taught the opposition of acid and alkali, and Stahl, soon after,
the phlogistic theory of combustion. Steno had remarked the most
important law of crystallography in 1669, that the angles of the same
kind of crystals are always equal. In the sciences of classification,
about 1680, Ray and Morison in England resumed the attempt to form a
systematic botany, which had been interrupted for a hundred years, from
the time of the memorable essay of Cæsalpinus. The grand discovery of
the circulation of the blood by Harvey about 1619, was followed in 1651
by Pecquet's discovery of the course of the chyle. There could now no
longer be any question whether science was progressive, or whether
observation could lead to new truths.

Among these cultivators of science, such sentiments as have been
already quoted became very familiar;--that knowledge is to be sought
from nature herself by observation and experiment;--that in such
matters tradition is of no force when opposed to experience, and that
mere reasonings without facts cannot lead to solid knowledge. But I
do not know that we find in these writers any more special rules of
induction and scientific research which have since been confirmed
and universally adopted. Perhaps too, as was natural in so great a
revolution, the writers of this time, especially the second-rate
ones, were somewhat too prone to disparage the labours and talents
of Aristotle and the ancients in general, and to overlook the ideal
element of our knowledge, in their zealous study of phenomena. They
urged, sometimes in an exaggerated manner, the superiority of modern
times in all that regards science, and the supreme and sole importance
of facts in scientific investigations. There prevailed among them also
a lofty and dignified tone of speaking of the condition and prospects
of science, such as we are accustomed to admire in the Verulamian
writings; for this, in a less degree, is epidemic among those who a
little after his time speak of the new philosophy.


5. _Otto Guericke, &c._--I need not illustrate these characteristics
at any great length. I may as an example notice Otto Guericke's
Preface to his _Experimenta Magdeburgica_ (1670). He quotes a passage
from Kircher's Treatise on the Magnetic Art, in which the author
says, "Hence it appears how all philosophy, except it be supported by
experiments, is empty, fallacious, and useless; what monstrosities
philosophers, in other respects of the highest and subtlest genius,
may produce in philosophy by neglecting experiment. Thus Experience
alone is the Dissolver of Doubts, the Reconciler of Difficulties, the
sole Mistress of Truth, who holds a torch before us in obscurity,
unties our knots, teaches us the true causes of things." Guericke
himself reiterates the same remark, adding that "philosophers,
insisting upon their own thoughts and arguments merely, cannot come
to any sound conclusion respecting the natural constitution of the
world." Nor were the Cartesians slow in taking up the same train of
reflection. Thus Gilbert Clark who, in 1660, published[212] a defence
of Descartes' doctrine of a _plenum_ in the universe, speaks in a
tone which reminds us of Bacon, and indeed was very probably caught
from him: "Natural philosophy formerly consisted entirely of loose
and most doubtful controversies, carried on in high-sounding words,
fit rather to delude than to instruct men. But at last (by the favour
of the Deity) there shone forth some more divine intellects, who
taking as their counsellors reason and experience together, exhibited
a new method of philosophizing. Hence has been conceived a strong hope
that philosophers may embrace, not a shadow or empty image of Truth,
but Truth herself: and that Physiology (Physics) scattering these
controversies to the winds, will contract an alliance with Mathematics.
Yet this is hardly the work of one age; still less of one man. Yet let
not the mind despond, or doubt not that, one party of investigators
after another following the same method of philosophizing, at last,
under good auguries, the mysteries of nature being daily unlocked as
far as human feebleness will allow, Truth may at last appear in full,
and these nuptial torches may be lighted."

As another instance of the same kind, I may quote the preface to the
First volume of the Transactions of the Academy of Sciences at Paris:
"It is only since the present century," says the writer, "that we can
reckon the revival of Mathematics and Physics. M. Descartes and other
great men have laboured at this work with so much success, that in this
department of literature, the whole face of things has been changed.
Men have quitted a sterile system of physics, which for several
generations had been always at the same point; the reign of words
and terms is passed; men will have things; they establish principles
which they understand, they follow those principles; and thus they
make progress. Authority has ceased to have more weight than Reason:
that which was received without contradiction because it had been
long received, is now examined, and often rejected: and philosophers
have made it their business to consult, respecting natural things,
Nature herself rather than the Ancients." These had now become the
commonplaces of those who spoke concerning the course and method of the
Sciences.


6. _Hooke._--In England, as might be expected, the influence of
Francis Bacon was more directly visible. We find many writers, about
this time, repeating the truths which Bacon had proclaimed, and in
almost every case showing the same imperfections in their views
which we have noticed in him. We may take as an example of this
Hooke's Essay, entitled "A General Scheme or Idea of the present
state of Natural Philosophy, and how its defects may be remedied by
a Methodical proceeding in the making Experiments and collecting
Observations; whereby to compile a Natural History as a solid basis
for the superstructure of true Philosophy." This Essay may be looked
upon as an attempt to adapt the _Novum Organon_ to the age which
succeeded its publication. We have in this imitation, as in the
original, an enumeration of various mistakes and impediments which had
in preceding times prevented the progress of knowledge; exhortations
to experiment and observation as the only solid basis of Science; very
ingenious suggestions of trains of inquiry, and modes of pursuing them;
and a promise of obtaining scientific truths when facts have been
duly accumulated. This last part of his scheme the author calls _a
Philosophical Algebra_; and he appears to have imagined that it might
answer the purpose of finding unknown causes from known facts, by means
of certain regular processes, in the same manner as Common Algebra
finds unknown from known quantities. But this part of the plan appears
to have remained unexecuted. The suggestion of such a method was a
result of the Baconian notion that invention in a discoverer might be
dispensed with. We find Hooke adopting the phrases in which this notion
is implied: thus he speaks of the understanding as "being very prone to
run into the affirmative way of judging, and wanting patience to follow
and prosecute the negative way of inquiry, by rejection of disagreeing
natures." And he follows Bacon also in the error of attempting at
once to obtain from the facts the discovery of a "nature," instead of
investigating first the measures and the laws of phenomena. I return to
more general notices of the course of men's thoughts on this subject.


7. _Royal Society._--Those who associated themselves together for the
prosecution of science quoted Bacon as their leader, and exulted in the
progress made by the philosophy which proceeded upon his principles.
Thus in Oldenburg's Dedication of the Transactions of the Royal Society
of London for 1670, to Robert Boyle, he says; "I am informed by such as
well remember the best and worst days of the famous Lord Bacon, that
though he wrote his _Advancement of Learning_ and his _Instauratio
Magna_ in the time of his greatest power, yet his greatest reputation
rebounded first from the most intelligent foreigners in many parts
of Christendom:" and after speaking of his practical talents and his
public employments, he adds, "much more justly still may we wonder how,
without any great skill in Chemistry, without much pretence to the
Mathematics or Mechanics, without optic aids or other engines of late
invention, he should so much transcend the philosophers then living,
in judicious and clear instructions, in so many useful observations
and discoveries, I think I may say beyond the records of many ages."
And in the end of the Preface to the same volume, he speaks with
great exultation of the advance of science all over Europe, referring
undoubtedly to facts then familiar. "And now let envy snarl, it
cannot stop the wheels of active philosophy, in no part of the known
world;--not in France, either in Paris or in Caen;--not in Italy,
either in Rome, Naples, Milan, Florence, Venice, Bononia or Padua;--in
none of the Universities either on this or on that side of the seas,
Madrid and Lisbon, all the best spirits in Spain and Portugal, and
the spacious and remote dominions to them belonging;--the Imperial
Court and the Princes of Germany; the Northern Kings and their best
luminaries; and even the frozen Muscovite and Russian have all taken
the operative ferment: and it works high and prevails every way, to the
encouragement of all sincere lovers of knowledge and virtue."

Again, in the Preface for 1672, he pursues the same thought into
detail: "We must grant that in the last age, when operative philosophy
began to recover ground, and to tread on the heels of triumphant
Philology; emergent adventures and great successes were encountered by
dangerous oppositions and strong obstructions. Galilæus and others in
Italy suffered extremities for their celestial discoveries; and here
in England Sir Walter Raleigh, when he was in his greatest lustrous,
was notoriously slandered to have erected a school of atheism, because
he gave countenance to chemistry, to practical arts, and to curious
mechanical operations, and designed to form the best of them into
a college. And Queen Elizabeth's Gilbert was a long time esteemed
extravagant for his magnetisms; and Harvey for his diligent researches
in pursuance of the circulation of the blood. But when our renowned
Lord Bacon had demonstrated the methods for a perfect restoration
of all parts of real knowledge; and the generous and philosophical
Peireskius had, soon after, agitated in all parts to redeem the most
instructive antiquities, and to excite experimental essays and fresh
discoveries; the success became on a sudden stupendous; and effective
philosophy began to sparkle, and even to flow into beams of shining
light all over the world."

The formation of the Royal Society of London and of the Academy
of Sciences of Paris, from which proceeded the declamations just
quoted, were among many indications, belonging to this period, of
the importance which states as well as individuals had by this time
begun to attach to the cultivation of science. The English Society was
established almost immediately when the restoration of the monarchy
appeared to give a promise of tranquillity to the nation (in 1660), and
the French Academy very soon afterwards (in 1666). These measures were
very soon followed by the establishment of the Observatories of Paris
and Greenwich (in 1667 and 1675); which may be considered to be a kind
of public recognition of the astronomy of observation, as an object
on which it was the advantage and the duty of nations to bestow their
wealth.


8. _Bacon's New Atalantis._--When philosophers had their attention
turned to the boundless prospect of increase to the knowledge and
powers and pleasures of man which the cultivation of experimental
philosophy seemed to promise, it was natural that they should think of
devising institutions and associations by which such benefits might be
secured. Bacon had drawn a picture of a society organized with a view
to such purpose, in his fiction of the "New Atalantis." The imaginary
teacher who explains this institution to the inquiring traveller,
describes it by the name of _Solomon's House_; and says[213], "The end
of our foundation is the knowledge of causes and secret motions of
things; and the enlarging the bounds of the human empire to effecting
of things possible." And, as parts of this House, he describes caves
and wells, chambers and towers, baths and gardens, parks and pools,
dispensatories and furnaces, and many other contrivances, provided
for the purpose of making experiments of many kinds. He describes
also the various employments of the Fellows of this College, who take
a share in its researches. There are _merchants of light_, who bring
books and inventions from foreign countries; _depredators_, who gather
the experiments which exist in books; _mystery-men_, who collect the
experiments of the mechanical arts; _pioneers_ or _miners_, who invent
new experiments; and _compilers_, "who draw the experiments of the
former into titles and tables, to give the better light for the drawing
of observations and axioms out of them." There are also _dowry-men_ or
_benefactors_, that cast about how to draw out of the experiments of
their fellows things of use and practice for man's life; _lamps_, that
direct new experiments of a more penetrating light than the former;
_inoculators_, that execute the experiments so directed. Finally, there
are the _interpreters of nature_, that raise the former discoveries by
experiments into greater observations (that is, more general truths),
axioms and aphorisms. Upon this scheme we may remark, that fictitious
as it undisguisedly is, it still serves to exhibit very clearly some of
the main features of the author's philosophy:--namely, his steady view
of the necessity of ascending from facts to the most general truths
by several stages;--an exaggerated opinion of the aid that could be
derived in such a task from technical separation of the phenomena and a
distribution of them into tables;--a belief, probably incorrect, that
the offices of experimenter and interpreter may be entirely separated,
and pursued by different persons with a certainty of obtaining
success!--and a strong determination to make knowledge constantly
subservient to the uses of life.


9. _Cowley._--Another project of the same kind, less ambitious but
apparently more directed to practice, was published a little later
(1657) by another eminent man of letters in this country. I speak of
Cowley's "Proposition for the Advancement of Experimental Philosophy."
He suggests that a College should be established at a short distance
from London, endowed with a revenue of four thousand pounds, and
consisting of twenty professors with other members. The objects of the
labours of these professors he describes to be, first, to examine all
knowledge of nature delivered to us from former ages and to pronounce
it sound or worthless; second, to recover the lost inventions of the
ancients; third, to improve all arts that we now have; lastly, to
discover others that we yet have not. In this proposal we cannot help
marking the visible declension from Bacon's more philosophical view.
For we have here only a very vague indication of improving old arts
and discovering new, instead of the two clear Verulamian antitheses,
Experiments and Axioms deduced from them, on the one hand, and on the
other an ascent to general Laws, and a derivation, from these, of Arts
for daily use. Moreover the prominent place which Cowley has assigned
to the verifying the knowledge of former ages and recovering "the lost
inventions and drowned lands of the ancients," implies a disposition to
think too highly of traditionary knowledge; a weakness which Bacon's
scheme shows _him_ to have fully overcome. And thus it has been up to
the present day, that with all Bacon's mistakes, in the philosophy of
scientific method few have come up to him, and perhaps none have gone
beyond him.

Cowley exerted himself to do justice to the new philosophy in verse as
well as prose, and his Poem to the Royal Society expresses in a very
noble manner those views of the history and prospects of philosophy
which prevailed among the men by whom the Royal Society was founded.
The fertility and ingenuity of comparison which characterize Cowley's
poetry are well known; and these qualities are in this instance largely
employed for the embellishment of his subject. Many of the comparisons
which he exhibits are apt and striking. Philosophy is a ward whose
estate (human knowledge) is, in his nonage, kept from him by his
guardians and tutors; (a case which the ancient rhetoricians were fond
of taking as a subject of declamation;) and these wrong-doers retain
him in unjust tutelage and constraint for their own purposes; until

      Bacon at last, a mighty man, arose,
      (Whom a wise King, and Nature, chose
      Lord Chancellor of both their laws,)
    And boldly undertook the injured pupil's cause.

Again, Bacon is one who breaks a scarecrow Priapus which stands in the
garden of knowledge. Again, Bacon is one who, instead of a picture of
painted grapes, gives us real grapes from which we press "the thirsty
soul's refreshing wine." Again, Bacon is like Moses, who led the
Hebrews forth from the barren wilderness, and ascended Pisgah;--

        Did on the very border stand
        Of the blest promised land,
    And from the mountain's top of his exalted wit
    Saw it himself and showed us it.

The poet however adds, that Bacon discovered, but did not conquer
this new world; and that the men whom he addresses must subdue these
regions. These "champions" are then ingeniously compared to Gideon's
band:

    Their old and empty pitchers first they brake,
    And with their hands then lifted up the light.

There were still at this time some who sneered at or condemned the new
philosophy; but the tide of popular opinion was soon strongly in its
favour. I have elsewhere[214] noticed a pasquinade of the poet Boileau
in 1682, directed against the Aristotelians. At this time, and indeed
for long afterwards, the philosophers of France were Cartesians. The
English men of science, although partially and for a time they accepted
some of Descartes' opinions, for the most part carried on the reform
independently, and in pursuance of their own views. And they very soon
found a much greater leader than Descartes to place at their head, and
to take as their authority, so far as they acknowledged authority,
in their speculations. I speak of Newton, whose influence upon the
philosophy of science I must now consider.


10. _Barrow._--I will, however, first mention one other writer who may,
in more than one way, be regarded as the predecessor of Newton. I speak
of Isaac Barrow, whom Newton succeeded as Professor of Mathematics in
the University of Cambridge, and who in his mathematical speculations
approached very near to Newton's method of Fluxions. He afterwards
(in 1673) became Master of Trinity College, which office he held
till his death in 1677. But the passages which I shall quote belong
to an earlier period, (when Barrow was about 22 years old,) and may
be regarded as expressions of the opinions which were then current
among active-minded and studious young men. They manifest a complete
familiarity with the writings both of Bacon and of Descartes, and a
very just appreciation of both. The discourse of which I speak is
an academical exercise delivered in 1652, on the thesis _Cartesiana
hypothesis haud satisfacit præcipuis naturæ phænomenis_. By the
"Cartesian hypothesis," he does not mean the hypothesis that the
planets are moved by vortices of etherial matter: I believe that this
Cartesian tenet never had any disciples in England; it certainly
never took any hold of Cambridge. By the Cartesian hypothesis, Barrow
means the doctrine that all the phenomena of nature can be accounted
for by matter and motion; and allowing that the motions of the planets
are to be so accounted for, (which is Newtonian as well as Cartesian
doctrine,) he denies that the Cartesian hypothesis accounts for "the
generations, properties, and specific operations of animals, plants,
minerals, stones, and other natural bodies," in doing which he shows
a sound philosophical judgment. But among the parts of this discourse
most bearing on our present purpose are those where he mentions Bacon.
"Against Cartesius," he says, "I pit the chymists and others, but
especially as the foremost champion of this battle, our Verulam, a man
of great name and of great judgment, who condemned this philosophy
before it was born." "He," adds Barrow, "several times in his
_Organon_, warned men against all hypotheses of this kind, and noticed
beforehand that there was not much to be expected from those principles
which are brought into being by violent efforts of argumentation from
the brains of particular men: for that, as upon the phenomena of the
stars, various constructions of the heavens may be devised, so also
upon the phenomena of the Universe, still more dogmas may be founded
and constructed; and yet all such are mere inventions: and as many
philosophies of this kind as are or shall be extant, so many fictitious
and theatrical worlds are made." The reference is doubtless to Aphorism
LXII. of the First Book of the _Novum Organon_, in which Bacon is
speaking of his "Idols of the Theatre." After making the remark which
Barrow has adopted, Bacon adds, "Such theatrical fables have also
this in common with those of dramatic poets, that the dramatic story
is more regular and elegant than true histories are, and is made so
as to be agreeable." Barrow, having this in his mind, goes on to say:
"And though Cartesius has dressed up the stage of his theatre more
prettily than any other person, and made his drama more like history,
still he is not exempt from the like censure." And he then refers to
Cartesius's own declaration, that he did not learn his system from
things themselves, but tried to impose his own laws upon things; thus
inverting the order of true philosophy.

Other parts of Bacon's work to which Barrow refers are those where
he speaks of the Form, or Formal Cause of a body, and says that in
comparison with that, the Efficient Cause and the Material Cause are
things unimportant and superficial, and contribute little to true and
active science[215]. And again, his classification of the various
kinds of motions[216],--the motus libertatis, motus nexus, motus
continuitatis, motus ad lucrum, fugæ, unionis, congregationis; and the
explanation of electrical attraction (about which Gilbert and others
had written) as _motus ad lucrum_.

These passages show that Barrow had read the _Novum Organon_ in a
careful and intelligent manner, and presumed his Cambridge hearers to
be acquainted with the work. Nor is his judgment of Descartes less wise
and philosophical. He rejects, as we have seen, his system as a true
scheme of the universe, and condemns altogether his _à priori_ mode
of philosophizing; but this does not prevent his accepting Descartes'
real discoveries, and admiring the boldness and vigour of his attempts
to reform philosophy. There is, in Barrow's works, academic verse, as
well as prose, on the subject of the Cartesian hypothesis. In this,
Descartes himself is highly praised, though his doctrines are very
partially accepted. The writer says: "Pardon us, great Cartesius, if
the Muse resists you. Pardon! We follow you, Inquiring Spirit that you
are, while we reject your system. As you have taught us free thought,
and broken down the rule of tyranny, we undauntedly speculate, even in
opposition to you."

Descartes is even yet spoken of, especially by French writers, as the
person who first asserted and established the freedom of inquiry which
is the boast of modern philosophy; but this is said with reference to
metaphysics, not to physics. In physical philosophy, though he caught
hold of some of the discoveries which were then coming into view, the
method in which he reasoned or professed to reason was altogether
vicious; and was, as I have already said, an attempt to undo what
the reformers, both theoretical and practical, had been doing:--to
discredit the philosophy of experience, and to restore the reign of _à
priori_ systems.

It was, however, now, too late to make any such attempt; and nothing
came of it to interrupt the progress of a better philosophy of
discovery.


FOOTNOTES:

[Footnote 200: _Anatomical Exercitations concerning the Generation of
Living Creatures_, 1653. Preface.]

[Footnote 201: He used similar expressions in conversation. George Ent,
who edited his _Generation of Animals_, visited him, "at that time
residing not far from the city; and found him very intent upon the
perscrutation of nature's works, and with a countenance as cheerful,
as mind unperturbed; Democritus-like, chiefly searching into the cause
of natural things." In the course of conversation the writer said, "It
hath always been your choice about the secrets of Nature, to consult
Nature herself." "'Tis true," replied he; "and I have constantly been
of opinion that from thence we might acquire not only the knowledge
of those less considerable secrets of Nature, but even a certain
admiration of that Supreme Essence, the Creator. And though I have
ever been ready to acknowledge, that many things have been discovered
by learned men of former times; yet do I still believe that the number
of those which remain yet concealed in the darkness of impervestigable
Nature is much greater. Nay, I cannot forbear to wonder, and sometimes
smile at those, who persuade themselves, that all things were so
consummately and absolutely delivered by Aristotle, Galen, or some
other great name, as that nothing was left to the superaddition of any
that succeeded."]

[Footnote 202: Lib. i. c. 2, 3.]

[Footnote 203: _Anal. Post._ ii.]

[Footnote 204: Pars iii. p. 45.]

[Footnote 205: See _Hist. Ind. Sc._ b. vi. c. ii.]

[Footnote 206: Cap. i. ii.]

[Footnote 207: _Hist. Ind. Sc._ b. ix. c. ii.]

[Footnote 208: _Meteorum_, c. viii. p. 187.]

[Footnote 209: Mackintosh, _Dissertation on Ethical Science_.]

[Footnote 210: _Hist. Ind. Sc._ b. vii. c. i.]

[Footnote 211: Castelli, Torricelli, Viviani, Baliani, Gassendi,
Mersenne, Borelli, Cavalleri.]

[Footnote 212: _De Plenitudine Mundi, in qua defenditur Cartesiana
Philosophia contra sententias Francisci Baconi, Th. Hobbii et Sethi
Wardi._]

[Footnote 213: Bacon's _Works_, vol. ii. 111.]

[Footnote 214: _Hist. Ind. Sc._ b. vii. c. i.]

[Footnote 215: _Nov. Org._ lib. ii. Aph. 2.]

[Footnote 216: _Ib._ lib. ii. Aph. 45.]




CHAPTER XVIII.

NEWTON.


1. Bold and extensive as had been the anticipations of those whose
minds were excited by the promise of the new philosophy, the
discoveries of Newton respecting the mechanics of the universe,
brought into view truths more general and profound than those earlier
philosophers had hoped or imagined. With these vast accessions to human
knowledge, men's thoughts were again set in action; and philosophers
made earnest and various attempts to draw, from these extraordinary
advances in science, the true moral with regard to the conduct and
limits of the human understanding. They not only endeavoured to verify
and illustrate, by these new portions of science, what had recently
been taught concerning the methods of obtaining sound knowledge;
but they were also led to speculate concerning many new and more
interesting questions relating to this subject. They saw, for the first
time, or at least far more clearly than before, the distinction between
the inquiry into the _laws_, and into the _causes_ of phenomena. They
were tempted to ask, how far the discovery of causes could be carried;
and whether it would soon reach, or clearly point to, the ultimate
cause. They were driven to consider whether the properties which they
discovered were essential properties of all matter, necessarily and
primarily involved in its essence, though revealed to us at a late
period by their derivative effects. These questions even now agitate
the thoughts of speculative men. Some of them have already, in this
work, been discussed, or arranged in the places which our view of the
philosophy of these subjects assigns to them. But we must here notice
them as they occurred to Newton himself and his immediate followers.


2. The general Baconian notion of the method of philosophizing,--that
it consists in ascending from phenomena, through various stages of
generalization, to truths of the highest order,--received, in Newton's
discovery of the universal mutual gravitation of every particle of
matter, that pointed actual exemplification, for want of which it had
hitherto been almost overlooked, or at least very vaguely understood.
That great truth, and the steps by which it was established, afford,
even now, by far the best example of the successive ascent, from one
scientific truth to another,--of the repeated transition from less to
more general propositions,--which we can yet produce; as may be seen
in the Table which exhibits the relation of these steps in Book II. of
the _Novum Organon Renovatum_. Newton himself did not fail to recognize
this feature in the truths which he exhibited. Thus he says[217], "By
the way of Analysis we proceed from compounds to ingredients, as from
motions to the forces producing them; and in general, from effects
to their causes, and from particular causes to more general ones,
till the argument ends in the most general." And in like manner in
another Query[218]: "The main business of natural philosophy is to
argue from phenomena without feigning hypotheses, and to deduce causes
from effects, till we come to the First Cause, which is certainly not
mechanical."


3. Newton appears to have had a horror of the term _hypothesis_,
which probably arose from his acquaintance with the rash and illicit
general assumptions of Descartes. Thus in the passage just quoted,
after declaring that gravity must have some other cause than matter,
he says, "Later philosophers banish the consideration of such a cause
out of Natural Philosophy, feigning hypotheses for explaining all
things mechanically, and referring other causes to metaphysics." In the
celebrated Scholium at the end of the _Principia_ he says, "Whatever
is not deduced from the phenomena, is to be termed _hypothesis_;
and hypotheses, whether metaphysical or physical, or occult causes,
or mechanical, have no place in experimental philosophy. In this
philosophy, propositions are deduced from phenomena, and rendered
general by induction." And in another place, he arrests the course
of his own suggestions, saying, "Verum hypotheses non fingo." I have
already attempted to show that this is, in reality, a superstitious and
self-destructive spirit of speculation. Some hypotheses are necessary,
in order to connect the facts which are observed; some new principle
of unity must be applied to the phenomena, before induction can be
attempted. What is requisite is, that the hypothesis should be close
to the facts, and not connected with them by the intermediation of
other arbitrary and untried facts; and that the philosopher should be
ready to resign it as soon as the facts refuse to confirm it. We have
seen in the _History_[219], that it was by such a use of hypotheses,
that both Newton himself, and Kepler, on whose discoveries those of
Newton were based, made their discoveries. The suppositions of a force
tending to the sun and varying inversely as the square of the distance;
of a mutual force between all the bodies of the solar system; of the
force of each body arising from the attraction of all its parts; not to
mention others, also propounded by Newton,--were all hypotheses before
they were verified as theories. It is related that when Newton was
asked how it was that he saw into the laws of nature so much further
than other men, he replied, that if it were so, it resulted from his
keeping his thoughts steadily occupied upon the subject which was to be
thus penetrated. But what is this occupation of the thoughts, if it be
not the process of keeping the phenomena clearly in view, and trying,
one after another, all the plausible hypotheses which seem likely to
connect them, till at last the true law is discovered? Hypotheses so
used are a necessary element of discovery.


4. With regard to the details of the process of discovery, Newton
has given us some of his views, which are well worthy of notice, on
account of their coming from him; and which are real additions to the
philosophy of this subject. He speaks repeatedly of the _analysis_
and _synthesis_ of observed facts; and thus marks certain steps in
scientific research, very important, and not, I think, clearly pointed
out by his predecessors. Thus he says[220], "As in Mathematics, so
in Natural Philosophy, the investigation of difficult things by the
method of analysis ought ever to precede the method of composition.
This analysis consists in making experiments and observations, and
in drawing general conclusions from them by induction, and admitting
of no objections against the conclusions, but such as are taken from
experiments or other certain truths. And although the arguing from
experiments and observations by induction be no demonstration of
general conclusions; yet it is the best way of arguing which the nature
of things admits of, and may be looked upon as so much the stronger,
by how much the induction is more general." And he then observes, as
we have quoted above, that by this way of analysis we proceed from
compounds to ingredients, from motions to forces, from effects to
causes, and from less to more general causes. The _analysis_ here
spoken of includes the steps which in _our_ Novum Organon we call the
_decomposition_ of facts, the exact _observation_ and _measurement_
of the phenomena, and the _colligation_ of facts; the necessary
intermediate step, the _selection_ and _explication_ of the appropriate
conception, being passed over by Newton, in the fear of seeming to
encourage the fabrication of hypotheses. The _synthesis_ of which
Newton here speaks consists of those steps of _deductive reasoning_,
proceeding from the conception once assumed, which are requisite for
the comparison of its consequences with the observed facts. This, his
statement of the process of research, is, as far as it goes, perfectly
exact.


5. In speaking of Newton's precepts on the subject, we are naturally
led to the celebrated "Rules of Philosophizing," inserted in the second
edition of the _Principia_. These rules have generally been quoted and
commented on with an almost unquestioning reverence. Such Rules, coming
from such an authority, cannot fail to be highly interesting to us; but
at the same time, we cannot here evade the necessity of scrutinizing
their truth and value, according to the principles which our survey of
this subject has brought into view. The Rules stand at the beginning of
that part of the _Principia_ (the Third Book) in which he infers the
mutual gravitation of the sun, moon, planets, and all parts of each.
They are as follows:

"Rule I. We are not to admit other causes of natural things than such
as both are true, and suffice for explaining their phenomena.

"Rule II. Natural effects of the same kind are to be referred to the
same causes, as far as can be done.

"Rule III. The qualities of bodies which cannot be increased or
diminished in intensity, and which belong to all bodies in which we
can institute experiments, are to be held for qualities of all bodies
whatever.

"Rule IV. In experimental philosophy, propositions collected from
phenomena by induction, are to be held as true either accurately
or approximately, notwithstanding contrary hypotheses; till other
phenomena occur by which they may be rendered either more accurate or
liable to exception."

In considering these Rules, we cannot help remarking, in the first
place, that they are constructed with an intentional adaptation to
the case with which Newton has to deal,--the induction of Universal
Gravitation; and are intended to protect the reasonings before which
they stand. Thus the first Rule is designed to strengthen the inference
of gravitation from the celestial phenomena, by describing it as a
_vera causa_, a true cause; the second Rule countenances the doctrine
that the planetary motions are governed by mechanical forces, as
terrestrial motions are; the third rule appears intended to justify the
assertion of gravitation, as a _universal_ quality of bodies; and the
fourth contains, along with a general declaration of the authority of
induction, the author's usual protest against hypotheses, levelled at
the Cartesian hypotheses especially.


6. _Of the First Rule._--We, however, must consider these Rules in
their general application, in which point of view they have often been
referred to, and have had very great authority allowed them. One of the
points which has been most discussed, is that maxim which requires that
the causes of phenomena which we assign should be true causes, _veræ
causæ_. Of course this does not mean that they should be _the_ true
or right cause; for although it is the philosopher's aim to discover
such causes, he would be little aided in his search of truth, by being
told that it is truth which he is to seek. The rule has generally
been understood to prescribe that in attempting to account for any
class of phenomena, we must assume such causes only, as _from other
considerations_, we know to exist. Thus gravity, which was employed in
explaining the motions of the moon and planets, was already known to
exist and operate at the earth's surface.

Now the Rule thus interpreted is, I conceive, an injurious limitation
of the field of induction. For it forbids us to look for a cause,
except among the causes with which we are already familiar. But if we
follow this rule, how shall we ever become acquainted with any new
cause? Or how do we know that the phenomena which we contemplate do
really arise from some cause which we already truly know? If they do
not, must we still insist upon making them depend upon some of our
known causes; or must we abandon the study of them altogether? Must we,
for example, resolve to refer the action of radiant heat to the air,
rather than to any peculiar fluid or ether, because the former is known
to exist, the latter is merely assumed for the purpose of explanation?
But why should we do this? Why should we not endeavour to learn the
cause from the effects, even if it be not already known to us? We
can infer causes, which are new when we first become acquainted with
them. Chemical Forces, Optical Forces, Vital Forces, are known to us
only by chemical and optical and vital phenomena; must we, therefore,
reject their existence or abandon their study? They do not conform to
the double condition, that they shall be sufficient and _also_ real:
they are true, only so far as they explain the facts, but are they,
therefore, unintelligible or useless? Are they not highly important
and instructive subjects of speculation? And if the gravitation which
rules the motions of the planets had not existed at the earth's
surface;--if it had been there masked and concealed by the superior
effect of magnetism, or some other extraneous force,--might not Newton
still have inferred, from Kepler's laws, the tendency of the planets to
the sun; and from their perturbations, their tendency to each other?
His discoveries would still have been immense, if the cause which he
assigned had not been a _vera causa_ in the sense now contemplated.


7. But what do we mean by calling gravity a "true cause"? How do
we learn its reality? Of course, by its effects, with which we are
familiar;--by the weight and fall of bodies about us. These strike even
the most careless observer. No one can fail to see that all bodies
which we come in contact with are heavy;--that gravity acts in our
neighbourhood here upon earth. Hence, it may be said, this cause is at
any rate a true cause, whether it explains the celestial phenomena or
not.

But if this be what is meant by a _vera causa_, it appears strange to
require that in all cases we should find such a one to account for
all classes of phenomena. Is it reasonable or prudent to demand that
we shall reduce every set of phenomena, however minute, or abstruse,
or complicated, to causes so obviously existing as to strike the most
incurious, and to be familiar among men? How can we expect to find
_such veræ causæ_ for the delicate and recondite phenomena which
an exact and skilful observer detects in chemical, or optical, or
electrical experiments? The facts themselves are too fine for vulgar
apprehension; their relations, their symmetries, their measures require
a previous discipline to understand them. How then can their causes be
found among those agencies with which the common unscientific herd of
mankind are familiar? What likelihood is there that causes held for
real by such persons, shall explain facts which such persons cannot see
or cannot understand?

Again: if we give authority to such a rule, and require that the causes
by which science explains the facts which she notes and measures and
analyses, shall be causes which men, without any special study, have
already come to believe in, from the effects which they casually
see around them, what is this, except to make our first rude and
unscientific persuasions the criterion and test of our most laborious
and thoughtful inferences? What is it, but to give to ignorance and
thoughtlessness the right of pronouncing upon the convictions of
intense study and long-disciplined thought? "Electrical atmospheres"
surrounding electrized bodies, were at one time held to be a "true
cause" of the effects which such bodies produce. These atmospheres, it
was said, are obvious to the senses; we feel them like a spider's web
on the hands and face. Æpinus had to answer such persons, by proving
that there are no atmospheres, no effluvia, but only repulsion. He
thus, for a _true cause_ in the vulgar sense of the term, substituted
an _hypothesis_; yet who doubts that what he did was an advance in the
science of electricity?


8. Perhaps some persons may be disposed to say, that Newton's Rule
does not enjoin us to take those causes only which we clearly know, or
suppose we know, to be really existing and operating, but only causes
_of such kinds_ as we have already satisfied ourselves do exist in
nature. It may be urged that we are entitled to infer that the planets
are governed in their motions by an attractive force, because we find,
in the bodies immediately subject to observation and experiment,
that such motions are produced by attractive forces, for example, by
that of the earth. It may be said that we might on similar grounds
infer forces which unite particles of chemical compounds, or deflect
particles of light, because we see adhesion and deflection produced by
forces.

But it is easy to show that the Rule, thus laxly understood, loses all
significance. It prohibits no hypothesis; for all hypotheses suppose
causes _such as_, in some case or other, we have seen in action. No
one would think of explaining phenomena by referring them to forces
and agencies altogether different from any which are known; for on
this supposition, how could he pretend to reason about the effects
of the assumed causes, or undertake to prove that they would explain
the facts? Some close similarity with some known kind of cause is
requisite, in order that the hypothesis may have the appearance of
an explanation. No forces, or virtues, or sympathies, or fluids, or
ethers, would be excluded by _this_ interpretation of _veræ causæ_.
Least of all, would such an interpretation reject the Cartesian
hypothesis of vortices; which undoubtedly, as I conceive, Newton
intended to condemn by his Rule. For that _such_ a case as a whirling
fluid, carrying bodies round a centre in orbits, does occur, is too
obvious to require proof. Every eddying stream, or blast that twirls
the dust in the road, exhibits examples of such action, and would
justify the assumption of the vortices which carry the planets in their
courses; as indeed, without doubt, such facts suggested the Cartesian
explanation of the solar system. The vortices, in this mode of
considering the subject, are at the least as _real_ a cause of motion
as gravity itself.


9. Thus the Rule which enjoins "true causes," is nugatory, if we take
_veræ causæ_ in the extended sense of any causes of a real _kind_,
and unphilosophical, if we understand the term of _those very_ causes
which we familiarly suppose to exist. But it may be said that we are to
designate as "true causes," not those which are collected in a loose,
confused and precarious manner, by undisciplined minds, from obvious
phenomena, but those which are justly and rigorously inferred. Such
a cause, it may be added, gravity is; for the facts of the downward
pressures and downward motions of bodies at the earth's surface lead
us, by the plainest and strictest induction, to the assertion of such
a force. Now to this interpretation of the Rule there is no objection;
but then, it must be observed, that on this view, terrestrial gravity
is inferred by the same process as celestial gravitation; and the
cause is no more entitled to be called "true," because it is obtained
from the former, than because it is obtained from the latter class of
facts. We thus obtain an intelligible and tenable explanation of a
_vera causa_; but then, by this explanation, its _verity_ ceases to be
distinguishable from its other condition, that it "suffices for the
explanation of the phenomena." The assumption of universal gravitation
accounts for the fall of a stone; it also accounts for the revolutions
of the Moon or of Saturn; but since both these explanations are of the
same kind, we cannot with justice make the one a criterion or condition
of the admissibility of the other.


10. But still, the Rule, so understood, is so far from being unmeaning
or frivolous, that it expresses one of the most important tests which
can be given of a sound physical theory. It is true, the explanation of
one set of facts may be of the same nature as the explanation of the
other class: but then, that the cause explains _both_ classes, gives it
a very different claim upon our attention and assent from that which
it would have if it explained one class only. The very circumstance
that the two explanations coincide, is a most weighty presumption in
their favour. It is the testimony of two witnesses in behalf of the
hypothesis; and in proportion as these two witnesses are separate
and independent, the conviction produced by their agreement is more
and more complete. When the explanation of two kinds of phenomena,
distinct, and not apparently connected, leads us to the same cause,
such a coincidence does give a reality to the cause, which it has
not while it merely accounts for those appearances which suggested
the supposition. This coincidence of propositions inferred from
separate classes of facts, is exactly what we noticed in the _Novum
Organon Renovatum_ (b. ii. c. 5, sect. 3), as one of the most decisive
characteristics of a true theory, under the name of _Consilience of
Inductions_.

That Newton's First Rule of Philosophizing, so understood, authorizes
the inferences which he himself made, is really the ground on which
they are so firmly believed by philosophers. Thus when the doctrine
of a gravity varying inversely as the square of the distance from
the body, accounted at the same time for the relations of times and
distances in the planetary orbits and for the amount of the moon's
deflection from the tangent of her orbit, such a doctrine became most
convincing: or again, when the doctrine of the universal gravitation of
all parts of matter, which explained so admirably the inequalities of
the moon's motions, also gave a satisfactory account of a phenomenon
utterly different, the precession of the equinoxes. And of the same
kind is the evidence in favour of the undulatory theory of light, when
the assumption of the length of an undulation, to which we are led by
the colours of thin plates, is found to be identical with that length
which explains the phenomena of diffraction; or when the hypothesis of
transverse vibrations, suggested by the facts of polarization, explains
also the laws of double refraction. When such a convergence of two
trains of induction points to the same spot, we can no longer suspect
that we are wrong. Such an accumulation of proof really persuades us
that we have to do with a _vera causa_. And if this kind of proof be
multiplied;--if we again find other facts of a sort uncontemplated in
framing our hypothesis, but yet clearly accounted for when we have
adopted the supposition;--we are still further confirmed in our belief;
and by such accumulation of proof we may be so far satisfied, as to
believe without conceiving it possible to doubt. In this case, when the
validity of the opinion adopted by us has been repeatedly confirmed by
its sufficiency in unforeseen cases, so that all doubt is removed and
forgotten, the theoretical cause takes its place among the realities
of the world, and becomes _a true cause_.


11. Newton's Rule then, to avoid mistakes, might be thus expressed:
That "we may, provisorily, assume such hypothetical cause as will
account for any given class of natural phenomena; but that when two
different classes of facts lead us to the same hypothesis, we may hold
it to be a _true cause_." And this Rule will rarely or never mislead
us. There are no instances, in which a doctrine recommended in this
manner has afterwards been discovered to be false. There have been
hypotheses which have explained many phenomena, and kept their ground
long, and have afterwards been rejected. But these have been hypotheses
which explained only one class of phenomena; and their fall took place
when another kind of facts was examined and brought into conflict with
the former. Thus the system of eccentrics and epicycles accounted
for all the observed _motions_ of the planets, and was the means of
expressing and transmitting all astronomical knowledge for two thousand
years. But then, how was it overthrown? By considering the _distances_
as well as motions of the heavenly bodies. Here was a second class of
facts; and when the system was adjusted so as to agree with the one
class, it was at variance with the other. These cycles and epicycles
could not be true, because they could not be made a just representation
of the facts. But if the measures of distance as well as of position
had conspired in pointing out the cycles and epicycles, as the paths of
the planets, the paths so determined could not have been otherwise than
their real paths; and the epicyclical theory would have been, at least
geometrically, true.


12. _Of the Second Rule._--Newton's Second Rule directs that "natural
events of the _same kind_ are to be referred to the _same causes_, so
far as can be done." Such a precept at first appears to help us but
little; for all systems, however little solid, profess to conform to
such a rule. When any theorist undertakes to explain a class of facts,
he assigns causes which, according to him, will by their natural
action, as seen in other cases, produce the effects in question. The
events which he accounts for by his hypothetical cause, are, he holds,
of the same kind as those which such a cause is known to produce.
Kepler, in ascribing the planetary motions to magnetism, Descartes, in
explaining them by means of vortices, held that they were referring
celestial motions to the causes which give rise to terrestrial motions
of the same kind. The question is, _Are_ the effects of the same kind?
This once settled, there will be no question about the propriety of
assigning them to the same cause. But the difficulty is, to determine
_when_ events are of the same kind. Are the motions of the planets of
the same kind with the motion of a body moving freely in a curvilinear
path, or do they not rather resemble the motion of a floating body
swept round by a whirling current? The Newtonian and the Cartesian
answered this question differently. How then can we apply this Rule
with any advantage?


13. To this we reply, that there is no way of escaping this uncertainty
and ambiguity, but by obtaining a clear possession of the ideas which
our hypothesis involves, and by reasoning rigorously from them. Newton
asserts that the planets move in free paths, acted on by certain
forces. The most exact calculation gives the closest agreement of
the results of this hypothesis with the facts. Descartes asserts
that the planets are carried round by a fluid. The more rigorously
the conceptions of force and the laws of motion are applied to this
hypothesis, the more signal is its failure in reconciling the facts
to one another. Without such calculation, we can come to no decision
between the two hypotheses. If the Newtonian hold that the motions
of the planets are _evidently_ of the _same kind_ as those of a body
describing a curve in free space, and therefore, like that, to be
explained by a force acting upon the body; the Cartesian denies that
the planets do move in free space. They are, he maintains, immersed
in a plenum. It is only when it appears that comets pass through this
plenum in all directions with no impediment, and that no possible form
and motion of its whirlpools can explain the forces and motions which
are observed in the solar system, that he is compelled to allow the
Newtonian's classification of events of the _same kind_.

Thus it does not appear that this Rule of Newton can be interpreted in
any distinct and positive manner, otherwise than as enjoining that, in
the task of induction, we employ clear ideas, rigorous reasoning, and
close and fair comparison of the results of the hypothesis with the
facts. These are, no doubt, important and fundamental conditions of a
just induction; but in this injunction we find no peculiar or technical
criterion by which we may satisfy ourselves that we are right, or
detect our errors. Still, of such general prudential rules, none can be
more wise than one which thus, in the task of connecting facts by means
of ideas, recommends that the ideas be clear, the facts, correct, and
the chain of reasoning which connects them, without a flaw.


14. _Of the Third Rule._--The Third Rule, that "qualities which are
observed without exception be held to be universal," as I have already
said, seems to be intended to authorize the assertion of gravitation
as a universal attribute of matter. We formerly stated, in treating of
Mechanical Ideas[221], that this application of such a Rule appears
to be a mode of reasoning far from conclusive. The assertion of the
universality of any property of bodies must be grounded upon the
reason of the case, and not upon any arbitrary maxim. Is it intended
by this Rule to prohibit any further examination how far gravity is
an original property of matter, and how far it may be resolved into
the result of other agencies? We know perfectly well that this was not
Newton's intention; since the cause of gravity was a point which he
proposed to himself as a subject of inquiry. It would certainly be very
unphilosophical to pretend, by this Rule of Philosophizing, to prejudge
the question of such hypotheses as that of Mosotti, That gravity is
the excess of the electrical attraction over electrical repulsion, and
yet to adopt this hypothesis, would be to suppose electrical forces
more truly universal than gravity; for according to the hypothesis,
gravity, being the inequality of the attraction and repulsion, is only
an accidental and partial relation of these forces. Nor would it be
allowable to urge this Rule as a reason of assuming that double stars
are attracted to each other by a force varying according to the inverse
square of the distance; without examining, as Herschel and others have
done, the orbits which they really describe. But if the Rule is not
available in such cases, what is its real value and authority? and in
what cases are they exemplified?


15. In a former work[222], it was shown that the fundamental laws of
motion, and the properties of matter which these involve, are, after a
full consideration of the subject, unavoidably assumed as universally
true. It was further shown, that although our knowledge of these laws
and properties be gathered from experience, we are strongly impelled,
(some philosophers think, authorized,) to look upon these as not only
universally, but necessarily true. It was also stated, that the law
of gravitation, though its universality may be deemed probable, does
not apparently involve the same necessity as the fundamental laws of
motion. But it was pointed out that these are some of the most abstruse
and difficult questions of the whole of philosophy; involving the
profound, perhaps insoluble, problem of the identity or diversity of
Ideas and Things. It cannot, therefore, be deemed philosophical to
cut these Gordian knots by peremptory maxims, which encourage us to
decide without rendering a reason. Moreover, it appears clear that
the reason which is rendered for this Rule by the Newtonians is quite
untenable; namely, that we know extension, hardness, and inertia, to
be universal qualities of bodies by experience alone, and that we have
the same evidence of experience for the universality of gravitation.
We have already observed that we cannot, with any propriety, say that
we _find_ by experience all bodies are extended. This could not be a
just assertion, unless we conceive the possibility of our finding the
contrary. But who can conceive our finding by experience some bodies
which are not extended? It appears, then, that the reason given for
the Third Rule of Newton involves a mistake respecting the nature and
authority of experience. And the Rule itself cannot be applied without
attempting to decide, by the casual limits of observation, questions
which necessarily depend upon the relations of ideas.


16. _Of the Fourth Rule._--Newton's Fourth Rule is, that "Propositions
collected from phenomena by induction, shall be held to be true,
notwithstanding contrary hypotheses; but shall be liable to be rendered
more accurate, or to have their exceptions pointed out, by additional
study of phenomena." This Rule contains little more than a general
assertion of the authority of induction, accompanied by Newton's usual
protest against hypotheses.

The really valuable part of the Fourth Rule is that which implies
that a constant verification, and, if necessary, rectification,
of truths discovered by induction, should go on in the scientific
world. Even when the law is, or appears to be, most certainly exact
and universal, it should be constantly exhibited to us afresh in the
form of experience and observation. This is necessary, in order to
discover exceptions and modifications if such exist: and if the law be
rigorously true, the contemplation of it, as exemplified in the world
of phenomena, will best give us that clear apprehension of its bearings
which may lead us to see the ground of its truth.

The concluding clause of this Fourth Rule appears, at first, to
imply that all inductive propositions are to be considered as merely
provisional and limited, and never secure from exception. But to judge
thus would be to underrate the stability and generality of scientific
truths; for what man of science can suppose that we shall hereafter
discover exceptions to the universal gravitation of all parts of the
solar system? And it is plain that the author did not intend the
restriction to be applied so rigorously; for in the Third Rule, as
we have just seen, he authorizes us to infer universal properties of
matter from observation, and carries the liberty of inductive inference
to its full extent. The Third Rule appears to encourage us to assert a
law to be universal, even in cases in which it has not been tried; the
Fourth Rule seems to warn us that the law may be inaccurate, even in
cases in which it has been tried. Nor is either of these suggestions
erroneous; but both the universality and the rigorous accuracy of our
laws are proved by reference to Ideas rather than to Experience; a
truth, which, perhaps, the philosophers of Newton's time were somewhat
disposed to overlook.


17. The disposition to ascribe all our knowledge to Experience, appears
in Newton and the Newtonians by other indications; for instance, it
is seen in their extreme dislike to the ancient expressions by which
the principles and causes of phenomena were described, as the _occult
causes_ of the Schoolmen, and the _forms_ of the Aristotelians, which
had been adopted by Bacon. Newton says[223], that the particles of
matter not only possess inertia, but also active principles, as
gravity, fermentation, cohesion; he adds, "These principles I consider
not as Occult Qualities, supposed to result from the Specific Forms of
things, but as General Laws of Nature, by which the things themselves
are formed: their truth appearing to us by phenomena, though their
causes be not yet discovered. For these are manifest qualities, and
their causes only are occult. And the Aristotelians gave the name of
_occult qualities_, not to manifest qualities, but to such qualities
only as they supposed to lie hid in bodies, and to the unknown causes
of manifest effects: such as would be the causes of gravity, and of
magnetick and electrick attractions, and of fermentations, if we
should suppose that these forces or actions arose from qualities
unknown to us, and incapable of being discovered and made manifest.
Such occult qualities put a stop to the improvement of Natural
Philosophy, and therefore of late years have been rejected. To tell
us that every species of things is endowed with an occult specific
quality by which it acts and produces manifest effects, is to tell us
nothing: but to derive two or three general principles of motion from
phenomena, and afterwards to tell us how the properties and actions
of all corporeal things follow from these manifest principles, would
be a great step in philosophy, though the causes of those principles
were not yet discovered: and therefore I scruple not to propose the
principles of motion above maintained, they being of very general
extent, and leave their causes to be found out."


18. All that is here said is highly philosophical and valuable; but we
may observe that the investigation of _specific forms_ in the sense in
which some writers had used the phrase, was by no means a frivolous
or unmeaning object of inquiry. Bacon and others had used _form_ as
equivalent to _law_[224]. If we could ascertain that arrangement of
the particles of a crystal from which its external crystalline form
and other properties arise, this arrangement would be the _internal
form_ of the crystal. If the undulatory theory be true, the _form_ of
light is transverse vibrations: if the emission theory be maintained,
the _form_ of light is particles moving in straight lines, and
deflected by various forces. Both the terms, _form_ and _law_, imply
an ideal connexion of sensible phenomena; form supposes matter which
is moulded to the form; law supposes objects which are governed by
the law. The former term refers more precisely to existences, the
latter to occurrences. The latter term is now the more familiar, and
is, perhaps, the better metaphor: but the former also contains the
essential antithesis which belongs to the subject, and might be used in
expressing the same conclusions.

But occult causes, employed in the way in which Newton describes,
had certainly been very prejudicial to the progress of knowledge, by
stopping inquiry with a mere word. The absurdity of such pretended
explanations had not escaped ridicule. The pretended physician in the
comedy gives an example of an occult cause or virtue.

        Mihi demandatur
        A doctissimo Doctore
      _Quare_ Opium facit dormire:
        Et ego respondeo,
        _Quia_ est in eo
        _Virtus dormitiva_,
    Cujus natura est sensus assoupire.


19. But the most valuable part of the view presented to us in
the quotation just given from Newton is the distinct separation,
already noticed as peculiarly brought into prominence by him, of the
determination of the _laws_ of phenomena, and the investigation of
their _causes_. The maxim, that the former inquiry must precede the
latter, and that if the general laws of facts be discovered, the result
is highly valuable, although the causes remain unknown, is extremely
important; and had not, I think, ever been so strongly and clearly
stated, till Newton both repeatedly promulgated the precept, and added
to it the weight of the most striking examples.

We have seen that Newton, along with views the most just and important
concerning the nature and methods of science, had something of the
tendency, prevalent in his time, to suspect or reject, at least
speculatively, all elements of knowledge except observation. This
tendency was, however, in him so corrected and restrained by his own
wonderful sagacity and mathematical habits, that it scarcely led to
any opinion which we might not safely adopt. But we must now consider
the cases in which this tendency operated in a more unbalanced manner,
and led to the assertion of doctrines which, if consistently followed,
would destroy the very foundations of all general and certain knowledge.


FOOTNOTES:

[Footnote 217: _Optics_, qu. 31, near the end.]

[Footnote 218: Qu. 28.]

[Footnote 219: _Hist. Ind. Sc._ b. v. and b. vii.]

[Footnote 220: _Optics_, qu. 31.]

[Footnote 221: _History of Ideas_, b. iii. c. x.]

[Footnote 222: _Ibid._ b. iii. c. ix. x. xi.]

[Footnote 223: _Opticks_, qu. 31.]

[Footnote 224: _Nov. Org._ l. ii. Aph. 2. "Licet enim in natura nihil
existet præter corpora individua, edentia actus puros individuos
ex lege; in doctrinis tamen illa ipsa lex, ejusque inquisitio, et
inventio, et explicatio, pro fundamento est tam ad sciendum quam ad
operandum. Eam autem _legem_, ejusque _paragraphos, formarum_ nomine
intelligimus; præsertim cum hoc vocabulum invaluerit, et familiariter
occurrat."

Aph. 17. "Eadem res est _forma_ calidi vel _forma_ luminis, et _lex_
calidi aut _lex_ luminis."]




CHAPTER XIX.

LOCKE AND HIS FRENCH FOLLOWERS.


1. In the constant opposition and struggle of the schools of
philosophy, which consider our Senses and our Ideas respectively,
as the principal sources of our knowledge, we have seen that at the
period of which we now treat, the tendency was to exalt the external
and disparage the internal element. The disposition to ascribe our
knowledge to observation alone, had already, in Bacon's time, led him
to dwell to a disproportionate degree upon that half of his subject;
and had tinged Newton's expressions, though it had not biassed his
practice. But this partiality soon assumed a more prominent shape,
becoming extreme in Locke, and extravagant in those who professed to
follow him.

Indeed Locke appears to owe his popularity and influence as a popular
writer mainly to his being one of the first to express, in a plain and
unhesitating manner, opinions which had for some time been ripening
in the minds of a large portion of the cultivated public. Hobbes had
already promulgated the main doctrines which Locke afterwards urged, on
the subject of the origin and nature of our knowledge: but in him these
doctrines were combined with offensive opinions on points of morals,
government, and religion, so that their access to general favour was
impeded: and it was to Locke that they were indebted for the extensive
influence which they soon after obtained. Locke owed this authority
mainly to the intellectual circumstances of the time. Although a writer
of great merit, he by no means possesses such metaphysical acuteness or
such philosophical largeness of view, or such a charm of writing, as
must necessarily give him the high place he has held in the literature
of Europe. But he came at a period when the reign of Ideas was
tottering to its fall. All the most active and ambitious spirits had
gone over to the new opinions, and were prepared to follow the fortunes
of the Philosophy of Experiment, then in the most prosperous and
brilliant condition, and full of still brighter promise. There were,
indeed, a few learned and thoughtful men who still remained faithful
to the empire of Ideas; partly, it may be, from a too fond attachment
to ancient systems; but partly, also, because they knew that there
were subjects of vast importance, in which experience did not form the
whole foundation of our knowledge. They knew, too, that many of the
plausible tenets of the new philosophy were revivals of fallacies which
had been discussed and refuted in ancient times. But the advocates of
mere experience came on with a vast store of weighty truth among their
artillery, and with the energy which the advance usually bestows. The
ideal system of philosophy could, for the present, make no effectual
resistance; Locke, by putting himself at the head of the assault,
became the hero of his day: and his name has been used as the watchword
of those who adhere to the philosophy of the senses up to our own times.


2. Locke himself did not assert the exclusive authority of the senses
in the extreme unmitigated manner in which some who call themselves
his disciples have done. But this is the common lot of the leaders
of revolutions, for they are usually bound by some ties of affection
and habit to the previous state of things, and would not destroy all
traces of that condition: while their followers attend, not to their
inconsistent wishes, but to the meaning of the revolution itself;
and carry out, to their genuine and complete results, the principles
which won the victory, and which have been brought out more sharp from
the conflict. Thus Locke himself does not assert that all our ideas
are derived from Sensation, but from Sensation _and Reflection_. But
it was easily seen that, in this assertion, two very heterogeneous
elements were conjoined: that while to pronounce Sensation the origin
of ideas, is a clear decided tenet, the acceptance or rejection of
which determines the general character of our philosophy; to make the
same declaration concerning Reflection, is in the highest degree vague
and ambiguous; since reflection may either be resolved into a mere
modification of sensation, as was done by one school, or may mean all
that the opposite school opposes to sensation, under the name of Ideas.
Hence the clear and strong impression which fastened upon men's minds,
and which does in fact represent all the systematic and consistent part
of Locke's philosophy, was, that in it all our ideas are represented as
derived from Sensation.


3. We need not spend much time in pointing out the inconsistencies into
which Locke fell; as all must fall into inconsistencies who recognize
no source of knowledge except the senses. Thus he maintains that our
Idea of Space is derived from the senses of sight and touch; our Idea
of Solidity from the touch alone. Our Notion of Substance is an unknown
support of unknown qualities, and is illustrated by the Indian fable
of the tortoise which supports the elephant, which supports the world.
Our Notion of Power or Cause is in like manner got from the senses.
And yet, though these ideas are thus mere fragments of our experience,
Locke does not hesitate to ascribe to them necessity and universality
when they occur in propositions. Thus he maintains the necessary truth
of geometrical properties: he asserts that the resistance arising from
solidity is absolutely insurmountable[225]; he conceives that nothing
short of Omnipotence can annihilate a particle of matter[226]; and he
has no misgivings in arguing upon the axiom that Every thing must have
a cause. He does not perceive that, upon his own account of the origin
of our knowledge, we can have no right to make any of these assertions.
If our knowledge of the truths which concern the external world were
wholly derived from experience, all that we could venture to say would
be,--that geometrical properties of figures are true _as far as we have
tried them_;--that we have seen _no example_ of a solid body being
reduced to occupy less space by pressure, or of a material substance
annihilated by natural means;--and that _wherever we have examined_,
we have found that every change has had a cause. Experience can never
entitle us to declare that what she has not seen is impossible; still
less, that things which she can not see are certain. Locke himself
intended to throw no doubt upon the certainty of either human or
divine knowledge; but his principles, when men discarded the temper in
which he applied them, and the checks to their misapplication which
he conceived that he had provided, easily led to a very comprehensive
skepticism. His doctrines tended to dislodge from their true bases the
most indisputable parts of knowledge; as, for example, pure and mixed
mathematics. It may well be supposed, therefore, that they shook the
foundations of many other parts of knowledge in the minds of common
thinkers.

It was not long before these consequences of the overthrow of
ideas showed themselves in the speculative world. I have already
in a previous work[227] mentioned Hume's skeptical inferences from
Locke's maxim, that we have no ideas except those which we acquire
by experience; and the doctrines set up in opposition to this by
the metaphysicians of Germany. I might trace the progress of the
sensational opinions in Britain till the reaction took place here
also: but they were so much more clearly and decidedly followed out in
France, that I shall pursue their history in that country.


4. _The French Followers of Locke, Condillac, &c._--Most of the
French writers who adopted Locke's leading doctrines, rejected the
"Reflection," which formed an anomalous part of his philosophy, and
declared that Sensation alone was the source of ideas. Among these
writers, Condillac was the most distinguished. He expressed the leading
tenet of their school in a clear and pointed manner by saying that "All
ideas are transformed sensations." We have already considered this
phrase[228], and need not here dwell upon it.

Opinions such as these tend to annihilate, as we have seen, one of the
two co-ordinate elements of our knowledge. Yet they were far from being
so prejudicial to the progress of science, or even of the philosophy
of science, as might have been anticipated. One reason of this was,
that they were practically corrected, especially among the cultivators
of Natural Philosophy, by the study of mathematics; for that study did
really supply all that was requisite on the ideal side of science, so
far as the ideas of space, time, and number, were concerned, and partly
also with regard to the idea of cause and some others. And the methods
of discovery, though the philosophy of them made no material advance,
were practically employed with so much activity, and in so many various
subjects, that a certain kind of prudence and skill in this employment
was very widely diffused.


5. _Importance of Language._--In one respect this school of
metaphysicians rendered a very valuable service to the philosophy of
science. They brought into prominent notice the great importance of
_words_ and _terms_ in the formation and progress of knowledge, and
pointed out that the office of language is not only to convey and
preserve our thoughts, but to perform the analysis in which reasoning
consists. They were led to this train of speculation, in a great
measure, by taking pure mathematical science as their standard example
of substantial knowledge. Condillac, rejecting, as we have said, almost
all those ideas on which universal and demonstrable truths must be
based, was still not at all disposed to question the reality of human
knowledge; but was, on the contrary, a zealous admirer of the evidence
and connexion which appear in those sciences which have the ideas of
space and number for their foundation, especially the latter. He looked
for the grounds of the certainty and reality of the knowledge which
these sciences contain; and found them, as he conceived, in the nature
of the _language_ which they employ. The _Signs_ which are used in
arithmetic and algebra enable us to keep steadily in view the identity
of the same quantity under all the forms which, by composition and
decomposition, it may be made to assume; and these Signs also not only
express the operations which are performed, but suggest the extension
of the operations according to analogy. Algebra, according to him,
is only a very perfect language; and language answers its purpose of
leading us to truth, by possessing the characteristics of algebra.
Words are the symbols of certain groups of impressions or facts; they
are so selected and applied as to exhibit the analogies which prevail
among these facts; and these analogies are the truths of which our
knowledge consists. "Every language is an analytical method; every
analytical method is a language[229];" these were the truths "alike new
and simple," as he held, which he conceived that he had demonstrated.
"The art of speaking, the art of writing, the art of reasoning, the
art of thinking, are only, at bottom, one and the same art[230]." Each
of these operations consists in a succession of analytical operations;
and words are the marks by which we are able to fix our minds upon the
steps of this analysis.


6. The analysis of our impressions and notions does in reality lead
to truth, not only in virtue of the identity of the whole with its
parts, as Condillac held, but also in virtue of certain Ideas which
govern the synthesis of our sensations, and which contain the elements
of universal truths, as we have all along endeavoured to show. But
although Condillac overlooked or rejected this doctrine, the importance
of words, as marking the successive steps of this synthesis and
analysis, is not less than he represented it to be. Every truth, once
established by induction from facts, when it is become familiar under
a brief and precise form of expression, becomes itself a fact; and is
capable of being employed, along with other facts of a like kind, as
the materials of fresh inductions. In this successive process, the
term, like the cord of a fagot, both binds together the facts which it
includes, and makes it possible to manage the assemblage as a single
thing. On occasion of most discoveries in science, the selection of a
technical term is an essential part of the proceeding. In the _History
of Science_, we have had numerous opportunities of remarking this; and
the List of technical terms given as an Index to that work, refers us,
by almost every word, to one such occasion. And these terms, which
thus have had so large a share in the formation of science, and which
constitute its language, do also offer the means of analyzing its
truths, each into its constituent truths; and these into facts more
special, till the original foundations of our most general propositions
are clearly exhibited. The relations of general and particular truths
are most evidently represented by the Inductive Tables given in
Book II. of the _Novum Organon Renovatum_. But each step in each of
these Tables has its proper form of expression, familiar among the
cultivators of science; and the analysis which our Tables display, is
commonly performed in men's minds, when it becomes necessary, by fixing
the attention successively upon a series of words, not upon the lines
of a Table. Language offers to the mind such a scale or ladder as the
Table offers to the eye; and since such Tables present to us, as we
have said, the Logic of Induction, that is, the formal conditions of
the soundness of our reasoning from facts, we may with propriety say
that a just analysis of the meaning of words is an essential portion of
Inductive Logic.

In saying this, we must not forget that a decomposition of general
truths into ideas, as well as into facts, belongs to our philosophy;
but the point we have here to remark, is the essential importance of
words to the latter of these processes. And this point had not ever
had its due weight assigned to it till the time of Condillac and other
followers of Locke, who pursued their speculations in the spirit I have
just described. The doctrine of the importance of terms is the most
considerable addition to the philosophy of science which has been made
since the time of Bacon[231].


7. _The French Encyclopedists._--The French _Encyclopédie_, published
in 1751, of which Diderot and Dalembert were the editors, may be
considered as representing the leading characters of European
philosophy during the greater part of the eighteenth century. The
writers in this work belong for the most part to the school of Locke
and Condillac; and we may make a few remarks upon them, in order to
bring into view one or two points in addition to what we have already
said of that school. The _Discours Préliminaire_, written by Dalembert,
is celebrated as containing a view of the origin of our knowledge, and
the connexion and classification of the sciences.

A tendency of the speculations of the Encyclopedists, as of the School
of Locke in general, is to reject all ideal principles of connexion
among facts, as something which experience, the only source of true
knowledge, does not give. Hence all certain knowledge consists only
in the recognition of the same thing under different aspects, or
different forms of expression. Axioms are not the result of an original
relation of ideas, but of the use, or it may be the abuse[232], of
words. In like manner, the propositions of Geometry are a series of
modifications,--of distortions, so to speak,--of one original truth;
much as if the proposition were stated in the successive forms of
expression presented by a language which was constantly growing more
and more artificial. Several of the sciences which rest upon physical
principles, that is, (says the writer,) truths of experience or simple
hypotheses, have only an experimental or hypothetical certainty.
Impenetrability added to the idea of extent is a mystery in addition:
the nature of motion is a riddle for philosophers: the metaphysical
principle of the laws of percussion is equally concealed from them. The
more profoundly they study the idea of matter and of the properties
which represent it, the more obscure this idea becomes; the more
completely does it escape them.


8. This is a very common style of reflection, even down to our own
times. I have endeavoured to show that concerning the Fundamental Ideas
of space, of force and resistance, of substance, external quality, and
the like, we know enough to make these Ideas the grounds of certain
and universal truths;--enough to supply us with axioms from which we
can demonstratively reason. If men wish for any other knowledge of
the nature of matter than that which ideas, and facts conformable to
ideas, give them, undoubtedly their desire will be frustrated, and
they will be left in a mysterious vacancy; for it does not appear
how such knowledge as they ask for could be knowledge at all. But in
reality, this complaint of our ignorance of the real nature of things
proceeds from the rejection of ideas, and the assumption of the senses
alone as the ground of knowledge. "Observation and calculation are
the only sources of truth:" this is the motto of the school of which
we now speak. And its import amounts to this:--that they reject all
ideas except the idea of number, and recognize the modifications which
parts undergo by addition and subtraction as the only modes in which
true propositions are generated. The laws of nature are assemblages of
facts: the truths of science are assertions of the identity of things
which are the same. "By the avowal of almost all philosophers," says
a writer of this school[233], "the most sublime truths, when once
simplified and reduced to their lowest terms, are converted into facts,
and thenceforth present to the mind only this proposition; the white is
white, the black is black."

These statements are true in what they positively assert, but they
involve error in the denial which by implication they convey. It
is true that observation and demonstration are the only sources of
scientific truth; but then, demonstration may be founded on other
grounds besides the elementary properties of number. It is true that
the theory of gravitation is but the assertion of a general fact; but
this is so, not because a sound theory does not involve ideas, but
because our apprehension of a fact does.


9. Another characteristic indication of the temper of the
Encyclopedists and of the age to which they belong, is the importance
by them assigned to those practical _Arts_ which minister to man's
comfort and convenience. Not only, in the body of the Encyclopedia, are
the Mechanical Arts placed side by side with the Sciences, and treated
at great length; but in the Preliminary Discourse, the preference
assigned to the liberal over the mechanical Arts is treated as a
prejudice[234], and the value of science is spoken of as measured
by its utility. "The discovery of the Mariner's Compass is not less
advantageous to the human race than the explanation of its properties
would be to physics.--Why should we not esteem those to whom we owe
the fusee and the escapement of watches as much as the inventors of
Algebra?" And in the classification of sciences which accompanies the
Discourse, the labours of artisans of all kinds have a place.

This classification of the various branches of science contained
in the Dissertation is often spoken of. It has for its basis the
classification proposed by Bacon, in which the parts of human knowledge
are arranged according to the faculties of the mind in which they
originate; and these faculties are taken, both by Bacon and by
Dalembert, as Memory, Reason, and Imagination. The insufficiency of
Bacon's arrangement as a scientific classification is so glaring, that
the adoption of it, with only superficial modifications, at the period
of the Encyclopedia, is a remarkable proof of the want of original
thought and real philosophy at the time of which we speak.


10. We need not trace further the opinion which derives all our
knowledge from the senses in its application to the philosophy of
Science. Its declared aim is to reduce all knowledge to the knowledge
of Facts; and it rejects all inquiries which involve the Idea of Cause,
and similar Ideas, describing them as "metaphysical," or in some other
damnatory way. It professes, indeed, to discard all Ideas; but, as we
have long ago seen, some Ideas or other are inevitably included even
in the simplest Facts. Accordingly the speculations of this school
are compelled to retain the relations of Position, Succession, Number
and Resemblance, which are rigorously ideal relations. The philosophy
of Sensation, in order to be consistent, ought to reject these Ideas
along with the rest, and to deny altogether the possibility of general
knowledge.

When the opinions of the Sensational School had gone to an extreme
length, a Reaction naturally began to take place in men's minds. Such
have been the alternations of opinion, from the earliest ages of human
speculation. Man may perhaps have existed in an original condition in
which he was only aware of the impressions of Sense; but his first
attempts to analyse his perceptions brought under his notice Ideas as
a separate element, essential to the existence of knowledge. Ideas
were thenceforth almost the sole subject of the study of philosophers;
of Plato and his disciples, professedly; of Aristotle, and still more
of the followers and commentators of Aristotle, practically. And this
continued till the time of Galileo, when the authority of the Senses
again began to be asserted; for it was shown by the great discoveries
which were then made, that the Senses had at least some share in
the promotion of knowledge. As discoveries more numerous and more
striking were supplied by Observation, the world gradually passed
over to the opinion that the share which had been ascribed to Ideas in
the formation of real knowledge was altogether a delusion, and that
Sensation alone was true. But when this was asserted as a general
doctrine, both its manifest falsity and its alarming consequences
roused men's minds, and made them recoil from the extreme point to
which they were approaching. Philosophy again oscillated back towards
Ideas; and over a great part of Europe, in the clearest and most
comprehensive minds, this regression from the dogmas of the Sensational
School is at present the prevailing movement. We shall conclude our
review by noticing a few indications of this state of things.


FOOTNOTES:

[Footnote 225: _Essay_, b. xi. c. iv. sect. 3.]

[Footnote 226: _Ibid._ c. xiii. sect. 22.]

[Footnote 227: _History of Ideas_, b. iii. c. iii. Modern Opinions
respecting the Idea of Cause.]

[Footnote 228: _Ibid._ b. i. c. iv.]

[Footnote 229: _Langue des Calculs_, p. 1.]

[Footnote 230: _Grammaire_, p. xxxvi.]

[Footnote 231: Since the selection and construction of terms is thus
a matter of so much consequence in the formation of science, it is
proper that systematic rules, founded upon sound principles, should be
laid down for the performance of this operation. Some such rules are
accordingly suggested in b. iv. of the _Nov. Org. Ren._]

[Footnote 232: _Disc. Prélim._ p. viii.]

[Footnote 233: Helvetius _Sur l'Homme_, c. xxiii.]

[Footnote 234: P. xiii.]




CHAPTER XX.

THE REACTION AGAINST THE SENSATIONAL SCHOOL.


1. When Locke's _Essay_ appeared, it was easily seen that its tendency
was to urge, in a much more rigorous sense than had previously been
usual, the ancient maxim of Aristotle, adopted by the schoolmen of
the middle ages, that "nothing exists in the intellect but what has
entered by the senses." Leibnitz expressed in a pointed manner the
limitation with which this doctrine had always been understood. "Nihil
est in intellectu quod non prius fuerit in sensu;--_nempe_," he added,
"_nisi intellectus ipse_." To this it has been objected[235], that we
cannot say that the intellect is _in_ the intellect. But this remark
is obviously frivolous; for the faculties of the understanding (which
are what the argument against the Sensational School requires us to
reserve) may be said to be _in_ the understanding, with as much justice
as we may assert there are _in_ it the impressions derived from sense.
And when we take account of these faculties, and of the Ideas to which,
by their operation, we necessarily subordinate our apprehension of
phenomena, we are led to a refutation of the philosophy which makes
phenomena, unconnected by Ideas, the source of all knowledge. The
succeeding opponents of the Lockian school insisted upon and developed
in various ways this remark of Leibnitz, or some equivalent view.


2. It was by inquiries into the foundations of Morals that English
philosophers were led to question the truth of Locke's theory. Dr.
Price, in his _Review of the Principal Questions in Morals_, first
published in 1757, maintained that we cannot with propriety assert
all our ideas to be derived from sensation and reflection. He pointed
out, very steadily, the other source. "The power, I assert, that
_understands_, or the faculty within us that discerns _truth_, and that
compares all the objects of thought and _judges_ of them, is a spring
of new ideas[236]." And he exhibits the antithesis in various forms.
"Were not _sense_ and _knowledge_ entirely different, we should rest
satisfied with sensible impressions, such as light, colours and sounds,
and inquire no further about them, at least when the impressions are
strong and vigorous: whereas, on the contrary, we necessarily desire
some further acquaintance with them, and can never be satisfied
till we have subjected them to the survey of reason. Sense presents
_particular_ forms to the mind, but cannot rise to any _general_ ideas.
It is the intellect that examines and compares the presented forms,
that rises above individuals to universal and abstract ideas; and
thus looks downward upon objects, takes in at one view an infinity of
particulars, and is capable of discovering general truths. Sense sees
only the outside of things, reason acquaints itself with their natures.
Sensation is only a mode of feeling in the mind; but knowledge implies
an active and vital energy in the mind[237]."


3. The necessity of refuting Hume's inferences from the mere sensation
system led other writers to limit, in various ways, their assent to
Locke. Especially was this the case with a number of intelligent
metaphysicians in Scotland, as Reid, Beattie, Dugald Stewart, and
Thomas Brown. Thus Reid asserts[238], "that the account which Mr.
Locke himself gives of the Idea of Power cannot be reconciled to
his favourite doctrine, that all our simple ideas have their origin
from sensation or reflection." Reid remarks, that our memory and our
reasoning power come in for a share in the origin of this idea: and
in speaking of reasoning, he obviously assumes the axiom that every
event must have a cause. By succeeding writers of this school, the
assumption of the fundamental principles, to which our nature in such
cases irresistibly directs us, is more clearly pointed out. Thus
Stewart defends the form of expression used by Price[239]: "A variety
of intuitive judgments might be mentioned, involving simple ideas,
which it is impossible to trace to any origin but to the power which
enables us to form these judgments. Thus it is surely an intuitive
truth that the sensations of which I am conscious, and all those I
remember, belong to one and the same being, which I call _myself_. Here
is an intuitive judgment involving the simple idea of _Identity_. In
like manner, the changes which I perceive in the universe impress me
with a conviction that some cause must have operated to produce them.
Here is an intuitive judgment involving the simple Idea of _Causation_.
When we consider the adjacent angles made by a straight line standing
upon another, and perceive that their sum is equal to two right angles,
the judgment we form involves a simple idea of _Equality_. To say,
therefore, that the Reason or the Understanding is a source of new
ideas, is not so exceptionable a mode of speaking as has been sometimes
supposed. According to Locke, _Sense_ furnishes our ideas, and Reason
perceives their agreements and disagreements. But the truth is, that
these agreements and disagreements are in many instances, simple
ideas, of which no analysis can be given; and of which the origin must
therefore be referred to Reason, according to Locke's own doctrine."
This view, according to which the Reason or Understanding is the source
of certain simple ideas, such as Identity, Causation, Equality, which
ideas are necessarily involved in the intuitive judgments which we
form, when we recognize fundamental truths of science, approaches very
near in effect to the doctrine which in several works I have presented,
of Fundamental Ideas belonging to each science, and manifesting
themselves in the axioms of the science. It may be observed, however,
that by attempting to enumerate these ideas and axioms, so as to
lay the foundations of the whole body of physical science, and by
endeavouring, as far as possible, to simplify and connect each group
of such Ideas, I have at least given a more systematic form to this
doctrine. I have, moreover, traced it into many consequences to which
it necessarily leads, but which do not appear to have been contemplated
by the metaphysicians of the Scotch school. But I gladly acknowledge
my obligations to the writers of that school; and I trust that in the
near agreement of my views on such points with theirs, there is ground
for believing the system of philosophy which I have presented, to be
that to which the minds of thoughtful men, who have meditated on such
subjects, are generally tending.


4. As a further instance that such a tendency is at work, I may make
a quotation from an eminent English philosophical writer of another
school. "If you will be at the pains," says Archbishop Whately[240],
"carefully to analyze the simplest description you hear of any
transaction or state of things, you will find that the process which
almost invariably takes place is, in logical language, this: that each
individual _has in his mind_ certain major premises or principles
relative to the subject in question;--that observation of what actually
presents itself to the senses, supplies minor premises; and that
the statement given (and which is reported as a thing experienced)
consists, in fact, of the _conclusions_ drawn from the combinations of
these premises." The major premises here spoken of are the Fundamental
Ideas, and the Axioms and Propositions to which they lead; and whatever
is regarded as a fact of observation is necessarily a conclusion in
which these propositions are assumed; for these contain, as we have
said, the conditions of our experience. Our experience conforms to
these axioms and their consequences, whether or not the connexion be
stated in a logical manner, by means of premises and a conclusion.


5. The same persuasion is also suggested by the course which the study
of metaphysics has taken of late years in France. In that country,
as we have seen, the Sensational System, which was considered as the
necessary consequence of the revolution begun by Locke, obtained a more
complete ascendancy than it did in England; and in that country too,
the reaction, among metaphysical and moral writers, when its time came,
was more decided and rapid than it was among Locke's own countrymen.
It would appear that M. Laromiguière was one of the first to give
expression to this feeling, of the necessity of a modification of the
sensational philosophy. He began by professing himself the disciple
of Condillac, even while he was almost unconsciously subverting the
fundamental principles of that writer. And thus, as M. Cousin justly
observes[241], his opinions had the more powerful effect from being
presented, not as thwarting and contradicting, but as sharing and
following out the spirit of his age. M. Laromiguière's work, entitled
_Essai sur les Facultés de l'Ame_, consists of lectures given to the
Faculty of Letters of the Academy of Paris, in the years 1811, 1812
and 1813. In the views which these lectures present, there is much
which the author has in common with Condillac. But he is led by his
investigation to assert[242], that it is not true that sensation is
the sole fundamental element of our thoughts and our understanding.
_Attention_ also is requisite: and here we have an element of quite
another kind. For sensation is passive; attention is active. Attention
does not spring out of sensation; the passive principle is not the
reason of the active principle. Activity and passivity are two facts
entirely different. Nor can this activity be defined or derived; being,
as the author says, a fundamental idea. The distinction is manifest
by its own nature; and we may find evidence of it in the very forms of
language. To _look_ is more than to _see_; to _hearken_ is more than
to _hear_. The French language marks this distinction with respect to
other senses also. "On _voit_, et l'on _regarde_; on _entend_, et l'on
_écoute_; on _sent_, et l'on _flaire_; on _goûte_, et l'on _savoure_."
And thus the mere sensation, or capacity of feeling, is only the
occasion on which the attention is exercised; while the attention is
the foundation of all the operations of the understanding.

The reader of my works will have seen how much I have insisted upon the
activity of the mind, as the necessary basis of all knowledge. In all
observation and experience, the mind is active, and by its activity
apprehends all sensations in subordination to its own ideas; and thus
it becomes capable of collecting knowledge from phenomena, since
ideas involve general relations and connexions, which sensations of
themselves cannot involve. And thus we see that, in this respect also,
our philosophy stands at that point to which the speculations of the
most reflecting men have of late constantly been verging.


6. M. Cousin himself, from whom we have quoted the above account
of Laromiguière, shares in this tendency, and has argued very
energetically and successfully against the doctrines of the Sensational
School. He has made it his office once more to bring into notice among
his countrymen, the doctrine of ideas as the sources of knowledge; and
has revived the study of Plato, who may still be considered as one of
the great leaders of the ideal school. But the larger portion of M.
Cousin's works refers to questions out of the reach of our present
review, and it would be unsuitable to dwell longer upon them in this
place.


7. We turn to speculations more closely connected with our present
subject. M. Ampère, a French man of science, well entitled by his
extensive knowledge, and large and profound views, to deal with the
philosophy of the sciences, published in 1834, his _Essai sur la
Philosophie des Sciences, ou Exposition analytique d'une Classification
Naturelle de toutes les Connaissances Humaines_. In this remarkable
work we see strong evidence of the progress of the reaction against
the system which derives our knowledge from sensation only. The
author starts from a maxim, that in classing the sciences, we must
not only regard the nature of the objects about which each science is
concerned, but also the point of view under which it considers them:
that is, the _ideas_ which each science involves. M. Ampère also gives
briefly his views of the intellectual constitution of man; a subject
on which he had long and sedulously employed his thoughts; and these
views are far from belonging to the Sensational School. Human thought,
he says, is composed of phenomena and of conceptions. Phenomena are
external, or _sensitive_; and internal, or _active_. Conceptions are
of four kinds; _primitive_, as space and motion, duration and cause;
_objective_, as our idea of matter and substance; _onomatic_, or those
which we associate with the general terms which language presents to
us; and _explicative_, by which we ascend to causes after a comparative
study of phenomena. He teaches further, that in deriving ideas from
sensation, the mind is not passive; but exerts an action which, when
voluntary, is called _attention_, but when it is, as it often is,
involuntary, may be termed _reaction_.

I shall not dwell upon the examination of these opinions[243]; but I
may remark, that both in the recognition of conceptions as an original
and essential element of the mind, and in giving a prominent place to
the active function of the mind, in the origin of our knowledge, this
view approaches to that which I have presented in preceding works;
although undoubtedly with considerable differences.


8. The classification of the sciences which M. Ampère proposes, is
founded upon a consideration of the sciences themselves; and is,
the author conceives, in accordance with the conditions of natural
classifications, as exhibited in Botany and other sciences. It is of
a more symmetrical kind, and exhibits more steps of subordination,
than that to which I have been led; it includes also practical Art as
well as theoretical Science; and it is extended to moral and political
as well as physical Sciences. It will not be necessary for me here
to examine it in detail: but I may remark, that it is throughout a
_dichotomous_ division, each higher member being subdivided into two
lower ones, and so on. In this way, M. Ampère obtains sciences of
the First Order, each of which is divided into two sciences of the
Second, and four of the Third Order. Thus Mechanics is divided into
_Cinematics_, _Statics_, _Dynamics_, and _Molecular Mechanics_; Physics
is divided into _Experimental Physics_, _Chemistry_, _Stereometry_,
and _Atomology_; Geology is divided into _Physical Geography_,
_Mineralogy_, _Geonomy_, and _Theory of the Earth_. Without here
criticizing these divisions or their principle, I may observe that
_Cinematics_, the doctrine of motion without reference to the force
which produces it, is a portion of knowledge which our investigation
has led us also to see the necessity of erecting into a separate
science; and which we have termed _Pure Mechanism_. Of the divisions of
Geology, _Physical Geography_, especially as explained by M. Ampère, is
certainly a part of the subject, both important and tolerably distinct
from the rest. _Geonomy_ contains what we have termed in the History,
_Descriptive Geology_;--the exhibition of the facts separate from the
inquiry into their causes; while our _Physical Geology_ agrees with M.
Ampère's _Theory of the Earth_. _Mineralogy_ appears to be placed by
him in a different place from that which it occupies in our scheme:
but in fact, he uses the term for a different science; he applies
it to the classification not of _simple minerals_, but of _rocks_,
which is a science auxiliary to geology, and which has sometimes been
called _Petralogy_. What we have termed _Mineralogy_, M. Ampère unites
with _Chemistry_. "It belongs," he says[244], "to Chemistry, and not
to Mineralogy, to inquire how many atoms of silicium and of oxygen
compose silica; to tell us that its primitive form is a rhombohedron of
certain angles, that it is called _quartz_, &c.; leaving, on one hand,
to Molecular Geometry the task of explaining the different secondary
forms which may result from the primitive form; and on the other hand,
leaving to Mineralogy the office of describing the different varieties
of quartz, and the rocks in which they occur, according as the quartz
is crystallized, transparent, coloured, amorphous, solid, or in sand."
But we may remark, that by adopting this arrangement, we separate from
Mineralogy almost all the knowledge, and absolutely all the general
knowledge, which books professing to treat of that science have
usually contained. The consideration of Mineralogical Classifications,
which, as may be seen in the _History of Science_, is so curious and
instructive, is forced into the domain of Chemistry, although many of
the persons who figure in it were not at all properly chemists. And we
lose, in this way, the advantage of that peculiar office which, in our
arrangement, Mineralogy fills; of forming a rigorous transition from
the sciences of classification to those which consider the mathematical
properties of bodies; and connecting the external characters and the
internal constitution of bodies by means of a system of important
general truths. I conceive, therefore, that our disposition of this
science, and our mode of applying the name, are far more convenient
than those of M. Ampère.


9. We have seen the reaction against the pure sensational doctrines
operating very powerfully in England and in France. But it was in
Germany that these doctrines were most decidedly rejected; and systems
in extreme opposition to these put forth with confidence, and received
with applause. Of the authors who gave this impulse to opinions in that
country, Kant was the first, and by far the most important. I have in
the _History of Ideas_ (b. iii. c. 3), endeavoured to explain how he
was aroused, by the skepticism of Hume, to examine wherein the fallacy
lay which appeared to invalidate all reasonings from effect to cause;
and how this inquiry terminated in a conviction that the foundations
of our reasonings on this and similar points were to be sought in
the mind, and not in the phenomena;--in the _subject_, and not in
the _object_. The revolution in the customary mode of contemplating
human knowledge which Kant's opinions involved, was most complete.
He himself, with no small justice, compares[245] it with the change
produced by Copernicus's theory of the solar system. "Hitherto," he
says, "men have assumed that all our knowledge must be regulated by
the objects of it; yet all attempts to make out anything concerning
objects _à priori_ by means of our conceptions," (as for instance their
geometrical properties) "must, on this foundation, be unavailing. Let
us then try whether we cannot make out something more in the problems
of metaphysics, by assuming that objects must be regulated by our
knowledge, since this agrees better with that supposition, which we are
prompted to make, that we can know something of them _à priori_. This
thought is like that of Copernicus, who, when he found that nothing
was to be made of the phenomena of the heavens so long as everything
was supposed to turn about the spectator, tried whether the matter
might not be better explained if he made the spectator turn, and left
the stars at rest. We may make the same essay in metaphysics, as to
what concerns our intuitive knowledge respecting objects. If our
apprehension of objects must be regulated by the properties of the
objects, I cannot comprehend how we can possibly know anything about
them _à priori_. But if the object, as apprehended by us, be regulated
by the constitution of our faculties of apprehension, I can readily
conceive this possibility." From this he infers that our experience
must be regulated by our conceptions.


10. This view of the nature of knowledge soon superseded entirely
the doctrines of the Sensational School among the metaphysicians of
Germany. These philosophers did not gradually modify and reject the
dogmas of Locke and Condillac, as was done in England and France[246];
nor did they endeavour to ascertain the extent of the empire of Ideas
by a careful survey of its several provinces, as we have been doing in
this series of works. The German metaphysicians saw at once that Ideas
and Things, the Subjective and the Objective elements of our knowledge,
were, by Kant's system, brought into opposition and correlation, as
equally real and equally indispensable. Seeing this, they rushed at
once to the highest and most difficult problem of philosophy,--to
determine what this correlation is;--to discover how Ideas and Things
are at the same time opposite and identical;--how the world, while it
is distinct from and independent of us, is yet, as an object of our
knowledge, governed by the conditions of our thoughts. The attempts
to solve this problem, taken in the widest sense, including the forms
which it assumes in Morals, Politics, the Arts, and Religion, as well
as in the Material Sciences, have, since that time, occupied the most
profound speculators of Germany; and have given rise to a number of
systems, which, rapidly succeeding each other, have, each in its day,
been looked upon as a complete solution of the problem. To trace the
characters of these various systems, does not belong to the business of
the present chapter: my task is ended when I have shown, as I have now
done, how the progress of thought in the philosophical world, followed
from the earliest up to the present time, has led to that recognition
of the co-existence and joint necessity of the two opposite elements
of our knowledge; and when I have pointed out processes adapted to
the extension of our knowledge, which a true view of its nature has
suggested or may suggest.

The latter portion of this task occupies the Third Book of the _Novum
Organon Renovatum_. With regard to the recent succession of German
systems of philosophy, I shall add something in a subsequent chapter:
and I shall also venture to trace further than I have yet done, the
bearing of the philosophy of science upon the theological view of the
universe and the moral and religious condition of man.


FOOTNOTES:

[Footnote 235: See Mr. Sharpe's _Essays_.]

[Footnote 236: Price's _Essays_, p. 16.]

[Footnote 237: P. 18.]

[Footnote 238: Reid, _Essays on the Powers of the Human Mind_, iii. 31.]

[Footnote 239: Stewart, _Outlines of Moral Phil._ p. 138.]

[Footnote 240: Whately, _Polit. Econ._ p. 76.]

[Footnote 241: Cousin, _Fragmens Philosophiques_, i. 53.]

[Footnote 242: _Ibid._ i. 67.]

[Footnote 243: See also the vigorous critique of Locke's _Essay_, by
Lemaistre, _Soirées de St. Petersbourg_.]

[Footnote 244: Ampère, _Essai_, p. 210.]

[Footnote 245: _Kritik der Reinen Vernunft_, Pref. p. xv.]

[Footnote 246: The sensational system never acquired in Germany the
ascendancy which it obtained in England and France; but I am compelled
here to pass over the history of philosophy in Germany, except so far
as it affects ourselves.]




CHAPTER XXI.

FURTHER ADVANCE OF THE SENSATIONAL SCHOOL.

M. AUGUSTE COMTE.


I shall now take the liberty of noticing the views published by a
contemporary writer; not that it forms part of my design to offer
any criticism upon the writings of all those who have treated of
those subjects on which we are now employed; but because we can
more distinctly in this manner point out the contrasts and ultimate
tendencies of the several systems of opinion which have come under
our survey: and since from among these systems we have endeavoured to
extract and secure the portion of truth which remains in each, and
to reject the rest, we are led to point out the errors on which our
attention is thus fixed, in recent as well as older writers.

M. Auguste Comte published in 1830 the first, and in 1835 the second
volume of his _Cours de Philosophie Positive_; of which the aim is not
much different from that of the present work, since as he states (p.
viii.) such a title as the _Philosophy of the Sciences_ would describe
a part of his object, and would be inappropriate only by excluding that
portion (not yet published) which refers to speculations concerning
social relations.


1. _M. Comte on Three States of Science._--By employing the term
_Philosophie Positive_, he wishes to distinguish the philosophy
involved in the present state of our sciences from the previous forms
of human knowledge. For according to him, each branch of knowledge
passes, in the course of man's history, through three different states;
it is first _theological_, then _metaphysical_, then _positive_. By
the latter term he implies a state which includes nothing but general
representations of facts;--phenomena _arranged according_ to relations
of succession and resemblance. This "positive philosophy" rejects all
inquiry after causes, which inquiry he holds to be void of sense[247]
and inaccessible. All such conceptions belong to the "metaphysical"
state of science which deals with abstract forces, real entities,
and the like. Still more completely does he reject, as altogether
antiquated and absurd, the "theological" view of phenomena. Indeed he
conceives[248] that any one's own consciousness of what passes within
himself is sufficient to convince him of the truth of the law of the
three phases through which knowledge must pass. "Does not each of us,"
he says, "in contemplating his own history, recollect that he has been
successively a _theologian_ in his infancy, a _metaphysician_ in his
youth, and a _physicist_ in his ripe age? This may easily be verified
for all men who are up to the level of their time."

It is plain from such statements, and from the whole course of his
work, that M. Comte holds, in their most rigorous form, the doctrines
to which the speculations of Locke and his successors led; and which
tended, as we have seen, to the exclusion of all ideas except those
of number and resemblance. As M. Comte refuses to admit into his
philosophy the fundamental idea of Cause, he of course excludes most of
the other ideas, which are, as we endeavoured to show, the foundations
of science; such as the ideas of Media by which secondary qualities are
made known to us; the ideas of Chemical Attraction, of Polar Forces,
and the like. He would reduce all science to the mere expression of
laws of phenomena, expressed in formulæ of space, time, and number; and
would condemn as unmeaning, and as belonging to an obsolete state of
science, all endeavours to determine the causes of phenomena, or even
to refer them to any of the other ideas just mentioned.


2. _M. Comte rejects the Search of Causes._--In a previous work[249]
I have shown, I trust decisively, that it is the genuine office
of science to inquire into the causes as well as the laws of
phenomena;--that such an inquiry cannot be avoided; and that it has
been the source of almost all the science we possess. I need not here
repeat the arguments there urged; but I may make a remark or two upon
M. Comte's hypothesis, that all science is first "metaphysical" and
then "positive;" since it is in virtue of this hypothesis that he
rejects the investigation of causes, as worthy only of the infancy
of science. All discussions concerning ideas, M. Comte would condemn
as "metaphysical," and would consider as mere preludes to positive
philosophy. Now I venture to assert, on the contrary, that discussions
concerning ideas, and real discoveries, have in every science gone
hand in hand. There is no science in which the pretended order of
things can be pointed out. There is no science in which the discoveries
of the laws of phenomena, when once begun, have been carried on
independently of discussions concerning ideas. There is no science
in which the expression of the laws of phenomena can at this time
dispense with ideas which have acquired their place in science in
virtue of metaphysical considerations. There is no science in which
the most active disquisitions concerning ideas did not come _after_,
not _before_, the first discovery of laws of phenomena. In Astronomy,
the discovery of the phenomenal laws of the epicyclical motions of the
heavens led to assumptions of the metaphysical principle of equable
circular motions: Kepler's discoveries would never have been made
but for his metaphysical notions. These discoveries of the laws of
phenomena did not lead immediately to Newton's theory, _because_ a
century of metaphysical discussions was requisite as a preparation.
Newton then discovered, not merely a law of phenomena, but a _cause_;
and _therefore_ he was the greatest of discoverers. The same is the
case in Optics; the ancients possessed some share of our knowledge
of facts; but meddled little with the metaphysical reasonings of the
subject. In modern times when men began to inquire into the _nature_
of light, they soon extended their knowledge of its _laws_. When this
series of discoveries had come to a pause, a new series of brilliant
discoveries of laws of phenomena went on, inseparably connected with a
new series of views of the nature and cause of light. In like manner,
the most modern discoveries in chemistry involve indispensably the idea
of polar forces. The metaphysics (in M. Comte's sense) of each subject
advances in a parallel line with the knowledge of physical laws. The
Explication of Conceptions must go on, as we have already shown, at the
same rate as the Colligation of Facts.

M. Comte will say[250] that Newton's discovery of gravitation only
consists in exhibiting the astronomical phenomena of the universe
as one single fact under different points of view. But this _fact_
involves the idea of _force_, that is, of _cause_. And that this idea
is not a mere modification of the ideas of time and space, we have
shown: if it were so, how could it lead to the axiom that attraction
is mutual, an indispensable part of the Newtonian theory? M. Comte
says[251] that we do not know what attraction is, since we can only
define it by identical phrases: but this is just as true of space,
or time, or motion; and is in fact exactly the characteristic of a
fundamental idea. We do not obtain such ideas from definitions, but we
possess them not the less truly because we cannot define them.

That M. Comte's hypothesis is historically false, is obvious by such
examples as I have mentioned. Metaphysical discussions have been
essential steps in the progress of each science. If we arbitrarily
reject all these portions of scientific history as useless trifling,
belonging to the first rude attempts at knowledge, we shall not only
distort the progress of things, but pervert the plainest facts. Of
this we have an example in M. Comte's account of Kepler's mechanical
speculations. We have seen, in the History of Physical Astronomy, that
Kepler's second law, (that the planets describe areas about the sun
proportional to the times,) was proved by him, by means of calculations
founded on the observations of Tycho; but that the mechanical reason
of it was not assigned till a later period, when it appeared as the
first proposition of Newton's _Principia_. It is plain from the
writings of Kepler, that it was impossible for him to show how this
law resulted from the forces which were in action; since the forces
which he considered were not those tending to the centre, which really
determine the property in question, but forces exerted by the sun _in
the direction of the planet's motion_, without which forces Kepler
conceived that the motion could not go on. In short, the state of
mechanical science in Kepler's time was such that no demonstration of
the law could be given. The terms in which such a demonstration must
be expressed had not at that time acquired a precise significance; and
it was in virtue of many subsequent _metaphysical_ discussions (as M.
Comte would term them) that these terms became capable of expressing
sound mechanical reasoning. Kepler did indeed pretend to assign what
he called a "physical proof" of his law, depending upon this, that the
sun's force is less at greater distances; a condition which does not
at all influence the result. Thus Kepler's reason for his law proves
nothing but the confusion of thought in which he was involved on such
subjects. Yet M. Comte assigns to Kepler the credit of having proved
this law by sound mechanical reasoning, as well as established it as
a matter of fact[252]. "This discovery by Kepler," he adds, "is the
more remarkable, inasmuch as it occurred before the science of dynamics
had really been created by Galileo." We may remark that inasmuch as M.
Comte perceived this incongruity in the facts as he stated them, it is
the more remarkable that he did not examine them more carefully.


3. _Causes in Physics._--The condemnation of the inquiry into causes
which is conveyed in M. Comte's notion of the three stages of Science,
he again expresses more in detail, in stating[253] what he calls his
_Fundamental theory of hypotheses_. This "theory" is, that we may
employ hypotheses in our natural philosophy, but these hypotheses
must always be such as admit of a positive verification. We must have
no suppositions concerning the agents by which effects are produced.
All such suppositions have an anti-scientific character, and can only
impede the real progress of physics. There can be no use in the ethers
and imaginary fluids to which some persons refer the phenomena of heat,
light, electricity and magnetism. And in agreement with this doctrine,
M. Comte in his account[254] of the Science of Optics, condemns, as
utterly unphilosophical and absurd, both the theory of emission and
that of undulation.

To this we reply, that theory of one kind or other is indispensable
to the expression of the phenomena; and that when the laws are
expressed, and apparently explained, by means of a theory, to forbid
us to inquire whether it be really true or false, is a pedantic and
capricious limitation of our knowledge, to which the intellect of man
neither can nor should submit. If any one holds the adoption of one or
other of these theories to be indifferent, let him express the _laws
of phenomena_ of diffraction in terms of the theory of emission[255].
If any one rejects the doctrine of undulation, let him point out some
other way of connecting double refraction with polarization. And
surely no man of science will contend that the beautiful branch of
science which refers to that connexion is not a portion of our positive
knowledge.

M. Comte's contempt for the speculations of the undulationists seems
to have prevented his acquainting himself with their reasonings, and
even with the laws of phenomena on which they have reasoned, although
these form by far the most striking and beautiful addition which
Science has received in modern times. He adduces, as an insuperable
objection to the undulatory theory, a difficulty which is fully
removed by calculation in every work on the subject:--the existence
of shadow[256]. He barely mentions the subject of diffraction, and
Young's law of interferences;--speaks of Fresnel as having applied this
principle to the phenomena of coloured rings, "on which the ingenious
labours of Newton left much to desire;" as if Fresnel's labours on
this subject had been the supplement of those of Newton: and after
regretting that "this principle of interferences has not yet been
distinctly disentangled from chemical conceptions on the nature of
light," concludes his chapter. He does not even mention the phenomena
of dipolarization, of circular and elliptical polarization, or of the
optical properties of crystals; discoveries of laws of phenomena quite
as remarkable as any which can be mentioned.

M. Comte's favourite example of physical research is Thermotics, and
especially Fourier's researches with regard to heat. It is shown[257]
in the History of Thermotics, that the general phenomena of radiation
required the assumption of a fluid to express them; as appears in the
_theory of exchanges_[258]. And the explanation of the principal laws
of radiation, which Fourier gives, depends upon the conception of
material molecular radiation. The _flux_ of caloric, of which Fourier
speaks, cannot be conceived otherwise than as implying a material
flow. M. Comte apologizes[259] for this expression, as too figurative,
and says that it merely indicates a _fact_. But what is the flow of a
current of fluid except a fact? And is it not evident that without such
expressions, and the ideas corresponding to them, Fourier could neither
have conveyed nor conceived his theory?

In concluding this discussion it must be recollected, that though
it is a most narrow and untenable rule to say that we will admit no
agency of ethers and fluids into philosophy; yet the reality of such
agents is only to be held in the way, and to the extent, which the laws
of phenomena indicate. It is not only allowable, but inevitable to
assume, as the vehicle of heat and light, a medium possessing some of
the properties of more familiar kinds of matter. But the idea of such
a medium, which we possess, and on which we cannot but reason, can be
fully developed only by an assiduous study of the cases in which it is
applicable. It may be, that as science advances, all our knowledge may
converge to one general and single aspect of the universe. We abandon
and reject this hope, if we refuse to admit those ideas which must
be our stepping-stones in advancing to such a point: and we no less
frustrate such an expectation, if we allow ourselves to imagine that
from our present position we can stride at once to the summit.


4. _Causes in other Sciences._--But if it is, in the sciences just
mentioned, impracticable to reduce our knowledge to laws of phenomena
alone, without referring to causes, media, and other agencies; how much
more plainly is it impossible to confine our thoughts to phenomena,
and to laws of succession and resemblance, in other sciences, as
chemistry, physiology, and geology? Who shall forbid us, or why should
we be forbidden, to inquire whether chemical and galvanic forces are
identical; whether irritability is a peculiar vital power; whether
geological causes have been uniform or paroxysmal? To exclude such
inquiries, would be to secure ourselves from the poison of error by
abstaining from the banquet of truth:--it would be to attempt to feed
our minds with the meagre diet of space and number, because we may find
too delightful a relish in such matters as cause and end, symmetry and
affinity, organization and development.

Thus M. Comte's arrangement of the progress of science as successively
metaphysical and positive, is contrary to history in fact, and contrary
to sound philosophy in principle. Nor is there any better foundation
for his statement that theological views are to be found only in the
rude infantine condition of human knowledge, and vanish as science
advances. Even in material sciences this is not the case. We have
shown in the chapter on Final Causes, that physiologists have been
directed in their remarks by the conviction of a purpose in every
part of the structure of animals; and that this idea, which had its
rise _after_ the first observations, has gone on constantly gaining
strength and clearness, so that it is now the basis of a large portion
of the science. We have seen, too, in the Book on the palætiological
sciences, that the researches of that class do by no means lead us to
reject an origin of the series of events, nor to suppose this origin
to be included in the series of natural laws. Science has not at all
shown any reason for denying either the creation or the purpose of the
universe.

This is true of those aspects of the universe which have become the
subjects of rigorous science: but how small a portion of the whole do
they form! Especially how minute a proportion does our knowledge bear
to our ignorance, if we admit into science, as M. Comte advises, only
the laws of phenomena! Even in the best explored fields of science, how
few such laws do we know! Meteorology, climate, terrestrial magnetism,
the colours and other properties of bodies, the conditions of musical
and articulate sound, and a thousand other facts of physics, are not
defined by any known laws. In physiology we may readily convince
ourselves how little we know of laws, since we can hardly study one
species without discovering some unguessed property, or apply the
microscope without seeing some new structure in the best known organs.
And when we go on to social and moral and political matters, we may
well doubt whether any one single rigorous rule of phenomena has ever
been stated, although on such subjects man's ideas have been busily
and eagerly working ever since his origin. What a wanton and baseless
assumption it would be, then, to reject those suggestions of a Governor
of the universe which we derive from man's moral and spiritual nature,
and from the institutions of society, because we fancy we see in the
small field of our existing "positive knowledge" a tendency to exclude
"theological views!" Because we can explain the motion of the stars by
a general Law which seems to imply no hyperphysical agency, and can
trace a few more limited laws in other properties of matter, we are
exhorted to reject convictions irresistibly suggested to us by our
bodies and our souls, by history and antiquities, by conscience and
human law.


5. _M. Comte's practical philosophy._--It is not merely as a
speculative doctrine that M. Comte urges the necessity of our thus
following the guidance of "positive philosophy." The fevered and
revolutionary condition of human society at present arises, according
to him[260], from the simultaneous employment of three kinds of
philosophy radically incompatible;--theological, metaphysical, and
positive philosophy. The remedy for the evil is to reject the two
former, and to refer everything to that positive philosophy, of which
the destined triumph cannot be doubtful. In like manner, our European
education[261], still essentially theological, metaphysical, and
literary, must be replaced by a _positive_ education, suited to the
spirit of our epoch.

With these practical consequences of M. Comte's philosophy we are not
here concerned: but the notice of them may serve to show how entirely
the rejection of the theological view pervades his system; and how
closely this rejection is connected with the principles which lead
him also to reject the fundamental ideas of the sciences as we have
presented them.


6. _M. Comte on Hypotheses._--In the detail of M. Comte's work, I do
not find any peculiar or novel remarks on the induction by which the
sciences are formed; except we may notice, as such, his permission of
hypotheses to the inquirer, already referred to. "There can only be,"
he says[262], "two general modes fitted to reveal to us, in a direct
and entirely rational manner, the true law of any phenomenon;--either
the immediate analysis of this phenomenon, or its exact and evident
relation to some more extended law, previously established;--in a word,
_induction_, or _deduction_. But both these ways would certainly be
insufficient, even with regard to the simplest phenomenon, in the eyes
of any one who fully comprehends the essential difficulties of the
intimate study of nature, if we did not often begin by anticipating
the result, and making a provisory supposition, at first essentially
conjectural, even with respect to some of the notions which constitute
the final object of inquiry. Hence the introduction, which is strictly
indispensable, of hypotheses in natural philosophy." We have already
seen that the "permissio intellectus" had been noticed as a requisite
step in discovery, as long before as the time of Bacon.


7. _M. Comte's Classification of Sciences._--I do not think it
necessary to examine in detail M. Comte's views of the philosophy of
the different sciences; but it may illustrate the object of the present
work, to make a remark upon his attempt to establish a distinction
between physical and chemical science. This distinction he makes to
consist in three points[263];--that Physics considers general and
Chemistry special properties;--that Physics considers masses and
Chemistry molecules;--that in Physics the mode of arrangement of
the molecules remains constant, while in Chemistry this arrangement
is necessarily altered. M. Comte however allows that these lines
of distinction are vague and insecure; for, among many others,
magnetism, a special property, belongs to physics, and breaks down
his first criterion; and molecular attractions are a constant subject
of speculation in physics, so that the second distinction cannot be
insisted on. To which we may add that the greater portion of chemistry
does not attend at all to the arrangement of the molecules, so that
the third character is quite erroneous. The real distinction of
these branches of science is, as we have seen, the fundamental ideas
which they employ. Physics deals with relations of space, time, and
number, media, and scales of qualities, according to intensity and
other differences; while chemistry has for its subject elements and
attractions as shown in composition; and polarity, though in different
senses, belongs to both. The failure of this attempt of M. Comte at
distinguishing these provinces of science by their objects, may be
looked upon as an illustration of the impossibility of establishing a
philosophy of the sciences on any other ground than the ideas which
they involve.

We have thus traced to its extreme point, so far as the nature
of science is concerned, one of those two antagonistic opinions,
of which the struggle began in the outset of philosophy, and has
continued during the whole of her progress;--namely, the opinions
which respectively make our sensations and our ideas the origin of our
knowledge. The former, if it be consistent with itself, must consider
all knowledge of causes as impossible, since no sensation can give us
the idea of cause. And when this opinion is applied to science, it
reduces it to the mere investigation of laws of phenomena, according
to relations of space, time, and number. I purposely abstain, as far
as possible, from the consideration of the other consequences, not
strictly belonging to the physical sciences, which were drawn from
the doctrine that all our ideas are only transformed sensations. The
materialism, the atheism, the sensualist morality, the anarchical
polity, which some of the disciples of the Sensational School erected
upon the fundamental dogmas of their sect, do not belong to our
present subject, and are matters too weighty to be treated of as mere
accessories.

       *       *       *       *       *

The above Remarks were written before I had seen the third volume of M.
Comte's work, or the subsequent volumes. But I do not find, in anything
which those volumes contain, any ground for altering what I have
written. Indeed they are occupied altogether with subjects which do not
come within the field of my present speculations.


FOOTNOTES:

[Footnote 247: i. p. 14.]

[Footnote 248: i. p. 7.]

[Footnote 249: _Hist. Ind. Sc._ b. xi. c. vii.]

[Footnote 250: P. 15.]

[Footnote 251: P. 16.]

[Footnote 252: M. Comte's statement is so entirely at variance with the
fact that I must quote it here. (_Phil. Pos._ vol. i. p. 705.)

"Le second théorème général de dynamique consiste dans le célèbre et
important _principe des aires_, dont le première idée est due à Kepler,
qui découvrit et démontra forte simplement cette propriété pour le cas
du mouvement d'une molecule unique, ou en d'autres terms, d'un corps
dont tous les points se meuvent identiquement. Kepler établit, par les
considérations les plus élémentaires, qui si la force accélératrice
totale dont une molecule est animée tend constamment vers un point
fixé, le rayon vecteur du mobile décrit autour de ce point des aires
égales en temps egaux, de telle sorte que l'aire décrite au bout d'un
temps quelconque croît proportionellement à ce temps. Il fit voir en
outre que réciproquement, si une semblable relation a été vérifiée
dans le mouvement d'un corps par rapport à un certain point, c'est une
preuve suffisante de l'action sur le corps d'un force dirigée sans
cesse vers ce point."

There is not a trace of the above propositions in the work _De Stellâ
Martis_, which contains Kepler's discovery of his law, nor, I am
convinced, in any other of Kepler's works. He is everywhere constant to
his conceptions of the _magnetic_ virtue residing in the sun, by means
of which the sun, revolving on his axis, carries the planets round with
him. M. Comte's statement so exactly expresses _Newton's_ propositions,
that one is led to suspect some extraordinary mistake, by which what
should have been said of the one was transferred to the other.]

[Footnote 253: Vol. ii. p. 433.]

[Footnote 254: Vol. ii. 640.]

[Footnote 255: I venture to offer this problem;--to express the
_laws of the phenomena_ of diffraction without the hypothesis of
undulations;--as a challenge to any one who holds such hypothesis to be
unphilosophical.]

[Footnote 256: ii. p. 641.]

[Footnote 257: ii. p. 673.]

[Footnote 258: _Hist. Ind. Sc._ ii. 489, b. x. c. i.]

[Footnote 259: ii. p. 561.]

[Footnote 260: i. 50.]

[Footnote 261: i. 41.]

[Footnote 262: ii. 433.]

[Footnote 263: _Phil. Pos._ ii. 392-398.]




CHAPTER XXII.

MR. MILL'S LOGIC[264].


The _History of the Inductive Sciences_ was published in 1837, and
the _Philosophy of the Inductive Sciences_ in 1840. In 1843 Mr. Mill
published his _System of Logic_, in which he states that without the
aid derived from the facts and ideas in my volumes, the corresponding
portion of his own would most probably not have been written, and
quotes parts of what I have said with commendation. He also, however,
dissents from me on several important and fundamental points, and
argues against what I have said thereon. I conceive that it may tend
to bring into a clearer light the doctrines which I have tried to
establish, and the truth of them, if I discuss some of the differences
between us, which I shall proceed to do[265].

Mr. Mill's work has had, for a work of its abstruse character, a
circulation so extensive, and admirers so numerous and so fervent, that
it needs no commendation of mine. But if my main concern at present
had not been with the points in which Mr. Mill _differs_ from me, I
should have had great pleasure in pointing out passages, of which there
are many, in which Mr. Mill appears to me to have been very happy in
promoting or in expressing philosophical truth.

There is one portion of his work indeed which tends to give it an
interest of a wider kind than belongs to that merely scientific truth
to which I purposely and resolutely confined my speculations in the
works to which I have referred. Mr. Mill has introduced into his work
a direct and extensive consideration of the modes of dealing with
moral and political as well as physical questions; and I have no doubt
that this part of his book has, for many of his readers, a more lively
interest than any other. Such a comprehensive scheme seems to give to
doctrines respecting science a value and a purpose which they cannot
have, so long as they are restricted to mere material sciences. I still
retain the opinion, however, upon which I formerly acted, that the
philosophy of science is to be extracted from the portions of science
which are universally allowed to be most certainly established, and
that those are the physical sciences. I am very far from saying, or
thinking, that there is no such thing as Moral and Political Science,
or that no method can be suggested for its promotion; but I think that
by attempting at present to include the Moral Sciences in the same
formulæ with the Physical, we open far more controversies than we
close; and that in the moral as in the physical sciences, the first
step towards showing how truth is to be discovered, is to study some
portion of it which is assented to so as to be beyond controversy.


1. _What is Induction?_--1. Confining myself, then, to the material
sciences, I shall proceed to offer my remarks on Induction with
especial reference to Mr. Mill's work. And in order that we may, as
I have said, proceed as intelligibly as possible, let us begin by
considering what we mean by _Induction_, as a mode of obtaining truth;
and let us note whether there is any difference between Mr. Mill and me
on this subject.

"For the purposes of the present inquiry," Mr. Mill says (i. 347[266]),
"Induction may be defined the operation of discovering and forming
general propositions:" meaning, as appears by the context, the
discovery of them from particular facts. He elsewhere (i. 370) terms
it "generalization from experience:" and again he speaks of it with
greater precision as the inference of a more general proposition from
less general ones.

2. Now to these definitions and descriptions I assent as far as they
go; though, as I shall have to remark, they appear to me to leave
unnoticed a feature which is very important, and which occurs in all
cases of Induction, so far as we are concerned with it. Science, then,
consists of general propositions, inferred from particular facts, or
from less general propositions, by Induction; and it is our object to
discern the nature and laws of _Induction_ in this sense. That the
propositions are general, or are more general than the facts from which
they are inferred, is an indispensable part of the notion of Induction,
and is essential to any discussion of the process, as the mode of
arriving at Science, that is, at a body of general truths.

3. I am obliged therefore to dissent from Mr. Mill when he includes, in
his notion of Induction, the process by which we arrive _at individual
facts_ from other facts _of the same order of particularity_.

Such inference is, at any rate, not Induction _alone_; if it be
Induction at all, it is Induction applied to an example.

For instance, it is a general law, obtained by Induction from
particular facts, that a body falling vertically downwards from rest,
describes spaces proportional to the squares of the times. But that a
particular body will fall through 16 feet in one second and 64 feet in
two seconds, is not an induction simply, it is a result obtained by
applying the inductive law to a particular case.

But further, such a process is often not induction _at all_. That a
ball striking another ball directly will communicate to it as much
momentum as the striking ball itself loses, is a law established
by induction: but if, from habit or practical skill, I make one
billiard-ball strike another, so as to produce the velocity which
I wish, without knowing or thinking of the general law, the term
_Induction_ cannot then be rightly applied. If I _know the law_ and
act upon it, I have in my mind both the general induction and its
particular application. But if I act by the ordinary billiard-player's
skill, without thinking of momentum or law, there is no Induction in
the case.

4. This distinction becomes of importance, in reference to Mr. Mill's
doctrine, because he has extended his use of the term _Induction_, not
only to the cases in which the general induction is consciously applied
to a particular instance; but to the cases in which the particular
instance is dealt with by means of experience, in that rude sense in
which _experience_ can be asserted of brutes; and in which, of course,
we can in no way imagine that the law is possessed or understood, as a
general proposition. He has thus, as I conceive, overlooked the broad
and essential difference between speculative knowledge and practical
action; and has introduced cases which are quite foreign to the idea
of science, alongside with cases from which we may hope to obtain some
views of the nature of science and the processes by which it must be
formed.

5. Thus (ii. 232) he says, "This inference of one particular fact from
another is a case of induction. It is of this sort of induction that
brutes are capable." And to the same purpose he had previously said (i.
251), "He [the burnt child who shuns the fire] is not generalizing:
he is inferring a particular from particulars. In the same way also,
brutes reason ... not only the burnt child, but the burnt dog, dreads
the fire."

6. This confusion, (for such it seems to me,) of knowledge with
practical tendencies, is expressed more in detail in other places. Thus
he says (i. 118), "I cannot dig the ground unless I have an idea of the
ground and of a spade, and of all the other things I am operating upon."

7. This appears to me to be a use of words which can only tend to
confuse our idea of knowledge by obliterating all that is distinctive
in _human_ knowledge. It seems to me quite false to say that I cannot
dig the ground, unless I have an idea of the ground and of my spade.
Are we to say that we cannot _walk_ the ground, unless we have an idea
of the ground, and of our feet, and of our shoes, and of the muscles of
our legs? Are we to say that a mole cannot dig the ground, unless he
has an idea of the ground and of the snout and paws with which he digs
it? Are we to say that a pholas cannot perforate a rock, unless he have
an idea of the rock, and of the acid with which he corrodes it?

8. This appears to me, as I have said, to be a line of speculation
which can lead to nothing but confusion. The knowledge concerning which
I wish to inquire is _human_ knowledge. And in order that I may have
any chance of success in the inquiry, I find it necessary to single
out that kind of knowledge which is especially and distinctively
human. Hence, I pass by, in this part of my investigation, all the
_knowledge_, if it is to be so called, which man has in no other way
than brutes have it;--all that merely shows itself in action. For
though action may be modified by habit, and habit by experience, in
animals as well as in men, such experience, so long as it retains
that merely practical form, is no part of the materials of science.
Knowledge in a _general_ form, is alone knowledge for that purpose;
and to _that_, therefore, I must confine my attention; at least till
I have made some progress in ascertaining its nature and laws, and am
thus prepared to compare such knowledge,--_human knowledge_ properly so
called,--with mere animal tendencies to action; or even with practical
skill which does not include, as for the most part practical skill does
not include, speculative knowledge.

9. And thus, I accept Mr. Mill's definition of Induction only in its
first and largest form; and reject, as useless and mischievous for our
purposes, his extension of the term to the practical influence which
experience of one fact exercises upon a creature dealing with similar
facts. Such influence cannot be resolved into _ideas_ and _induction_,
without, as I conceive, making all our subsequent investigation vague
and heterogeneous, indefinite and inconclusive. If we must speak of
animals as _learning_ from experience, we may at least abstain from
applying to them terms which imply that they learn, in the same way
in which men learn astronomy from the stars, and chemistry from the
effects of mixture and heat. And the same may be said of the language
which is to be used concerning what _men_ learn, when their _learning_
merely shows itself in action, and does not exist as a general thought.
_Induction_ must not be applied to such cases. _Induction_ must be
confined to cases where we have in our minds general propositions, in
order that the sciences, which are our most instructive examples of the
process we have to consider, may be, in any definite and proper sense,
_Inductive_ Sciences.

10. Perhaps some persons may be inclined to say that this difference
of opinion, as to the extent of meaning which is to be given to the
term _Induction_, is a question merely of words; a matter of definition
only. This is a mode in which men in our time often seem inclined to
dispose of philosophical questions; thus evading the task of forming
an opinion upon such questions, while they retain the air of looking
at the subject from a more comprehensive point of view. But as I have
elsewhere said, such questions of definition are never questions
of definition merely. A proposition is always implied along with
the definition; and the truth of the proposition depends upon the
settlement of the definition. This is the case in the present instance.
We are speaking of _Induction_, and we mean that kind of Induction
by which the sciences now existing among men have been constructed.
On this account it is, that we cannot include, in the meaning of the
term, mere practical tendencies or practical habits; for science is not
constructed of these. No accumulation of these would make up any of the
acknowledged sciences. The elements of such sciences are something of a
kind different from practical habits. The elements of such sciences are
principles which we _know_; truths which can be contemplated as being
_true_. Practical habits, practical skill, instincts and the like,
appear in action, and in action only. Such endowments or acquirements
show themselves when the occasion for action arrives, and then, show
themselves in the act; without being put, or being capable of being
put, in the form of truths contemplated by the intellect. But the
elements and materials of Science are necessary truths contemplated by
the intellect. It is by consisting of such elements and such materials,
that Science _is_ Science. Hence a use of the term _Induction_ which
requires us to obliterate this distinction, must make it impossible for
us to arrive at any consistent and intelligible view of the nature of
Science, and of the mental process by which Sciences come into being.
We must, for the purpose which Mr. Mill and I have in common, retain
his larger and more philosophical definition of Induction,--that it is
the inference of a more general proposition from less general ones.

11. Perhaps, again, some persons may say, that practical skill and
practical experience _lead_ to science, and may therefore be included
in the term _Induction_, which describes the formation of science. But
to this we reply, that these things lead to science as occasions only,
and do not form part of science; and that science begins then only
when we look at the facts in a general point of view. This distinction
is essential to the philosophy of science. The rope-dancer may, by
his performances, suggest, to himself or to others, properties of
the center of gravity; but this is so, because man has a tendency to
speculate and to think of general truths, as well as a tendency to
dance on a rope on special occasions, and to acquire skill in such
dancing by practice. The rope-dancer does not dance by Induction,
any more than the dancing dog does. To apply the terms Science and
Induction to such cases, carries us into the regions of metaphor;
as when we call birds of passage "wise meteorologists," or the bee
"a natural chemist, who turns the flower-dust into honey." This is
very well in poetry: but for our purposes we must avoid recognizing
these cases as really belonging to the sciences of meteorology and
chemistry,--as really cases of Induction. Induction for us is general
propositions, _contemplated as such_, derived from particulars.

Science may result _from_ experience and observation _by_ Induction;
but Induction is not therefore the same thing as experience and
observation. Induction is experience or observation _consciously_
looked at in a _general_ form. This consciousness and generality are
necessary parts of that knowledge which is science. And accordingly,
on the other hand, science cannot result from mere Instinct, as
distinguished from Reason; because Instinct by its nature is not
conscious and general, but operates blindly and unconsciously in
particular cases, the actor not seeing or thinking of the rule which he
obeys.

12. A little further on I shall endeavour to show that not only a
general _thought_, but a general _word_ or phrase is a requisite
element in Induction. This doctrine, of course, still more decidedly
excludes the case of animals, and of mere practical knowledge in man.
A burnt child dreads the fire; but reason must be unfolded, before the
child learns to understand the words "fire will hurt you." The burnt
dog never thus learns to understand words. And this difference points
to an entirely different state of thought in the two cases: or rather,
to a difference between a state of rational thought on the one hand,
and of mere practical instinct on the other.

13. Besides this difference of speculative thought and practical
instinct which thus are, as appears to me, confounded in Mr. Mill's
philosophy, in such a way as tends to destroy all coherent views of
human knowledge, there is another set of cases to which Mr. Mill
applies the term _Induction_, and to which it appears to me to be
altogether inapplicable. He employs it to describe the mode in which
superstitious men, in ignorant ages, were led to the opinion that
striking natural events presaged or accompanied calamities. Thus he
says (i. 389), "The opinion so long prevalent that a comet or any
other unusual appearance in the heavenly regions was the precursor of
calamities to mankind, or at least to those who witnessed it; the
belief in the oracles of Delphi and Dodona; the reliance on astrology,
or on the weather-prophecies in almanacs; were doubtless inductions
supposed to be grounded on experience;" and he speaks of these
insufficient inductions being extinguished by the stronger inductions
subsequently obtained by scientific inquiry. And in like manner,
he says in another place (i. 367), "Let us now compare different
predictions: the first, that eclipses will occur whenever one planet
or satellite is so situated as to cast its shadow upon another: the
second, that they will occur whenever some great calamity is impending
over mankind."

14. Now I cannot see how anything but confusion can arise from
applying the term _Induction_ to superstitious fancies like those
here mentioned. They are not imperfect truths, but entire falsehoods.
Of that, Mr. Mill and I are agreed: how then can they exemplify the
progress towards truth? They were not collected from the facts by
seeking a law of their occurrence; but were suggested by an imagination
of the anger of superior powers shown by such deviations from the
ordinary course of nature. If we are to speak of _inductions_ to any
purpose, they must be such inductions as represent the facts, in some
degree at least. It is not meant, I presume, that these opinions are in
any degree true: to what purpose then are they adduced? If I were to
hold that my dreams predict or conform to the motions of the stars or
of the clouds, would this be an induction? It would be so, as much one
as those here so denominated: yet what but confusion could arise from
classing it among scientific truths? Mr. Mill himself has explained
(ii. 389) the way in which such delusions as the prophecies of
almanac-makers, and the like, obtain credence; namely, by the greater
effect which the positive instances produce on ordinary minds in
comparison with the negative, when the rule has once taken possession
of their thoughts. And this being, as he says, the recognized
explanation of such cases, why should we not leave them to their due
place, and not confound and perplex the whole of our investigation by
elevating them to the rank of "inductions"? The very condemnation of
such opinions is that they are not at all inductive. When we have made
any progress in our investigation of the nature of science, to attempt
to drive us back to the wearisome discussion of such elementary points
as these, is to make progress hopeless.


II. _Induction or Description?_--15. In the cases hitherto noticed, Mr.
Mill extends the term _Induction_, as I think, too widely, and applies
it to cases to which it is not rightly applicable. I have now to notice
a case of an opposite kind, in which he does not apply it where I do,
and condemns me for using it in such a case. I had spoken of Kepler's
discovery of the Law, that the planets move round the sun in ellipses,
as an example of Induction. The separate facts of any planet (Mars, for
instance,) being in certain places at certain times, are all included
in the general proposition which Kepler discovered, that Mars describes
an ellipse of a certain form and position. This appears to me a very
simple but a very distinct example of the operation of discovering
general propositions; general, that is, with reference to particular
facts; which operation Mr. Mill, as well as myself, says is Induction.
But Mr. Mill denies this operation in this case to be Induction at
all (i. 357). I should not have been prepared for this denial by the
previous parts of Mr. Mill's book, for he had said just before (i.
350), "such facts as the magnitudes of the bodies of the solar system,
their distances from each other, the figure of the earth and its
rotation ... are proved indirectly, by the aid of inductions founded
on other facts which we can more easily reach." If the figure of the
earth and its rotation are proved by Induction, it seems very strange,
and is to me quite incomprehensible, how the figure of the earth's
orbit and its revolution (and of course, of the figure of Mars's orbit
and his revolution in like manner,) are not also proved by Induction.
No, says Mr. Mill, Kepler, in putting together a number of places of
the planet into one figure, only performed an act of _description_.
"This descriptive operation," he adds (i. 359), "Mr. Whewell, by an
aptly chosen expression, has termed Colligation of Facts." He goes on
to commend my observations concerning this process, but says that,
according to the old and received meaning of the term, it is not
Induction at all.

16. Now I have already shown that Mr. Mill himself, a few pages
earlier, had applied the term _Induction_ to cases undistinguishable
from this in any essential circumstance. And even in this case, he
allows that Kepler did really perform an act of Induction (i. 358),
"namely, in concluding that, because the observed places of Mars were
correctly represented by points in an imaginary ellipse, therefore Mars
would continue to revolve in that same ellipse; and even in concluding
that the position of the planet during the time which had intervened
between the two observations must have coincided with the intermediate
points of the curve." Of course, in Kepler's Induction, of which I
speak, I include all this; all this is included in speaking of the
_orbit_ of Mars: a continuous line, a periodical motion, are implied
in the term _orbit_. I am unable to see what would remain of Kepler's
discovery, if we take from it these conditions. It would not only not
be an induction, but it would not be a description, for it would not
recognize that Mars moved in an orbit. Are particular positions to be
conceived as points in a curve, without thinking of the intermediate
positions as belonging to the same curve? If so, there is no law at
all, and the facts are not bound together by any intelligible tie.

In another place (ii. 209) Mr. Mill returns to his distinction of
Description and Induction; but without throwing any additional light
upon it, so far as I can see.

17. The only meaning which I can discover in this attempted distinction
of Description and Induction is, that when particular facts are bound
together by their relation in _space_, Mr. Mill calls the discovery
of the connexion _Description_, but when they are connected by other
general relations, as time, cause and the like, Mr. Mill terms the
discovery of the connexion _Induction_. And this way of making a
distinction, would fall in with the doctrine of other parts of Mr.
Mill's book, in which he ascribes very peculiar attributes to space
and its relations, in comparison with other Ideas, (as I should call
them). But I cannot see any ground for this distinction, of connexion
according to space and other connexions of facts.

To stand upon such a distinction, appears to me to be the way to miss
the general laws of the formation of science. For example: The ancients
discovered that the planets revolved in recurring periods, and thus
connected the observations of their motions according to the Idea of
_Time_. Kepler discovered that they revolved in ellipses, and thus
connected the observations according to the Idea of _Space_. Newton
discovered that they revolved in virtue of the Sun's attraction, and
thus connected the motions according to the Idea of _Force_. The first
and third of these discoveries are recognized on all hands as processes
of Induction. Why is the second to be called by a different name? or
what but confusion and perplexity can arise from refusing to class it
with the other two? It is, you say, Description. But such Description
is a kind of Induction, and must be spoken of as Induction, if we are
to speak of Induction as the process by which Science is formed: for
the three steps are all, the second in the same sense as the first
and third, in co-ordination with them, steps in the formation of
astronomical science.

18. But, says Mr. Mill (i. 363), "it is a fact surely that the planet
does describe an ellipse, and a fact which we could see if we had
adequate visual organs and a suitable position." To this I should
reply: "Let it be so; and it is a fact, surely, that the planet does
move periodically: it is a fact, surely, that the planet is attracted
by the sun. Still, therefore, the asserted distinction fails to find a
ground." Perhaps Mr. Mill would remind us that the elliptical form of
the orbit is a fact which we could see if we had adequate visual organs
and a suitable position: but that force is a thing which we cannot
see. But this distinction also will not bear handling. Can we not see
a tree blown down by a storm, or a rock blown up by gunpowder? Do we
not here see force:--see it, that is, by its effects, the only way in
which we need to see it in the case of a planet, for the purposes of
our argument? Are not such operations of force, Facts which may be the
objects of sense? and is not the operation of the sun's Force a Fact
of the same kind, just as much as the elliptical form of orbit which
results from the action? If the latter be "surely a Fact," the former
is a Fact no less surely.

19. In truth, as I have repeatedly had occasion to remark, all attempts
to frame an argument by the exclusive or emphatic appropriation of
the term _Fact_ to particular cases, are necessarily illusory and
inconclusive. There is no definite and stable distinction between Facts
and Theories; Facts and Laws; Facts and Inductions. Inductions, Laws,
Theories, which are true, _are_ Facts. Facts involve Inductions. It is
a fact that the moon is attracted by the earth, just as much as it is a
Fact that an apple falls from a tree. That the former fact is collected
by a more distinct and conscious Induction, does not make it the less
a Fact. That the orbit of Mars is a Fact--a true Description of the
path--does not make it the less a case of Induction.

20. There is another argument which Mr. Mill employs in order to
show that there is a difference between mere colligation which is
description, and induction in the more proper sense of the term. He
notices with commendation a remark which I had made (i. 364), that
at different stages of the progress of science the facts had been
successfully connected by means of very different conceptions, while
yet the later conceptions have not contradicted, but included, so far
as they were true, the earlier: thus the ancient Greek representation
of the motions of the planets by means of epicycles and eccentrics,
was to a certain degree of accuracy true, and is not negatived, though
superseded, by the modern representation of the planets as describing
ellipses round the sun. And he then reasons that this, which is thus
true of Descriptions, cannot be true of Inductions. He says (i. 367),
"Different descriptions therefore may be all true: but surely not
different explanations." He then notices the various explanations of
the motions of the planets--the ancient doctrine that they are moved
by an inherent virtue; the Cartesian doctrine that they are moved by
impulse and by vortices; the Newtonian doctrine that they are governed
by a central force; and he adds, "Can it be said of these, as was said
of the different descriptions, that they are all true as far as they
go? Is it not true that one only can be true in any degree, and that
the other two must be altogether false?"

21. And to this questioning, the history of science compels me to reply
very distinctly and positively, in the way which Mr. Mill appears to
think extravagant and absurd. I am obliged to say, Undoubtedly, all
these explanations _may_ be true and consistent with each other, and
would be so if each had been followed out so as to show in what manner
it could be made consistent with the facts. And this was, in reality,
in a great measure done[267]. The doctrine that the heavenly bodies
were moved by vortices was successively modified, so that it came to
coincide in its results with the doctrine of an inverse-quadratic
centripetal force, as I have remarked in the _History_[268]. When this
point was reached, the vortex was merely a machinery, well or ill
devised, for producing such a centripetal force, and therefore did not
contradict the doctrine of a centripetal force. Newton himself does
not appear to have been averse to explaining gravity by impulse. So
little is it true that if the one theory be true the other must be
false. The attempt to explain gravity by the impulse of streams of
particles flowing through the universe in all directions, which I have
mentioned in the _Philosophy_[269] so far from being inconsistent
with the Newtonian theory, that it is founded entirely upon it. And
even with regard to the doctrine, that the heavenly bodies move by
an inherent virtue; if this doctrine had been maintained in any such
way that it was brought to agree with the facts, the inherent virtue
must have had its laws determined; and then, it would have been found
that the virtue had a reference to the central body; and so, the
"inherent virtue" must have coincided in its effect with the Newtonian
force; and then, the two explanations would agree, except so far as
the word "inherent" was concerned. And if such a part of an earlier
theory as this word _inherent_ indicates, is found to be untenable,
it is of course rejected in the transition to later and more exact
theories, in Inductions of this kind, as well as in what Mr. Mill calls
Descriptions. There is therefore still no validity discoverable in the
distinction which Mr. Mill attempts to draw between "descriptions" like
Kepler's law of elliptical orbits, and other examples of induction.

22. When Mr. Mill goes on to compare what he calls different
predictions--the first, the true explanation of eclipses by the shadows
which the planets and satellites cast upon one another, and the
other, the belief that they will occur whenever some great calamity
is impending over mankind, I must reply, as I have stated already,
(Art. 17), that to class such superstitions as the last with cases of
Induction, appears to me to confound all use of words, and to prevent,
as far as it goes, all profitable exercise of thought. What possible
advantage can result from comparing (as if they were alike) the
relation of two descriptions of a phenomenon, each to a certain extent
true, and therefore both consistent, with the relation of a scientific
truth to a false and baseless superstition?

23. But I may make another remark on this example, so strangely
introduced. If, under the influence of fear and superstition, men
may make such mistakes with regard to laws of nature, as to imagine
that eclipses portend calamities, are they quite secure from mistakes
in _description_? Do not the very persons who tell us how eclipses
predict disasters, also describe to us fiery swords seen in the air,
and armies fighting in the sky? So that even in this extreme case,
at the very limit of the rational exercise of human powers, there is
nothing to distinguish Description from Induction.

I shall now leave the reader to judge whether this feature in the
history of science,--that several views which appear at first quite
different are yet all true,--which Mr. Mill calls a curious and
interesting remark of mine, and which he allows to be "strikingly true"
of the Inductions which he calls _Descriptions_, (i. 364) is, as he
says, "unequivocally false" of other Inductions. And I shall confide
in having general assent with me, when I continue to speak of Kepler's
_Induction_ of the elliptical orbits.

I now proceed to another remark.


III. _In Discovery a new Conception is introduced._--

24. There is a difference between Mr. Mill and me in our view of the
essential elements of this Induction of Kepler, which affects all other
cases of Induction, and which is, I think, the most extensive and
important of the differences between us. I must therefore venture to
dwell upon it a little in detail.

I conceive that Kepler, in discovering the law of Mars's motion,
and in asserting that the planet moved in an ellipse, did this;--he
bound together particular observations of separate places of Mars
by the notion, or, as I have called it, the _conception_, of an
_ellipse_, which was supplied by his own mind. Other persons, and he
too, before he made this discovery, had present to their minds the
facts of such separate successive positions of the planet; but could
not bind them together rightly, because they did not apply to them
this conception of an _ellipse_. To supply this conception, required
a special preparation, and a special activity in the mind of the
discoverer. He, and others before him, tried other ways of connecting
the special facts, none of which fully succeeded. To discover such
a connexion, the mind must be conversant with certain relations of
space, and with certain kinds of figures. To discover the right figure
was a matter requiring research, invention, resource. To hit upon
the right conception is a difficult step; and when this step is once
made, the facts assume a different aspect from what they had before:
that done, they are seen in a new point of view; and the catching
this point of view, is a special mental operation, requiring special
endowments and habits of thought. Before this, the facts are seen as
detached, separate, lawless; afterwards, they are seen as connected,
simple, regular; as parts of one general fact, and thereby possessing
innumerable new relations before unseen. Kepler, then, I say, bound
together the facts by superinducing upon them the _conception_ of an
_ellipse_; and this was an essential element in his Induction.

25. And there is the same essential element in all Inductive
discoveries. In all cases, facts, before detached and lawless, are
bound together by a new thought. They are reduced to law, by being
seen in a new point of view. To catch this new point of view, is an
act of the mind, springing from its previous preparation and habits.
The facts, in other discoveries, are brought together according to
other relations, or, as I have called them, _Ideas_;--the Ideas of
Time, of Force, of Number, of Resemblance, of Elementary Composition,
of Polarity, and the like. But in all cases, the mind performs the
operation by an apprehension of some such relations; by singling out
the one true relation; by combining the apprehension of the true
relation with the facts; by applying to them the Conception of such a
relation.

26. In previous writings, I have not only stated this view generally,
but I have followed it into detail, exemplifying it in the greater part
of the History of the principal Inductive Sciences in succession. I
have pointed out what are the Conceptions which have been introduced in
every prominent discovery in those sciences; and have noted to which of
the above Ideas, or of the like Ideas, each belongs. The performance
of this task is the office of the greater part of my _Philosophy
of the Inductive Sciences_. For that work is, in reality, no less
historical than the _History_ which preceded it. The _History of the
Inductive Sciences_ is the history of the discoveries, mainly so far
as concerns the _Facts_ which were brought together to form sciences.
The _Philosophy_ is, in the first ten Books, the history of the _Ideas_
and _Conceptions_, by means of which the facts were connected, so as
to give rise to scientific truths. It would be easy for me to give a
long list of the Ideas and Conceptions thus brought into view, but
I may refer any reader who wishes to see such a list, to the Tables
of Contents of the _History_, and of the first ten Books of the
_Philosophy_.

27. That these Ideas and Conceptions are really distinct elements of
the scientific truths thus obtained, I conceive to be proved beyond
doubt, not only by considering that the discoveries never were made,
nor could be made, till the right Conception was obtained, and by
seeing how difficult it often was to obtain this element; but also, by
seeing that the Idea and the Conception itself, as distinct from the
Facts, was, in almost every science, the subject of long and obstinate
controversies;--controversies which turned upon the possible relations
of Ideas, much more than upon the actual relations of Facts. The first
ten Books of the _Philosophy_ to which I have referred, contain the
history of a great number of these controversies. These controversies
make up a large portion of the history of each science; a portion quite
as important as the study of the facts; and a portion, at every stage
of the science, quite as essential to the progress of truth. Men, in
seeking and obtaining scientific knowledge, have always shown that they
found the formation of right conceptions in their own minds to be an
essential part of the process.

28. Moreover, the presence of a Conception of the mind as a special
element of the inductive process, and as the tie by which the
particular facts are bound together, is further indicated, by there
being some special new _term_ or _phrase_ introduced in every
induction; or at least some term or phrase thenceforth steadily
applied to the facts, which had not been applied to them before; as
when Kepler asserted that Mars moved round the sun in an _elliptical
orbit_, or when Newton asserted that the planets _gravitate_ towards
the sun; these new terms, _elliptical orbit_, and _gravitate_, mark
the new conceptions on which the inductions depend. I have in the
_Philosophy_[270] further illustrated this application of "technical
terms," that is, fixed and settled terms, in every inductive discovery;
and have spoken of their use in enabling men to proceed from each such
discovery to other discoveries more general. But I notice these terms
here, for the purpose of showing the existence of a conception in the
discoverer's mind, corresponding to the term thus introduced; which
conception, the term is intended to convey to the minds of those to
whom the discovery is communicated.

29. But this element of discovery,--right conceptions supplied by
the mind in order to bind the facts together,--Mr. Mill denies to be
an element at all. He says, of Kepler's discovery of the elliptical
orbit (i. 363), "It superadded nothing to the particular facts
which it served to bind together;" yet he adds, "except indeed the
knowledge that a resemblance existed between the planetary orbit
and other ellipses;" that is, except the knowledge that it _was_ an
ellipse;--precisely the circumstance in which the discovery consisted.
Kepler, he says, "asserted as a fact that the planet moved in an
ellipse. But this fact, which Kepler did not add to, but found in the
motion of the planet ... was the very fact, the separate parts of
which had been separately observed; it was the sum of the different
observations."

30. That the fact of the elliptical motion was not merely the _sum_ of
the different observations, is plain from this, that other persons, and
Kepler himself before his discovery, did not find it by adding together
the observations. The fact of the elliptical orbit was not the sum of
the observations _merely_; it was the sum of the observations, _seen
under a new point of view_, which point of view Kepler's mind supplied.
Kepler found it in the facts, because it was there, no doubt, for one
reason; but also, for another, because he had, in his mind, those
relations of thought which enabled him to find it. We may illustrate
this by a familiar analogy. We too find the law in Kepler's book; but
if we did not understand Latin, we should not find it there. We must
learn Latin in order to find the law in the book. In like manner, a
discoverer must know the language of science, as well as look at the
book of nature, in order to find scientific truth. All the discussions
and controversies respecting Ideas and Conceptions of which I have
spoken, may be looked upon as discussions and controversies respecting
the grammar of the language in which nature speaks to the scientific
mind. Man is the _Interpreter_ of Nature; not the Spectator merely,
but the Interpreter. The study of the language, as well as the mere
sight of the characters, is requisite in order that we may read the
inscriptions which are written on the face of the world. And this
study of the language of nature, that is, of the necessary coherencies
and derivations of the relations of phenomena, is to be pursued by
examining Ideas, as well as mere phenomena;--by tracing the formation
of Conceptions, as well as the accumulation of Facts. And this is what
I have tried to do in the books already referred to.

31. Mr. Mill has not noticed, in any considerable degree, what I have
said of the formation of the Conceptions which enter into the various
sciences; but he has, in general terms, denied that the Conception is
anything different from the facts themselves. "If," he says (i. 301),
"the facts are rightly classed under the conceptions, it is because
there is in the facts themselves, something of which the conception
is a copy." But it is a copy which cannot be made by a person without
peculiar endowments; just as a person cannot copy an ill-written
inscription, so as to make it convey sense, unless he understand the
language. "Conceptions," Mr. Mill says (ii. 217), "do not develope
themselves from within, but are impressed from without." But what comes
from without is not enough: they must have both origins, or they cannot
make knowledge. "The conception," he says again (ii. 221), "is not
furnished _by_ the mind till it has been furnished _to_ the mind." But
it is furnished to the mind by its own activity, operating according to
its own laws. No doubt, the conception may be formed, and in cases of
discovery, must be formed, by the suggestion and excitement which the
facts themselves produce; and must be so moulded as to agree with the
facts. But this does not make it superfluous to examine, out of what
_materials_ such conceptions are formed, and _how_ they are capable of
being moulded so as to express laws of nature; especially, when we see
how large a share this part of discovery--the examination how our ideas
can be modified so as to agree with nature,--holds, in the history of
science.

32. I have already (Art. 28) given, as evidence that the conception
enters as an element in every induction, the constant introduction
in such cases, of a new fixed term or phrase. Mr. Mill (ii. 282)
notices this introduction of a new phrase in such cases as important,
though he does not appear willing to allow that it is necessary. Yet
the necessity of the conception at least, appears to result from the
considerations which he puts forward. "What darkness," he says, "would
have been spread over geometrical demonstration, if wherever the word
_circle_ is used, the definition of a circle was inserted instead of
it." "If we want to make a particular combination of ideas permanent
in the mind, there is nothing which clenches it like a name specially
devoted to express it." In my view, the new conception is the _nail_
which connects the previous notions, and the name, as Mr. Mill says,
_clenches_ the junction.

33. I have above (Art. 30) referred to the difficulty of getting
hold of the right conception, as a proof that induction is not a
mere juxtaposition of facts. Mr. Mill does not dispute that it is
often difficult to hit upon the right conception. He says (i. 360),
"that a conception of the mind is introduced, is indeed most certain,
and Mr. Whewell has rightly stated elsewhere, that to hit upon the
right conception is often a far more difficult, and more meritorious
achievement, than to prove its applicability when obtained. But," he
adds, "a conception implies and corresponds to something conceived; and
although the conception itself is not in the facts, but in our mind, it
must be a conception of something which really is in the facts." But to
this I reply, that its being really in the facts, does not help us at
all towards knowledge, if we cannot see it there. As the poet says,

    It is the mind that sees: the outward eyes
    Present the object, but the mind descries.

And this is true of the sight which produces knowledge, as well as of
the sight which produces pleasure and pain, which is referred to in the
Tale.

34. Mr. Mill puts his view, as opposed to mine, in various ways, but,
as will easily be understood, the answers which I have to offer are
in all cases nearly to the same effect. Thus, he says (ii. 216), "the
tardy development of several of the physical sciences, for example,
of Optics, Electricity, Magnetism, and the higher generalizations of
Chemistry, Mr. Whewell ascribes to the fact that mankind had not yet
possessed themselves of the idea of Polarity, that is, of opposite
properties in opposite directions. But what was there to suggest such
an idea, until by a separate examination of several of these different
branches of knowledge it was shown that the facts of each of them did
present, in some instances at least, the curious phenomena of opposite
properties in opposite directions?" But on this I observe, that these
facts did not, nor do yet, present this conception to ordinary minds.
The opposition of properties, and even the opposition of directions,
which are thus apprehended by profound cultivators of science, are
of an abstruse and recondite kind; and to conceive any one kind of
polarity in its proper generality, is a process which few persons
hitherto appear to have mastered; still less, have men in general
come to conceive of them all as modifications of a general notion of
Polarity. The description which I have given of Polarity in general,
"opposite properties in opposite directions," is of itself a very
imperfect account of the manner in which corresponding antitheses are
involved in the portions of science into which Polar relations enter.
In excuse of its imperfection, I may say, that I believe it is the
first attempt to define Polarity in general; but yet, the conception
of Polarity has certainly been strongly and effectively present in the
minds of many of the sagacious men who have discovered and unravelled
polar phenomena. They attempted to convey this conception, each in his
own subject, sometimes by various and peculiar expressions, sometimes
by imaginary mechanism by which the antithetical results were produced;
their mode of expressing themselves being often defective or imperfect,
often containing what was superfluous; and their meaning was commonly
very imperfectly apprehended by most of their hearers and readers.
But still, the conception was there, gradually working itself into
clearness and distinctness, and in the mean time, directing their
experiments, and forming an essential element of their discoveries. So
far would it be from a sufficient statement of the case to say, that
they conceived polarity because they saw it;--that they saw it as soon
as it came into view;--and that they described it as they saw it.

35. The way in which such conceptions acquire clearness and
distinctness is often by means of Discussions of Definitions. To define
well a thought which already enters into trains of discovery, is often
a difficult matter. The business of such definition is a part of the
business of discovery. These, and other remarks connected with these,
which I had made in the _Philosophy_, Mr. Mill has quoted and adopted
(ii. 242). They appear to me to point very distinctly to the doctrine
to which he refuses his assent,--that there is a special process in the
mind, in addition to the mere observation of facts, which is necessary
at every step in the progress of knowledge. The Conception must be
_formed_ before it can be _defined_. The Definition gives the last
stamp of distinctness to the Conception; and enables us to express, in
a compact and lucid form, the new scientific propositions into which
the new Conception enters.

36. Since Mr. Mill assents to so much of what has been said in the
_Philosophy_, with regard to the process of scientific discovery, how,
it may be asked, would he express these doctrines so as to exclude that
which he thinks erroneous? If he objects to our saying that when we
obtain a new inductive truth, we connect phenomena by applying to them
a new Conception which fits them, in what terms would he describe the
process? If he will not agree to say, that in order to discover the law
of the facts, we must find an appropriate Conception, what language
would he use instead of this? This is a natural question; and the
answer cannot fail to throw light on the relation in which his views
and mine stand to each other.

Mr. Mill would say, I believe, that when we obtain a new inductive law
of facts, we find something in which the facts _resemble each other_;
and that the business of making such discoveries is the business of
discovering such resemblances. Thus, he says (of me,) (ii. 211),
"his Colligation of Facts by means of appropriate Conceptions, is
but the ordinary process of finding by a comparison of phenomena, in
what consists their agreement or resemblance." And the Methods of
experimental Inquiry which he gives (i. 450, &c.), proceed upon the
supposition that the business of discovery may be thus more properly
described.

37. There is no doubt that when we discover a law of nature by
induction, we find some point in which all the particular facts agree.
All the orbits of the planets agree in being ellipses, as Kepler
discovered; all falling bodies agree in being acted on by a uniform
force, as Galileo discovered; all refracted rays agree in having
the sines of incidence and refraction in a constant ratio, as Snell
discovered; all the bodies in the universe agree in attracting each
other, as Newton discovered; all chemical compounds agree in being
constituted of elements in definite proportions, as Dalton discovered.
But it appears to me a most scanty, vague, and incomplete account of
these steps in science, to say that the authors of them discovered
something in which the facts in each case agreed. The point in which
the cases agree, is of the most diverse kind in the different cases--in
some, a relation of space, in others, the action of a force, in others,
the mode of composition of a substance;--and the point of agreement,
visible to the discoverer alone, does not come even into his sight,
till after the facts have been connected by thoughts of his own, and
regarded in points of view in which he, by his mental acts, places
them. It would seem to me not much more inappropriate to say, that an
officer, who disciplines his men till they move together at the word of
command, does so by finding something in which they agree. If the power
of consentaneous motion did not exist in the individuals, he could not
create it: but that power being there, he finds it and uses it. Of
course I am aware that the parallel of the two cases is not exact; but
in the one case, as in the other, that in which the particular things
are found to agree, is something formed in the mind of him who brings
the agreement into view.


IV. _Mr. Mill's Four Methods of Inquiry._--38. Mr. Mill has not only
thus described the business of scientific discovery; he has also given
rules for it, founded on this description. It may be expected that we
should bestow some attention upon the methods of inquiry which he thus
proposes. I presume that they are regarded by his admirers as among the
most valuable parts of his book; as certainly they cannot fail to be,
if they describe methods of scientific inquiry in such a manner as to
be of use to the inquirer.

Mr. Mill enjoins four methods of experimental inquiry, which he calls
_the Method of Agreement_, _the Method of Difference_, _the Method
of Residues_, and _the Method of Concomitant Variations_[271]. They
are all described by formulæ of this kind:--Let there be, in the
observed facts, combinations of antecedents, _ABC_, _BC_, _ADE_, &c.
and combinations of corresponding consequents, _abc_, _bc_, _ade_, &c.;
and let the object of inquiry be, the consequence of some cause _A_, or
the cause of some consequence _a_. The Method of Agreement teaches us,
that when we find by experiment such facts as _abc_ the consequent of
_ABC_, and _ade_ the consequent of _ADE_, then _a_ is the consequent of
_A_. The Method of Difference teaches us that when we find such facts
as _abc_ the consequent of _ABC_, and _bc_ the consequent of _BC_, then
_a_ is the consequent of _A_. The Method of Residues teaches us, that
if _abc_ be the consequent of _ABC_, and if we have already ascertained
that the effect of _A_ is _a_, and the effect of _B_ is _b_, then we
may infer that the effect of _C_ is _c_. The Method of Concomitant
Variations teaches us, that if a phenomenon _a_ varies according as
another phenomenon _A_ varies, there is some connexion of causation
direct or indirect, between _A_ and _a_.

39. Upon these methods, the obvious thing to remark is, that they take
for granted the very thing which is most difficult to discover, the
reduction of the phenomena to formulæ such as are here presented to
us. When we have any set of complex facts offered to us; for instance,
those which were offered in the cases of discovery which I have
mentioned,--the facts of the planetary paths, of falling bodies, of
refracted rays, of cosmical motions, of chemical analysis; and when, in
any of these cases, we would discover the law of nature which governs
them, or, if any one chooses so to term it, the feature in which all
the cases agree, where are we to look for our _A_, _B_, _C_ and _a_,
_b_, _c_? Nature does not present to us the cases in this form; and
how are we to reduce them to this form? You say, _when_ we find the
combination of _ABC_ with _abc_ and _ABD_ with _abd_, then we may
draw our inference. Granted: but when and where are we to find such
combinations? Even now that the discoveries are made, who will point
out to us what are the _A_, _B_, _C_ and _a_, _b_, _c_ elements of the
cases which have just been enumerated? Who will tell us which of the
methods of inquiry those historically real and successful inquiries
exemplify? Who will carry these formulæ through the history of the
sciences, as they have really grown up; and show us that these four
methods have been operative in their formation; or that any light is
thrown upon the steps of their progress by reference to these formulæ?

40. Mr. Mill's four methods have a great resemblance to Bacon's
"Prerogatives of Instances;" for example, the Method of Agreement to
the _Instantiæ Ostensivæ_; the Method of Differences to the _Instantiæ
Absentiæ in Proximo_, and the _Instantiæ Crucis_; the Method of
Concomitant Variations to the _Instantiæ Migrantes_. And with regard to
the value of such methods, I believe all study of science will convince
us more and more of the wisdom of the remarks which Sir John Herschel
has made upon them[272].

"It has always appeared to us, we must confess, that the help which
the classification of instances under their different titles of
prerogative, affords to inductions, however just such classification
may be in itself, is yet more apparent than real. The force of the
instance must be felt in the mind before it can be referred to
its place in the system; and before it can be either referred or
appreciated it must be known; and when it _is_ appreciated, we are
ready enough to weave our web of induction, without greatly troubling
ourselves whence it derives the weight we acknowledge it to have in our
decisions.... No doubt such instances as these are highly instructive;
but the difficulty in physics is to find such, not to perceive their
force when found."


V. _His Examples._--41. If Mr. Mill's four methods had been applied by
him in his book to a large body of conspicuous and undoubted examples
of discovery, well selected and well analysed, extending along the
whole history of science, we should have been better able to estimate
the value of these methods. Mr. Mill has certainly offered a number
of examples of his methods; but I hope I may say, without offence,
that they appear to me to be wanting in the conditions which I have
mentioned. As I have to justify myself for rejecting Mr. Mill's
criticism of doctrines which I have put forward, and examples which I
have adduced, I may, I trust, be allowed to offer some critical remarks
in return, bearing upon the examples which he has given, in order to
illustrate his doctrines and precepts.

42. The first remark which I have to make is, that a large proportion
of his examples (i. 480, &c.) is taken from one favourite author;
who, however great his merit may be, is too recent a writer to have
had his discoveries confirmed by the corresponding investigations and
searching criticisms of other labourers in the same field, and placed
in their proper and permanent relation to established truths; these
alleged discoveries being, at the same time, principally such as deal
with the most complex and slippery portions of science, the laws of
vital action. Thus Mr. Mill has adduced, as examples of discoveries,
Prof. Liebig's doctrine--that death is produced by certain metallic
poisons through their forming indecomposable compounds; that the effect
of respiration upon the blood consists in the conversion of peroxide
of iron into protoxide--that the antiseptic power of salt arises from
its attraction for moisture--that chemical action is contagious; and
others. Now supposing that we have no doubt of the truth of these
discoveries, we must still observe that they cannot wisely be cited,
in order to exemplify the nature of the progress of knowledge, till
they have been verified by other chemists, and worked into their places
in the general scheme of chemistry; especially, since it is tolerably
certain that in the process of verification, they will be modified and
more precisely defined. Nor can I think it judicious to take so large
a proportion of our examples from a region of science in which, of all
parts of our material knowledge, the conceptions both of ordinary
persons, and even of men of science themselves, are most loose and
obscure, and the genuine principles most contested; which is the case
in physiology. It would be easy, I think, to point out the vague and
indeterminate character of many of the expressions in which the above
examples are propounded, as well as their doubtful position in the
scale of chemical generalization; but I have said enough to show why I
cannot give much weight to these, as cardinal examples of the method
of discovery; and therefore I shall not examine in detail how far they
support Mr. Mill's methods of inquiry.

43. Mr. Liebig supplies the first and the majority of Mr. Mill's
examples in chapter IX. of his Book on Induction. The second is
an example for which Mr. Mill states himself to be indebted to
Mr. Alexander Bain; the law established being this, that (i. 487)
electricity cannot exist in one body without the simultaneous
excitement of the opposite electricity in some neighbouring body, which
Mr. Mill also confirms by reference to Mr. Faraday's experiments on
voltaic wires.

I confess I am quite at a loss to understand what there is in the
doctrine here ascribed to Mr. Bain which was not known to the
electricians who, from the time of Franklin, explained the phenomena of
the Leyden vial. I may observe also that the mention of an "electrified
atmosphere" implies a hypothesis long obsolete. The essential point in
all those explanations was, that each electricity produced by induction
the opposite electricity in neighbouring bodies, as I have tried to
make apparent in the _History_[273]. Faraday has, more recently,
illustrated this universal co-existence of opposite electricities with
his usual felicity.

But the conjunction of this fact with voltaic phenomena, implies a
non-recognition of some of the simplest doctrines of the subject.
"Since," it is said (i. 488), "common or machine electricity, and
voltaic electricity may be considered for the present purpose to be
identical, Faraday wished to know, &c." I think Mr. Faraday would be
much astonished to learn that he considered electricity in equilibrium,
and electricity in the form of a voltaic current, to be, for any
purpose, identical. Nor do I conceive that he would assent to the
expression in the next page, that "from the nature of a voltaic charge,
the two opposite currents necessary to the existence of each other are
both accommodated in one wire." Mr. Faraday has, as it appears to me,
studiously avoided assenting to this hypothesis.

44. The next example is the one already so copiously dwelt upon by Sir
John Herschel, Dr. Wells's researches on the production of Dew. I have
already said[274] that "this investigation, although it has sometimes
been praised as an original discovery, was in fact only resolving the
phenomenon into principles already discovered namely, the doctrine of a
_constituent temperature_ of vapour, the different conducting power of
different bodies, and the like. And this agrees in substance with what
Mr. Mill says (i. 497); that the discovery, when made, was corroborated
by deduction from the known laws of aqueous vapour, of conduction, and
the like. Dr. Wells's researches on Dew tended much in this country
to draw attention to the general principles of Atmology; and we may
see, in this and in other examples which Mr. Mill adduces, that the
explanation of special phenomena by means of general principles,
already established, has, for common minds, a greater charm, and
is more complacently dwelt on, than the discovery of the general
principles themselves.

45. The next example, (i. 502) is given in order to illustrate the
Method of Residues, and is the discovery by M. Arago that a disk
of copper affects the vibrations of the magnetic needle. But this
apparently detached fact affords little instruction compared with the
singularly sagacious researches by which Mr. Faraday discovered the
cause of this effect to reside in the voltaic currents which the motion
of the magnetic needle developed in the copper. I have spoken of this
discovery in the _History_[275]. Mr. Mill however is quoting Sir John
Herschel in thus illustrating the Method of Residues. He rightly gives
the Perturbations of the Planets and Satellites as better examples of
the method[276].

46. In the next chapter (c. x.) Mr. Mill speaks of Plurality of causes
and of the Intermixture of effects, and gives examples of such cases.
He here teaches (i. 517) that chemical synthesis and analysis, (as when
oxygen and hydrogen compose water, and when water is resolved into
oxygen and hydrogen,) is properly _transformation_, but that because we
find that the weight of the compound is equal to the sum of the weights
of the elements, we take up the notion of chemical _composition_. I
have endeavoured to show[277] that the maxim, that the sum of the
weights of the elements is equal to the weight of the compound, was,
historically, not _proved_ from experiment, but _assumed_ in the
reasonings upon experiments.

47. I have now made my remarks upon nearly all the examples which Mr.
Mill gives of scientific inquiry, so far as they consist of knowledge
which has really been obtained. I may mention, as points which
appear to me to interfere with the value of Mr. Mill's references to
examples, expressions which I cannot reconcile with just conceptions
of scientific truth; as when he says (i. 523), "some other force which
_impinges on_ the first force;" and very frequently indeed, of the
"tangential _force_," as co-ordinate with the centripetal force.

When he speaks (ii. 20, Note) of "the doctrine now universally received
that the earth is a great natural magnet with two poles," he does not
recognize the recent theory of Gauss, so remarkably coincident with a
vast body of facts[278]. Indeed in his statement, he rejects no less
the earlier views proposed by Halley, theorized by Euler, and confirmed
by Hansteen, which show that we are compelled to assume at least _four_
poles of terrestrial magnetism; which I had given an account of in the
first edition of the _History_.

There are several other cases which he puts, in which, the knowledge
spoken of not having been yet acquired, he tells us how he would
set about acquiring it; for instance, if the question were (i. 526)
whether mercury be a cure for a given disease; or whether the brain be
a voltaic pile (ii. 21); or whether the moon be inhabited (ii. 100);
or whether all crows are black (ii. 124); I confess that I have no
expectation of any advantage to philosophy from discussions of this
kind.

48. I will add also, that I do not think any light can be thrown upon
scientific methods, at present, by grouping along with such physical
inquiries as I have been speaking of, speculations concerning the
human mind, its qualities and operations. Thus he speaks (i. 508) of
human characters, as exemplifying the effect of plurality of causes;
of (i. 518) the phenomena of our mental nature, which are analogous to
chemical rather than to dynamical phenomena; of (i. 518) the reason why
susceptible persons are imaginative; to which I may add, the passage
where he says (i. 444), "let us take as an example of a phenomenon
which we have no means of fabricating artificially, a human mind."
These, and other like examples, occur in the part of his work in which
he is speaking of scientific inquiry in general, not in the Book on the
Logic of the Moral Sciences; and are, I think, examples more likely to
lead us astray than to help our progress, in discovering the laws of
Scientific Inquiry, in the ordinary sense of the term.


VI. _Mr. Mill against Hypothesis._--49. I will now pass from Mr. Mill's
methods, illustrated by such examples as those which I have been
considering, to the views respecting the conditions of Scientific
Induction to which I have been led, by such a survey as I could
make, of the whole history of the principal Inductive Sciences; and
especially, to those views to which Mr. Mill offers his objections[279].

Mr. Mill thinks that I have been too favourable to the employment
of hypotheses, as means of discovering scientific truth; and that
I have countenanced a laxness of method, in allowing hypotheses to
be established, merely in virtue of the accordance of their results
with the phenomena. I believe I should be as cautious as Mr. Mill, in
accepting mere hypothetical explanations of phenomena, in any case in
which we had the phenomena, and their relations, placed before both of
us in an equally clear light. I have not accepted the Undulatory theory
of Heat, though recommended by so many coincidences and analogies[280].
But I see some grave reasons for not giving any great weight to Mr.
Mill's admonitions;--reasons drawn from the language which he uses on
the subject, and which appears to me inconsistent with the conditions
of the cases to which he applies it. Thus, when he says (ii. 22) that
the condition of a hypothesis accounting for all the known phenomena
is "often fulfilled equally well by two conflicting hypotheses," I can
only say that I know of no such case in the history of Science, where
the phenomena are at all numerous and complicated; and that if such
a case were to occur, one of the hypotheses might always be resolved
into the other. When he says, that "this evidence (the agreement of the
results of the hypothesis with the phenomena) cannot be of the smallest
value, because we cannot have in the case of such an hypothesis the
assurance that if the hypothesis be false it must lead to results at
variance with the true facts," we must reply, with due submission, that
we have, in the case spoken of, the most complete evidence of this;
for any change in the hypothesis would make it incapable of accounting
for the facts. When he says that "if we give ourselves the license
of inventing the causes as well as their laws, a person of fertile
imagination might devise a hundred modes of accounting for any given
fact;" I reply, that the question is about accounting for a large and
complex series of facts, of which the laws have been ascertained: and
as a test of Mr. Mill's assertion, I would propose as a challenge to
any person of fertile imagination to devise any _one_ other hypothesis
to account for the perturbations of the moon, or the coloured fringes
of shadows, besides the hypothesis by which they have actually been
explained with such curious completeness. This challenge has been
repeatedly offered, but never in any degree accepted; and I entertain
no apprehension that Mr. Mill's supposition will ever be verified by
such a performance.

50. I see additional reason for mistrusting the precision of Mr. Mill's
views of that accordance of phenomena with the results of a hypothesis,
in several others of the expressions which he uses (ii. 23). He speaks
of a hypothesis being a "_plausible_ explanation of all or most of the
phenomena;" but the case which we have to consider is where it gives an
_exact_ representation of all the phenomena in which its results can be
traced. He speaks of its being certain that the laws of the phenomena
are "_in some measure analogous_" to those given by the hypothesis; the
case to be dealt with being, that they are in every way identical. He
speaks of this analogy being certain, from the fact that the hypothesis
can be "for a moment _tenable_;" as if any one had recommended a
hypothesis which is tenable only while a small part of the facts
are considered, when it is inconsistent with others which a fuller
examination of the case discloses. I have nothing to say, and have said
nothing, in favour of hypotheses which are _not_ tenable. He says there
are many such "_harmonies_ running through the laws of phenomena in
other respects radically distinct;" and he gives as an instance, the
laws of light and heat. I have never alleged such harmonies as grounds
of theory, unless they should amount to identities; and if they should
do this, I have no doubt that the most sober thinkers will suppose
the causes to be of the same kind in the two harmonizing instances.
If chlorine, iodine and brome, or sulphur and phosphorus, have, as
Mr. Mill says, analogous properties, I should call these substances
_analogous_: but I can see no temptation to frame an hypothesis that
they are _identical_ (which he seems to fear), so long as Chemistry
proves them distinct. But any hypothesis of an analogy in the
constitution of these elements (suppose, for instance, a resemblance
in their atomic form or composition) would seem to me to have a fair
claim to trial; and to be capable of being elevated from one degree of
probability to another by the number, variety, and exactitude of the
explanations of phenomena which it should furnish.


VII. _Against prediction of Facts._--51. These expressions of Mr.
Mill have reference to a way in which hypotheses may be corroborated,
in estimating the value of which, it appears that he and I differ.
"It seems to be thought," he says (ii. 23), "that an hypothesis of
the sort in question is entitled to a more favourable reception, if,
besides accounting for the facts previously known, it has led to the
anticipation and prediction of others which experience afterwards
verified." And he adds, "Such predictions and their fulfilment are
indeed well calculated to strike the ignorant vulgar;" but it is
strange, he says, that any considerable stress should be laid upon such
a coincidence by scientific thinkers. However strange it may seem to
him, there is no doubt that the most scientific thinkers, far more than
the ignorant vulgar, have allowed the coincidence of results predicted
by theory with fact afterwards observed, to produce the strongest
effects upon their conviction; and that all the best-established
theories have obtained their permanent place in general acceptance
in virtue of such coincidences, more than of any other evidence. It
was not the ignorant vulgar alone, who were struck by the return of
Halley's comet, as an evidence of the Newtonian theory. Nor was it the
ignorant vulgar, who were struck with those facts which did so much
strike men of science, as curiously felicitous proofs of the undulatory
theory of light,--the production of darkness by two luminous rays
interfering in a special manner; the refraction of a single ray of
light into a conical pencil; and other complex yet precise results,
predicted by the theory and verified by experiment. It must, one would
think, strike all persons in proportion to their thoughtfulness, that
when Nature thus does our bidding, she acknowledges that we have learnt
her true language. If we can predict new facts which we have not seen,
as well as explain those which we have seen, it must be because our
explanation is not a mere formula of observed facts, but a truth of a
deeper kind. Mr. Mill says, "If the laws of the propagation of light
agree with those of the vibrations of an elastic fluid in so many
respects as is necessary to make the hypothesis a plausible explanation
of all or most of the phenomena known at the time, it is nothing
strange that they should accord with each other in one respect more."
Nothing strange, if the theory be true; but quite unaccountable,
if it be not. If I copy a long series of letters of which the last
half-dozen are concealed, and if I guess those aright, as is found to
be the case when they are afterwards uncovered, this must be because
I have made out the import of the inscription. To say, that because I
have copied all that I could see, it is nothing strange that I should
guess those which I cannot see, would be absurd, without supposing such
a ground for guessing. The notion that the discovery of the laws and
causes of phenomena is a loose haphazard sort of guessing, which gives
"plausible" explanations, accidental coincidences, casual "harmonies,"
laws, "in some measure analogous" to the true ones, suppositions
"tenable" for a time, appears to me to be a misapprehension of the
whole nature of science; as it certainly is inapplicable to the case to
which it is principally applied by Mr. Mill.

52. There is another kind of evidence of theories, very closely
approaching to the verification of untried predictions, and to which,
apparently, Mr. Mill does not attach much importance, since he has
borrowed the term by which I have described it, _Consilience_, but
has applied it in a different manner (ii. 530, 563, 590). I have
spoken, in the _Philosophy_[281], of the _Consilience of Inductions_,
as one of the _Tests of Hypotheses_, and have exemplified it by many
instances; for example, the theory of universal gravitation, obtained
by induction from the motions of the planets, was found to explain
also that peculiar motion of the spheroidal earth which produces the
Precession of the Equinoxes. This, I have said, was a striking and
surprising coincidence which gave the theory a stamp of truth beyond
the power of ingenuity to counterfeit. I may compare such occurrences
to a case of interpreting an unknown character, in which two different
inscriptions, deciphered by different persons, had given the same
alphabet. We should, in such a case, believe with great confidence
that the alphabet was the true one; and I will add, that I believe the
history of science offers no example in which a theory supported by
such consiliences, had been afterwards proved to be false.

53. Mr. Mill accepts (ii. 21) a rule of M. Comte's, that we may apply
hypotheses, provided they are capable of being afterwards verified as
facts. I have a much higher respect for Mr. Mill's opinion than for
M. Comte's[282]; but I do not think that this rule will be found of
any value. It appears to me to be tainted with the vice which I have
already noted, of throwing the whole burthen of explanation upon the
unexplained word _fact_--unexplained in any permanent and definite
opposition to theory. As I have said, the Newtonian theory _is_ a
fact. Every true theory is a fact. Nor does the distinction become
more clear by Mr. Mill's examples. "The vortices of Descartes would
have been," he says, "a perfectly legitimate hypothesis, if it had
been possible by any mode of explanation which we could entertain
the hope of possessing, to bring the question whether such vortices
exist or not, within the reach of our observing faculties." But this
was possible, and was done. The free passage of comets through the
spaces in which these vortices should have been, convinced men that
these vortices did not exist. In like manner Mr. Mill rejects the
hypothesis of a luminiferous ether, "because it can neither be seen,
heard, smelt, tasted, or touched." It is a strange complaint to make of
the vehicle of light, that it cannot be heard, smelt, or tasted. Its
vibrations _can_ be seen. The fringes of shadows for instance, show its
vibrations, just as the visible lines of waves near the shore show the
undulations of the sea. Whether this can be touched, that is, whether
it resists motion, is hardly yet clear. I am far from saying there are
not difficulties on this point, with regard to _all_ theories which
suppose a _medium_. But there are no more difficulties of this kind in
the undulatory theory of light, than there are in Fourier's theory of
heat, which M. Comte adopts as a model of scientific investigation; or
in the theory of voltaic _currents_, about which Mr. Mill appears to
have no doubt; or of electric _atmospheres_, which, though generally
obsolete, Mr. Mill appears to favour; for though it had been said that
we _feel_ such atmospheres, no one had said that they have the other
attributes of matter.


VIII. _Newton's Vera Causa._--54. Mr. Mill conceives (ii. 17) that his
own rule concerning hypotheses coincides with Newton's Rule, that the
cause assumed must be a _vera causa_. But he allows that "Mr. Whewell
... has had little difficulty in showing that his (Newton's) conception
was neither precise nor consistent with itself." He also allows that
"Mr. Whewell is clearly right in denying it to be necessary that the
cause assigned should be a cause already known; else how could we ever
become acquainted with new causes?" These points being agreed upon, I
think that a little further consideration will lead to the conviction
that Newton's Rule of philosophizing will best become a valuable guide,
if we understand it as asserting that when the explanation of two or
more different kinds of phenomena (as the revolutions of the planets,
the fall of a stone, and the precession of the equinoxes,) lead us to
_the same_ cause, such a coincidence gives a reality to the cause. We
have, in fact, in such a case, a Consilience of Inductions.

55. When Mr. Mill condemns me (ii. 24) (using, however, expressions of
civility which I gladly acknowledge,) for having recognized no mode of
Induction except that of trying hypothesis after hypothesis until one
is found which fits the phenomena, I must beg to remind the readers of
our works, that Mr. Mill himself allows (i. 363) that the process of
finding a conception which binds together observed facts "is tentative,
that it consists of a succession of guesses, many being rejected until
one at last occurs fit to be chosen." I must remind them also that I
have given a Section upon the _Tests of Hypotheses_, to which I have
just referred,--that I have given various methods of Induction, as
the _Method of Gradation_, the _Method of Natural Classification_,
the _Method of Curves_, the _Method of Means_, the _Method of Least
Squares_, the _Method of Residues_: all which I have illustrated by
conspicuous examples from the History of Science; besides which, I
conceive that what I have said of the Ideas belonging to each science,
and of the construction and explication of conceptions, will point
out in each case, in what region we are to look for the Inductive
Element in order to make new discoveries. I have already ventured to
say, elsewhere, that the methods which I have given, are as definite
and practical as any others which have been proposed, with the
great additional advantage of being the methods by which all great
discoveries in science have really been made.


IX. _Successive Generalizations._--56. There is one feature in the
construction of science which Mr. Mill notices, but to which he does
not ascribe, as I conceive, its due importance: I mean, that process by
which we not only ascend from particular facts to a general law, but
when this is done, ascend from the first general law to others more
general; and so on, proceeding to the highest point of generalization.
This character of the scientific process was first clearly pointed
out by Bacon, and is one of the most noticeable instances of his
philosophical sagacity. "There are," he says, "two ways, and can
be only two, of seeking and finding truth. The one from sense and
particulars, takes a flight to the most general axioms, and from these
principles and their truth, settled once for all, invents and judges of
intermediate axioms. The other method collects axioms from sense and
particulars, ascending _continuously and by degrees_, so that in the
end it arrives at the most general axioms:" meaning by _axioms_, laws
or principles. The structure of the most complete sciences consists
of several such steps,--_floors_, as Bacon calls them, of successive
generalization; and thus this structure may be exhibited as a kind
of scientific pyramid. I have constructed this pyramid in the case
of the science of Astronomy[283]: and I am gratified to find that
the illustrious Humboldt approves of the design, and speaks of it as
executed with complete success[284]. The capability of being exhibited
in this form of successive generalizations, arising from particulars
upward to some very general law, is the condition of all tolerably
perfect sciences; and the steps of the successive generalizations are
commonly the most important events in the history of the science.

57. Mr. Mill does not reject this process of generalization; but he
gives it no conspicuous place, making it only one of three modes of
reducing a law of causation into other laws. "There is," he says (i.
555), "the _subsumption_ of one law under another; ... the gathering up
of several laws into one more general law which includes them all. He
adds afterwards, that the general law is the _sum_ of the partial ones
(i. 557), an expression which appears to me inadequate, for reasons
which I have already stated. The general law is not the mere sum of
the particular laws. It is, as I have already said, their amount _in a
new point of view_. A new conception is introduced; thus, Newton did
not merely add together the laws of the motions of the moon and of the
planets, and of the satellites, and of the earth; he looked at them
altogether as the result of a universal force of mutual gravitation;
and therein consisted his generalization. And the like might be pointed
out in other cases.

58. I am the more led to speak of Mr. Mill as not having given due
importance to this process of successive generalization, by the way in
which he speaks in another place (ii. 525) of this doctrine of Bacon.
He conceives Bacon "to have been radically wrong when he enunciates,
as a universal rule, that induction should proceed from the lowest to
the middle principles, and from those to the highest, never reversing
that order, and consequently, leaving no room for the discovery of new
principles by way of deduction[285] at all."

59. I conceive that the Inductive Table of Astronomy, to which I have
already referred, shows that in that science,--the most complete which
has yet existed,--the history of the science has gone on, as to its
general movement, in accordance with the view which Bacon's sagacity
enjoined. The successive generalizations, _so far as they were true_,
were made by successive generations. I conceive also that the Inductive
Table of Optics shows the same thing; and this, without taking for
granted the truth of the Undulatory Theory; for with regard to all the
steps of the progress of the science, lower than that highest one,
there is, I conceive, no controversy.

60. Also, the Science of Mechanics, although Mr. Mill more especially
refers to it, as a case in which the highest generalizations (for
example the Laws of Motion) were those earliest ascertained with any
scientific exactness, will, I think, on a more careful examination of
its history, be found remarkably to confirm Bacon's view. For, in that
science, we have, in the first place, very conspicuous examples of the
vice of the method pursued by the ancients in flying to the highest
generalizations first; as when they made their false distinctions of
the laws of _natural_ and _violent_ motions, and of _terrestrial_
and _celestial_ motions. Many erroneous laws of motion were asserted
through neglect of facts or want of experiments. And when Galileo and
his school had in some measure succeeded in discovering some of the
true laws of the motions of terrestrial bodies, they did not at once
assert them as general: for they did not at all apply those laws to
the celestial motions. As I have remarked, all Kepler's speculations
respecting the causes of the motions of the planets, went upon the
supposition that the First Law of terrestrial Motion did not apply to
celestial bodies; but that, on the contrary, some continual force was
requisite to keep up, as well as to originate, the planetary motions.
Nor did Descartes, though he enunciated the Laws of Motion with more
generality than his predecessors, (but not with exactness,) venture
to trust the planets to those laws; on the contrary, he invented his
machinery of Vortices in order to keep up the motions of the heavenly
bodies. Newton was the first who extended the laws of terrestrial
motion to the celestial spaces; and in doing so, he used all the laws
of the celestial motions which had previously been discovered by
more limited inductions. To these instances, I may add the gradual
generalization of the Third Law of motion by Huyghens, the Bernoullis,
and Herman, which I have described in the _History_[286] as preceding
that Period of Deduction, to which the succeeding narrative[287] is
appropriated. In Mechanics, then, we have a cardinal example of the
historically gradual and successive ascent of science from particulars
to the most general laws.

61. The Science of Hydrostatics may appear to offer a more favourable
example of the ascent to the most general laws, without going through
the intermediate particular laws; and it is true, with reference
to this science, as I have observed[288], that it does exhibit the
_peculiarity_ of our possessing the most general principles on which
the phenomena depend, and from which many cases of special facts are
explained by deduction; while other cases cannot be so explained,
from the want of principles intermediate between the highest and the
lowest. And I have assigned, as the reason of this peculiarity, that
the general principles of the Mechanics of Fluids were not obtained
with reference to the science itself, but by extension from the sister
science of the Mechanics of Solids. The two sciences are parts of the
same Inductive Pyramid; and having reached the summit of this Pyramid
on one side, we are tempted to descend on the other from the highest
generality to more narrow laws. Yet even in this science, the best
part of our knowledge is mainly composed of inductive laws, obtained
by inductive examination of particular classes of facts. The mere
mathematical investigations of the laws of waves, for instance, have
not led to any results so valuable as the experimental researches of
Bremontier, Emy, the Webers, and Mr. Scott Russell. And in like manner
in Acoustics, the Mechanics of Elastic Fluids[289], the deductions of
mathematicians made on general principles have not done so much for
our knowledge, as the cases of vibrations of plates and pipes examined
experimentally by Chladni, Savart, Mr. Wheatstone and Mr. Willis. We
see therefore, even in these sciences, no reason to slight the wisdom
which exhorts us to ascend from particulars to intermediate laws,
rather than to hope to deduce these latter better from the more general
laws obtained once for all.

62. Mr. Mill himself indeed, notwithstanding that he slights Bacon's
injunction to seek knowledge by proceeding from less general to more
general laws, has given a very good reason why this is commonly
necessary and wise. He says (ii. 526), "Before we attempt to explain
deductively, from more general laws, any new class of phenomena, it is
desirable to have gone as far as is practicable in ascertaining the
empirical laws of these phenomena; so as to compare the results of
deduction, not with one individual instance after another, but with
general propositions expressive of the points of agreement which have
been found among many instances. For," he adds with great justice,
"if Newton had been obliged to verify the theory of gravitation, not
by deducing from it Kepler's laws, but by deducing all the observed
planetary positions which had served Kepler to establish those laws,
the Newtonian theory would probably never have emerged from the state
of an hypothesis." To which we may add, that it is certain, from the
history of the subject, that in that case the hypothesis would never
have been framed at all.


X. _Mr. Mill's Hope from Deduction._--63. Mr. Mill expresses a hope
of the efficacy of Deduction, rather than Induction, in promoting
the future progress of Science; which hope, so far as the physical
sciences are concerned, appears to me at variance with all the lessons
of the history of those sciences. He says (i. 579), "that the advances
henceforth to be expected even in physical, and still more in mental
and social science, will be chiefly the result of deduction, is evident
from the general considerations already adduced:" these considerations
being, that the phenomena to be considered are very complex, and are
the result of many known causes, of which we have to disentangle the
results.

64. I cannot but take a very different view from this. I think that
any one, looking at the state of physical science, will see that there
are still a vast mass of cases, in which we do not at all know the
causes, at least, in their full generality; and that the knowledge of
new causes, and the generalization of the laws of those already known,
can only be obtained by new _inductive_ discoveries. Except by new
Inductions, equal, in their efficacy for grouping together phenomena
in new points of view, to any which have yet been performed in the
history of science, how are we to solve such questions as those which,
in the survey of what we already know, force themselves upon our minds?
Such as, to take only a few of the most obvious examples--What is the
nature of the connexion of heat and light? How does heat produce the
expansion, liquefaction and vaporization of bodies? What is the nature
of the connexion between the optical and the chemical properties of
light? What is the relation between optical, crystalline and chemical
polarity? What is the connexion between the atomic constitution and
the physical qualities of bodies? What is the tenable definition of a
mineral species? What is the true relation of the apparently different
types of vegetable life (monocotyledons, dicotyledons, and cryptogamous
plants)? What is the relation of the various types of animal life
(vertebrates, articulates, radiates, &c.)? What is the number, and
what are the distinctions of the Vital Powers? What is the internal
constitution of the earth? These, and many other questions of equal
interest, no one, I suppose, expects to see solved by deduction from
principles already known. But we can, in many of them, see good hope of
progress by a large use of induction; including, of course, copious and
careful experiments and observations.

65. With such questions before us, as have now been suggested, I
can see nothing but a most mischievous narrowing of the field and
enfeebling of the spirit of scientific exertion, in the doctrine that
"Deduction is the great scientific work of the present and of future
ages;" and that "A revolution is peaceably and progressively effecting
itself in philosophy the reverse of that to which Bacon has attached
his name." I trust, on the contrary, that we have many new laws of
nature still to discover; and that our race is destined to obtain a
sight of wider truths than any we yet discern, including, as cases, the
general laws we now know, and obtained from these known laws as they
must be, by Induction.

66. I can see, however, reasons for the comparatively greater favour
with which Mr. Mill looks upon Deduction, in the views to which he has
mainly directed his attention. The explanation of remarkable phenomena
by known laws of Nature, has, as I have already said, a greater charm
for many minds than the discovery of the laws themselves. In the case
of such explanations, the problem proposed is more definite, and the
solution more obviously complete. For the process of induction includes
a mysterious step, by which we pass from particulars to generals,
of which step the reason always seems to be inadequately rendered
by any words which we can use; and this step to most minds is not
demonstrative, as to few is it given to perform it on a great scale.
But the process of explanation of facts by known laws is deductive,
and has at every step a force like that of demonstration, producing
a feeling peculiarly gratifying to the clear intellects which are
most capable of following the process. We may often see instances in
which this admiration for deductive skill appears in an extravagant
measure; as when men compare Laplace with Newton. Nor should I think
it my business to argue against such a preference, unless it were
likely to leave us too well satisfied with what we know already, to
chill our hope of scientific progress, and to prevent our making any
further strenuous efforts to ascend, higher than we have yet done, the
mountain-chain which limits human knowledge.

67. But there is another reason which, I conceive, operates in leading
Mr. Mill to look to Deduction as the principal means of future progress
in knowledge, and which is a reason of considerable weight in the
subjects of research which, as I conceive, he mainly has in view. In
the study of our own minds and of the laws which govern the history of
society, I do not think that it is very likely that we shall hereafter
arrive at any wider principles than those of which we already possess
some considerable knowledge; and this, for a special reason; namely,
that our knowledge in such cases is not gathered by mere external
observation of a collection of external facts; but acquired by
attention to internal facts, our own emotions, thoughts, and springs of
action; facts are connected by ties existing in our own consciousness,
and not in mere observed juxtaposition, succession, or similitude.
How the character, for instance, is influenced by various causes, (an
example to which Mr. Mill repeatedly refers, ii. 518, &c.), is an
inquiry which may perhaps be best conducted by considering what we know
of the influence of education and habit, government and occupation,
hope and fear, vanity and pride, and the like, upon men's characters,
and by tracing the various effects of the intermixture of such
influences. Yet even here, there seems to be room for the discovery
of laws in the way of experimental inquiry: for instance, what share
race or family has in the formation of character; a question which can
hardly be solved to any purpose in any other way than by collecting
and classing instances. And in the same way, many of the principles
which regulate the material wealth of states, are obtained, if not
exclusively, at least most clearly and securely, by induction from
large surveys of facts. Still, however, I am quite ready to admit that
in Mental and Social Science, we are much less likely than in Physical
Science, to obtain new truths by any process which can be distinctively
termed _Induction_; and that in those sciences, what may be called
_Deductions_ from principles of thought and action of which we are
already conscious, or to which we assent when they are felicitously
picked out of our thoughts and put into words, must have a large share;
and I may add, that this observation of Mr. Mill appears to me to be
important, and, in its present connexion, new.


XI. _Fundamental opposition of our doctrines._--68. I have made nearly
all the remarks which I now think it of any consequence to make upon
Mr. Mill's _Logic_, so far as it bears upon the doctrines contained
in my _History_ and _Philosophy_. And yet there remains still
untouched one great question, involving probably the widest of all the
differences between him and me. I mean the question whether geometrical
axioms, (and, as similar in their evidence to these, _all_ axioms,) be
truths derived from experience, or be necessary truths in some deeper
sense. This is one of the fundamental questions of philosophy; and all
persons who take an interest in metaphysical discussions, know that the
two opposite opinions have been maintained with great zeal in all ages
of speculation. To me it appears that there are _two_ distinct elements
in our knowledge, Experience, without, and the Mind, within. Mr. Mill
derives all our knowledge from Experience _alone_. In a question thus
going to the root of all knowledge, the opposite arguments must needs
cut deep on both sides. Mr. Mill cannot deny that our knowledge of
geometrical axioms and the like, _seems_ to be _necessary_. I cannot
deny that our knowledge, axiomatic as well as other, _never is_
acquired _without experience_.

69. Perhaps ordinary readers may despair of following our reasonings,
when they find that they can only be made intelligible by supposing,
on the one hand, a person who thinks distinctly and yet has never seen
or felt any external object; and on the other hand, a person who is
transferred, as Mr. Mill supposes (ii. 117), to "distant parts of the
stellar regions where the phenomena may be entirely unlike those with
which we are acquainted," and where even the axiom, that every effect
must have a cause, does not hold good. Nor, in truth, do I think it
necessary here to spend many words on this subject. Probably, for those
who take an interest in this discussion, most of the arguments on each
side have already been put forwards with sufficient repetition. I have,
in an "Essay on the Fundamental Antithesis of Philosophy," and in some
accompanying "Remarks," printed[290] at the end of the second edition
of my _Philosophy_, given my reply to what has been said on this
subject, both by Mr. Mill, and by the author of a very able critique on
my _History_ and _Philosophy_ which appeared in the _Quarterly Review_
in 1841: and I will not here attempt to revive the general discussion.

70. Perhaps I may be allowed to notice, that in one part of Mr. Mill's
work where this subject is treated, there is the appearance of one of
the parties to the controversy pronouncing judgment in his own cause.
This indeed is a temptation which it is especially difficult for an
author to resist, who writes a treatise upon _Fallacies_, the subject
of Mr. Mill's fifth Book. In such a treatise, the writer has an easy
way of disposing of adverse opinions by classing them as "Fallacies,"
and putting them side by side with opinions universally acknowledged to
be false. In this way, Mr. Mill has dealt with several points which are
still, as I conceive, matters of controversy (ii. 357, &c.).

71. But undoubtedly, Mr. Mill has given his argument against my
opinions with great distinctness in another place (i. 319). In order
to show that it is merely habitual association which gives to an
experimental truth the character of a necessary truth, he quotes
the case of the laws of motion, which were really discovered from
experiment, but are now looked upon as the only conceivable laws; and
especially, what he conceives as "the _reductio ad absurdum_ of the
theory of inconceivableness," an opinion which I had ventured to throw
out, that if we could conceive the Composition of bodies distinctly,
we might be able to see that it is necessary that the modes of their
composition should be definite. I do not think that readers in general
will see anything absurd in the opinion, that the laws of Mechanics,
and even the laws of the Chemical Composition of bodies, may depend
upon principles as necessary as the properties of space and number; and
that this necessity, though not at all perceived by persons who have
only the ordinary obscure and confused notions on such subjects, may
be evident to a mind which has, by effort and discipline, rendered its
ideas of Mechanical Causation, Elementary Composition and Difference of
Kind, clear and precise. It may easily be, I conceive, that while such
necessary principles are perceived to be necessary only by a few minds
of highly cultivated insight, such principles as the axioms of Geometry
and Arithmetic may be perceived to be necessary by _all_ minds which
have any habit of abstract thought at all: and I conceive also, that
though these axioms are brought into distinct view by a certain degree
of intellectual cultivation, they may still be much better described
as conditions of experience, than as results of experience:--as laws
of the mind and of its activity, rather than as facts impressed upon a
mind merely passive.


XII. _Absurdities in Mr. Mill's Logic._--72. I will not pursue the
subject further: only, as the question has arisen respecting the
absurdities to which each of the opposite doctrines leads, I will point
out opinions connected with this subject, which Mr. Mill has stated in
various parts of his book.

He holds (i. 317) that it is merely from habit that we are unable to
conceive the _last point_ of space or the _last instant_ of time.
He holds (ii. 360) that it is strange that any one should rely upon
the _à priori_ evidence that space or extension is infinite, or that
nothing can be made of nothing. He holds (i. 304) that the first law
of _motion_ is _rigorously true_, but that the axioms respecting
the _lever_ are only _approximately_ true. He holds (ii. 110) that
there may be sidereal firmaments in which events succeed each other
at random, without obeying any laws of causation; although one might
suppose that even if space and cause are both to have their limits,
still they might terminate together: and then, even on this bold
supposition, we should no _where_ have a world in which events were
_casual_. He holds (ii. 111) that the axiom, that every event must
have a cause, is established by means of an "induction by simple
enumeration:" and in like manner, that the principles of number and
of geometry are proved by this method of simple enumeration alone. He
ascribes the proof (i. 162) of the axiom, "things which are equal to
the same are equal to each other," to the fact that this proposition
has been perpetually _found_ true and never false. He holds (i. 338)
that "In all propositions concerning numbers, a condition is implied,
without which none of them would be true; and that condition is an
assumption which _may be false_. _The condition is that_ 1 = 1."

73. Mr. Mill further holds (i. 309), that it is a characteristic
property of geometrical forms, that they are capable of being painted
in the imagination with a distinctness equal to reality:--that our
ideas of forms exactly resemble our sensations: which, it is implied,
is not the case with regard to any other class of our ideas;--that we
thus may have mental pictures of all possible combinations of lines
and angles, which are as fit subjects of geometrical experimentation
as the realities themselves. He says, that "we know that the imaginary
lines exactly resemble real ones;" and that we obtain this knowledge
respecting the characteristic property of the idea of space by
experience; though it does not appear _how_ we can compare our _ideas_
with the _realities_, since we know the realities only _by_ our ideas;
or why this property of their resemblance should be confined to _one
class_ of ideas alone.

74. I have now made such remarks as appear to me to be necessary, on
the most important parts of Mr. Mill's criticism of my _Philosophy_. I
hope I have avoided urging any thing in a contentious manner; as I have
certainly written with no desire of controversy, but only with a view
to offer to those who may be willing to receive it, some explanation of
portions of my previous writings. I have already said, that if this had
not have been my especial object, I could with pleasure have noted the
passages of Mr. Mill's _Logic_ which I admire, rather than the points
in which we differ. I will in a very few words refer to some of these
points, as the most agreeable way of taking leave of the dispute.

I say then that Mr. Mill appears to me especially instructive in
his discussion of the nature of the proof which is conveyed by the
syllogism; and that his doctrine, that the force of the syllogism
consists in an _inductive assertion, with an interpretation added
to it_, solves very happily the difficulties which baffle the
other theories of this subject. I think that this doctrine of his
is made still more instructive, by his excepting from it the cases
of Scriptural Theology and of Positive Law (i. 260), as cases in
which general propositions, not particular facts, are our original
data. I consider also that the recognition of _Kinds_ (i. 166) as
classes in which we have, not a finite but an _inexhaustible_ body of
resemblances among individuals, and as groups made by nature, not by
mere definition, is very valuable, as stopping the inroad to an endless
train of false philosophy. I conceive that he takes the right ground
in his answer to Hume's argument against miracles (ii. 183): and I
admire the acuteness with which he has criticized Laplace's tenets on
the Doctrine of Chances, and the candour with which he has, in the
second edition, acknowledged oversights on this subject made in the
first. I think that much, I may almost say all, which he says on the
subject of Language, is very philosophical; for instance, what he says
(ii. 238) of the way in which words acquire their meaning in common
use. I especially admire the acuteness and force with which he has
shown (ii. 255) how moral principles expressed in words degenerate into
formulas, and yet how the formula cannot be rejected without a moral
loss. This "perpetual oscillation in spiritual truths," as he happily
terms it, has never, I think, been noted in the same broad manner,
and is a subject of most instructive contemplation. And though I have
myself refrained from associating moral and political with physical
science in my study of the subject, I see a great deal which is full of
promise for the future progress of moral and political knowledge in Mr.
Mill's sixth Book, "On the Logic of the Moral and Political Sciences."
Even his arrangement of the various methods which have been or may
be followed in "the Social Science,"--"the Chemical or Experimental
Method," "the Geometrical or Abstract Method," "the Physical or
Concrete Deductive Method," "the Inverse Deductive or Historical
Method," though in some degree fanciful and forced, abounds with
valuable suggestions; and his estimate of "the interesting philosophy
of the Bentham school," the main example of "the geometrical method,"
is interesting and philosophical. On some future occasion, I may,
perhaps, venture into the region of which Mr. Mill has thus essayed
to map the highways: for it is from no despair either of the great
progress to be made in such truth as that here referred to, or of the
effect of philosophical method in arriving at such truth, that I have,
in what I have now written, confined myself to the less captivating but
more definite part of the subject.


FOOTNOTES:

[Footnote 264: [_A System of Logic, Ratiocinative and Inductive, being
a connected view of the Principles of Evidence, and of the Methods of
Scientific Investigation._ By John Stuart Mill.]]

[Footnote 265: These Remarks were published in 1849, under the title
_Of Induction, with especial reference to Mr. J. S. Mill's System of
Logic_.]

[Footnote 266: My references are throughout (except when otherwise
expressed) to the volume and the page of Mr. Mill's first edition of
his _Logic_.]

[Footnote 267: On this subject see an Essay _On the Transformation of
Hypotheses_, given in the Appendix.]

[Footnote 268: B. vii. c. iii. sect. 3.]

[Footnote 269: B. iii. c. ix. art. 7.]

[Footnote 270: B. i. c. iii.]

[Footnote 271: B. iii. c. viii.]

[Footnote 272: _Discourse_, Art. 192.]

[Footnote 273: B. xi. c. xi.]

[Footnote 274: _Phil._ b. xiii. c. ix. art. 7.]

[Footnote 275: B. xiii. c. viii.]

[Footnote 276: Given also in the _Phil. Ind. Sc._ b. xiii. c. vii.
sect. 17.]

[Footnote 277: _Ibid._ b. vi. c. iv.]

[Footnote 278: See _Hist. Ind. Sc._ b. xii. note D, in the second
edition.]

[Footnote 279: There are some points in my doctrines on the subject
of the Classificatory Sciences to which Mr. Mill objects, (ii. 314,
&c.), but there is nothing which I think it necessary to remark here,
except one point. After speaking of Classification of organized beings
in general, Mr. Mill notices (ii. 321) as an additional subject, the
arrangement of natural groups into a Natural Series; and he says, that
"all who have attempted a theory of natural arrangement, including
among the rest Mr. Whewell, have stopped short of this: all except M.
Comte." On this I have to observe, that I stopped short of, or rather
passed by, the doctrine of a Series of organized beings, because I
thought it bad and narrow philosophy: and that I sufficiently indicated
that I did this. In the _History_ (b. xvi. c. vi.) I have spoken of the
doctrine of Circular Progression propounded by Mr. Macleay, and have
said, "so far as this view _negatives_ a mere _linear_ progression in
nature, which would place each genus in contact with the preceding and
succeeding ones, and so far as it requires us to attend to the more
varied and ramified resemblances, there can be no doubt that it is
supported by the result of all the attempts to form natural systems."
And with regard to the difference between Cuvier and M. de Blainville,
to which Mr. Mill refers (ii. 321), I certainly cannot think that M.
Comte's suffrage can add any weight to the opinion of either of those
great naturalists.]

[Footnote 280: _Hist. Ind. Sc._ b. x. note (VA) in the second edition.]

[Footnote 281: B. xi. c. v. art. 11.]

[Footnote 282: I have given elsewhere (see last chapter) reasons why I
cannot assign to M. Comte's _Philosophie Positive_ any great value as a
contribution to the philosophy of science. In this judgment I conceive
that I am supported by the best philosophers of our time. M. Comte
owes, I think, much of the notice which has been given to him to his
including, as Mr. Mill does, the science of society and of human nature
in his scheme, and to his boldness in dealing with these. He appears
to have been received with deference as a mathematician: but Sir John
Herschel has shown that a supposed astronomical discovery of his is a
mere assumption. I conceive that I have shown that his representation
of the history of science is erroneous, both in its details and in its
generalities. His distinction of the three stages of sciences, the
theological, metaphysical, and positive, is not at all supported by the
facts of scientific history. Real discoveries always involve what he
calls _metaphysics_; and the doctrine of final causes in physiology,
the main element of science which can properly be called _theological_,
is retained at the end, as well as the beginning of the science, by all
except a peculiar school.]

[Footnote 283: I have also, in the same place, given the Inductive
Pyramid for the science of Optics. These Pyramids are necessarily
inverted in their form, in order that, in reading in the ordinary way,
we may proceed _to_ the vertex. _Phil. Ind. Sc._ b. xi. c. vi.]

[Footnote 284: _Cosmos_, vol. ii. note 35.]

[Footnote 285: The reader will probably recollect that as _Induction_
means the inference of general propositions from particular cases,
_Deduction_ means the inference by the application of general
propositions to particular cases, and by combining such applications;
as when from the most general principles of Geometry or of Mechanics,
we prove some less general theorem; for instance, the number of the
possible regular solids, or the principle of _vis viva_.]

[Footnote 286: B. vi. c. v.]

[Footnote 287: c. vi.]

[Footnote 288: _Hist._ b. vi. c. vi. sect. 13.]

[Footnote 289: _Hist. Ind. Sc._ b. viii.]

[Footnote 290: Reprinted in the Appendix to this volume.]




CHAPTER XXIII.

POLITICAL ECONOMY AS AN INDUCTIVE SCIENCE.


(_Moral Sciences._)--1. Both M. Comte and Mr. Mill, in speaking of the
methods of advancing science, aim, as I have said, at the extension of
their methods to moral subjects, and aspire to suggest means for the
augmentation of our knowledge of ethical, political, and social truths.
I have not here ventured upon a like extension of my conclusions,
because I wished to confine my views of the philosophy of discovery
to the cases in which all allow that solid and permanent discoveries
have been made. Moreover in the case of moral speculations, we have
to consider not only observed external facts and the ideas by which
they are colligated, but also internal facts, in which the instrument
of observation is consciousness, and in which observations and ideas
are mingled together, and act and react in a peculiar manner. It may
therefore be doubted whether the methods which have been effectual
in the discovery of physical theories will not require to be greatly
modified, or replaced by processes altogether different, when we would
make advances in ethical, political, or social knowledge. In ethics, at
least, it seems plain that we must take our starting-point not without
but within us. Our mental powers, our affections, our reason, and any
other faculties which we have, must be the basis of our convictions.
And in this field of knowledge, the very form of our highest
propositions is different from what it is in the physical sciences. In
Physics we examine what _is_, in a form more or less general: in Ethics
we seek to determine what OUGHT _to be_, as the highest rule, which is
supreme over all others. In this case we cannot expect the methods of
physical discovery to aid us.

But others of the subjects which I have mentioned, though strongly
marked and influenced by this ethical element, are still of a mixed
character, and require also observation of external facts of human,
individual, and social conduct, and generalizations derived from
such observations. The facts of political constitutions and social
relations in communities of men, and the histories of such communities,
afford large bodies of materials for political and social science;
and it seems not at all unlikely that such science may be governed,
in its formation and progress, by laws like those which govern the
physical sciences, and may be steered clear of errors and directed
towards truths by an attention to the forms which error and truth have
assumed in the most stable and certain sciences. The different forms
of society, and the principal motives which operate upon men regarded
in masses, may be classified as facts; and though our consciousness of
what we ourselves are and the affections which we ourselves feel are
always at work in our interpretations of such facts, yet the knowledge
which we thus obtain may lead us to bodies of knowledge which we may
call _Sciences_, and compare with the other sciences as to their form
and maxims.


(_Political Economy._)--2. Among such bodies of knowledge, I may notice
as a specimen, the science of _Political Economy_, and may compare it
with other sciences in the respects which have been referred to.

M. Comte has given a few pages to the discussion of this science of
Political Economy[291]; but what he has said amounts only to a few
vague remarks on Adam Smith and Destutt de Tracy; his main object
being, it would seem, to introduce his usual formula, and to condemn
all that has hitherto been done (with which there is no evidence that
he is adequately acquainted) as worthless, because it is "theological,"
"metaphysical," "literary," and not "_positive_."

Mr. Mill has much more distinctly characterized the plan and form
of Political Economy in his system[292]. He regards this science as
that which deals with the results which take place in human society
in consequence of the desire of wealth. He explains, however, that
it is only for the sake of convenience that one of the motives which
operate upon man is thus insulated and treated as if it were the only
one:--that there are other principles, for instance, the principles on
which the progress of population depends, which co-operate with the
main principle, and materially modify its results: and he gives reasons
why this mode of simplifying the study of social phenomena tends to
promote the progress of systematic knowledge.

Instead of discussing these reasons, I will notice the way in which the
speculations of political economists have exemplified tendencies to
error, and corrections of those tendencies, of the same nature as those
which we have already noticed in speaking of other sciences.


(_Wages, Profits, and Rent._)--3. We may regard as one of the first
important steps in this science, Adam Smith's remark, that the value
or price of any article bought and sold consists of three elements,
_Wages_, _Profits_, and _Rent_. Some of the most important of
subsequent speculations were attempts to determine the laws of each of
these three elements. At first it might be supposed that there ought to
be added to them a fourth element, _Materials_. But upon consideration
it will be seen that materials, as an element of price, resolves itself
into wages and rent; for all materials derive their value from the
labour which is bestowed upon them. The iron of the ploughshare costs
just what it costs to sink the mine, dig up and smelt the iron. The
wood of the frame costs what it costs to cut down the tree, together
with the rent of the ground on which it grows.


(_Premature Generalizations._)--4. But what determines Wages?--The
amount of persons seeking work, that is, speaking loosely, the
population; and the amount of money which is devoted to the payment of
wages. And what determines the population? It was replied,--the means
of subsistence. And how does the population tend to increase?--In a
geometrical ratio. And how does the subsistence tend to increase?--At
most in an arithmetical ratio. And hence it was inferred that the
population tends constantly to run beyond the means of subsistence,
and will be limited by a threatened deficiency of these means. And
the wages paid must be such as to form this limit. And therefore the
wages paid will always be such as just to keep up the population in its
ordinary state of progress. Here was one general proposition which was
gathered from summary observations of society.

Again: as to Rent: Adam Smith had treated Rent as if it were a monopoly
price--the result of a monopoly of the land by the landowners. But
subsequent writers acutely remarked that land is of various degrees of
fertility, and there is some land which barely pays the cultivator, if
cultivating it he pay no rent. And rent can be afforded for other land
only in so far as it is better than this bad land. And thus, there was
obtained another general proposition; that the Rent of good land was
just equal to the excess of its produce over the worst cultivable land.

Now these two propositions are examples of a hasty and premature
generalization, like that from which the sweeping physical systems
of antiquity were derived. They were examples of that process which
Francis Bacon calls _anticipation_; in which we leap at once from a few
facts to propositions of the highest generality; and supposing these
to be securely established, proceed to draw a body of conclusions from
them, and thus frame a system.

And what is the sounder and wiser mode of proceeding in order to obtain
a science of such things? We must classify the facts which we observe,
and take care that we do not ascribe to the facts in our immediate
neighbourhood or specially under our notice, a generality of prevalence
which does not belong to them. We must proceed by the ladder of
Induction, and be sure we have obtained the narrower generalizations,
before we aspire to the widest.


(_Correction of them by Induction. Rent._)--5. For instance; in the
case of the latter of the above two propositions--that Rent is the
excess of the produce of good soils over the worst--that is the case
in England and Scotland; but is it the case in other countries? Let us
see. Why is it the case in England? Because if the rent demanded for
good land were _more_ than the excess of the produce over bad land, the
farmer would prefer the bad land as more gainful. If the rent demanded
for good land were _less_ than the excess, the bad land would be
abandoned by the farmer.

But all this goes upon the supposition that the farmer can remove from
good land to bad, or from bad to good, or apply his capital in some
other way than farming, according as it is more gainful. This is true
in England; but is it true all over the world?

By no means. It is true in scarcely any other part of the world. In
almost every other part of the world the cultivator is bound to the
land, so that he cannot remove himself and his capital from it; and
cannot, because he is not satisfied with his position upon it, seek and
find a position and a subsistence elsewhere. On the contrary, he is
bound by the laws and customs of the country, by constitution, history
and character, so that he cannot, or can only with great difficulty,
change his plan and mode of life. And thus over great part of the world
the fundamental supposition on which rests the above generalization
respecting Rent is altogether false.

An able political economist[293] has taken the step, which as we have
said, sound philosophy would have prescribed: he has classified the
states of society which exist or have existed on the earth, as they
bear on this point, the amount of Rent. He has classified the modes
in which the produce is, in different countries and different stages
of society, divided between the cultivator and the proprietor: and he
finds that the natural divisions are these:--_Serf Rents_, that is,
labour rents paid by the Cultivator to the Landowner, as in Russia:
_Métayer Rents_, where the produce is divided between the Cultivator
and the Landowner, as in Central Europe: _Ryot Rents_, where a portion
of the produce is paid to the Sovereign as Landlord, as in India:
_Cottier Rents_, where a money-rent is paid by a Cultivator who raises
his own subsistence from the soil; and _Farmers' Rents_, where a
covenanted Rent is paid by a person employing labourers. In this last
case alone is it true that the Rent is equal to the excess of good over
bad soils.

The error of the conclusion, in this case, arises from assuming the
mobility of capital and labour in cases in which it is not moveable:
which is much as if mechanicians had reasoned respecting rigid bodies,
supposing them to be fluid bodies.

But the error of method was in not classifying the facts of societies
before jumping to a conclusion which was to be applicable to all
societies.


(_Wages._)--6. And in like manner there is an error of the same kind
in the assertion of the other general principles:--that wages are
determined by the capital which is forthcoming for the payment of
wages; and that population is determined in its progress by wages. For
there is a vast mass of population on the surface of the earth which
does not live upon wages: and though in England the greater part of the
people lives upon wages, in the rest of the world the part that does so
is small. And in this case, as in the other, we must class these facts
as they exist in different nations, before we can make assertions of
any wide generality.

Mr. Jones[294] classed the condition of labourers in different
countries in the same inductive manner in which he classed the tenure
of land. He pointed out that there are three broad distinct classes
of them: _Unhired Labourers_, who cultivate the ground which they
occupy, and live on _self-produced wages_; _Paid Dependants_, who are
paid out of the _revenue_ or income of their employers, as the military
retainers and domestic artizans of feudal times in Europe, and the
greater part of the people of Asia at the present day; and _Hired
Labourers_, who are paid wages from _capital_.

This last class, though taken as belonging to the normal condition of
society by many political economists, is really the exceptional case,
taking the world at large; and no propositions concerning the structure
and relations of ranks in society can have any wide generality which
are founded on a consideration of this case alone.


(_Population._)--7. And again: with regard to the proposition that
the progress of population depends merely on the rate of wages, a
very little observation of different communities, and of the same
communities at different times, will show that this is a very rash and
hasty generalization. When wages rise, whether or not population shall
undergo a corresponding increase depends upon many other circumstances
besides this single fact of the increase of wages. The effect of a
rise of wages upon population is affected by the form of the wages,
the time occupied by the change, the institutions of the society
under consideration, and other causes: and a due classification of
the conditions of the society according to these circumstances, is
requisite in order to obtain any general proposition concerning the
effect of a rise or fall of wages upon the progress of the population.

And thus those precepts of the philosophy of discovery which we have
repeated so often, which are so simple, and which seem so obvious,
have been neglected or violated in the outset of Political Economy as
in so many other sciences:--namely, the precepts that we must classify
our facts before we generalize, and seek for narrower generalizations
and inductions before we aim at the widest. If these maxims had been
obeyed, they would have saved the earlier speculators on this subject
from some splendid errors; but, on the other hand, it may be said, that
if these earlier speculators had not been thus bold, the science could
not so soon have assumed that large and striking form which made it so
attractive, and to which it probably owes a large part of its progress.


FOOTNOTES:

[Footnote 291: _Phil. Pos._ t. iv. p. 264.]

[Footnote 292: _Logic_, b. vi. c. 3.]

[Footnote 293: Jones, _On Rent_, 1833.]

[Footnote 294: _Literary Remains_, 1859.]




CHAPTER XXIV.

MODERN GERMAN PHILOSOPHY[295].


I. _Science is the Idealization of Facts._

1. I have spoken, a few chapters back, of the Reaction against the
doctrines of the Sensational School in England and France. In Germany
also there was a Reaction against these doctrines;--but there, this
movement took a direction different from its direction in other
countries. Omitting many other names, Kant, Fichte, Schelling and Hegel
may be regarded as the writers who mark, in a prominent manner, this
Germanic line of speculation. The problem of philosophy, in the way in
which they conceived it, may best be explained by reference to that
Fundamental Antithesis of which I had occasion to speak in the _History
of Scientific Ideas_[296]. And in order to characterize the steps taken
by these modern German philosophers, I must return to what I have said
concerning the Fundamental Antithesis.

This Antithesis, as I have there remarked, is stated in various
ways:--as the Antithesis of Thoughts and Things; of Ideas and
Sensations; of Theory and Facts; of Necessary Truth and Experience; of
the Subjective and Objective elements of our knowledge; and in other
phrases. I have further remarked that the elements thus spoken of,
though opposed, are inseparable. We cannot have the one without the
other. We cannot have thoughts without thinking of Things: we cannot
have things before us without thinking of them.

Further, it has been shown, I conceive, that our knowledge derives
from the former of these two elements, namely our Ideas, its form
and character of knowledge; our ideas being the necessary _Forms_ of
knowledge, while the _Matter_ of our knowledge in each case is supplied
by the appropriate perception or outward experience.

Thus our Ideas of Space and Time are the necessary Forms of our
geometrical and arithmetical knowledge; and no sensations or experience
are needed as the matter of such knowledge, except in so far as
sensation and experience are needed to evoke our Ideas in any degree.
And hence these sciences are sometimes called _Formal_ sciences. All
other Sciences involve, along with the experience and observation
appropriate to each, a development of the ideal conditions of knowledge
existing in our minds; and I have given the history, both of this
development of ideas and of the matter derived from experience, in two
former works, the _History of Scientific Ideas_, and the _History of
the Inductive Sciences_. I have there traced this history through the
whole body of the physical sciences.

But though Ideas and Perceptions are thus separate elements in our
philosophy, they cannot in fact be distinguished and separated, but are
different aspects of the same thing. And the only way in which we can
approach to truth is by gradually and successively, in one instance
after another, advancing from the perception to the idea; from the fact
to the theory.

2. I would now further observe, that in this progression from fact
to theory, we advance (when the theory is complete and completely
possessed by the mind) from the apprehension of truths as _actual_ to
the apprehension of them as _necessary_; and thus Facts which were
originally observed merely as Facts become the consequences of theory,
and are thus brought within the domain of Ideas. That which was a part
of the objective world becomes also a part of the subjective world; a
necessary part of the thoughts of the theorist. And in this way the
progress of true theory is the _Idealization of Facts_.

Thus the Progress of Science consists in a perpetual reduction of Facts
to Ideas. Portions are perpetually transferred from one side to another
of the Fundamental Antithesis: namely, from the Objective to the
Subjective side. The Centre or Fulcrum of the Antithesis is shifted by
every movement which is made in the advance of science, and is shifted
so that the ideal side gains something from the real side.

3. I will proceed to illustrate this Proposition a little further.
Necessary Truths belong to the Subjective, Observed Facts to the
Objective side of our knowledge. Now in the progress of that exact
speculative knowledge which we call Science, Facts which were at a
previous period merely Observed Facts, come to be known as Necessary
Truths; and the attempts at new advances in science generally introduce
the representation of known truths of fact, as included in higher and
wider truths, and therefore, so far, necessary.

We may exemplify this progress in the history of the science of
Mechanics. Thus the property of the lever, the inverse proportion of
the weights and arms, was known as a fact before the time of Aristotle,
and known as no more; for he gives many fantastical and inapplicable
reasons for the fact. But in the writings of Archimedes we find this
fact brought within the domain of necessary truth. It was there
transferred from the empirical to the ideal side of the Fundamental
Antithesis; and thus a progressive step was made in science. In like
manner, it was at first taken by Galileo as a mere fact of experience,
that in a falling body, the velocity increases in proportion to the
time; but his followers have seen in this the necessary effect of the
uniform force of gravity. In like manner, Kepler's empirical Laws were
shown by Newton to be necessary results of a central force attracting
inversely as the square of the distance. And if it be still, even at
present, doubtful whether this is the _necessary_ law of a central
force, as some philosophers have maintained that it is, we cannot doubt
that if now or hereafter, those philosophers could establish their
doctrine as certain, they would make an important step in science, in
addition to those already made.

And thus, such steps in science are made, whenever empirical facts
are discerned to be necessary laws; or, if I may be allowed to use a
briefer expression, whenever _facts are idealized_.

4. In order to show how widely this statement is applicable, I will
exemplify it in some of the other sciences.

In Chemistry, not to speak of earlier steps in the science, which
might be presented as instances of the same general process, we may
remark that the analyses of various compounds into their elements,
according to the quantity of the elements, form a vast multitude of
facts, which were previously empirical only, but which are reduced
to a law, and therefore to a certain kind of ideal necessity, by the
discovery of their being compounded according to definite and multiple
proportions. And again, this very law of definite proportions, which
may at first be taken as a law given by experience only, it has been
attempted to make into a necessary truth, by asserting that bodies
must necessarily consist of atoms, and atoms must necessarily combine
in definite small numbers. And however doubtful this Atomic Theory may
at present be, it will not be questioned that any chemical philosopher
who could establish it, or any other Theory which would produce an
equivalent change in the aspect of the science, would make a great
scientific advance. And thus, in this Science also, the Progress of
Science consists in the transfer of facts from the empirical to the
necessary side of the antithesis; or, as it was before expressed, in
the idealization of facts.

5. We may illustrate the same process in the Natural History
Sciences. The discovery of the principle of Morphology in plants
was the reduction of a vast mass of Facts to an _Idea_; as Schiller
said to Göthe when he explained the discovery; although the latter,
cherishing a horror of the term _Idea_, which perhaps is quite as
common in England as in Germany, was extremely vexed at being told
that he possessed such furniture in his mind. The applications of this
Principle to special cases, for instance, to Euphorbia by Brown, to
Reseda by Lindley, have been attempts to idealize the facts of these
special cases.

6. We may apply the same view to steps in Science which are still
under discussion;--the question being, whether an advance has really
been made in science or not. For instance, in Astronomy, the Nebular
Hypothesis has been propounded, as an explanation of many of the
observed phenomena of the Universe. If this Hypothesis could be
conceived ever to be established as a true Theory, this must be done
by its taking into itself, as necessary parts of the whole Idea, many
Facts which have already been observed; such as the various form of
nebulæ;--many Facts which it must require a long course of years to
observe, such as the changes of nebulæ from one form to another;--and
many facts which, so far as we can at present judge, are utterly
at variance with the Idea, such as the motions of satellites, the
relations of the material elements of planets, the existence of
vegetable and animal life upon their surfaces. But if all these Facts,
when fully studied, should appear to be included in the general Idea
of Nebular Condensation according to the Laws of Nature, the Facts
so idealized would undoubtedly constitute a very remarkable advance
in science. But then, we are to recollect that we are not to suppose
that the Facts will agree with the Idea, merely because the Idea,
considered by itself, and without carefully attending to the Facts,
is a large and striking Idea. And we are also to recollect that the
Facts may be compared with another Idea, no less large and striking;
and that if we take into our account, (as, in forming an Idea of the
Course of the Universe, we must do,) not only vegetable and animal,
but also _human_ life, this other Idea appears likely to take into it
a far larger portion of the known Facts, than the Idea of the Nebular
Hypothesis. The other Idea which I speak of is the Idea of Man as the
principal Object in the Creation; to whose sustenance and development
the other parts of the Universe are subservient as means to an end; and
although, in our attempts to include all known Facts in this Idea, we
again meet with many difficulties, and find many trains of Facts which
have no apparent congruity with the Idea; yet we may say that, taking
into account the Facts of man's intellectual and moral condition, and
his history, as well as the mere Facts of the material world, the
difficulties and apparent incongruities are far less when we attempt
to idealize the Facts by reference to this Idea, of Man as the End of
Creation, than according to the other Idea, of the World as the result
of Nebular Condensation, without any conceivable End or Purpose. I am
now, of course, merely comparing these two views of the Universe, as
supposed steps in science, according to the general notion which I
have just been endeavouring to explain, that a step in science is some
Idealization of Facts.

7. Perhaps it will be objected, that what I have said of the
Idealization of Facts, as the manner in which the progress of science
goes on, amounts to no more than the usual expressions, that the
progress of science consists in reducing Facts to Theories. And to this
I reply, that the advantage at which I aim, by the expression which
I have used, is this, to remind the reader, that Fact and Theory, in
every subject, are not marked by separate and prominent features of
difference, but only by their present opposition, which is a transient
relation. They are related to each other no otherwise than as the poles
of the fundamental antithesis: the point which separates those poles
shifts with every advance of science; and then, what was Theory becomes
Fact. As I have already said elsewhere, a true Theory is a Fact; a Fact
is a familiar Theory. If we bear this in mind, we express the view
on which I am now insisting when we say that the progress of science
consists in reducing Facts to Theories. But I think that speaking of
_Ideas_ as opposed to Facts, we express more pointedly the original
Antithesis, and the subsequent identification of the Facts with the
Idea. The expression appears to be simple and apt, when we say, for
instance, that the Facts of Geography are identified with the Idea
of globular Earth; the Facts of Planetary Astronomy with the Idea of
the Heliocentric system; and ultimately, with the Idea of Universal
Gravitation.

8. We may further remark, that though by successive steps in science,
successive Facts are reduced to Ideas, this process can never be
complete. However the point may shift which separates the two poles,
the two poles will always remain. However, far the ideal element may
extend, there will always be something beyond it. However far the
phenomena may be idealized, there will always remain some which are
not idealized, and which are mere phenomena. This also is implied
by making our expressions refer to the fundamental antithesis: for
because the antithesis _is_ fundamental, its two elements will always
be present; the objective as well as the subjective. And thus, in the
contemplation of the universe, however much we understand, there must
always be something which we do not understand; however far we may
trace necessary truths, there must always be things which are to our
apprehension arbitrary: however far we may extend the sphere of our
internal world, in which we feel power and see light, it must always
be surrounded by our external world, in which we see no light, and
only feel resistance. Our subjective being is inclosed in an objective
shell, which, though it seems to yield to our efforts, continues entire
and impenetrable beyond our reach, and even enlarges in its extent
while it appears to give up to us a portion of its substance.


II. _Successive German Philosophies._

9. The doctrine of the Fundamental Antithesis of two elements of which
the union is involved in all knowledge, and of which the separation
is the task of all philosophy, affords us a special and distinct mode
of criticizing the philosophies which have succeeded each other in the
world; and we may apply it to the German Philosophies of which we have
spoken.

The doctrine of the Fundamental Antithesis is briefly this:

_That in every act of knowledge (1) there are two opposite elements
which we may call Ideas and Perceptions; but of which the opposition
appears in various other antitheses; as Thoughts and Things, Theories
and Facts, Necessary Truths and Experiential Truths; and the like: (2)
that our knowledge derives from the former of these elements, namely
our Ideas, its form and character as knowledge, our Ideas of space
and time being the necessary forms, for instance, of our geometrical
and arithmetical knowledge; (3) and in like manner, all our other
knowledge involving a development of the ideal conditions of knowledge
existing in our minds: (4) but that though ideas and perceptions are
thus separate elements in our philosophy, they cannot, in fact, be
distinguished and separated, but are different aspects of the same
thing; (5) that the only way in which we can approach to truth is by
gradually and successively, in one instance after another, advancing
from the perception to the idea; from the fact to the theory; from
the apprehension of truths as actual to the apprehension of them as
necessary. (6) This successive and various progress from fact to theory
constitutes the history of science; (7) and this progress, though
always leading us nearer to that central unity of which both the idea
and the fact are emanations, can never lead us to that point, nor to
any measurable proximity to it, or definite comprehension of its place
and nature._

10. Now the doctrine being thus stated, successive sentences of the
statement contain successive steps of German philosophy, as it has
appeared in the series of celebrated authors whom I have named.

Ideas, and Perceptions or Sensations, being regarded as the two
elements of our knowledge, Locke, or at least the successors of
Locke, had rejected the former element, Ideas, and professed to
resolve all our knowledge into Sensation. After this philosophy had
prevailed for a time, Kant exposed, to the entire conviction of the
great body of German speculators, the untenable nature of this account
of our knowledge. He taught (one of the first sentences of the above
statement) that (2) _Our knowledge derives from our Ideas its form
and character as knowledge; our Ideas of space and time being, for
instance, the necessary forms of our geometrical and arithmetical
knowledge_. Fichte carried still further this view of our knowledge,
as derived from our Ideas, or from its nature as knowledge; and held
that (3) _all our knowledge is a development of the ideal conditions of
knowledge existing in our minds_ (one of our next following sentences).
But when the ideal element of our knowledge was thus exclusively
dwelt upon, it was soon seen that this ideal system no more gave a
complete explanation of the real nature of knowledge, than the old
sensational doctrine had done. Both elements, Ideas and Sensations,
must be taken into account. And this was attempted by Schelling, who,
in his earlier works, taught (as we have also stated above) that (4)
_Ideas and Facts are different aspects of the same thing_:--this thing,
the central basis of truth in which both elements are involved and
identified, being, in Schelling's language, the _Absolute_, while each
of the separate elements is subjected to _conditions_ arising from
their union. But this Absolute, being a point inaccessible to us, and
inconceivable by us, as _our_ philosophy teaches (as above), cannot
to any purpose be made the basis of our philosophy: and accordingly
this _Philosophy of the Absolute_ has not been more permanent than
its predecessors. Yet the philosophy of Hegel, which still has a wide
and powerful sway in Germany, is, in the main, a development of the
same principle as that of Schelling;--the identity of the idea and the
fact; and Hegel's _Identity-System_, is rather a more methodical and
technical exposition of Schelling's Philosophy of the Absolute than
a new system. But Hegel traces the manifestation of the identity of
the idea and fact in the _progress_ of human knowledge; and thus in
some measure approaches to our doctrine (above stated), that (5) _the
way in which we approach to truth is by gradually and successively, in
one instance after another_, that is, _historically, advancing from
the perception to the idea, from the fact to the theory_: while at the
same time Hegel has not carried out this view in any comprehensive or
complete manner, so as to show that (6) _this process constitutes the
history of science_: and as with Schelling, his system shows an entire
want of the conviction (above expressed as part of our doctrine),
(7) that _we can never, in our speculations reach or approach to the
central unity of which both idea and fact are emanations_.

11. This view of the relation of the Sensational School, of the Schools
of Kant, Fichte, Schelling, and Hegel, and of the fundamental defects
of all, may be further illustrated. It will, of course, be understood
that our illustration is given only as a slight and imperfect sketch of
these philosophies; but their relation may perhaps become more apparent
by the very brevity with which it is stated; and the object of the
present chapter is not the detailed criticism of systems, but this very
relation of systems to each other.

The actual and the ideal, the external and the internal elements
of knowledge, were called by the Germans the _objective_ and the
_subjective_ elements respectively. The forms of knowledge and
especially space and time, were pronounced by Kant to be essentially
_subjective_; and this view of the nature of knowledge, more fully
unfolded and extended to all knowledge, became the _subjective
ideality_ of Fichte. But the subjective and the objective are, as
we have said, in their ultimate and supreme form, one; and hence
we are told of the _subjective-objective_, a phrase which has also
been employed by Mr. Coleridge. Fichte had spoken of the subjective
element as the _Me_, (das Ich); and of the objective element as the
_Not-me_, (das Nicht-Ich); and has deduced the _Not-me_ from the _Me_.
Schelling, on the contrary, laboured with great subtlety to deduce
the _Me_ from the _Absolute_ which includes both. And this Absolute,
or Subjective-objective, is spoken of by Schelling as unfolding itself
into endless other antitheses. It was held that from the assumption of
such a principle might be deduced and explained the oppositions which,
in the contemplation of nature, present themselves at every step, as
leading points of general philosophy:--for example, the opposition
of matter as _passive_ and _active_, as _dead_ and _organized_,
as _unconscious_ or _conscious_; the opposition of _individual_
and _species_, of _will_ and _moral rule_. And this antithetical
development was carried further by Hegel, who taught that the Absolute
Idea developes itself so as to assume qualities, limitations, and
seeming oppositions, and then completes the cycle of its development by
returning into unity.

12. That there is, in the history of Science, much which easily lends
itself to such a formula, the views which I have endeavoured to
expound, show and exemplify in detail. But yet the attempts to carry
this view into detail by conjecture--by a sort of divination--with
little or no attention to the historical progress and actual
condition of knowledge, (and such are those which have been made by
the philosophers whom I have mentioned,) have led to arbitrary and
baseless views of almost every branch of knowledge. Such oppositions
and differences as are found to exist in nature, are assumed as the
representatives of the elements of necessary antitheses, in a manner
in which scientific truth and inductive reasoning are altogether
slighted. Thus, this peculiar and necessary antithetical character is
assumed to be displayed in attraction and repulsion, in centripetal and
centrifugal forces, in a supposed positive and negative electricity,
in a supposed positive and negative magnetism; in still more doubtful
positive and negative elements of light and heat; in the different
elements of the atmosphere, which are, quite groundlessly, assumed to
have a peculiar antithetical character: in animal and vegetable life:
in the two sexes; in gravity and light. These and many others, are
given by Schelling, as instances of the radical opposition of forces
and elements which necessarily pervades all nature. I conceive that the
heterogeneous and erroneous principles involved in these views of the
material world show us how unsafe and misleading is the philosophical
assumption on which they rest. And the Triads of Hegel, consisting of
Thesis, Antithesis, and Union, are still more at variance with all
sound science. Thus we are told that matter and motion are determined
as _inertia_, _impulsion_, _fall_; that Absolute Mechanics determines
itself as _centripetal force_, _centrifugal force_, _universal
gravitation_. Light, it is taught, is a secondary determination of
matter. Light is the most intimate element of nature, and might be
called _the Me_ of nature: it is limited by what we may call negative
light, which is darkness.

13. In these rash and blind attempts to construct physical science
_à priori_, we may see how imperfect the Hegelian doctrines are as
a complete philosophy. In the views of moral and political subjects
the results of such a scheme are naturally less obviously absurd, and
may often be for a moment striking and attractive, as is usually the
case with attempts to reduce history to a formula. Thus we are told
that _the State_ appears under the following determinations:--first
as one, substantial, self-included: next, varied, individual, active,
disengaging itself from the substantial and motionless unity: next,
as two principles, altogether distinct, and placed front to front in
a marked and active opposition: then, arising out of the ruins of the
preceding, the idea appears afresh, one, identical, harmonious. And the
East, Greece, Rome, Germany, are declared to be the historical forms
of these successive determinations. Whatever amount of real historical
colour there may be for this representation, it will hardly, I think,
be accepted as evidence of a profound political philosophy; but on such
parts of the subject I shall not here dwell.

14. I may observe that in the series of philosophical systems now
described, the two elements of the Fundamental Antithesis are
alternately dwelt upon in an exaggerated degree, and then confounded.
The Sensational School could see in human knowledge nothing but
facts: Kant and Fichte fixed their attention almost entirely upon
ideas: Schelling and Hegel assume the identity of the two, (a point
we never can reach,) as the origin of their philosophy. The external
world in Locke's school was all in all. In the speculations of
Kant this external world became a dim and unknown region. Things
were acknowledged to be _something_ in themselves, but _what_, the
philosopher could not tell. Besides the _phænomenon_ which we see, Kant
acknowledged a _noumenon_ which we think of; but this assumption, for
such it is, exercises no influence upon his philosophy.

15. We may for the sake of illustration imagine to ourselves each
system of philosophy as a Drama in which _Things_ are the _Dramatis
Personæ_ and the _Idea_ which governs the system is the _Plot_ of the
drama. In Kant's Drama, Things in themselves are merely a kind of 'Mute
Personages,' κωφὰ πρόσωπα, which stand on the stage to be pointed at
and talked about, but which do not tell us anything, or enter into the
action of the piece. Fichte carries this further, and if we go on with
the same illustration, we may say that he makes the whole drama into
a kind of Monologue; in which the author tells the story, and merely
names the persons who appear. If we would still carry on the image,
we may say that Schelling, going upon the principle that the whole of
the drama is merely a progress to the Denouement, which denouement
contains the result of all the preceding scenes and events, starts
with the last scene of the piece; and bringing all the characters on
the stage in their final attitudes, would elicit the story from this.
While the true mode of proceeding is, to follow the drama Scene by
Scene, learning as much as we can of the Action and the Characters,
but knowing that we shall not be allowed to see the Denouement, and
that to do so is probably not the lot of our species on earth. So far
as any philosopher has thus followed the historical progress of the
grand spectacle offered to the eyes of speculative man, in which the
Phenomena of Nature are the Scenes, and the Theory of them the Plot, he
has taken the course by which knowledge really has made its advances.
But those who have partially done this, have often, like Hegel, assumed
that they had divined the whole course and end of the story, and have
thus criticised the scenes and the characters in a spirit quite at
variance with that by which any real insight into the import of the
representation can be obtained.

If it be asked which position we can assign, in this dramatic
illustration, to those who hold that all our knowledge is derived from
facts only, and who reject the supposition of ideas; we may say that
they look on with a belief that the drama has _no_ plot, and that these
scenes are improvised without connexion or purpose.

16. I will only offer one more illustration of the relative position
of these successive philosophies. Kant compares the change which he
introduced into philosophy to the change which Copernicus introduced
into astronomical theory. When Copernicus found that nothing could be
made of the phenomena of the heavens so long as everything was made
to turn round the spectator, he tried whether the matter might not be
better explained if he made the spectator turn, and left the stars
at rest. So Kant conceives that our experience is regulated by our
own faculties, as the phenomena of the heavens are regulated by our
own motions. But accepting and carrying out this illustration, we may
say that Kant, in explaining the phenomena of the heavens by means
of the motions of the earth, has almost forgotten that the planets
have their own proper motions, and has given us a system which hardly
explains anything besides broadest appearances, such as the annual and
daily motions of the sun; and that Fichte appears as if he wished to
deduce all the motions of the planets, as well as of the sun, from the
conditions of the spectator;--while Schelling goes to the origin of
the system, like Descartes, and is not content to show how the bodies
move, without also proving that from some assumed original condition,
all the movements and relations of the system must necessarily be what
they are. It may be that a theory which explains how the planets,
with their orbits and accompaniments, have come into being, may offer
itself to bold speculators, like those who have framed and produced
the nebular hypothesis. But I need not remind my readers either how
precarious such a hypothesis is; or, that if it be capable of being
considered probable, its proofs must gradually dawn upon us, step by
step, age after age: and that a system of doctrine which assumes such
a scheme as a certain and fundamental truth, and deduces the whole of
astronomy from it, must needs be arbitrary, and liable to the gravest
error at every step. Such a precarious and premature philosophy, at
best, is that of Schelling and Hegel; especially as applied to those
sciences in which, by the past progress of all sure knowledge, we are
taught what the real cause and progress of knowledge is: while at the
same time we may allow that all these forms of philosophy, since they
do recognize the condition and motion of the spectator, as a necessary
element in the explanation of the phenomena, are a large advance upon
the Ptolemaic scheme--the view of those who appeal to phenomena alone
as the source of our knowledge, and say that the sun, the moon, and
the planets move as we see them move, and that all further theory is
imaginary and fantastical.


FOOTNOTES:

[Footnote 295: The substance of this and the next chapter was printed
as a communication to the Cambridge Phil. Soc. in 1840.]

[Footnote 296: Or in the earlier editions, in the _Philosophy of the
Inductive Sciences_.]




CHAPTER XXV.

THE FUNDAMENTAL ANTITHESIS AS IT EXISTS IN THE MORAL WORLD.


1. We have hitherto spoken of the Fundamental Antithesis as the ground
of our speculations concerning the material world, at least mainly.
We have indeed been led by the physical sciences, and especially by
Biology, to the borders of Psychology. We have had to consider not only
the mechanical effects of muscular contraction, but the sensations
which the nerves receive and convey:--the way in which sensations
become perceptions; the way in which perceptions determine actions. In
this manner we have been led to the subject of volition or will[297],
and this brings us to a new field of speculation, the moral nature of
man; and this moral nature is a matter not only of speculative but
of practical interest. On this subject I shall make only a few brief
remarks.

2. Even in the most purely speculative view, the moral aspect of man's
nature differs from the aspect of the material universe, in this
respect, that in the moral world, external events are governed in
some measure by the human will. When we speculate concerning the laws
of material nature, we suppose that the phenomena of nature follow a
course and order which we may perhaps, in some measure, discover and
understand, but which we cannot change or control. But when we consider
man as an agent, we suppose him able to determine some at least of the
events of the external world; and thus, able to determine the actions
of other men, and to lay down laws for them. He cannot alter the
properties of fire and metals, stones and fluids, air and light; but he
can use fire and steel so as to compel other men's actions; stone-walls
and ocean-shores so as to control other men's motions; gold and gems
so as to have a hold on other men's desires; articulate sounds and
intelligible symbols so as to direct other men's thoughts and move
their will. There is an external world of Facts; and in this, the Facts
are such as he makes them by his Acts.

3. But besides this, there is also, standing over against this external
world of Facts, an internal world of Ideas. The Moral Acts without are
the results of Moral Ideas within. Men have an Idea of Justice, for
instance, according to which they are led to external acts, as to use
force, to make a promise, to perform a contract, as individuals; or to
make war and peace, to enact laws and to execute them, as a nation.

4. Some such internal moral Idea necessarily exists, along with
all properly human actions. Man feels not only pain and anger, but
indignation and the sentiment of wrong, which feelings imply a moral
idea of right and wrong. Again, what he thinks of as wrong, he tries to
prevent; what he deems right, he attempts to realize. The Idea gives
a character to the Act; the Act embodies the Idea. In the moral world
as in the natural world, the Antithesis is universal and inseparable.
It is an Antithesis of inseparable elements. In human action, there is
ever involved the Idea of what is right, and the external Act in which
this idea is in some measure embodied.

5. But the moral Ideas, such as that of Justice, of Rightness, and
the like, are always embodied incompletely in the world of external
action. Although men's actions are to a great extent governed by the
Ideas of Justice, Rightness and the like; (for it must be recollected
that we include in their actions, laws, and the enforcement of laws;)
yet there is a large portion of human actions which is not governed by
such ideas: (actions which result from mere desire, and violations of
law). There is a perpetual Antithesis of Ideas and Facts, which is the
fundamental basis of moral as of natural philosophy. In the former as
in the latter subject, besides what is ideal, there is an Actual which
the ideal does not include. This Actual is the region in which the
results of mere desire, of caprice, of apparent accident, are found. It
is the region of history, as opposed to justice; it is the region of
what _is_, as distinct from what _ought_ to be.

6. Now what I especially wish here to remark, is this;--that the
progress of man as a moral being consists in a constant extension of
the Idea into the region of Facts. This progress consists in making
human actions conform more and more to the moral Ideas of Justice,
Rightness, and the like; including in human actions, as we have said,
Laws, the enforcement of Laws, and other collective acts of bodies of
men. The History of Man _as_ Man consists in this extension of moral
Ideas into the region of Facts. It is not that the actual history of
what men do has always consisted in such an extension of moral Ideas;
for there has ever been, in the actual doings of men, a large portion
of facts which had no moral character; acts of desire, deeds of
violence, transgressions of acknowledged law, and the like. But such
events are not a part of the genuine progress of humanity. They do
not belong to the history of man as man, but to the history of man as
brute. On the other hand, there are events which belong to the history
of man as man, events which belong to the genuine progress of humanity;
such as the establishment of just laws; their enforcement; their
improvement by introducing into them a fuller measure of moral Ideas.
By such means there is a constant progress of man as a moral being.
By this _realization of moral Ideas_ there is a constant progress of
Humanity.

7. I have made this reflection, because it appears to me to bring
into view an analogy between the Progress of Science and the Progress
of Man, or of Humanity, in the sense in which I have used the term.
In both these lines of Progress, Facts are more and more identified
with Ideas. In both, there is a fundamental Antithesis of Ideas
and Facts, and progress consists in a constant advance of the point
which separates the two elements of this Antithesis. In both, Facts
are constantly won over to the domain of Ideas. But still, there is
a difference in the two cases; for in the one case the Facts are
beyond our control. We cannot make them other than they are; and all
that we can do, if we can do that, is to shape our Ideas so that they
shall coincide with the Facts, and still have the manifest connexion
which belongs to them as Ideas. In the other case, the Facts are, to
a certain extent, in our power. They are what we make them, for they
are what we do. In this case, the Facts ought to come towards the
Ideas, rather than the Ideas towards the Facts. As we called the former
process the Idealization of Facts, we may call this the Realization of
Ideas; and the analogy which I have here wished to bring into view may
be expressed by saying, that the Progress of Physical Science consists
in a constant successive Idealization of Physical Facts; and the
Progress of man's Moral Being is a constant successive Realization of
Moral Ideas.

8. Thus the necessary co-existence of an objective and a subjective
element belongs not only to human knowledge, as was before explained,
but also to human action. The objective and the subjective element are
inseparable in this case as in the other. We have always the Fact of
Positive Law, along with the Idea of Absolute Justice; the Facts of
Gain or Loss, along with the Idea of Rights. The Idea of Justice is
inseparable from historical facts, for justice gives to each his own,
and history determines what that is. We cannot even conceive justice
without society, or society without law, and thus in the moral and in
the natural world the fundamental antithesis is inseparable, even in
thought. The two elements must always subsist; for however far the
moral ideas be realized in the world, there will always remain much in
the world which is not conformable to moral ideas, even if it were only
through its necessary dependence on an unmoral and immoral past. As
in the physical world so in the moral, however much the ideal sphere
expands, it is surrounded by a region which is not conformable to the
idea, although in one case the expansion takes place by educing ideas
out of facts, in the other, by producing facts from ideas.

I shall hereafter venture to pursue further this train of speculation,
but at present I shall make some remarks on writers who may be regarded
as the successors amongst ourselves of these German schools of
Philosophy.


FOOTNOTES:

[Footnote 297: _Phil. of Biol._ c. v.]




CHAPTER XXVI.

OF THE "PHILOSOPHY OF THE INFINITE."


In the last Chapter but one I stated that Schelling propounded a
Philosophy of the Absolute, the Absolute being the original basis
of truth in which the two opposite elements, Ideas and Facts, are
identified, and that Hegel also founded his philosophy on the Identity
of these two elements. These German philosophies appear to me, as I
have ventured to intimate, of small or no value in their bearing on
the history of actual science. I have in the history of the sciences
noted instances in which these writers seem to me to misconceive
altogether the nature and meaning of the facts of scientific history;
as where[298] Schelling condemns Newton's Opticks as a fabric of
fallacies: and where[299] Hegel says that the glory due to Kepler has
been unjustly transferred to Newton. As it appears to me important that
English philosophers should form a just estimate of Hegel's capacity of
judging and pronouncing on this subject, I will print in the Appendix a
special discussion of what he has said respecting Newton's discovery of
the law of gravitation.

Recently attempts have been made to explain to English readers
these systems of German philosophy, and in these attempts there are
some points which may deserve our notice as to their bearing on the
philosophy of science. I find some difficulty in discussing these
attempts, for they deal much with phrases which appear to me to
offer no grasp to man's power of reason. What, for instance, is the
_Absolute_, which occupies a prominent place in these expositions? It
is, as I have stated, in Schelling, the central basis of truth in which
things and thoughts are united and identified. To attempt to reason
about such an "Absolute" appears to me to be an entire misapprehension
of the power of reason. Again; one of the most eminent of the
expositors has spoken of each system of this kind as a _Philosophy of
the Unconditioned_[300]. But what, we must ask, is the _Unconditioned_?
That which is subject to no conditions, is subject to no conditions
which distinguish it from any thing else, and so, cannot be a matter of
thought. But again; this _Absolute_ or _Unconditioned_ is (if I rightly
understand) said to be described also by various other names; _unity_,
_identity_, _substance_, _absolute cause_, the _infinite_, _pure
thought_, &c. As each of these terms expresses some condition on which
the name fixes our thoughts, I cannot understand why they should any of
them be called the _Unconditioned_; and as they express very different
thoughts, I cannot understand why they should be called by the same
name. From speculations starting from such a point, I can expect
nothing but confusion and perplexity; nor can I find that anything else
has come of them. They appear to me more barren, and more certain to be
barren, of any results which have any place in our real knowledge, than
the most barren speculations of the schoolmen of the middle ages: which
indeed they much resemble in all their features--their acuteness, their
learning, their ambitious aim, and their actual failure.

2. But leaving the Absolute and the Unconditioned, as notions which
cannot be dealt with by our reason without being something entirely
different from their definitions, we may turn for a moment to another
notion which is combined with them by the expositors of whom I speak,
and which has some bearing upon our positive science, because it enters
into the reasonings of mathematics: I mean the notion of _Infinite_.
Some of those who hold that we can know nothing concerning the
Absolute and the Unconditioned, (which they pretend to prove, though
concerning such words I do not conceive that anything can be true or
false,) hold also that the Infinite is in the same condition;--that we
can know nothing concerning what is Infinite;--therefore, I presume,
nothing concerning infinite space, infinite time, infinite number, or
infinite degrees.

To disprove this doctrine, it might be sufficient to point out that
there is a vast mass of mathematical science which includes the notion
of infinites, and leads to a great body of propositions concerning
Infinites. The whole of the infinitesimal calculus depends upon
conceiving finite magnitudes divided into an infinite number of parts:
these parts are infinitely small, and of these parts there are other
infinitesimal parts infinitely smaller still, and so on, as far as we
please to go. And even those methods which shun the term _infinite_, as
Newton's method of Ultimate Ratios, the method of Indivisibles, and the
method of Exhaustions of the ancient geometers, do really involve the
notion of infinite; for they imply a process continued without limit.

3. But perhaps it will be more useful to point out the fallacies of
the pretended proofs that we can know nothing concerning Infinity and
infinite things.

The argument offered is, that of infinity we have no notion but the
negation of a limit, and that from this negative notion no positive
result can be deduced.

But to this I reply: It is not at all true that our notion of what is
infinite is merely that it is _that_ which has no limit. We must ask
further that _what_? that space? that time? that number?--And if that
space, that what kind of space? That line? that surface? that solid
space?--And if that line, that line bounded at one end, or not? If that
surface, that surface bounded on one, or on two, or on three sides?
or on none? However any of these questions are answered, we may still
have an infinite space. Till they are answered, we can assert nothing
about the space; not because we can assert nothing about infinites; but
because we are not told what _kind_ of infinite we are talking of.

In reality the definition of an Infinite Quantity is not negative
merely, but contains a positive part as well. We assume a quantity
of a certain kind which may be augmented by carrying onward its
limits in one or more directions: this is a finite quantity of a
given kind. We _then_--when we have thus positively determined the
kind of the quantity--suppose the limit in one or more directions to
be annihilated, and thus we have an infinite quantity. But in this
infinite quantity there remain the positive properties from which we
began, as well as the negative property, the negation of a limit; and
the positive properties joined with the negative property may and do
supply grounds of reasoning respecting the infinite quantity.

4. This is lore so elementary to mathematicians that it appears almost
puerile to dwell upon it; but this seems to have been overlooked, in
the proof that we can have no knowledge concerning infinites. In such
proof it is assumed as quite evident, that all infinites are equal.
Yet, as we have seen, infinites may differ infinitely among themselves,
both in quantity and in kind. A German writer is quoted[301] for an
"ingenious" proof of this kind. In his writings, the opponent is
supposed to urge that a line _BAC_ may be made infinite by carrying
the extremity _C_ infinitely to the right, and again infinite by
carrying the extremity _B_ infinitely to the left; and thus the line
infinitely extended both ways would be double of the line infinite on
one side only. The supposed reply to this is, that it cannot be so,
because one infinite is equal to another: and moreover that what is
bounded at one end _A_, cannot be infinite: both which assumptions are
without the smallest ground. That one infinite quantity may be double
of another, is just as clear and certain as that one finite quantity
may. For instance, if one leaf of the book which the reader has before
him were produced infinitely upwards it would be an infinite space,
though bounded at the bottom and at both sides. If the other leaf were
in like manner produced infinitely upwards it would in like manner be
infinite; and the two together, though each infinite, would be double
of either of them.

5. As I have said, infinite quantities are conceived by conceiving
finite quantities increased by the transfer of a certain limit, and
then by negativing this limit altogether. And thus an infinite number
is conceived by assuming the series 1, 2, 3, 4, and so on, up to a
limit, and then removing this limit altogether. And this shows the
baselessness of another argument quoted from Werenfels. The opponent
asks, Are there in the infinite line an infinite number of feet?
Then in the double line there must be twice as many; and thus the
former infinite number did not contain all the (possible) unities;
(numerus infinitus non omnes habet unitates, sed præter eum concipi
possunt totidem unitates, quibus ille careat, eique possunt addi).
To which I reply, that the definition of an infinite number is not
that it contains all possible unities: but this--that the progress of
numeration being begun according to a certain law, goes on without
limit. And accordingly it is easy to conceive how one infinite number
may be larger than another infinite number, in any proportion. If, for
instance, we take, instead of the progression of the natural numbers 1,
2, 3, 4, &c. and the progression of the square numbers 1, 4, 9, 16, &c.
any term of the latter series will be greater than the corresponding
term of the other series in a ratio constantly increasing, and the
infinite term of the one, infinitely greater than the corresponding
infinite term of the other.

6. In the same manner we form a conception of infinite time, by
supposing time to begin now, and to go on, after the nature of time,
without limit; or by going back in thought from the present to a past
time, and by continuing this retrogression without limit. And thus we
have time infinite _a parte ante_ and _a parte post_, as the phrase
used to run; and time infinite both ways includes both, and is the most
complete notion of eternity.

7. Perhaps those who thus maintain that we cannot conceive anything
infinite, mean that we cannot form to ourselves a definite image of
anything infinite. And this of course is true. We cannot form to
ourselves an image of anything of which one of the characteristics is
that it is, in a certain way, unlimited. But this impossibility does
not prevent our reasoning about infinite quantities; combining as
elements of our reasoning, the absence of a limit with other positive
characters.

8. One of the consequences which is drawn by the assertors of the
doctrine that we cannot know anything about Infinity, is that we cannot
obtain from science any knowledge concerning God: And I have been the
more desirous to show the absence of proof of this doctrine, because I
conceive that science _does_ give us some knowledge, though it be very
little, of the nature of God: as I shall endeavour to show hereafter.

For instance, I conceive that when we say that God is an _eternal_
Being, this phraseology is not empty and unmeaning. It has been used
by the wisest and most thoughtful men in all ages, and, as I conceive,
may be used with undiminished, or with increased propriety, after
all the light which science and philosophy have thrown upon such
declarations. The reader of Newton will recollect how emphatically he
uses this expression along with others of a cognate character[302]:
"God is eternal and infinite, ... that is, He endures from eternity
to eternity, and is present from infinity to infinity.... He is not
eternity and infinity, but eternal and infinite. He is not duration and
space, but He endures and is present. He endures always, and is present
everywhere, and by existing always and everywhere He constitutes
duration and space." We shall see shortly that the view to which we are
led may be very fitly expressed by this language.

But I will first notice some other aspects of this philosophy.


FOOTNOTES:

[Footnote 298: _Hist. Ind. Sc._ b. ix. c. iii.]

[Footnote 299: _Ibid._ b. vii. c. ii.]

[Footnote 300: Sir W. Hamilton's Note on the _Philosophy of the
Unconditioned_.]

[Footnote 301: Werenfels in Mr. Mansel's _Bampton Lectures_, lect. ii.
Note 15.]

[Footnote 302: _Scholium Generale_ at the end of the _Principia_.]




CHAPTER XXVII.

SIR WILLIAM HAMILTON ON INERTIA AND WEIGHT.


In a preceding chapter I have spoken of Sir William Hamilton as the
expositor, to English readers, of modern German systems, and especially
of the so-called "Philosophy of the Unconditioned." But the same writer
is also noticeable as a continuator of the speculations of English and
Scottish philosophers concerning primary and secondary qualities; and
these speculations bear so far upon the philosophy of science that it
is proper to notice them here.


1. In our survey of the sciences, we have spoken of a class which we
have termed the Secondary Mechanical Sciences; these being the sciences
which explain certain sensible phenomena, as sound, light, and heat, by
means of a medium interposed between external bodies and our organs of
sense. In these cases, we ascribe to bodies certain qualities: we call
them resonant, bright, red or green, hot or cold. But in the sciences
which relate to these subjects, we explain these qualities by the
figure, size and motions of the parts of the medium which intervenes
between the object and the ear, eye, or other sensible organ. And those
former qualities, sound, warmth and colour, are called _secondary
qualities_ of the bodies; while the latter, figure, size and motion,
are called the _primary qualities_ of body.


2. This distinction, in its substance, is of great antiquity. The
atomic theory which was set up at an early period of Greek philosophy
was an attempt to account for the secondary qualities of bodies by
means of their primary qualities. And this is really the scientific
ground of the distinction. _Those_ are primary qualities or attributes
of body by means of which we, in a scientific view, explain and derive
their other qualities. But the explanation of the sensible qualities
of bodies by means of their operation through a medium has till now
been very defective, and is so still. We have to a certain extent
theories of Sound, Light and Heat, which reduce these qualities to
scales and standards, and in some measure account mechanically for
their differences and gradations. But we have as yet no similar theory
of Smells and Tastes. Still, we do not doubt that fragrance and flavour
are perceived by means of an aerial medium in which odours float, and
a fluid medium in which sapid matters are dissolved. And the special
odour and flavour which are thus perceived must depend upon the size,
figure, motion, number, &c. of the particles thus conveyed to the
organs of taste and smell: that is, _those_ secondary qualities, as
well as the others, must depend upon the primary qualities of the parts
of the medium.


3. In this way the distinction of primary and secondary qualities is
definite and precise. But when men attempt to draw the distinction
by guess, without any scientific principle, the separation of
the two classes is vague and various. I have, in the _History of
Scientific Ideas_[303], pointed out some of the variations which
are to be found on this subject in the writings of philosophers.
Sir William Hamilton[304] has given an account of many more which
he has compared and analysed with great acuteness. He has shown how
this distinction is treated, among others, by the ancient atomists,
Leucippus and Democritus, by Aristotle, Galen, Galileo, Descartes,
Boyle, Malebranche, Locke, Reid, Stewart, Royer-Collard. He then
proceeds to give his own view; which is, that we may most properly
divide the qualities of bodies into _three_ classes, which he calls
_Primary_, _Secundo-primary_, and _Secondary_. The former he enumerates
as 1, Extension; 2, Divisibility; 3, Size; 4, Density or Rarity; 5,
Figure; 6, Incompressibility absolute; 7, Mobility; 8, Situation.
The Secundo-primary are Gravity, Cohesion, Inertia, Repulsion. The
Secondary are those commonly so called, Colour, Sound, Flavour,
Savour, and Tactical Sensation; to which he says may be added the
muscular and cutaneous sensation which accompany the perception of the
Secundo-primary qualities. "Such, though less directly the result of
foreign causes, are Titillation, Sneezing, Horripilation, Shuddering,
the feeling of what is called Setting-the-teeth-on-edge, &c."

The Secundo-primary qualities Sir William Hamilton traces in further
detail. He explains that with reference to Gravity, bodies are _heavy_
or _light_. With reference to Cohesion, there are many coordinate
pairs, of which he enumerates these:--_hard_ and _soft_; _firm_
and _fluid_,--the fluid being subdivided into _thick_ and _thin_;
_viscid_ and _friable_; _tough_ and _brittle_; _rigid_ and _flexible_;
_fissile_ and _infissile_; _ductile_ and _inductile_; _retractile_
and _irretractile_; _rough_ and _smooth_; _slippery_ and _tenacious_.
With reference to Repulsion he gives these qualities:--_compressible_
and _incompressible_; _elastic_ and _inelastic_. And with reference to
Inertia he mentions only _moveable_ and _immoveable_.

I do not see what advantage is gained to philosophy by such an
enumeration of qualities as this, which, after all, does not pretend
to completeness; nor do I see anything either precise or fundamental
in such distinctions as that of elasticity, a mode of cohesion, and
elasticity, a mode of repulsion. But a question in which our philosophy
is really concerned is how far any of these qualities are _universal_
qualities of matter. Sir W. Hamilton holds that they are none of them
necessary qualities of matter, and therefore of course not universal,
and argues this point at some length. With regard to one of his
Secundo-primary qualities, I will make some remarks.


4. _Inertia._--In discussing the Ideas which enter into the Mechanical
Sciences[305], I have stated that the Idea of Force and Resistance to
Force, that is, of _Force_ and _Matter_, are the necessary foundations
of those sciences. Force cannot act without matter to act on; Matter
cannot exist without Force to keep its parts together and to keep it in
its place. But Force acting upon matter may either be Force producing
rest, or Force producing motion. If we consider Force producing motion,
the motion produced, that is, the velocity produced, must depend upon
the quantity of matter moved. It cannot be that the same power, acting
in the same way, shall produce the same velocity by pushing a small
pebble and a large rock. If this were so, we could have no science on
such matters. It must needs be that the same force produces a smaller
velocity in the larger body; and this according to some measure of
its largeness. The measure of the degree in which the body thus
resists this communication of motion is _inertia_. And the inertia is
necessarily supposed to be proportional to the quantity of matter,
because it is by this inertia that this existence and quantity of the
matter is measured. If therefore any Science concerning Force and
Matter is to exist, matter must have inertia, and the inertia must be
proportional to the quantity of matter.


5. Sir W. Hamilton, in opposition to this, says, that we can conceive
a body occupying space, and yet without attraction or repulsion for
another body, and wholly indifferent to this or that position, in
space, to motion and to rest. He infers thence that inertia is not a
necessary quality of bodies.

To this I reply, that even if we can conceive such bodies, (which in
fact man, living in a world of matter cannot conceive,) at any rate
we cannot conceive any _science_ about such bodies. If bodies were
indifferent to motion and rest, Forces could not be measured by their
effects; nor could be measured or known in any way. Such bodies might
float about like clouds, visible to the eye, but intangible, and
governed by no laws of motion. But if we have any science about bodies,
they must be tangible, and governed by laws of motion. Not, then, from
any observed properties of bodies, but from the possibility of any
science about bodies, does it follow that all bodies have inertia.


6. _Gravity._--Reasoning of the same kind may be employed about weight.
We can conceive, it is urged, matter without weight. But I reply,
we cannot conceive a _science_ which deals with matter that has no
weight:--a science, I mean, which deals with the quantity of matter of
bodies, as arising from the sum of their elements. For the quantity of
matter of bodies is and must be measured by those sensible properties
of matter which undergo quantitative addition, subtraction and
division, as the matter is added, subtracted, and divided. The quantity
of matter cannot be known in any other way. But this mode of measuring
the quantity of matter, in order to be true at all, must be universally
true. If it were only partially true--if some kinds of matter had
weight and others had not--the limits of the mode of measuring matter
by weight would be arbitrary: and therefore the whole procedure
would be arbitrary, and as a mode of obtaining philosophical truth,
altogether futile. But we suppose truth respecting the composition of
bodies to be attainable; therefore we must suppose the rule, which is
the necessary basis of such truth, to be itself true.

Sir W. Hamilton has replied to these arguments, but, as I conceive,
without affecting the force of them. I will repeat here the answer
which I have already given[306], and will reprint in the Appendix the
Memoir by which his objections were occasioned.

He says, (1), that our reasoning assumes that we must necessarily have
it in our power to ascertain the Quantity of Matter; whereas this may
be a problem out of the reach of human determination.

To this I reply, that my reasoning _does_ assume that there is a
science, or sciences, which make assertions concerning the Quantity
of Matter: Mechanics and Chemistry are such sciences. My assertion
is, that to make such sciences possible, Quantity of Matter must
be proportional to Weight. If my opponent deny that Mechanics and
Chemistry can exist as science, he may invalidate my proof; but not
otherwise.

(2) He says that there are two conceivable ways of estimating the
Quantity of Matter: by the Space occupied, and by the Weight or
Inertia; and that I assume the second measure gratuitously.

To which I reply, that the most elementary steps in Mechanics and
in Chemistry contradict the notion that the Quantity of Matter is
proportionate to the Space. They proceed necessarily on a distinction
between Space and Matter:--between mere Extension and material
Substance.

(3) He allows that we cannot make the Extension of a body the
measure of the Quantity of Matter, because, he says, we do not
know if "the compressing force" is such as to produce "the closest
compression." That is, he assumes a compressing force, assumes a
"closest compression," assumes a peculiar (and very improbable) atomic
hypothesis; and all this, to supply a reason why we are not to believe
the first simple principle of Mechanics and Chemistry.

(4) He speaks of "a series of apparent fluids (as Light or its vehicle,
the Calorific, the Electro-galvanic, and Magnetic agents) which we can
neither denude of their character of substance, nor clothe with the
attribute of weight."

To which my reply is, that precisely because I cannot "clothe" these
agents with the attribute of Weight, I _do_ "denude them of the
character of Substance." They are not substances, but agencies. These
Imponderable Agents are not properly called "Imponderable Fluids." This
I conceive that I have proved; and the proof is not shaken by denying
the conclusion without showing any defect in the reasoning.

(5) Finally, my critic speaks about "a logical canon," and about "a
criterion of truth, subjectively necessary and objectively certain;"
which matters I shall not waste the reader's time by discussing.


FOOTNOTES:

[Footnote 303: B. iv. c. i.]

[Footnote 304: Reid's _Works_, Supplementary Dissertation D.]

[Footnote 305: _Hist. Sc. Id._ b. iii.]

[Footnote 306: _Hist. Sc. Id._ b. vi. c. iii.]




CHAPTER XXVIII.

INFLUENCE OF GERMAN SYSTEMS OF PHILOSOPHY IN BRITAIN.


The philosophy of Kant, as I have already said, involved a definite
doctrine on the subject of the Fundamental Antithesis, and a correction
of some of the errors of Locke and his successors. It was not however
at first favourably received among British philosophers, and those who
accepted it were judged somewhat capriciously and captiously. I will
say a word on these points[307].

1. (_Stewart_)--Dugald Stewart, in his _Dissertation on the Progress
of the Moral Sciences_, repeatedly mentions Kant's speculations, and
always unfavourably. In Note I to Part I. of the Dissertation he says,
"In our own times, Kant and his followers seem to have thought that
they had thrown a strong light on the nature of _space_ and also of
_time_, when they introduced the word _form_ (_form of the intellect_)
as a common term applicable to both. Is not this to revert to the
scholastic folly of verbal generalization?" And in Part II. he gives a
long and laborious criticism of a portion of Kant's speculations; of
which the spirit may be collected from his describing them as resulting
in "the metaphysical _conundrum_, that the human mind (considered as
a _noumenon_ and not as a _phenomenon_) neither exists in space nor
time." And after mentioning Meiners and Herder along with Kant, he
adds, "I am ashamed to say that in Great Britain the only one of these
names which has been much talked of is Kant." And again in Note EE, he
translates some portion of the German philosopher, adding, that to the
expressions so employed he can attach no meaning.

Stewart, in his criticism of Kant's doctrines, remarks that, in
asserting that the human mind possesses, in its own ideas, an element
of necessary and universal truth, not derived from experience, Kant had
been anticipated by Price, by Cudworth, and even by Plato; to whose
_Theætetus_ both Price and Cudworth refer, as containing views similar
to their own. And undoubtedly this doctrine of ideas, as indispensable
sources of necessary truths, was promulgated and supported by weighty
arguments in the _Theætetus_; and has ever since been held by many
philosophers, in opposition to the contrary doctrine, also extensively
held, that all truth is derived from experience. But, in pointing out
this circumstance as diminishing the importance of Kant's speculations,
Stewart did not sufficiently consider that doctrines, fundamentally the
same, may discharge a very different office at different periods of
the history of philosophy. Plato's Dialogues did not destroy, nor even
diminish, the value of Cudworth's "Immutable Morality." Notwithstanding
Cudworth's publications, Price's doctrines came out a little afterwards
with the air and with the effect of novelties. Cudworth's assertion of
ideas did not prevent the rise of Hume's skepticism; and it was Hume's
skepticism which gave occasion to Kant's new assertion of necessary
and universal truth, and to his examination into the grounds of the
possibility and reality of such truth. To maintain such doctrine
_after_ the appearance of intermediate speculations, and with reference
to them, was very different from maintaining it before; and this is the
merit which Kant's admirers claim for him. Nor can it be denied that
his writings produced an immense effect upon the mode of treating such
questions in Germany; and have had, even in this country, an influence
far beyond what Mr. Stewart would have deemed their due.


2. (_Mr. G. H. Lewes._)--But as injustice has thus been done to Kant by
confounding his case with that of his predecessors of like opinions,
so on the other hand, injustice has also been done, both to him and
those who have followed him in the assertion of ideas, by confounding
_their_ case with his. This injustice seems to me to be committed by a
writer on the History of Philosophy, who has given an account of the
successive schools of philosophy up to our own time;--has assigned
to Kant an important and prominent place in the recent history of
metaphysics;--but has still maintained that Kant's philosophy, and
indeed every philosophy, is and must be a failure. In order to prove
this thesis, the author naturally has to examine Kant's doctrines and
the reasons assigned for them, and to point out what he conceives to be
the fallacy of these arguments. This accordingly he professes to do;
but as soon as he has entered upon the argument, he substitutes, as
his opponent, for the philosopher of Königsberg, a writer of our own
time and country, who does not profess himself a Kantian, who has been
repeatedly accused, with whatever justice, of misrepresenting what he
has borrowed from Kant, and whose main views are, in the opinion of
the writer himself, very different from Kant's. Mr. Lewes[308], in the
chapter entitled "Examination of Kant's Fundamental Principles," after
a preliminary statement of the points he intends to consider, says "Now
to the question. As Kant confessedly was led to his own system by the
speculations of Hume," and so on; and forthwith he introduces the name
of _Dr. Whewell_ as the writer whose views he has to criticize, without
stating how he connects him with Kant, and goes on arguing against
_him_ for a dozen pages to the end of the Chapter.

3. It is true, however, that I had adopted some of Kant's views, or at
least some of his arguments. The chapters[309] on the Ideas of Space
and Time in the _Philosophy of the Inductive Sciences_, were almost
literal translations of chapters in the _Kritik der Reinen Vernunft_.
Yet the author was charged by a reviewer at the time, with explaining
these doctrines "in a manner incompatible with the clear views of
Emanuel Kant." It appeared to be assumed by the English admirers of the
Kantian philosophy, that Kant's views were true and clear in Germany,
but became untenable when adopted in England.


4. (_Mr. Mansel_)--But the most important of my critics on this
ground is Mr. Mansel, who has revived the censure of my speculations
as not doing justice to the Kantian philosophy. "It is much to be
regretted," he says[310], "that Dr. Whewell, who has made good use of
Kantian principles in many parts of his _Philosophy of the Inductive
Sciences_," has not more accurately observed Kant's distinction between
the necessary laws under which all men think, and the contingent
laws under which certain men think of certain things. And further on
Mr. Mansel, after giving great praise to the general spirit of the
_Philosophy of the Inductive Sciences_, says, "It is to be regretted
that the accuracy of his theory has been in so many instances vitiated
by a stumble at the threshold of the Critical Philosophy." Mr. Mansel
is, indeed, by much the most zealous English Kantian whose writings I
have seen;--among those, I mean, who have brought original powers of
philosophical thought to bear upon such subjects; and have not been, as
some have been, enslaved by an admiration of German systems, just as
bigotted as the contempt of them which others feel. And as Mr. Mansel
has stated distinctly some of the points in which he conceives that I
have erred in deviating from the doctrines of Kant, I should wish to
make a few remarks on those points.

5. Kant considers that Space and Time are conditions of perception,
and hence sources of necessary and universal truth. Dr. Whewell agrees
with Kant in placing in the mind certain sources of necessary truth;
he calls these Fundamental Ideas, and reckons, besides Space and Time,
others, as Cause, Likeness, Substance, and several more. Mr. Mill,
the most recent and able expounder of the opposite doctrine, derives
all truths from Observation, and denies that there is such a separate
source of truth as Ideas. Mr. Mansel does not agree either with Mr.
Mill or Dr. Whewell; he adheres to the original Kantian thesis, that
Space and Time are sources of necessary truths, but denies the office
to the other Fundamental Ideas of Dr. Whewell. In reading what has
been said by Mr. Mill, Mr. Mansel, and other critics, on the subject
of what I have called _Fundamental Ideas_, I am led to perceive that
I have expressed myself incautiously, with regard to the identity of
character between the first two of these Fundamental Ideas, namely,
Space and Time, and the others, as Force, Composition, and the like.
And I am desirous of explaining, to those who take an interest in these
speculations, how far I claim for the other Fundamental Ideas the same
character and attributes as for Space and Time.

6. The special and characteristic property of all the Fundamental Ideas
is what I have already mentioned, that they are the mental sources of
necessary and universal scientific truths. I call them _Ideas_, as
being something not derived from sensation, but governing sensation,
and consequently giving form to our experience;--_Fundamental_, as
being the foundation of knowledge, or at least of Science. And the way
in which those Ideas become the foundations of Science is, that when
they are clearly and distinctly entertained in the mind, they give rise
to inevitable convictions or intuitions, which may be expressed as
_Axioms_; and these Axioms are the foundations of Sciences respective
of each Idea. The Idea of Space, when clearly possessed, gives rise
to geometrical Axioms, and is thus the foundation of the Science of
Geometry. The Idea of Mechanical Force, (a modification of the Idea of
Cause,) when clearly developed in the mind, gives birth to Axioms which
are the foundation of the Science of Mechanics. The Idea of Substance
gives rise to the Axiom which is universally accepted,--that we cannot,
by any process, (for instance, by chemical processes,) create or
destroy matter, but can only combine and separate elements;--and thus
gives rise to the Science of Chemistry.


7. Now it may be observed, that in giving this account of the
foundation of Science, I lay stress on the condition that the Ideas
must be _clearly and distinctly possessed_. The Idea of Space must be
quite clear in the mind, or else the Axioms of Geometry will not be
seen to be true: there will be no _intuition_ of their truth; and for
a mind in such a state, there can be no Science of Geometry. A man may
have a confused and perplexed, or a vacant and inert state of mind, in
which it is not clearly apparent to him, that two straight lines cannot
inclose a space. But this is not a frequent case. The Idea of Space is
much more commonly clear in the minds of men than the other Ideas on
which science depends, as Force, or Substance. It is much more common
to find minds in which these latter Ideas are not so clear and distinct
as to make the Axioms of Mechanics or of Chemistry self-evident.
Indeed the examples of a state of mind in which the Ideas of Force
or of Substance are so clear as to be made the basis of science, are
comparatively few. They are the examples of minds scientifically
cultivated, at least to some extent. Hence, though the Axioms of
Mechanics or of Chemistry may be, in their own nature, as evident as
those of Geometry, they are not evident to so many persons, nor at so
early a period of intellectual or scientific culture. And this being
the case, it is not surprising that some persons should doubt whether
these Axioms are evident at all;--should think that it is an error to
assert that there exist, in such sciences as Mechanics or Chemistry,
Fundamental Ideas, fit to be classed with Space, as being, like it, the
origin of Axioms.

In speaking of all the Fundamental Ideas as being alike the source of
Axioms when clearly possessed, without dwelling sufficiently upon the
amount of mental discipline which is requisite to give the mind this
clear possession of most of them; and in not keeping before the reader
the different degrees of evidence which, in most minds, the Axioms
of different sciences naturally have, I have, as I have said, given
occasion to my readers to misunderstand me. I will point out one or two
passages which show that this misunderstanding has occurred, and will
try to remove it.

8. The character of axiomatic truths seen by intuition is, that
they are not only seen to be true, but to be necessary;--that the
contrary of them is not only false, but inconceivable. But this
inconceivableness depends entirely upon the clearness of the Ideas
which the axioms involve. So long as those Ideas are vague and
indistinct, the contrary of an Axiom may be assented to, though it
cannot be distinctly conceived. It may be assented to, not because it
is possible, but because _we_ do not see clearly what _is_ possible. To
a person who is only beginning to think geometrically, there may appear
nothing absurd in the assertion, that two straight lines may inclose
a space. And in the same manner, to a person who is only beginning
to think of mechanical truths, it may not appear to be absurd, that
in mechanical processes, Reaction should be greater or less than
Action; and so, again, to a person who has not thought steadily
about Substance, it may not appear inconceivable, that by chemical
operations, we should generate new matter, or destroy matter which
already exists.

Here then we have a difficulty:--the test of Axioms is that the
contrary of them is inconceivable; and yet persons, till they have in
some measure studied the subject, do not see this inconceivableness.
Hence our Axioms must be evident only to a small number of thinkers;
and seem not to deserve the name of self-evident or necessary truths.

This difficulty has been strongly urged by Mr. Mill, as supporting
his view, that all knowledge of truth is derived from experience. And
in order that the opposite doctrine, which I have advocated, may not
labour under any disadvantages which really do not belong to it, I must
explain, that I do not by any means assert that those truths which
I regard as necessary, are all equally evident to common thinkers,
or evident to persons in all stages of intellectual development. I
may even say, that some of those truths which I regard as necessary,
and the necessity of which I believe the human mind to be capable of
seeing, by due preparation and thought, are still such, that this
amount of preparation and thought is rare and peculiar; and I will
willingly grant, that to attain to and preserve such a clearness and
subtlety of mind as this intuition requires, is a task of no ordinary
difficulty and labour.

9. This doctrine,--that some truths may be seen by intuition, but yet
that the intuition of them may be a rare and difficult attainment,--I
have not, it would seem, conveyed with sufficient clearness to obviate
misapprehension. Mr. Mill has noticed a passage of my _Philosophy_
on this subject, which he has understood in a sense different from
that which I intended. Speaking of the two Principles of Chemical
Science,--that combinations are definite in kind, and in quantity,--I
had tried to elevate myself to the point of view in which these
Principles are seen, not only to be true, but to be necessary. I was
aware that even the profoundest chemists had not ventured to do this;
yet it appeared to me that there were considerations which seemed to
show that any other rule would imply that the world was a world on
which the human mind could not employ itself in scientific speculation
at all. These considerations I ventured to put forwards, not as views
which could at present be generally accepted, but as views to which
chemical philosophy appeared to me to tend. Mr. Mill, not unnaturally,
I must admit, supposed me to mean that the two Principles of Chemistry
just stated, are self-evident, in the same way and in the same
degree as the Axioms of Geometry are so. I afterwards explained that
what I meant to do was, to throw out an opinion, that _if_ we could
conceive the composition of bodies _distinctly_, we might be able to
see that it is necessary that the modes of this composition should
be definite. This Mr. Mill does not object to[311]: but he calls it
a great attenuation of my former opinion; which he understood to be
that we, (that is, men in general,) already see, or may see, or ought
to see, this necessity. Such a general apprehension of the necessity
of definite chemical composition I certainly never reckoned upon;
and even in my own mind, the thought of such a necessity was rather
an anticipation of what the intuitions of philosophical chemists in
another generation would be, than an assertion of what they now are or
ought to be; much less did I expect that persons, neither chemists nor
philosophers, would already, or perhaps ever, see that a proposition,
so recently discovered to be true, is not only true, but necessary.

10. Of the bearing of this view on the question at issue between Mr.
Mill and me, I may hereafter speak; but I will now notice other persons
who have misunderstood me in the same way.

An able writer in the _Edinburgh Review_[312] has, in like manner,
said, "Dr. Whewell seems to us to have gone much too far in reducing
to necessary truths what assuredly the generality of mankind will not
feel to be so." It is a fact which I do not at all contest, that the
_generality of mankind_ will not feel the Axioms of Chemistry, or even
of Mechanics, to be necessary truths. But I had said, not that the
generality of mankind would feel this necessity, but (in a passage
just before quoted by the Reviewer) that the mind under certain
circumstances _attains a point of view_ from which it can pronounce
mechanical (and other) fundamental truths to be necessary in their
nature, though disclosed to us by experience and observation.

Both the Edinburgh Reviewer and Mr. Mansel appear to hold a distinction
between the fundamental truths of Geometry, and those of the other
subjects which I have classed with them. The latter says, that
perhaps metaphysicians may hereafter establish the existence of other
subjective conditions of intuitions (or, as I should call them,
Fundamental Ideas,) besides Space and Time, but that in asserting
such to exist in the science of Mechanics, I certainly go too far:
and he gives as an instance my Essay,--"Demonstration that all matter
is heavy." I certainly did not expect that the Principles asserted
in that Essay would be assented to as readily or as generally as the
Axioms of Geometry; but I conceive that I have there proved that
Chemical Science, using the balance as one of its implements, cannot
admit "imponderable bodies" among its elements. This impossibility
will, I think, not only be found to exist in fact, but seen to exist
necessarily, by chemists, in proportion as they advance towards general
propositions of Chemical Science in which the so-called "imponderable
fluids" enter. But even if I be right in this opinion, to how few will
this necessity be made apparent, and how slowly will the intuition
spread! I am as well aware as my critics, that the necessity will
probably never be apparent to ordinary thinkers.


11. Though Mr. Mansel does not acknowledge any subjective conditions
of intuition besides Space and Time, he does recognize other _kinds
of necessity_, which I should equally refer to Fundamental Ideas;
because they are, no less than Space and Time, the foundations of
universal and necessary truths in science. Such are[313] the Principle
of Substance;--All Qualities exist in some subject: and the Principle
of Causality;-- Every Event has its Cause. To these Principles he
ascribes a "metaphysical necessity," the nature and grounds of which
he analyses with great acuteness. But what I have to observe is, that
whatever _differences_ may be pointed out between the _grounds_ of
the necessity, in this case of _metaphysical_ necessity, and in that
which Mr. Mansel calls _mathematical_ necessity which belongs to the
Conditions or Ideas of Space and of Time; still, it is not the less
true that the Ideas of Substance and of Cause, _do_ afford a foundation
for necessary truths, and that on these truths are built Sciences. That
every Change must have a Cause, with the corresponding Axioms,--that
the Cause is known by the Effect, and Measured by it,--is the basis
of the Science of Mechanics. That there is a Substance to which
qualities belong, with the corresponding Axiom,--that we cannot create
or destroy Substance, though we may alter Qualities by combining and
separating Substances,--is the basis of the Science of Chemistry. And
that this doctrine of the Indestructibility of Substance is a primary
axiomatic truth, is certain; both because it has been universally taken
for granted by men seeking for general truths; and because it is not
and cannot be proved by experience[314]. So that I have here, even
according to Mr. Mansel's own statement, other grounds besides Space
and Time, for necessary truths in Science.

12. Besides mathematical and metaphysical necessity, Mr. Mansel
recognizes also a _logical necessity_. I will not pretend to say
that this kind of necessity is exactly represented by any of those
Fundamental Ideas which are the basis of Science; but yet I think it
will be found that this logical necessity mainly operates through
the attribution of Names to things; and that a large portion of its
cogency arises from these maxims,--that names must be so imposed that
General Propositions shall be possible,--and so that Reasoning shall be
possible. Now these maxims are really the basis of Natural History,
and are so stated in the _Philosophy of the Inductive Sciences_. The
former maxim is the principle of all Classification; and though we have
no syllogisms in Natural History, the apparatus of _genus_, _species_,
_differentia_, and the like, which was introduced in the analysis of
syllogistic reasoning, is really more constantly applied in Natural
History than in any other science.

13. Besides the different kinds of necessity which Mr. Mansel thus
acknowledges, I do not see why he should not, on his own principles,
recognize others; as indeed he appears to me to do. He acknowledges,
I think, the distinction of Primary and Secondary qualities; and
this must involve him in the doctrine that Secondary Qualities are
necessarily perceived by means of a _Medium_. Again: he would, I
think, acknowledge that in organized bodies, the parts exist for a
_Purpose_; and Purpose is an Idea which cannot be inferred by reasoning
from facts, without being possessed and applied as an Idea. So that
there would, I conceive, exist, in his philosophy, all the grounds of
necessary truth which I have termed Fundamental Ideas; only that he
would further subdivide, classify, and analyse, the kinds and grounds
of this necessity.

In this he would do well; and some of his distinctions and analyses
of this kind are, in my judgment, very instructive. But I do not see
what objection there can be to my putting together all these kinds of
necessity, when my purpose requires it; and, inasmuch as they all are
the bases of Science, I may call them by a general name; for instance,
Grounds of Scientific Necessity; and these are precisely what I mean by
_Fundamental Ideas_.

That some steady thought, and even some progress in the construction
of Science, is needed in order to see the necessity of the Axioms thus
introduced, is true, and is repeatedly asserted and illustrated in the
History of the Sciences. The necessity of such Axioms is seen, but it
is not seen at first. It becomes clearer and clearer to each person,
and clear to one person after another, as the human mind dwells more
and more steadily on the several subjects of speculation. _There are
scientific truths which are seen by intuition, but this intuition
is progressive._ This is the remark which I wish to make in answer
to those of my critics who have objected that truths which I have
propounded as Axioms, are not evident to all.


14. That the Axioms of Science are not evident _to all_, is true
enough, and too true. Take the Axiom of Substance:--that we may change
the condition of a substance in various ways, but cannot destroy it.
This has been assumed as evident by philosophers in all ages; but if
we ask an ordinary person whether a body can be destroyed by fire, or
diminished, will he unhesitatingly reply, that it cannot? It requires
some thought to say[315], as the philosopher said, that the weight of
the smoke is to be found by subtracting the weight of the ashes from
that of the fuel; nay, even when this is said, it appears, at first,
rather an epigram than a scientific truth. Yet it is by thinking only,
not by an experiment, that, from a happy guess it becomes a scientific
truth. And the thought is the basis, not the result, of experimental
truths; for which reason I ascribe it to a Fundamental Idea. And so,
such truths are the genuine growth of the human mind; not innate,
as if they needed not to grow; still less, dead twigs plucked from
experience and stuck in from without; not universal, as if they grew
up everywhere; but not the less, under favourable circumstances, the
genuine growth of the scientific intellect.

15. Not only do I hold that the Axioms, on which the truths of science
rest, grow from guesses into Axioms in various ways, and often
gradually, and at different periods in different minds, and partially,
even in the end; but I conceive that this may be shown by the history
of science, as having really happened, with regard to all the most
conspicuous of such principles. The scientific insight which enabled
discoverers to achieve their exploits, implied that they were among
the first to acquire an intuitive conviction of the Axioms of their
Science: the controversies which form so large a portion of the history
of science, arise from the struggles between the clear-sighted and
the dimsighted, between those who were forwards and those who were
backwards in the progress of ideas; and these controversies have very
often ended in diffusing generally a clearness of thought, on the
controverted subject, which at first, the few only, or perhaps not
even they, possessed. The History of Science consists of the History
of Ideas, as well as of the History of Experience and Observation.
The latter portion of the subject formed the principal matter of my
_History_ of the Inductive Sciences; the former occupied a large
portion of the _Philosophy_ of the Inductive Sciences[316]; which, I
may perhaps be allowed to explain, is, for the most part, a Historical
Work no less than the other; and was written in a great measure, at the
same time, and from the same survey of the works of scientific writers.

16. I am aware that the explanation which I have given, may naturally
provoke the opponents of the doctrine of scientific necessity to
repeat their ordinary fundamental objections, in a form adapted to
the expressions which I have used. They may say, the fact that these
so-called Axioms thus become evident only during the progress of
experience, proves that they are derived from experience: they may,
in reply to our image, say, that truths are stuck into the mind by
experience, as seeds are stuck into the ground; and that to maintain
that they can grow under any other conditions, is to hold the
doctrine of spontaneous generation, which is equally untenable in the
intellectual and in the physical world. I shall not however here resume
the general discussion; but shall only say briefly in reply, that
Axioms,--for instance, this Axiom, that _material substances cannot be
created or annihilated by any process which we can apply_,--though it
becomes evident in the progress of experience, cannot be derived from
experience; for it is a proposition which never has nor can be proved
by experience; but which, nevertheless, has been always assumed by men,
seeking for general truths, as necessarily true, and as controlling
and correcting all possible experience. And with regard to the image
of vegetable development, I may say, that as such development implies
both inherent forms in the living seed, and nutritive powers in earth
and air; so the development of our scientific ideas implies both a
formative power, and materials acted on; and that, though the analogy
must be very defective, we conceive that we best follow it by placing
the formative power in the living mind, and in the external world the
materials acted on: while the doctrine that all truth is derived from
experience only, appears to reject altogether one of these elements, or
to assert the two to be one.


FOOTNOTES:

[Footnote 307: The remarks contained in this chapter have for the most
part been already printed and circulated in a _Letter to the Author of
Prolegomena Logica_, 1852.]

[Footnote 308: _Biographical History of Philosophy_, 1846. In a more
recent edition the author of this work has modified his expressions,
but still employs himself in arguing against Dr. Whewell, in order to
overthrow Kant. So far as his arguments affect my philosophy, they are,
as I conceive, answered in the various expositions which I have given
of that philosophy.]

[Footnote 309: B. ii. The Philosophy of the Pure Sciences. Chap.
ii. Of the Idea of Space. Chap. iii. Of some peculiarities of the
Idea of Space. Chap. vii. Of the Idea of Time. Chap. viii. Of some
peculiarities of the Idea of Time.]

[Footnote 310: _Prolegomena Logica_, by H. L. Mansel, M.A. 1851.]

[Footnote 311: _Logic_, i. p. 273, 3rd edit.]

[Footnote 312: No. 193, p. 29.]

[Footnote 313: _Prol. Log._ p. 123.]

[Footnote 314: See _Phil. Ind. Sc._ b. vi. c. iii.]

[Footnote 315: Kant.]

[Footnote 316: Republished as _The History of Scientific Ideas_.]




CHAPTER XXIX.

NECESSARY TRUTH IS PROGRESSIVE.


OBJECTIONS CONSIDERED.

The doctrine that necessary truth is progressive is a doctrine very
important in its bearing upon the nature of the human mind; and, as
I conceive, in its theological bearing also. But it is a doctrine to
which objections are likely to be made from various quarters, and I
will consider some of these objections.

1. Necessary truths, it will be said, cannot increase in number. New
ones cannot be added to the old ones. For necessary truths are those of
which the necessity is plain and evident to all mankind--to the common
sense of man; such as the axioms of geometry. But that which is evident
to all mankind must be evident from the first: that which is plain to
the common sense of man cannot require scientific discovery: that which
is necessarily true cannot require accumulated proof.

To this I reply, that necessary truths require for their apprehension
a certain growth and development of the human mind. Though it is seen
that they are necessarily true, this is seen only by those who think
steadily and clearly, and to think steadily and clearly on any kind
of subject, requires time and attention;--requires mental culture.
This may be seen even in the case of the axioms of geometry. These
axioms are self-evident: but to _whom_ are they self-evident? Not to
uncultured savages, or young children; or persons of loose vague habits
of thought. To see the truth and necessity of geometrical axioms, we
need geometrical culture.

Therefore that any axioms are not evident without patient thought and
continued study of the subject, does not disprove their necessity.
Principles may be axiomatic and necessary, although they require time,
and the progress of thought and of knowledge, to bring them to light.
And axioms may be thus gradually brought to light by the progress of
knowledge.

Nor is it difficult to give examples of such axioms, other than
geometrical. There is an axiom which has obtained currency among
thoughtful men from the time that man began to speculate about himself
and the universe:--_E nihilo nil fit_: Nothing can be made of nothing.
No material substance can be produced or destroyed by natural causes,
though its form and consistence may be changed indefinitely. Is not
this an axiom? a necessary truth? Yet it is not evident to all men
at first, and without mental culture. At first and before habits of
steady and consistent thought are formed, men think familiarly of the
creation and destruction of matter. Only when the mind has received
some philosophical culture does it see the truth and necessity of the
axiom of substance, and _then_ it does see it.

And the axioms on which the science of mechanics rests, that the cause
is measured by the effects, that reaction is equal and opposite to
action, and the like,--are not these evident to a mind cultivated by
steady thought on such subjects? and do they not require such culture
of the mind in order to see them? Are they not obscure or uncertain
to those who are not so cultured, that is to common thinkers: to the
general bulk of mankind? Thus then it requires the discipline of the
science of mechanics to enable the mind to see the axioms of that
science.

And does not this go further, as science and the careful study of
the grounds of science go further? To a person well disciplined in
mechanical reasoning it has become, not a conclusion, but a principle,
that in mechanical action what is gained in power is lost in time:
or that in any change, the force gained is equal to the force lost,
so that new force cannot be generated, any more than new matter, by
natural changes. Is this an axiom? a necessary fundamental truth? It
appears so to at least one great thinker and discoverer now alive
among us. If it do not appear so to us, or not in the same sense,
may not this be because we have not yet reached his point of view?
May not the conviction which is now his alone become hereafter the
conviction of the philosophical world? And whatever the case may be
in this instance, have there not been examples of this progress? Did
not Galileo and the disciples of Galileo reduce several mechanical
principles to the character of necessary truths, after they had by
experiment and reasoning discovered them to be actually true? And
have we not in these cases so many proofs that necessary truth is
progressive, along with the progress of knowledge?

2. But, it will be said, the necessary character claimed for such
truths is an illusion. The propositions so brought into view are really
established by observation: by the study of external facts: and it is
only the effect of habit and familiarity which makes men of science,
when they well know them to be true, think them to be necessarily true.
They are really the results of experience, as their history shows; and
therefore cannot be necessary and _à priori_ truths.

To which I reply: Such principles as I have mentioned,--that material
substance cannot be produced or destroyed--that the cause is measured
by the effect--that reaction is equal and opposite to action: are not
the results of experience, nor can be. No experience can prove them;
they are necessarily assumed as the interpretation of experience.
They were not proved in the course of scientific investigations, but
brought to light as such investigations showed their necessity. They
are not the results, but the conditions of experimental sciences.
If the Axiom of Substance were not true, and were not assumed, we
could not have such a science as Chemistry, that is, we could have
no knowledge at all respecting the changes of form of substances.
If the Axioms of Mechanics were not true and were not assumed, we
could have no science of Mechanics, that is, no knowledge of the laws
of force acting on matter. It is not any special _results_ of the
science in such cases; but the _existence_, the _possibility_, of
any science, which establishes the necessity of these axioms. They
are not the consequences of knowledge, acquired from without, but
the internal condition of our being able to know. And when we are to
_know_ concerning any new subject contained in the universe, it is not
inconceivable nor strange that there should be new conditions of our
knowledge.

It is not inconceivable or strange, therefore, that as new sciences
are formed, new axioms, the foundations of such sciences, should come
into view. As the light of clear and definite knowledge is kindled in
successive chambers of the universe, it may disclose, not only the
aspect of those new apartments, but also the form and structure of the
lamp which man is thus allowed to carry from point to point, and to
transmit from hand to hand. And though the space illumined to man's
vision may always be small in comparison with the immeasurable abyss of
darkness by which it is surrounded, and though the light may be dim and
feeble, as well as partial; this need not make us doubt that, so far as
we can by the aid of this lamp, we see truly: so far as we discern the
necessary laws of the universe, the laws are true, and their truth is
rooted in that in which the being of the universe is rooted.

And, to dwell for a moment longer on this image, we may also
conceive that all that this lamp--the intellect of man cultivated by
science,--does, by the light which it gives, is this--that it dispels a
darkness which is dark for man alone, and discloses to him some things
in some measure as all things lie in clear and perfect light before the
eye of God. To the Divine Mind all the laws of the universe are plain
and clear in all their multiplicity, extent and depth. The human mind
is capable of seeing some of these laws, though only a few; to some
extent, though but a little way; to some depth, though never to the
bottom. But the Human Mind, can, in the course of ages and generations,
by the long exercise of thought, successfully employed in augmenting
knowledge, improve its powers of vision; and may thus come to see more
laws than at first, to trace their extent more largely, to understand
them more thoroughly; and thus the inward intellectual light of man may
become broader and broader from age to age, though ever narrow when
compared with completeness.

3. Is it strange to any one that inward light, as well as outward
knowledge, should thus increase in the course of man's earthly career?
that as knowledge extends, the foundations of knowledge should expand?
that as man goes on discovering new truths, he should also discover
something concerning the conditions of truth? Is it wonderful that
as science is progressive the philosophy of science also should be
progressive? that as we know more of everything else, we should also
come to know more of our powers of knowing?

This does not seem to have been supposed by philosophers in general;
or rather, they have assumed that they could come to know more about
the powers of knowing by thinking about them, even without taking
into account the light thrown upon the nature of knowledge by the
progress of knowledge. From Plato downwards, through Aristotle,
through the Schoolmen, to Descartes, to Locke, to Kant, Schelling and
Hegel, philosophers have been perpetually endeavouring to explore
the nature, the foundations, the consequences of our knowledge. But
since Plato, scarcely one of them has ever proceeded as if new light
were thrown upon knowledge by new knowledge. They have, many or all
of them, attempted to establish fundamental truths, some of them new
fundamental truths, about the human mind and the nature and conditions
of its knowledge. These attempts show that they do not deny or doubt
that there may be such new fundamental truths. Such new fundamental
truths respecting the human mind and respecting knowledge must be, in
many cases at least, (as it will be seen that they _are_, on examining
the systems proposed by the philosophers just mentioned,) seen by
their own light to be true. They are _new axioms_ in philosophy. These
philosophers therefore, or their disciples, cannot consistently blame
us for holding the possibility of new axioms being introduced into
philosophy from age to age, as there arise philosophers more and more
clear-sighted.

4. But though _they_ have no ground for rejecting _our_ new axioms
merely because they are new, _we_ may have good ground for doubting
the value of _their_ new axioms, that is, of the foundations of their
systems; because they are new truths about knowledge gathered by
merely exploring the old fields of knowledge. We found our hopes of
obtaining a larger view of the constitution of the human mind than the
early philosophers had, on this:--that we obtain our view by studying
the operation of the human mind _since their time_; its progress
in acquiring a large stock of uncontested truths and in obtaining
a wide and real knowledge of the universe. Here are new materials
which the ancients had not; and which may therefore justify the hope
that we may build our philosophy higher than the ancients did. But
modern philosophers who use only the same materials as the ancient
philosophers used, have not the same grounds for hope which we have. If
they borrow all their examples and illustrations of man's knowledge of
the universe, from the condition of the universe as existing in Space
and Time, that is, from the geometrical condition of the universe, they
may fail to obtain the light which might be obtained if they considered
that the universe is also subject to conditions of _Substance_, of
_Cause_ and _Effect_, of _Force_ and _Matter_: is filled with _Kinds_
of things, in whose structure we assume _Design_ and _Ends_; and so on;
and if they reflected that these conditions or _Ideas_ are not mere
vague notions, but the bases of sciences which all thoughtful persons
allow to be certain and real.

It is then, as I have said, from taking advantage of the progressive
character which physical science, in the history of man, has been
found to possess, that I hope to learn more of the nature and
prospects of the human mind and soul, than those can learn who still
take their stand on the old limited ground of man's knowledge.
The knowledge of Geometry by the Greeks was the starting-point of
their sound philosophy. It showed that something might be certainly
known, and it showed, in some degree, how it was known. It thus
refuted the skepticism which was destroying philosophy, and offered
specimens of solid truth for the philosopher to analyse. But the
Greeks tried to go beyond geometry in their knowledge of the universe.
They tried to construct a science of Astronomy--of Harmonics--of
Optics--of Mechanics. In the two former subjects, they succeeded to
a very considerable extent. The question then arose, What was the
philosophical import of these new sciences? What light did they throw
on the nature of the universe, on the nature of knowledge, on the
nature of the human mind? These questions Plato attempted to answer. He
said that the lesson of these new sciences is this:--that the universe
is framed upon the _Divine Ideas_; that man can to a certain extent
obtain sight of these Ideas; and that when he does this, he _knows_
concerning the universe. And again, he also put the matter otherwise:
there is an _Intelligible World_, of which the Visible and Sensible
world is only a dim image. _Science_ consists in understanding the
Intelligible World, which man is to a certain extent able to do, by the
nature of his understanding. This was Plato's philosophy, founded upon
the progress which human knowledge had made up to his time. Since his
time, knowledge, that is science, has made a large additional progress.
What is the philosophical lesson to be derived from this progress,
and from the new provinces thus added to human knowledge? This is a
question which I have tried to answer. I am not aware that any one
since Plato has taken this line of speculation;--I mean, has tried
to spell out the lesson of philosophy which is taught us, not by one
specimen, or a few only, of the knowledge respecting the universe which
man has acquired; but by including in his survey all the provinces of
human knowledge, and the whole history of each. At any rate, whatever
any one else may have done in this way, it seems to me that new
inferences remain to be drawn, of the nature of those which Plato drew:
and those I here attempt to deduce and to illustrate.




CHAPTER XXX.

THE THEOLOGICAL BEARING OF THE PHILOSOPHY OF DISCOVERY.


That necessary truth is progressive;--that science is the idealization
of facts, and that this process goes on from age to age, and advances
with the advance of scientific discovery;--these are doctrines which
I have endeavoured to establish and to elucidate. If these doctrines
are true, they are so important that I may be excused should I return
to them again and again, and trace their consequences in various
directions. Especially I would examine the bearing of these doctrines
upon our religious philosophy. I have hitherto abstained in a great
measure from discussing religious doctrines; but such a reserve carried
too far must deprive our philosophy of all completeness. No philosophy
of science can be complete which is not also a philosophy of the
universe; and no philosophy of the universe can satisfy thoughtful
men, which does not include a reference to the power by which the
universe came to be what it is. Supposing, then, such a reference to be
admitted, let us see what aspect our doctrines give to it.


1. (_How can there be necessary truths concerning the actual
universe?_)--In looking at the bearing of our doctrine on the
philosophy of the universe, we are met by a difficulty, which is
indeed, only a former difficulty under a new aspect. When we are come
to the conclusion that science consists of facts idealized, we are led
to ask, How this can be? _How can_ facts be idealized? How can that
which is a fact of external observation become a result of internal
thought? How can that which was known _à posteriori_ become known _à
priori_? How can the world of things be identified with the world
of thoughts? How can we discover a necessary connexion among mere
phenomena?

Or to put the matter otherwise: How is it that the deductions of the
intellect are verified in the world of sense? How is it that the truths
of science obtained _à priori_ are exemplified in the general rules of
facts observed _à posteriori_? How is it that facts, in science, always
do correspond to our ideas?

I have propounded this paradox in various forms, because I wish it
to be seen that it is, at first sight, a real, not merely a verbal
contradiction, or at least a difficulty. If we can discover the
solution of this difficulty in any one form, probably we can transpose
the answer so as to suit the other forms of the question.

2. Suppose the case to be as I have stated it; that in some sciences at
least, laws which were at first facts of observation come to be seen as
necessary truths; and let us see to what this amounts in the several
sciences.

It amounts to this: the truths of Geometry, such as we discern them by
the exercise of our own thoughts, are always verified in the world of
observation. The laws of space, derived from our Ideas, are universally
true in the external world.

In the same way, as to number: the laws or truths respecting number,
which are deduced from our Idea of Number, are universally true in the
external world.

In the same way, as to the science which deals with matter and force:
the truths of which I have spoken as derived from Ideas:--that
action is equal to reaction; and that causes are measured by their
effects;--are universally verified in all the laws of phenomena of the
external world, which are disclosed by the science of Mechanics.

In the same way with regard to the composition and resolution of bodies
into their elements; the truths derived from our Idea of Matter:--that
no composition or resolution can increase or diminish the quantity
of matter in the world, and that the properties of compounds are
determined by their composition;--are truths derived from Ideas of
quantity of matter, and of composition and resolution; but these truths
are universally verified when we come to the facts of Chemistry.

In the same way it is a truth flowing from the Ideas of the Kinds of
things, (as the possible subject of general propositions expressed in
language,) that the kinds of things must be definite; and this law is
verified whenever we express general propositions in general terms: for
instance, when we distinguish species in Mineralogy.

3. This last example may appear to most readers doubtful. I have
purposely pursued the enumeration till I came to a doubtful example,
because it is, and I conceive always will be, impossible to extend this
general view to _all_ the Sciences. On the contrary, this doctrine
applies at present to only a very few of the sciences, even in the eyes
of those who hold the existence of ideal truths. The doctrine extends
at present to a few only of the sciences, even if it extend to one
or two besides those which have been mentioned--Geometry, Mechanics,
Chemistry, Mineralogy: and though it may hereafter appear that Ideal
Truths are possible and attainable for a few other sciences, yet the
laws disclosed by sciences which cannot be reduced to ideal elements
will, I conceive, always very far outnumber those which can be so
reduced. The great body of our scientific knowledge will always be
knowledge obtained by mere observation, not knowledge obtained by the
use of theories alone.

4. The survey of the history and philosophy of the Sciences which we
have attempted in previous works enables us to offer a sort of estimate
of the relative portions of science which have and which have not
thus been idealized. For the Aphorisms[317] which we have collected
from that survey, contain Axioms which may be regarded as the Ideal
portions of the various sciences; and the inspection of that series of
aphorisms will show us to how such a portion of science, anything of
this axiomatic or ideal character can he applied. These Axioms are the
Axioms of Geometry (Aphorism XXVI); of Arithmetic (XXXVI); of Causation
(XLVII); of a medium for the sensation of secondary qualities (LVIII),
and their measure (LXIX); of Polarity (LXXII); of Chemical Affinity
(LXXVI); of Substance (LXXVII); of Atoms (LXXIX).

Have we any axioms in the sciences which succeed these in our survey,
as Botany, Zoology, Biology, Palæontology?

There is the Axiom of Symmetry (LXXX); of Kind, (already in some
measure spoken of, (LXXXIII)); of Final Cause (CV); of First Cause
(CXVI).


5. (_Small extent of necessary truth._)--It is easily seen how small
a portion of each of these latter sciences is included in these
axioms: while, with regard to the sciences first mentioned, the Axioms
include, in a manner, the whole of the science. The science is only
the consequence of the Axioms. The whole science of Mechanics is only
the development of the Axioms concerning action and reaction, and
concerning cause and its measures, which I have mentioned as a part of
our Ideal knowledge.

In fact, beginning from Geometry and Arithmetic, and going through
the sciences of Mechanics, of Secondary Qualities, and of Chemistry,
onwards to the sciences which deal with Organized Beings, we find that
our ideal truths occupy a smaller and smaller share of the sciences
in succession, and that the vast variety of facts and phenomena
which nature offers to us, is less and less subject to any rules or
principles which we can perceive to be necessary.

But still, that there are principles,--necessary principles, which
prevail universally even in these higher parts of the natural
sciences,--appears on a careful consideration of the axioms which I
have mentioned:--that in symmetrical natural bodies the similar parts
are similarly affected;--that every event must have a cause;--that
there must be a First Cause, and the like.

6. It being established, then, that in the progress of science,
facts are idealized--that _à posteriori_ truths become _à priori_
truths;--that the world of things is identified with the world of
thoughts to a certain extent;--to an extent which grows larger as we
see into the world of things more clearly; the question recurs which I
have already asked: How can this be?

How can it be that the world without us is thus in some respects
identical with the world within us?--that is our question.


7. (_How did things come to be as they are?_)--It would seem that we
may make a step in the solution of this question, if we can answer this
other: How did the world without us and the world within us come to be
what they are?

To this question, two very different answers are returned by those who
do and those who do not believe in a Supreme Mind or Intelligence, as
the cause and foundation of the world.

Those who do not believe that the world has for its cause and
foundation a Supreme Intelligence, or who do not connect their
philosophy with this belief, would reply to our inquiry, that the
reason why man's thoughts and ideas agree with the world is, that they
are borrowed from the world; and that the persuasion that these Ideas
and truths derived from them have any origin except the world without
us, is an illusion.

On this view I shall not now dwell; for I wish to trace out the
consequences of the opposite view, that there exists a Supreme Mind,
which is the cause and foundation of the universe. Those who hold this,
and who also hold that the human mind can become possessed of necessary
truths, if they are asked how it is that these necessary truths are
universally verified in the material world, will reply, that it is
so because the Supreme Creative-Mind has made it so to be:--that the
truths which exist or can be generated in man's mind agree with the
laws of the universe, because He who has made and sustains man and the
universe has caused them to agree:--that our Ideas correspond to the
Facts of the world, and the Facts to our Ideas, because our Ideas are
given us by the same power which made the world, and given so that
these can and must agree with the world so made.


8. (_View of the Theist_).--This, in its general form, would be the
answer of the _theist_, (so we may call him who believes in a Supreme
Intelligent Cause of the world and of man,) to the questions which we
have propounded--the perplexity or paradox which we have tried to bring
into view. But we must endeavour to trace this view--this answer--more
into detail.

If a Supreme Intelligence be the cause of the world and of the Laws
which prevail among its phenomena, these Laws must exist as Acts of
that Intelligence--as Laws caused by the thoughts of the Supreme
Mind--as Ideas in the Mind of God. And then the question would be, How
we are to conceive these thoughts, these Ideas, to be at the same time
Divine and human:--to be at the same time Ideas in the Divine Mind, and
necessary truths in the human mind; and this is the question which I
would now inquire into.


9. (_Is this Platonism?_)--To the terms in which the inquiry is now
propounded it may be objected that I am taking for granted the Platonic
doctrine, that the world is constituted according to the Ideas of the
Divine Mind. It may be said that this doctrine is connected with gross
extravagancies of speculation and fiction, and has long been obsolete
among sound philosophers.

To which I reply, that if such doctrines have been pushed into
extravagancies, with _them_ I have nothing to do, nor have I any
disposition or wish to revive them. But I do not conceive the doctrine,
to the extent to which I have stated it, to be at all obsolete:--that
the Cause and Foundation of the Universe is a Divine Mind: and from
that doctrine it necessarily follows, that the laws of the Universe are
in the Ideas of the Divine Mind.

I would then, as I have said, examine the consequences of this
doctrine, in reference to the question of which I have spoken. And
in order to do this, it may help us, if we consider separately the
bearing of this doctrine upon separate portions of our knowledge of
the universe;--separately its bearing upon the laws which form the
subject-matter of different sciences:--if we take particular human
Ideas, and consider what the Divine Ideas must be with regard to each
of them.

10. (_Idea of Space._)--Let us take, in the first place, the Idea
of Space. Concerning this Idea we possess necessary truths; namely,
the Axioms of Geometry; and, as necessarily resulting from them, the
whole body of Geometry. And our former inquiry, as narrowed within the
limits of this Idea, will be, How is it that the truths of Geometry--_à
priori_ truths--are universally verified in the observed phenomena of
the universe? And the theist's answer which we have given will now
assume this form:--This is so because the Supreme Mind has constituted
and constitutes the universe according to the Idea of Space. The
universe conforms to the Idea of Space, and the Idea of Space exists
in the human mind;--is necessarily evoked and awakened in the human
mind existing in the universe. And since the Idea of Space, which is
a constituent of the universe, is also a constituent of the human
mind, the consequences of this Idea in the universe and in the human
mind necessarily coincide; that is, the _spacial_ Laws of the universe
necessarily coincide with the _spacial_ Science which man elaborates
out of his mind.

11. To this it may be objected, that we suppose the Idea of Space in
the Divine Mind (according to which Idea, among others, the universe is
constituted,) to be identical with the Idea of Space in the human mind;
and this, it may be urged, is too limited and material a notion of the
Divine Mind to be accepted by a reverent philosophy.

I reply, that I suppose the Divine Idea of Space and the human Idea
of Space to coincide, _only so far_ as the human Idea goes; and
that the Divine Idea may easily have so much more luminousness and
comprehensiveness as Divine Ideas may be supposed to have compared with
human. Further, that this Idea of Space, the first of the Ideas on
which human science is founded, is the most luminous and comprehensive
of such Ideas; and there are innumerable other Ideas, the foundations
of sciences more or less complete, which are extremely obscure and
limited in the human mind, but which must be conceived to be perfectly
clear and unlimitedly comprehensive in the Divine Mind. And thus, the
distance between the human and the Divine Mind, even as to the views
which constitute the most complete of the human sciences, is as great
in our view as in any other.

12. That the Idea of Space in the human mind, though sufficiently clear
and comprehensive to be the source of necessary truths, is far too
obscure and limited to be regarded as identical with the Divine Idea,
will be plain to us, if we call to mind the perplexities which the
human mind falls into when it speculates concerning space infinite.
An Intelligence in which all these perplexities should vanish by the
light of the Idea itself, would be infinitely elevated in clearness and
comprehensiveness of intellectual vision above human intelligence, even
though its Idea of Space should coincide with the human Idea as far as
the human Idea goes.

I do not shrink from saying, therefore, that the Idea of Space which
is a constituent of the human mind existing in the universe is, as far
as it goes, identical with the Idea of Space which is a constituent of
the universe. And this I give as the answer to the question, How it is
that the necessary truths of Geometry universally coincide with the
relations of the phenomena of the universe? And this doctrine, it is
to be remembered, carries us to the further doctrine, that the Idea of
Space in the human mind is, so far as it goes, coincident with the Idea
of Space in the Divine Mind.


13. (_Idea of Time._)--What I have said of the Idea of Space, may
be repeated, for the most part, with regard to the Idea of Time;
except that the Idea of Time, as such, does not give rise to a large
collection of necessary truths, such as the propositions of Geometry.
Some philosophers regard Number as a modification or derivative of
the Idea of Time. If we accept this view, we have, in the Science of
Arithmetic, a body of necessary truths which flow from the Idea of
Time. But this doctrine, whichever way held, does not bear much on
the question with which we are now concerned. That which we do hold
is, that the Idea of Time in the human mind is, so far as it goes,
coincident with the Idea of Time in the Divine Mind: and that this
is the reason why the events of the universe, as contemplated by us,
conform to necessary laws of succession: while at the same time we must
suppose that all the perplexities in the Idea of Time which embarrass
the human mind--the perplexities, for instance, which arise from
contemplating a past and a future eternity, are, in the Divine Mind,
extinguished in the Light of the Idea itself.

Space and Time have, and have generally been regarded as having,
peculiar prerogatives in our speculations concerning the constitution
of the universe. We see and perceive all things as subject to the laws
of Space and Time; or rather (for the term _Law_ does not here satisfy
us), as being and happening _in_ space and _in_ time: and probably most
persons will have no repugnance to the doctrine that the Divine Mind,
as well as the human, so regards them, and has so constituted them and
us that they _must_ be so regarded. Space and Time are human Ideas
which include all objects and events, and are the foundation of all
human Science. And we can conceive that Space and Time are also Divine
Ideas which the Divine Mind causes to include all objects and events,
and makes to be the foundation of all existence. So far as these Ideas
go, our doctrine is not difficult or new.


14. (_Ideas of Force and Matter._)--But what are we to say of the
Ideas which come next in the survey of the sciences, Force and Matter?
These are human Ideas--the foundations of several sciences--of the
mechanical sciences in particular. But are they the foundations of
necessary truths? Have we necessary truths respecting Force and Matter?
We have endeavoured to prove that we have:--that certain fundamental
propositions in the Science of Mechanics, although, historically
speaking, they were discovered by observation and experience, are yet,
philosophically speaking, necessary propositions. And being such, the
facts of the universe must needs conform to these propositions; and
the reason why they do so, we hold, in this as in the former case,
to be, that these Ideas, Force and Matter, are Ideas in the Divine
Mind:--Ideas according to which the universe is, by the Divine Cause,
constituted and established.

15. That Force and Matter are Ideas existing in the Divine Mind, and
coincident with the Idea of Force and Matter in the human mind, as
far as these go, is a doctrine which is important in our view of the
universe in relation to its Cause and Foundation.

These are very comprehensive and fundamental Ideas, and there are
certain universal relations among external things which rest upon these
Ideas. The two, Force and Matter, are, in a certain way, the necessary
antithesis and opposite condition each of the other. Force (that is
Mechanical Force, Pressure or Impulse) cannot act without matter to
act upon. Matter (that is Body) cannot exist without Force by which
it is kept in its place, by which its parts are held together, and by
which it excludes every other body from the place which it occupies. We
cannot conceive Force without Matter, or Matter without Force; the two
are, as Action and Reaction, necessarily co-ordinate and coexistent.
In every part of the universe they must be so. In every part of the
universe, if there be material objects, there must be Force; if there
be Force, there must be material objects.

Our apprehension of this universal necessity arises from our having the
Ideas of Force and Matter which are human Ideas. The actuality of this
universal antithesis arises from the Ideas of Force and Matter being
Ideas in the Divine Mind;--Ideas realized as a part of the fundamental
constitution of the universe.

That Force and Matter are thus among the Ideas in the Divine Mind,
and that, with them, the Ideas of Force and Matter in the human mind,
regarded in their most general form, agree so far as they go, is
another step in the doctrine which I am trying to unfold. That the
Ideas of Force and Matter in the Divine Mind are such as to banish by
their own light, innumerable contradictions and perplexities which
darken these Ideas in the human mind, is to be supposed: and thus the
Divine Mind is infinitely luminous and comprehensive compared with the
human mind.


16. (_Creation of Matter._)--It may perhaps be urged, as an objection
to this doctrine, that it asserts Matter to be a necessary constituent
of the universe, and thus involves the assertion of the eternity of
Matter. But in reality the doctrine asserts Matter to be eternal, only
in the way in which time and space are eternal. Whether we hold that
there was a creation before which time and space did not exist,--with
the poet who says

  Ere Time and Space _were_ Time and Space were _not_,--

is not essential to our present inquiry. Certainly we cannot conceive
such a state, and therefore cannot reason about it. We have no occasion
here to speak of Creation, nor have spoken of it. What I have said
is, that Space and Time, Force and Matter are universal elements,
principles, constituents, of the universe as it is--and necessary
Ideas of the human mind existing in that universe. If there ever
was a Creation before which Matter did not exist, it was a Creation
before which Force did not exist. And in the universe as it is, the
two are necessarily co-existent in the human thought because they are
co-existent in the Divine Thought which makes the world.

We apply then to Force and Matter the doctrine--the Platonic doctrine,
if any one please so to call it,--that the world is constituted
according to the Ideas of the Divine Mind, and that the human mind
apprehends the inward and most fundamental relations of the universe by
sharing in some measure of those same Ideas.


17. (_Platonic Ideas._)--But do we go on with Plato to extend this
doctrine of Ideas to all the objects and all the aspects of objects
which constitute the material universe? Do we say with Plato that there
is not only an Idea of a Triangle by conformity to which a figure is a
triangle, but an Idea of Gold, by conformity to which a thing is gold,
and Idea of a Table, by conformity to which a thing is a table?

We say none of these things. We say nothing which at all approaches to
them. We do not say that there is an Idea of a Triangle, the archetype
of all triangles; we only say that man has an Idea of Space, which is
an Idea of a fundamental reality; and that therefore from this Idea
flow real and universal truths--about triangles and other figures.
Still less do we say that we have an archetypal Idea of Gold, or of a
Metal in general, or of any of the kinds of objects which exist in the
world. Here we part company with Plato altogether.

But have we any Ideas at all with regard to objects which we thus speak
of as separable into Kinds? We can have knowledge,--even exact and
general knowledge, that is, science--with regard to such things--with
regard to plants and metals--gold and iron. Do we possess in our minds,
with regard to those objects, any Ideas, any universal principles, such
as we possess with regard to geometrical figures or mechanical actions?
And if so, are those human Ideas verified in the universe, as the Ideas
hitherto considered are? and do they thus afford us further examples
of Ideas in the human mind which are also Ideas in the Divine Mind,
manifested in the constitution of the universe?


18. (_Idea of Kinds._)--We answer _Yes_ to these questions, on this
ground:--the objects that exist in the world, plants and metals, gold
and iron, for example, in order that they may be objects with regard
to which we can have any knowledge, must be objects of distinct and
definite thought. Plant must differ from metal, gold from iron, in
order that we may know anything at all about any of these objects.
The differences by which such objects differ need not necessarily
be expressed by _definitions_, as the difference of a triangle and
a square are expressed; but there must manifestly _be_ fixed and
definite differences, in order that we may have any knowledge about
them. These Kinds of things must be so far distinct and definite, as
to be objects of distinct and definite thought. The _Kinds_ of natural
objects must differ, and we must think of things as of different Kinds,
in order that we may know anything about natural objects. Living in a
world in which we exercise our Intellect upon the natural objects which
surround us, we must regard them as distinct from each other in Kind.
We must have an Idea of Kinds of natural objects.

19. The Idea of a Kind involves this principle: That where the Kind
differs the Properties may differ, but so far as the Kind is the same
the Properties contemplated in framing the notion of each Kind are the
same. Gold cannot have the distinctive properties of Iron without being
Iron.

In the case of human knowledge, each Kind is marked by a _word_--a
_name_; and the doctrine that the notion of the Kind must be so applied
that this same Kind of object shall have the same properties, has
been otherwise expressed by saying that Names must be so applied that
general propositions may be possible. We must so apply the name of Gold
that we may be able to say, gold has a specific gravity of a certain
amount and is ductile in a certain degree.

20. But this condition of the names of Kinds,--that they must be
such that general propositions about these Kinds of objects shall be
possible;--is it a necessary result of the Idea of Kind? And if so, can
the Idea of Kind, thus implying the use of language, and a condition
depending on the use of language, be an Idea in the Divine as well as
in the human mind? Can it be, in this respect, like the Ideas which we
have already considered, Space and Time, Force and Matter?

We cannot suppose that the Ideas which exist in the Divine Mind imply,
in the Supreme Intelligence, the need of language, like human language.
But there is no incongruity in supposing that they imply that which
we take as the _condition_ of such language as we speak of, namely,
distinct thought. There is nothing incongruous in supposing that the
Supreme Intelligence regards the objects which exist in the universe as
distinct in Kind: and that the Idea of Kind in the human mind agrees
with the Idea of Kind in the Divine Mind, as far as it goes. And as
we have seen, the Idea of Properties is correlative and coexistent
with the Idea of Kind, so that the one changing, the other changes
also. There is nothing incongruous in supposing that the Divine Mind
manifests in the universe of which it is the Cause and Foundation,
these two, its co-ordinate Ideas: and that the human mind sees that
these two Ideas are co-ordinate and coexistent, in virtue of its
participating in these Ideas of the Divine Mind. The universe is full
of things which man perceives do and must differ correspondingly in
kind and in properties; and this is so, because the Ideas of various
Kinds and various Properties are part of the scheme of the universe in
the Divine Mind.

21. That the Ideas of Kinds and Properties as coordinate and
interdependent, though common, to a certain extent, to the human and
the Divine Mind, are immeasurably more luminous, penetrating and
comprehensive in the Divine than in the human mind, is abundantly
evident. In fact, though man assents to such axioms as these,--that
the Properties of Things depend upon their Kinds, and that the Kinds
of Things are determined by their Properties,--yet the nature of
connexion of Kinds and Properties is a matter in which man's mind is
all but wholly dark, and on which the Divine Mind must be perfectly
clear. For in how few cases--if indeed in any one--can we know what
is the essence of any Kind;--what is the real nature of the connexion
between the character of the Kind and its Properties! Yet on this point
we must suppose that the Divine Intellect, which is the foundation of
the world, is perfectly clear. Every Kind of thing, every genus and
species of object, appears to Him in its essential character, and its
properties follow as necessary consequences. He sees the essences of
things through all time and through all space; while we, slowly and
painfully, by observation and experiment, which we cannot idealize or
can idealize only in the most fragmentary manner, make out a few of the
properties of each Kind of thing. Our Science here is but a drop in the
ocean of that truth, which is known to the Divine Mind but kept back
from us; but still, that we can know and do know anything, arises from
our taking hold of that principle, human as well as Divine, that there
are differences of Kinds of things, and corresponding differences of
their properties.


22. (_Idea of Substance._)--I shall not attempt to enumerate all
the Ideas which, being thus a part of the foundation of Science in
the human mind and of Existence in the universe, are shown to be at
the same time Ideas in the Divine and in the human mind. But there
is one other of which the necessary and universal application is so
uncontested, that it may well serve further to exemplify our doctrine.
In all reasonings concerning the composition and resolution of the
elements of bodies, it is assumed that the quantity of matter cannot be
increased or diminished by anything which we can do to them. We have an
Idea of _Substance_, as something which may have its qualities altered
by our operations upon it, but cannot have its quantity changed.
And this Idea of Substance is universally verified in the facts of
observation and experiment. Indeed it cannot fail to be so; for it
regulates and determines the way in which we interpret the facts of
observation and experiment. It authorized the philosopher who was asked
the weight of a column of smoke to reply, "Subtract the weight of the
ashes from that of the fuel, and you have the weight of the smoke:"
for in virtue of that idea we assume that, in combustion, or in any
other operation, all the substance which is subjected to the operation
must exist in the result in some form or other. Now why may we
reasonably make this assumption, and thus, as it were, prescribe laws
to the universe? Our reply is, Because Substance is one of the Ideas
according to which the universe is constituted. The material things
which make up the universe are substance according to this Idea. They
are substance according to this Idea in the Divine Mind, and they are
substance according to this Idea in the human mind, because the human
mind has this Idea, to a certain extent, in common with the Divine
Mind. In this, as in the other cases, the Idea must be immeasurably
more clear and comprehensive in the Divine Mind than in the human.
The human Idea of substance is full of difficulty and perplexity: as
for instance; how a substance can assume successively a solid, fluid
and airy form; how two substances can be combined so as entirely to
penetrate one another and have new qualities: and the like. All these
perplexities and difficulties we must suppose to vanish in the Divine
Idea of Substance. But still there remains in the human, as in the
Divine Idea, the source and root of the universal truth, that though
substances may be combined or separated or changed in form in the
processes of nature or of art, no portion of substance can come into
being or cease to be.


23. (_Idea of Final Cause._)--There is yet one other Idea which I shall
mention, though it is one about which difficulties have been raised,
since the consideration of such difficulties may be instructive:
the Idea of a purpose, or as it is often termed, a _Final Cause_,
in organized bodies. It has been held, and rightly[318], that the
assumption of a Final Cause of each part of animals and plants is as
inevitable as the assumption of an efficient cause of every event.
The maxim, that in organized bodies nothing is _in vain_, is as
necessarily true as the maxim that nothing happens _by chance_. I have
elsewhere[319] shown fully that this Idea is not deduced from any
special facts, but is assumed as a law governing all facts in organic
nature, directing the researches and interpreting the observations
of physiologists. I have also remarked that it is not at variance
with that other law, that plants and that animals are constructed
upon general plans, of which plans, it may be, we do not see the
necessity, though we see how wide is their generality. This Idea of a
purpose,--of a Final Cause,--then, thus supplied by our minds, is found
to be applicable throughout the organic world. It is in virtue of this
Idea that we conceive animals and plants as subject to _disease_; for
disease takes place when the parts do not fully answer their _purpose_;
when they do not do what they _ought_ to do. How is it then that we
thus find an Idea which is _supplied_ by our own minds, but which is
_exemplified_ in every part of the organic world? Here perhaps the
answer will be readily allowed. It is because this Idea is an Idea of
the Divine Mind. There _is_ a Final Cause in the constitution of these
parts of the universe, and therefore we can interpret them by means of
the Idea of Final Cause. We can _see_ a purpose, because there _is_
a purpose. Is it too presumptuous to suppose that we can thus enter
into the Ends and Purposes of the Divine Mind? We willingly grant and
declare that it would be presumptuous to suppose that we can enter into
them to any but a very small degree. They doubtless go immeasurably
beyond our mode of understanding or conceiving them. But to a certain
extent we _can_ go. We can go so far as to see that they _are_ Ends and
Purposes. It is _not_ a vain presumption in us to suppose that we know
that the eye was made for seeing and the ear for hearing. In this the
most pious of men see nothing impious: the most cautious philosophers
see nothing rash. And that we can see thus far into the designs of
the Divine Mind, arises, we hold, from this:--that we have an Idea of
Design and of Purpose which, so far as it is merely _that_, is true;
and so far, is Design and Purpose in the same sense in the one case and
in the other.

I am very far from having exhausted the list of Fundamental Ideas which
the human mind possesses and which have been made the foundations of
Sciences. Of all such Ideas, I might go on to remark, that they are of
universal validity and application in the region of external Facts. In
all the cases I might go on to inquire, How is it that man's Ideas,
developed in his internal world, are found to coincide universally
with the laws of the external world? By what necessity, on what ground
does this happen? And in all cases I should have had to reply, that
this happens, and must happen, because these Ideas of the human mind
are also Ideas of the Divine Mind according to which the universe is
constituted. Man has these thoughts, and sees them verified in the
universe, because God had these thoughts and exemplifies them in the
universe.


24. (_Human immeasurably inferior to Divine_).--But of all these Ideas,
I should also have to remark, that the way in which man possesses them
is immeasurably obscure and limited in comparison with the way in
which God must be supposed to possess them. These human Ideas, though
clear and real as far as they go, in every case run into obscurity and
perplexity, from which the Ideas of the Divine Mind must be supposed to
be free. In every case, man, by following the train of thought involved
in each Idea, runs into confusion and seeming contradictions. It may
be that by thinking more and more, and by more and more studying the
universe, he may remove some of this confusion and solve some of these
contradictions. But when he has done in this way all that he can, an
immeasurable region of confusion and contradiction will still remain;
nor can he ever hope to advance very far, in dispelling the darkness
which hangs over the greater part of the universe. His knowledge, his
science, his Ideas, extend only so far as he can keep his footing
in the shallow waters which lie on the shore of the vast ocean of
unfathomable truth.

25. But further, we have not, even so, exhausted our estimate of the
immeasurable distance between the human mind and the Divine Mind:--very
far from it: we have only spoken of the smallest portion of the region
of truth,--that about which we have Sciences and Scientific Ideas.
In that region alone do we claim for man the possession of Ideas the
clearness of which has in it something divine. But how narrow is the
province of Science compared with the whole domain of human thought! We
may enumerate the sciences of which we have been speaking, and which
involve such Ideas as I have mentioned. How many are they? Geometry,
Arithmetic, Chemistry, Classification, Physiology. To these we might
have added a few others; as the sciences which deal with Light, Heat,
Polarities; Geology and the other Palætiological Sciences; and there
our enumeration at present must stop. For we can hardly as yet claim to
have Sciences, in the rigorous sense in which we use the term, about
the Vital Powers of man, his Mental Powers, his historical attributes,
as Language, Society, Arts, Law, and the like. On these subjects few
philosophers will pretend to exhibit to us Ideas of universal validity,
prevailing through all the range of observation. Yet all these things
proceed according to Ideas in the Divine Mind by which the universe,
and by which man, is constituted. In such provinces of knowledge,
at least, we have no difficulty in seeing or allowing how blind man
is with regard to their fundamental and constituent principles; how
weak his reason; how limited his view. If on some of the plainest
portions of possible knowledge, man have Ideas which may be regarded
as coincident to a certain extent with those by which the universe is
really constituted; still on by far the largest portion of the things
which most concern him, he has no knowledge but that which he derives
from experience, and which he cannot put in so general a form as to
have any pretensions to rest it upon a foundation of connate Ideas.


26. (_Science advances towards the Divine Ideas._)--But there is yet
one remark tending somewhat in the opposite direction, which I must
make, as a part of the view which I wish to present. Science, in the
rigorous sense of the term, involves, we have said, Ideas which to a
certain extent agree with the Ideas of the Divine Mind. But science in
that sense is progressive; new sciences are formed and old sciences
extended. Hence it follows that the Ideas which man has, and which
agree with the Ideas of the Divine Mind, may receive additions to their
number from time to time. This may seem a bold assertion; yet this is
what, with due restriction, we conceive to be true. Such Ideas as we
have spoken of receive additions, in respect of their manifestation
and development. The Ideas, the germ of them at least, were in the
human mind before; but by the progress of scientific thought they are
unfolded into clearness and distinctness. That this takes place with
regard to scientific Ideas, the history of science abundantly shows.
The Ideas of Space and Time indeed, were clear and distinct from the
first, and accordingly the Sciences of Geometry and Arithmetic have
existed from the earliest times of man's intellectual history. But the
Ideas upon which the Science of Mechanics depends, having been obscure
in the ancient world, are become clear in modern times. The Ideas of
Composition and Resolution have only in recent centuries become so
clear as to be the basis of a definite science. The Idea of Substance
indeed was always assumed, though vaguely applied by the ancients; and
the Idea of a Design or End in vital structures is at least as old as
Socrates. But the Idea of Polarities was never put forth in a distinct
form till quite recently; and the Idea of Successive Causation, as
applied in Geology and in the other Palætiological Sciences, was never
scientifically applied till modern times: and without attempting to
prove the point by enumeration, it will hardly be doubted that many
Scientific Ideas are clear and distinct among modern men of science
which were not so in the ancient days.

Now all such scientific Ideas are, as I have been urging, points on
which the human mind is a reflex of the Divine Mind. And therefore in
the progress of science, we obtain, not indeed new points where the
human mind reflects the Divine, but new points where this reflection is
clear and luminous. We do not assert that the progress of science can
bring _into existence_ new elements of truth in the human mind, but it
may bring them _into view_. It cannot add to the characters of Divine
origin in the human mind, but it may add to or unfold the _proofs_ of
such an origin. And this is what we conceive it does. And though we
do not conceive that the Ideas which science thus brings into view
are the most important of man's thoughts in other respects, yet they
may, and we conceive do, supply a proof of the Divine nature of the
human mind, which proof is of peculiar cogency. What other proofs may
be collected from other trains of human thought, we shall hereafter
consider.


27. (_Recapitulation._)--This, then, is the argument to which we
have been led by the survey of the sciences in which we have been
engaged:--That the human mind can and does put forth, out of its
natural stores, duly unfolded, certain Ideas as the bases of scientific
truths: These Ideas are universally and constantly verified in the
universe: And the reason of this is, that they agree with the Ideas
of the Divine Mind according to which the universe is constituted and
sustained: The human mind has thus in it an element of resemblance to
the Divine Mind: To a certain extent it looks upon the universe as
the Divine Mind does; and therefore it is that it can see a portion
of the truth: And not only can the human mind thus see a portion of
the truth, as the Divine Mind sees it: but this portion, though at
present immeasurably small, and certain to be always immeasurably small
compared with the whole extent of truth which with greater intellectual
powers, he might discern, nevertheless may increase from age to age.

This is then, I conceive, one of the results of the progress of
scientific discovery--the Theological Result of the Philosophy of
Discovery, as it may, I think, not unfitly be called:--That by every
step in such discovery by which external facts assume the aspect of
necessary consequences of our Ideas, we obtain a fresh proof of the
Divine nature of the human mind: And though these steps, however far
we may go in this path, can carry us only a very little way in the
knowledge of the universe, yet that such knowledge, so far as we do
obtain it, is Divine in its kind, and shows that the human mind has
something Divine in its nature.

The progress by which external facts assume the aspect of necessary
consequences of our Ideas, we have termed the idealization of facts;
and in this sense we have said, that the progress of science consists
in the Idealization of Facts. But there is another way in which the
operation of man's mind may be considered--an opposite view of the
identification of Ideas with Facts; which we must consider, in order to
complete our view of the bearing of the progress of human thought upon
the nature of man.


FOOTNOTES:

[Footnote 317: Given in the _Novum Organon Renovatum_.]

[Footnote 318: _Nov. Org. Ren._ Aph. cv.]

[Footnote 319: _Hist. Sc. Id._ b. ix. c. vi.]




CHAPTER XXXI.

MAN'S KNOWLEDGE OF GOD.


1. Man's powers and means of knowledge are so limited and imperfect
that he can know _little_ concerning God. It is well that men in their
theological speculations should recollect that it is so, and should
pursue all such speculations in a modest and humble spirit.

But this humility and modesty defeat their own ends, when they lead us
to think that we can know _nothing_ concerning God: for to be modest
and humble in dealing with this subject, implies that we know _this_,
at least, that God is a proper object of modest and humble thought.

2. Some philosophers have been led, however, by an examination of man's
faculties and of the nature of being, to the conclusion that man can
know _nothing_ concerning God. But we may very reasonably doubt the
truth of this conclusion. We may ask, How can we _know_ that we _can_
know nothing? If we can know nothing, we cannot even know that.

It is much more reasonable to begin with things that we really do know,
and to examine how far such knowledge can carry us, respecting God, as
well as anything else. This is the course which we have been following,
and its results are very far from being trifling or unimportant.

In thus beginning from what we know, we start from two points, on each
of which we have, we conceive, some real and sure knowledge:--namely,
mathematical and physical knowledge of the universe without us; and a
knowledge of our own moral and personal nature within us.


3. (_From Nature we learn something of God._)--In pursuing the first
line of thought, we are led to reason thus. The universe is governed
by certain Ideas: for instance, everything which exists and happens in
the universe, exists and happens IN _Space_ and _Time_. Why is this?
It is, we conceive, because God has constituted and constitutes the
universe so that it may be so; that is, because the Ideas of Space and
of Time are Ideas according to which God has established and upholds
the universe.

But we may proceed further in this way, as we have already said.
The universe not only exists in space and time, but it has in it
substances--material substances: or taking it collectively, Material
_Substance_. Can we know anything concerning this substance? Yes:
something we can know; for we know that material substance cannot be
brought into being or annihilated by any natural process. We have then
an Idea of Substance which is a Law of the universe. How is this?--We
reply, that it is because our Idea of Substance is an Idea on which God
has established and upholds the universe.

Can we proceed further still? Can we discern any other Ideas according
to which the universe is constituted? Yes: as we have already remarked,
we can discern several, though as we go on from one to another
they become gradually fainter in their light, less cogent in their
necessity. We can see that Force as well as Material Substance is
an Idea on which the universe is constituted, and that _Force_ and
_Matter_ are a necessary and universal antithesis: we can see that
the Things which occupy the universe must be of definite _Kinds_, in
order that an intelligent mind may occupy itself about them, and thus
that the Idea of Kind is a constitutive Idea of the universe. We can
see that some kinds of things have life, and our Idea of Life is,
that every part of a living thing is a means to an End; and thus we
recognize _End_, or Final Cause, as an Idea which prevails throughout
the universe, and we recognize this Idea as an Idea according to which
God constitutes and upholds the universe.

Since we know so much concerning the universe, and since every Law of
the universe which is a necessary form of thought about the universe
must exist in the _Divine_ Mind, in order that it may find a place in
_our_ minds, how can we say that we can know nothing concerning the
Divine Mind?


4. (_Though but Little._)--But on the other hand, we easily see how
little our knowledge is, compared with what we do not know. Even the
parts of our knowledge which are the clearest are full of perplexities;
and of the Laws of the universe, including living as well as lifeless
things, how small a portion do we know at all!

Even the parts of our knowledge which are the clearest, I say, are
full of perplexities. Infinite Space and an infinite Past, an infinite
Future,--how helplessly our reason struggles with these aspects of
our Ideas! And with regard to _Substance_, how did ingenerable and
indestructible substance come into being? And with regard to _Matter_,
how can passive Matter be endued with living force? And with regard to
_Kinds_, how immeasurably beyond our power of knowing are their numbers
and their outward differences: still more their internal differences
and central essence! And with regard to the _Design_ which we see in
the organs of living things, though we can confidently say we see it,
how obscurely is it shown, and how much is our view of it disturbed by
other Laws and Analogies! And the Life of things, the end to which such
Design tends, how full of impenetrable mysteries is it! or rather how
entirely a mass of mystery into which our powers of knowledge strive in
vain to penetrate!

There is therefore no danger that by following this train of thought
we should elevate our view of man too high, or bring down God in our
thoughts to the likeness of man. Even if we were to suppose the Idea
of the Divine Mind to be of the same kind as the Ideas of the human
mind, the very few Ideas of this kind, which man possesses, compared
with the whole range of the universe, and the scanty length to which
he can follow each, make his knowledge so small and imperfect, that
he has abundant reason to be modest and humble in his contemplations
concerning the Intelligence that knows all and constitutes all. He can,
as I have already said, wade but a few steps into the margin of the
boundless and unfathomable ocean of truth.

5. But the Ideas of the Divine Mind must necessarily be different in
kind, as well as in number and extent, from the Ideas of the human
mind, on this very account, that they are complete and perfect. The
Mind which can conceive all the parts and laws of the universe in all
their mutual bearings, fundamental reasons, and remote consequences,
must be different in kind, as well as in extent, from the mind which
can only trace a few of these parts, and see these laws in a few of
their aspects, and cannot sound the whole depth of any of them. The
Divine Mind differs from the human, in the way in which we must needs
suppose what is Divine to differ from what is human.

6. It has sometimes been said that the Divine Mind differs from the
human as the Infinite from the finite. And this has been given as a
reason why we cannot know anything concerning God; for we cannot,
it is said, know _anything_ concerning the Infinite. Our conception
of the Infinite being merely negative, (the negation of a limit,)
makes all knowledge about it impossible. But this is not truly said.
Our conception of the Infinite is _not_ merely negative. As I have
elsewhere remarked, our conception of the Infinite is positive in this
way:--that in order to form this conception, we begin to follow a given
Idea in a given direction; and then, having thus begun, we suppose that
the progress of thought goes on in that direction without limit. To
arrive at our Idea of infinite space, for example, we must determine
what kind of space we mean,--line, area or solid; and from what origin
we begin: and infinite space has different attributes as we take
different beginnings in this way.

And so with regard to the kinds of infinity (for there are many) which
belong to the Divine Mind. _We_ have a few Ideas which represent the
Laws of the universe:--as Space, Time, Substance, Force, Matter, Kind,
End; of such Ideas the Divine Mind may have an infinite number. These
Ideas in the human mind are limited in depth and clearness: in the
Divine Mind they must be infinitely clearer than the clearest human
Intuition; infinitely more profound than the profoundest human thought.
And in this way, and, as we shall see, in other ways also, the Divine
Mind infinitely transcends the human mind when most fully instructed
and unfolded.

In this way and in other ways also, I say. For we have hitherto spoken
of the human mind only as contemplating the external world;--as
discerning, to a certain small extent, the laws of the universe. We
have spoken of the world of things without: we must now speak of the
world within us;--of the world of our thoughts, our being, our moral
and personal being.


7. (_From ourselves we learn something concerning God._)--We must
speak of this: for this is, as I have said, another starting point and
another line in which we may proceed from what we know, and see how far
our knowledge carries us, and how far it teaches us anything concerning
God.

Looking at ourselves, we perceive that we have to act, as well as
to contemplate: we are practical as well as speculative beings. And
tracing the nature and conditions of our actions, in the depths of our
thought we find that there is in the aspect of actions a supreme and
inevitable distinction of right and wrong. We cannot help judging of
our actions as right and wrong. We acknowledge that there must be such
a judgment appropriate to them. We have these Ideas of _right_ and
_wrong_ as attributes of actions; and thus we are _moral_ beings.

8. And again: the actions are _our_ actions. _We_ act in this way or
that. And _we_ are not mere _things_, which move and change as they
are acted on, but which do not themselves act, as man acts. I am not a
Thing but a _Person_; and the men with whom I act, who act with me--act
in various ways towards me, well or ill--are also persons. Man is a
personal being.

The Ideas of right and wrong--the _moral_ Ideas of man--are then a part
of the scheme of the universe to which man belongs. Could they be this,
if they were not also a part of the nature of that Divine Mind which
constitutes the universe?--It would seem not: the Moral Law of the
universe must be a Law of the Divine Mind, in order that it may be a
Law felt and discerned by man.


9. (_Objection answered._)--But, it may be objected, the Moral Law
of the universe is a Law in a different sense from the Laws of the
universe of which we spoke before--the mathematical and physical laws
of the universe. Those were laws according to which things _are_, and
events _occur_: but Moral Laws are Laws according to which men _ought_
to act, and according to which actions _ought_ to be. There is a
difference, so that we cannot reason from the human to the Divine Mind
in the same manner in this case as in the other.

True: we cannot reason _in the same manner_. But we can reason still
more confidently. For the Law directing what _ought to be_ is the
_Supreme Law_, and the mind which constitutes the Supreme Law is the
_Supreme Mind_, that is, the Divine Mind.

10. That the Moral Law is not verified among men in fact, is not a
ground for doubting that it is a Law of the Divine Mind; but it is a
ground for inquiring what consequences the Divine Mind has annexed to
the violation of the Law; and in what manner the supremacy of the Law
will be established in the total course of the history of the universe,
including, it may be, the history of other worlds than that in which we
now live.

Considering how dimly and imperfectly we see what consequences the
Divine Governor has annexed to the violation of the Moral Law, He who
sees all these consequences and has provided for the establishment of
His Law in the whole history of the human race, must be supposed to be
infinitely elevated above man in wisdom;--more even in virtue of this
aspect of His nature, than in virtue of that which is derived from the
contemplation of the universe.

11. Man is a person; and his personality is his _highest_ attribute,
or at least, that which makes all his highest attributes possible.
And the highest attribute which belongs to the finite minds which
exist in the universe must exist also in the Infinite Mind which
constitutes the universe as it is. The Divine Mind must reside in a
_Divine Person_. And as man, by his personality, acts in obedience to
or in transgression of a moral law, so God, by His Personality, acts in
establishing the Law and in securing its supremacy in the whole history
of the world.


12. (_Creation._)--Acknowledging a Divine Mind which is the foundation
and support of the world as it is, constituting and upholding its laws,
it may be asked, Does this view point to a beginning of the world?
Was there a time when the Divine Mind called into being the world,
before non-existent? Was there a Creation of the world?

I do not think that an answer to this question, given either way,
affects the argument which I have been urging. The Laws of the
Universe discoverable by the human mind, are the Laws of the Divine
Mind, whether or not there was a time when these Laws first came into
operation, or first produced the world which we see. The argument
respecting the nature of the Divine Mind is the same, whether or not we
suppose a Creation.

But, in point of fact, every part of our knowledge of the Universe does
seem to point to a beginning. Every part of the world has been, so far
as we can see, formed by natural causes out of something different
from what it now is. The Earth, with its lands and seas, teeming with
innumerable forms of living things, has been produced from an earth
formed of other lands and seas, occupied with quite different forms of
life: and if we go far enough back, from an earth in which there was
no life. The stars which we call _fixed_ move and change; the nebulæ
in their shape show that they too are moving and changing. The Earth
was, some at least hold, produced by the condensation of a nebula.
The history of man, as well as of others of its inhabitants, points
to a beginning. Languages, Arts, Governments, Histories, all seem to
have begun from a starting-point, however remote. Indeed not only a
beginning, but a beginning at no remote period, appears to be indicated
by most of the sciences which carry us backwards in the world's history.

But we must allow, on the other hand, that though all such lines of
research point _towards_ a beginning, none of them can be followed _up
to_ a beginning. All the lines converge, but all melt away before they
reach the point of convergence. As I have elsewhere said[320], in no
science has man been able to arrive at a beginning which is homogeneous
with the known course of events, though we can often go very far
back, and limit the hypotheses respecting the origin. We have, in the
impossibility of thus coming to any conclusion by natural reason on the
subject of creation, another evidence of the infinitely limited nature
of the human mind, when compared with the Creative or Constitutive
Divine Mind.


13. (_End of the World._)--But if our natural reason, aided by all
that science can teach, can tell us nothing respecting the origin
and beginning of this world, still less can reason tell us anything
with regard to the _End_ of this world. On this subject, the natural
sciences are even more barren of instruction than on the subject of
Creation. Yet we may say that as the Constitution of the Universe, and
its conformity to a Collection of eternal and immutable Ideas as its
elements, are not inconsistent with the supposition of a Beginning of
the present course of the world, so neither are they inconsistent with
the supposition of an End. Indeed it would not be at all impossible
that physical inquiries should present the prospect of an End, even
more clearly than they afford the retrospect of a Beginning. If, for
instance, it should be found that the planets move in a resisting
medium which constantly retards their velocity, and must finally
make them fall in upon the central sun, there would be an end of the
earth as to its present state. We cannot therefore, on the grounds of
Science, deny either a Beginning or an End of the present world.


14. But here another order of considerations comes into play, namely,
those derived from moral and theological views of the world. On these
we must, in conclusion, say a few words.

It is very plain that these considerations may lead us to believe in
a view of the Beginning, Middle, and End of the history of the world,
very different from anything which the mere physical and natural
sciences can disclose to us. And these expressions to which I have
been led, the _Beginning_, the _Middle_, and the _End_ of the world's
history according to theological views, are full of suggestions of the
highest interest. But the interest which belongs to these suggestions
is of a solemn and peculiar kind; and the considerations to which
such suggestions point are better, I think, kept apart from such
speculations as those with which I have been concerned in the present
volume.


FOOTNOTES:

[Footnote 320: _Hist. Ind. Sc._ b. xviii. c. vi. sect. 5]




CHAPTER XXXII.

ANALOGIES OF PHYSICAL AND RELIGIOUS PHILOSOPHY.


1. Any assertion of analogy between physical and religious philosophy
will very properly be looked upon with great jealousy as likely to
be forced and delusive; and it is only in its most general aspects
that a sound philosophy on the two subjects can offer any points of
resemblance. But in some of its general conditions the discovery of
truth in the one field of knowledge and in the other may offer certain
analogies, as well as differences, which it may be instructive to
notice; and to some such aspects of our philosophy I shall venture to
refer.

For the physical sciences--the sciences of observation and
speculation--the progress of our exact and scientific knowledge, as
I have repeatedly said, consists in reducing the objects and events
of the universe to a conformity with Ideas which we have in our own
minds:--the Ideas, for instance, of Space, Force, Substance, and the
like. In this sense, the intellectual progress of men consists in the
Idealization of Facts.

2. In moral subjects, on the other hand, where man has not merely to
observe and speculate, but also to act;--where he does not passively
leave the facts and events of the world such as they are, but tries
actively to alter them and to improve the existing state of things,
his progress consists in doing this. He makes a moral advance when he
succeeds in doing what he thus attempts:--when he really improves the
state of things with which he has to do by removing evil and producing
good:--when he makes the state of things, namely, the relations between
him and other persons, his acts and their acts, conform more and
more to Ideas which he has in his own mind:--namely, to the Ideas of
Justice, Benevolence, and the like. His moral progress thus consists in
the realization of Ideas.

And thus we are led to the Aphorism, as we may call it, that _Man's
Intellectual Progress consists in the Idealization of Facts, and his
Moral Progress consists in the Realization of Ideas_.


3. But further, though that progress of science which consists in
the idealization of facts may be carried through several stages, and
indeed, in the history of science, has been carried through many
stages, yet it is, and always must be, a progress exceedingly imperfect
and incomplete, when compared with the completeness to which its nature
points. Only a few sciences have made much progress; none are complete;
most have advanced only a step or two. In none have we reduced all the
Facts to Ideas. In all or almost all the unreduced Facts are far more
numerous and extensive than those which have been reduced. The general
mass of the facts of the universe are mere facts, unsubdued to the rule
of science. The Facts are not Idealized. The intellectual progress
is miserably scanty and imperfect, and would be so, even if it were
carried much further than it is carried. How can we hope that it will
ever approach to completeness?

4. And in like manner, the _moral_ progress of man is still more
miserably scanty and incomplete. In how small a degree has he in this
sense realized his Ideas! In how small a degree has he carried into
real effect, and embodied in the relations of society, in his own acts
and in those of others with whom he is concerned, the Ideas of Justice
and Benevolence and the like! How far from a complete realization of
such moral Ideas are the acts of the best men, and the relations of
the best forms of society! How far from perfection in these respects
is man! and how certain it is that he will always be very far from
perfection! Far below even such perfection as he can conceive, he will
always be in his acts and feelings. The moral progress of man, of each
man, and of each society, is, as I have said, miserably scanty and
incomplete; and when regarded as the realization of his moral Ideas,
its scantiness and incompleteness become still more manifest than
before.

Hence we are led to another Aphorism:--_that man's progress in the
realization of Moral Ideas, and his progress in the Scientific
idealization of Facts, are, and always will be, exceedingly scanty and
incomplete_.


5. But there is another aspect of Ideas, both physical and moral,
in which this scantiness and incompleteness vanish. In the Divine
Mind, all the physical Ideas are entertained with complete fulness
and luminousness; and it is because they are so entertained in the
Divine Mind, and it is because the universe is constituted and framed
upon them, that we find them verified in every part of the universe,
whenever we make our observation of facts and deduce their laws.

In like manner the Moral Ideas exist in the Divine Mind in complete
fulness and luminousness; and we are naturally led to believe and
expect that they must be exemplified in the moral universe, as
completely and universally as the physical laws are exemplified in the
physical universe. Is this so? or under what conditions can we conceive
this to be?

6. In answering this question, we must consider how far the moral,
still more even than the physical Ideas of the Divine Mind, are
elevated above our human Ideas; but yet not so far as to have no
resemblance to our corresponding human Ideas; for if this were so, we
could not reason about them at all.

In speaking of man's moral Ideas, Benevolence, Justice, and the like,
we speak of them as belonging to man's _Soul_, rather than to his
_Mind_, which we have commonly spoken of as the seat of his physical
Ideas. A distinction is thus often made between the intellectual and
the moral faculties of man; but on this distinction we here lay no
stress. We may speak of man's _Mind_ and _Soul_, meaning that part of
his being in which are all his Ideas, intellectual and moral.

And now let us consider the question which has just been asked:--how we
can conceive the Divine Benevolence and Justice to be completely and
universally realized in the moral world, as the Ideas of Space, Time,
&c. are in the physical world?


7. Our Ideas of Benevolence, Justice, and of other Virtues, may be
elevated above their original narrowness, and purified from their
original coarseness, by moral culture; as our Ideas of Force and
Matter, of Substance and Elements, and the like, may be made clear
and convincing by philosophical and scientific culture. This appears,
in some degree, in the history of moral terms, as the progress of
clearness and efficacy in the Idea of the material sciences appears in
the history of the terms belonging to such sciences. Thus among the
Romans, while they confined their kindly affections within their own
class, a stranger was universally an enemy; _peregrinus_ was synonymous
with _hostis_. But at a later period, they regarded all _men_ as having
a claim on their kindness; and he who felt and acted on this claim was
called _humane_. This meaning of the word _humanity_ shows the progress
(in their Ideas at least) of the virtue which the word _humanity_
designates.

8. And as man can thus rise to a point of view where he sees that man
is to be loved as man, so the humane and loving man inevitably assumes
that God loves all men; and thus assumes that there is, or may be, a
love of man in man's heart, which represents and resembles in kind,
however remote in degree, the love of God to man.

But as in man's love of man there are very widely different stages,
rising from the narrow love of a savage to his family or his tribe,
to the widest and warmest feelings of the most enlightened and loving
universal philanthropist;--so must we suppose that there are stages
immeasurably wider by which God's love of man is more comprehensive and
more tender than any love of man for man. The religious philosopher
will fully assent to the expressions of this conviction delivered by
pious men in all ages. "The eternal God is thy refuge, and beneath
thee are the everlasting arms." "When my father and my mother forsake
me the Lord taketh me up," is the expression of Divine Love, consistent
with philosophy as well as with revelation. But as the Divine Love is
more comprehensive and enduring than any human love, so is it in an
immeasurably greater degree, more enlightened. It is not a love that
seeks merely the pleasure and gratification of its object; _that_
even an enlightened human love does not do. It seeks the good of its
objects; and such a good as is the greatest good, to an Intelligence
which can embrace all cases, causes, and contingencies. To our limited
understanding, evil seems often to be inflicted, and the good of a
part seems inconsistent with the good of another part. Our attempts to
conceive a Supreme and complete Good provided for all the creatures
which exist in the universe, baffle and perplex us, even more than our
attempts to conceive infinite space, infinite time, and an infinite
chain of causation. But as the most careful attention which we can
give to the Ideas of Space, Time, and Causation convinces us that
these Ideas are perfectly clear and complete in the Divine Mind, and
that _our_ perplexity and confusion on these subjects arise only from
the vast distance between the Divine Mind and our human mind, so is
it reasonable to suppose the same to be the source of the confusion
which we experience when we attempt to determine what most conduces to
the good of our fellow-creatures; and when, urged by love to them, we
endeavour to promote this good. We can do little of what Infinite Love
would do, yet are we not thereby dispensed from seeking in some degree
to imitate the working of Divine Love. We can see but little of what
Infinite Intelligence sees, and this should be one source of confidence
and comfort, when we stumble upon perplexities produced by the seeming
mixture of good and evil in the world.

9. But when we ask the questions which have already been stated:
Whether this Infinite Divine Love is realized in the world, and if
so, How: I conceive that we are irresistibly impelled to reply to the
former question, that it is: and we then turn to the latter. We are
led to assume that there is in God an Infinite Love of man, a creature
in a certain degree of a Divine nature. We must, as a consequence of
this, assume that the Love of God to man, necessarily is, in the end,
and on the whole, completely and fully realized in the history of the
world. But what is the complete history of the world! Is it that which
consists in the lives of men such as we see them between their birth
and their death? If the minds or souls of men are alive after the death
of the body, that future life, as well as this present life, belongs to
the history of the world;--to that providential history, of which the
totality, as we have said, must be governed by Infinite Divine Love.
And in addition to all other reasons for believing that the minds and
souls of men do thus survive their present life, is this:--that we thus
can conceive, what otherwise it is difficult or impossible to conceive,
the operation of Infinite Love in the whole of the history of mankind.
If there be a Future State in which men's souls are still under the
authority and direction of the Divine Governor of the world, all that
is here wanting to complete the scheme of a perfect government of
Intelligent Love may thus be applied: all seeming and partial evil may
be absorbed and extinguished in an ultimate and universal good.


10. The Idea of Justice as belonging to God suggests to us some of the
same kind of reflexions as those which we have made respecting the
Divine Love. We believe God to be just: otherwise, as has been said,
He would not be God. And as we thus, from the nature of our minds and
souls, believe God to be just, we must, in this belief, understand
Justice according to the Idea which we have of Justice; that is, in
some measure, according to the Idea of Justice, as exemplified in
human actions and feelings. It would be absurd to combine the two
propositions, that we necessarily believe that God is just, and that by
_just_, we mean something entirely different from the common meaning of
the word.

But though the Divine Idea of Justice must necessarily, in some
measure, coincide with our Idea of Justice, we must believe in this,
as in other cases, that the Divine Idea is immeasurably more profound,
comprehensive, and clear, than the human Idea. Even the human Idea of
Justice is susceptible of many and large progressive steps, in the way
of clearness, consistency, and comprehensiveness. In the moral history
of man this Idea advances from the hard rigour of inflexible written
Law to the equitable estimation of the real circumstances of each case;
it advances also from the narrow Law of a single community to a larger
Law, which includes and solves the conflicts of all such Laws. Further,
the administration of human Law is always imperfect, often erroneous,
in consequence of man's imperfect knowledge of the facts of each case,
and still more, from his ignorance of the designs and feelings of the
actors. If the Judge could see into the heart of the person accused,
and could himself rise higher and higher in judicial wisdom, he might
exemplify the Idea of Justice in a far higher degree than has ever yet
been done.

11. But all such advance in the improvement of human Justice must
still be supposed to stop immeasurably short of the Divine Justice,
which must include a perfect knowledge of all men's actions, and all
men's hearts and thoughts; and a universal application of the wisest
and most comprehensive Laws. And the difference of the Divine and of
the human Idea of Justice may, like the differences of other Divine
and human Ideas, include the solution of all the perplexities in which
we find ourselves involved when we would trace the Idea to all its
consequences. The Divine Idea is immeasurably elevated above the human
Idea; in the Divine Idea all inconsistency, defect, and incompleteness
vanish, and Justice includes in its administration every man, without
any admixture of injustice. This is what we must conceive of the Divine
administration, since God is perfectly just.

12. But here, as before, we have another conclusion suggested to us. We
are, by the considerations just now spoken of, led to believe that, in
the Divine administration of the world is an administration of perfect
Justice;--that is, such is the Divine Administration in the end and on
the whole, taking into account the whole of the providential history of
the world. But the course of the world, taking into account only what
happens to man in this present life, is not, we may venture to say, a
complete and entire administration of justice. It often happens that
injustice is successful and triumphant, even in the end, so far as the
end is seen here. It happens that wrong is done, and is not remedied
or punished. It happens that blameless and virtuous men are subjected
to pain, grief, violence, and oppression, and are not protected,
extricated, or avenged. In the affairs of this world, the prevalence of
injustice and wrong-doing is so apparent, as to be a common subject of
complaint: and though the complaint may be exaggerated, and though a
calm and comprehensive view may often discern compensating and remedial
influences which are not visible at first sight, still we cannot regard
the lot of happiness or misery which falls to each man in this world
and this life as apportioned according to a scheme of perfect and
universal justice, such as in our thoughts we cannot but require the
Divine administration to be.

13. Here then we are again led to the same conviction by regarding the
Divine administration of the world as the realization of the Divine
Justice, to which we were before led by regarding it as the realization
of the Divine Love. Since the Idea is not fully or completely realized
in man's life in this present world, this present world cannot be the
whole of the Divine Administration. To complete the realization of the
Idea of Justice, as an element of the Divine Administration, there
must be a life of man after his life in this present world. If man's
mind and soul, the part of him which is susceptible of happiness and
misery, survive this present life, and be still subject to the Divine
Administration, the Idea of Divine Justice may still be completely
realized, notwithstanding all that here looks like injustice or
defective justice; and it belongs to the Idea of Justice to remedy
and compensate, not to prevent wrong. And thus by this supposition
of a Future State of man's existence, we are enabled to conceive
that, in the whole of the Divine Government of the universe, all
seeming injustice and wrong may be finally corrected and rectified,
in an ultimate and universal establishment of a reign of perfect
Righteousness.


14. Admitting the view thus presented, we may again discern a
remarkable analogy between what we have called our _physical_ Ideas
(those of Space, Time, Cause, Substance, and the like), and our _moral_
Ideas, (those of Benevolence, Justice, &c.). In both classes we must
suppose that our human Ideas represent, though very incompletely and at
an immeasurable distance, the Divine Ideas. Even our physical Ideas,
when pursued to their consequences, are involved in a perplexity
and confusion from which the Divine Ideas are free. Our Ideas of
Benevolence and Justice are still more full of imperfections and
inconsistency, when we would frame them into a complete scheme, and
yet from such imperfections and inconsistency we must suppose that
the Divine Benevolence and Justice are exempt. Our physical Ideas we
find in every case exactly exemplified and realized in the universe,
and we account for this by considering that they are the Divine Ideas,
on which the universe is constituted. Our moral Ideas, the Ideas of
Benevolence and Justice in particular, must also be realized in the
universe, as a scheme of Divine Government. But they are not realized
in the world as constituted of man living this present life. The Divine
Scheme of the world, therefore, extends beyond this present life of
man. If we could include in our survey the future life as well as the
present life of man, and the future course of the Divine Government, we
should have a scheme of the Moral Government of the universe, in which
the Ideas of Perfect Benevolence and Perfect Justice are as completely
and universally exemplified and realized, as the Ideas of Space, Time,
Cause, Substance, and the like, are in the physical universe.


15. There is one other remark bearing upon this analogy, which seems
to deserve our attention. As I have said in the last chapter, the
scheme of the world, as governed by our physical Ideas, seems to point
to a Beginning of the world, or at least of the present course of the
world: and if we suppose a Beginning, our thoughts naturally turn to
an End. But if our physical Ideas point to a Beginning and suggest an
End, do our Ideas of Divine Benevolence and Justice in any way lend
themselves to this suggestion?--Perhaps we might venture to say that in
some degree they do, even to the eye of a mere philosophical reason.
Perhaps our reason alone might suggest that there is a progression in
the human race, in various moral attributes--in art, in civilization,
and even in humanity and in justice, which implies a beginning. And
that at any rate there is nothing inconsistent with our Idea of the
Divine Government in the supposition that the history of this world has
a Beginning, a Middle and an End.

16. If therefore there should be conveyed to us by some channel
especially appropriated to the communication and development of moral
and religious Ideas, the knowledge that the world, as a scheme of
Divine Government, has _a Beginning_, _a Middle_, and _an End_, of
a Kind, or at least, invested with circumstances quite different
from any which our physical Ideas can disclose to us, there would
be, in such a belief, nothing at all inconsistent with the analogies
which our philosophy--the philosophy of our Ideas illustrated by the
whole progress of science--has impressed upon us. On the grounds of
this philosophy, we need find no difficulty in believing that as the
visible universe exhibits the operation of the Divine Ideas of Space,
Time, Cause, Substance, and the like, and discloses to us traces of
a Beginning of the present mode of operation, so the moral universe
exhibits to us the operation of the Divine Benevolence and Justice; and
that these Divine attributes wrought in a special and peculiar manner
in the Beginning; interposed in a peculiar and special manner in the
Middle; and will again act in a peculiar and special manner in the End
of the world. And thus the conditions of the physical universe, and the
Government of the Moral world, are both, though in different ways, a
part of the work which God is carrying on from the Beginning of things
to the End--_opus quod Deus operator a principio usque ad finem_.


17. We are led by such analogies as I have been adducing to believe
that the whole course of events in which the minds and souls of men
survive the present life, and are hereafter subjected to the Divine
government in such a way as to complete all that is here deficient in
the world's history, is a scheme of perfect Benevolence and Justice.
Now, can we discern in man's mind or soul itself any indication of a
destiny like this? Are there in us any powers and faculties which seem
as if they were destined to immortality? If there be, we have in such
faculties a strong confirmation of that belief in the future life of
man which has already been suggested to us as necessary to render the
Divine government conceivable.


18. According to our philosophy there are powers and faculties which
do thus seem fitted to endure, and not fitted to terminate and be
extinguished. The Ideas which we have in our minds--the physical
Ideas, as we have called them, according to which the universe is
constituted,--agree, as far as they go, with the Ideas of the Divine
Mind, seen in the constitution of the universe. But these Divine
Ideas are eternal and imperishable: we therefore naturally conclude
that the human mind which includes such elements, is also eternal and
imperishable. Since the mind can take hold of eternal truths, it must
be itself eternal. Since it is, to a certain extent, the image of God
in its faculties, it cannot ever cease to be the image of God. When it
has arrived at a stage in which it sees several aspects of the universe
in the same form in which they present themselves to the Divine Mind,
we cannot suppose that the Author of the human mind will allow it and
all its intellectual light to be extinguished.

19. And our conviction that this extinction of the human mind cannot
take place becomes stronger still, when we consider that the mind,
however imperfect and scanty its discernment of truth may be, is
still capable of a vast, and even of an unlimited progress in the
pursuit and apprehension of truth. The mind is capable of accepting
and appropriating, through the action of its own Ideas, every step in
science which has ever been made--every step which shall hereafter
be made. Can we suppose that this vast and boundless capacity exists
for a few years only, is unfolded only into a few of its simplest
consequences, and is then consigned to annihilation? Can we suppose
that the wonderful powers which carry man on, generation by generation,
from the contemplation of one great and striking truth to another, are
buried with each generation? May we not rather suppose that that mind,
which is capable of indefinite progression, is allowed to exist in an
infinite duration, during which such progression may take place?

20. I propose this argument as a ground of hope and satisfactory
reflexion to those who love to dwell on the natural arguments for the
Immortality of the Soul. I do not attempt to follow it into detail.
I know too well how little such a cause can gain by obstinate and
complicated argumentation, to attempt to urge the argument in that
manner: and probably different persons, among those who accept the
argument as valid, would give different answers to many questions of
detail, which naturally arise out of the acceptance of this argument.
I will not here attempt to solve, or even to propound these questions.
My main purpose in offering these views and this argument at all, is
to give some satisfaction to those who would think it a sad and blank
result of this long survey of the nature and progress of science in
which we have been so long engaged (through this series of works), that
it should in no way lead to a recognition of the Author of that world
about which our Science is, and to the high and consolatory hopes which
lift man beyond this world. No survey of the universe can be at all
satisfactory to thoughtful men, which has not a theological bearing;
nor can any view of man's powers and means of knowing be congenial to
such men, which does not recognize an infinite destination for the mind
which has an infinite capacity; an eternal being of the Faculty which
can take a steady hold of eternal being.


21. And as we may derive such a conviction from our physical Ideas, so
too may we no less from our moral Ideas. Our minds apprehend Space and
Time and Force and the like, as Ideas which are not dependent on the
body; and hence we believe that our minds shall not perish with our
bodies. And in the same manner our souls conceive pure Benevolence and
perfect Justice, which go beyond the conditions of this mortal life;
and hence we believe that our souls have to do with a life beyond this
mortal life.

It is more difficult to speak of man's indefinite moral progression
even than of his indefinite intellectual progression. Yet in every
path of moral speculation we have such a progression suggested to us.
We may begin, for instance, with the ordinary feelings and affections
of our daily nature:--Love, Hate, Scorn. But when we would elevate the
Soul in our imagination, we ascend above these ordinary affections, and
take the repulsive and hostile ones as fitted only to balance their own
influences. And thus the poet, speaking of a morally poetical nature,
describes it:

  The Poet in a golden clime was born,
    With golden stars above.
  He felt the hate _of_ hate, the scorn _of_ scorn,
    The love _of_ love.

But the loftier moralist can rise higher than this, and can, and will,
reject altogether Hate and Scorn from his view of man's better nature.
His description would rather be--

  The good man in a loving clime was born,
    With loving stars above.
  He felt sorrow for hate, pity for scorn,
    And love of love.

He would, in his conception of such a character, ascribe to it all
the virtues which result from the control and extinction of these
repulsive and hostile affections:--the virtues of magnanimity,
forgivingness, unselfishness, self-devotion, tenderness, sweetness. And
these we can conceive in a higher and higher degree, in proportion as
our own hearts become tender, forgiving, pure and unselfish. And though
in every human stage of such a moral proficiency, we must suppose
that there is still some struggle with the remaining vestiges of our
unkind, unjust, angry and selfish affections, we can see no limit to
the extent to which this struggle may be successful; no limit to the
degree in which these traces of the evil of our nature may be worn
out by an enduring practice and habit of our better nature. And when
we contemplate a human character which has, through a long course of
years, and through many trials and conflicts, made a large progress in
this career of melioration, and is still capable, if time be given,
of further progress towards moral perfection, is it not reasonable to
suppose that He who formed man capable of such progress, and who, as we
must needs believe, looks with approval on such progress where made,
will not allow the progress to stop when it has gone on to the end of
man's short earthly life? Is it not rather reasonable to suppose that
the pure and elevated and all-embracing affection, extinguishing all
vices and including all virtues, to which the good man thus tends,
shall continue to prevail in him as a permanent and ever-during
condition, in a life after this?

But can man raise himself to such a stage of moral progress, by his own
efforts? Such a progress is an approximation towards the perfection of
moral Ideas, and therefore an approximation towards the image of God,
in whom that perfection resides: is it not then reasonable to suppose
that man needs a Divine Influence to enable him to reach this kind of
moral completeness? And is it not also reasonable to suppose that,
as he needs such aid, in order that the Idea of his moral progress
may be realized, so he will receive such aid from the Divine Power
which realizes the Idea of Divine Love in the world; and to do so,
must realize it in those human souls which are most fitted for such a
purpose?

But these questions remind me how difficult, and indeed, how impossible
it is to follow such trains of reflexion by the light of philosophy
alone. To answer such questions, we need, not Religious Philosophy
only, but Religion: and as I do not here venture beyond the domain of
philosophy, I must, however abruptly, conclude.


THE END.




APPENDIX.


APPENDIX A.

OF THE PLATONIC THEORY OF IDEAS.

(_Cam. Phil. Soc._ Nov. 10, 1856.)


Though Plato has, in recent times, had many readers and admirers
among our English scholars, there has been an air of unreality and
inconsistency about the commendation which most of these professed
adherents have given to his doctrines. This appears to be no captious
criticism, for instance, when those who speak of him as immeasurably
superior in argument to his opponents, do not venture to produce
his arguments in a definite form as able to bear the tug of modern
controversy;--when they use his own Greek phrases as essential to the
exposition of his doctrines, and speak as if these phrases could not be
adequately rendered in English;--and when they assent to those among
the systems of philosophy of modern times which are the most clearly
opposed to the system of Plato. It seems not unreasonable to require,
on the contrary, that if Plato is to supply a philosophy for us, it
must be a philosophy which can be expressed in our own language;--that
his system, if we hold it to be well founded, shall compel us to deny
the opposite systems, modern as well as ancient;--and that, so far as
we hold Plato's doctrines to be satisfactorily established, we should
be able to produce the arguments for them, and to refute the arguments
against them. These seem reasonable requirements of the adherents of
_any_ philosophy, and therefore, of Plato's.

I regard it as a fortunate circumstance, that we have recently had
presented to us an exposition of Plato's philosophy which does conform
to those reasonable conditions; and we may discuss this exposition with
the less reserve, since its accomplished author, though belonging to
this generation, is no longer alive. I refer to the _Lectures_ on the
History of Ancient Philosophy, by the late Professor Butler of Dublin.
In these Lectures, we find an account of the Platonic Philosophy which
shows that the writer had considered it as, what it is, an attempt
to solve large problems, which in all ages force themselves upon the
notice of thoughtful men. In Lectures VIII. and X., of the Second
Series, especially, we have a statement of the Platonic Theory of
Ideas, which may be made a convenient starting point for such remarks
as I wish at present to make. I will transcribe this account; omitting,
as I do so, the expressions which Professor Butler uses, in order to
present the theory, not as a dogmatical assertion, but as a view, at
least not extravagant. For this purpose, he says, of the successive
portions of the theory, that one is "not too absurd to be maintained;"
that another is "not very extravagant either;" that a third is "surely
allowable;" that a fourth presents "no incredible account" of the
subject; that a fifth is "no preposterous notion in substance, and no
unwarrantable form of phrase." Divested of these modest formulæ, his
account is as follows: [Vol. II. p. 117.]

"Man's soul is made to contain not merely a consistent scheme of its
own notions, but a direct apprehension of _real and eternal laws beyond
it_. These real and eternal laws are things _intelligible_, and not
things sensible.

"These laws impressed upon creation by its Creator, and apprehended
by man, are something distinct equally from the Creator and from man,
and the whole mass of them may fairly be termed the World of Things
Intelligible.

"Further, there are qualities in the supreme and ultimate Cause of all,
which are manifested in His creation, and not merely manifested, but,
in a manner--after being brought out of his super-essential nature into
the stage of being [which is] below him, but next to him--are then by
the causative act of creation deposited in things, differencing them
one from the other, so that the things partake of them (μετέχουσι),
communicate with them (κοινωνοῦσι).

"The intelligence of man, excited to reflection by the impressions
of these objects thus (though themselves transitory) participant of
a divine quality, may rise to higher conceptions of the perfections
thus faintly exhibited; and inasmuch as these perfections are
unquestionably _real_ existences, and _known_ to be such in the very
act of contemplation,--this may be regarded as a direct intellectual
apperception of them,--a Union of the Reason with the Ideas in that
sphere of being which is common to both.

"Finally, the Reason, in proportion as it learns to contemplate the
Perfect and Eternal, _desires_ the enjoyment of such contemplations in
a more consummate degree, and cannot be fully satisfied, except in the
actual fruition of the Perfect itself.

"These suppositions, taken together, constitute the Theory of Ideas."

In remarking upon the theory thus presented, I shall abstain from any
discussion of the theological part of it, as a subject which would
probably be considered as unsuited to the meetings of this Society,
even in its most purely philosophical form. But I conceive that it will
not be inconvenient, if it be not wearisome, to discuss the Theory of
Ideas as an attempt to explain the existence of real knowledge; which
Prof. Butler very rightly considers as the necessary aim of this and
cognate systems of philosophy[321].

I conceive, then, that one of the primary objects of Plato's Theory
of Ideas is, to explain the existence of real knowledge, that is, of
demonstrated knowledge, such as the propositions of geometry offer
to us. In this view, the Theory of Ideas is one attempt to solve a
problem, much discussed in our times, What is the ground of geometrical
truth? I do not mean that this is the whole object of the Theory, or
the highest of its claims. As I have said, I omit its theological
bearings; and I am aware that there are passages in the Platonic
Dialogues, in which the Ideas which enter into the apprehension and
demonstration of geometrical truths are spoken of as subordinate to
Ideas which have a theological aspect. But I have no doubt that one
of the main motives to the construction of the Theory of Ideas was,
the desire of solving the Problem, "How is it possible that man should
apprehend necessary and eternal truths?" That the truths are necessary,
makes them eternal, for they do not depend on time; and that they are
eternal, gives them at once a theological bearing.

That Plato, in attempting to explain the nature and possibility of
real knowledge, had in his mind geometrical truths, as examples of
such knowledge is, I think, evident from the general purport of his
discourses on such subjects. The advance of Greek geometry into a
conspicuous position, at the time when the Heraclitean sect were
proving that nothing could be proved and nothing could be known,
naturally suggested mathematical truth as the refutation of the
skepticism of mere sensation. On the one side it was said, we can
know nothing except by our sensations; and that which we observe with
our senses is constantly changing; or at any rate, may change at any
moment. On the other hand it was said, we _do_ know geometrical truths,
and as truly as we know them, that they cannot change. Plato was quite
alive to the lesson, and to the importance of this kind of truths.
In the _Meno_ and in the _Phædo_ he refers to them, as illustrating
the nature of the human mind: in the _Republic_ and the _Timæus_ he
again speaks of truths which far transcend anything which the senses
can teach, or even adequately exemplify. The senses, he argues in the
_Theætetus_, cannot give us the knowledge which we have; the source
of it must therefore be in the mind itself; in the _Ideas_ which
it possesses. The impressions of sense are constantly varying, and
incapable of giving any certainty: but the Ideas on which real truth
depends are constant and invariable, and the certainty which arises
from these is firm and indestructible. Ideas are the permanent, perfect
objects, with which the mind deals when it contemplates necessary and
eternal truths. They belong to a region superior to the material world,
the world of sense. They are the objects which make up the furniture of
the Intelligible World; with which the Reason deals, as the Senses deal
each with its appropriate Sensation.

But, it will naturally be asked, what is the Relation of Ideas to the
Objects of Sense? Some connexion, or relation, it is plain, there
must be. The objects of sense can suggest, and can illustrate real
truths. Though these truths of geometry cannot be proved, cannot even
be exactly exemplified, by drawing diagrams, yet diagrams are of use
in helping ordinary minds to see the proof; and to all minds, may
represent and illustrate it. And though our conclusions with regard to
objects of sense may be insecure and imperfect, they have some show of
truth, and therefore some resemblance to truth. What does this arise
from? How is it explained, if there is no truth except concerning Ideas?

To this the Platonist replied, that the phenomena which present
themselves to the senses partake, in a certain manner, of Ideas, and
thus include so much of the nature of Ideas, that they include also
an element of Truth. The geometrical diagram of Triangles and Squares
which is drawn in the sand of the floor of the Gymnasium, partakes of
the nature of the true Ideal Triangles and Squares, so that it presents
an imitation and suggestion of the truths which are true of them. The
real triangles and squares are in the mind: they are, as we have said,
objects, not in the Visible, but in the Intelligible World. But the
Visible Triangles and Squares make us call to mind the Intelligible;
and thus the objects of sense suggest, and, in a way, exemplify the
eternal truths.

This I conceive to be the simplest and directest ground of two primary
parts of the Theory of Ideas;--The Eternal Ideas constituting an
Intelligible World; and the Participation in these Ideas ascribed to
the objects of the world of sense. And it is plain that so far, the
Theory meets what, I conceive, was its primary purpose; it answers the
questions, How can we have certain knowledge, though we cannot get it
from Sense? and, How can we have knowledge, at least apparent, though
imperfect, about the world of sense?

But is this the ground on which Plato himself rests the truth of his
Theory of Ideas? As I have said, I have no doubt that these were the
questions which suggested the Theory; and it is perpetually applied
in such a manner as to show that it was held by Plato in this sense.
But his applications of the Theory refer very often to another part
of it;--to the Ideas, not of Triangles and Squares, of space and its
affections; but to the Ideas of Relations--as the Relations of Like and
Unlike, Greater and Less; or to things quite different from the things
of which geometry treats, for instance, to Tables and Chairs, and other
matters, with regard to which no demonstration is possible, and no
general truth (still less necessary an eternal truth) capable of being
asserted.

I conceive that the Theory of Ideas, thus asserted and thus supported,
stands upon very much weaker ground than it does, when it is
asserted concerning the objects of thought about which necessary and
demonstrable truths are attainable. And in order to devise arguments
against _this_ part of the Theory, and to trace the contradictions to
which it leads, we have no occasion to task our own ingenuity. We find
it done to our hands, not only in Aristotle, the open opponent of the
Theory of Ideas, but in works which stand among the Platonic Dialogues
themselves. And I wish especially to point out some of the arguments
against the Ideal Theory, which are given in one of the most noted of
the Platonic Dialogues, the _Parmenides_.

The _Parmenides_ contains a narrative of a Dialogue held between
Parmenides and Zeno, the Eleatic Philosophers, on the one side, and
Socrates, along with several other persons, on the other. It may be
regarded as divided into two main portions; the first, in which the
Theory of Ideas is attacked by Parmenides, and defended by Socrates;
the second, in which Parmenides discusses, at length, the Eleatic
doctrine that _All things are One_. It is the former part, the
discussion of the Theory of Ideas, to which I especially wish to direct
attention at present: and in the first place, to that extension of
the Theory of Ideas, to things of which no general truth is possible;
such as I have mentioned, tables and chairs. Plato often speaks of
a Table, by way of example, as a thing of which there must be an
Idea, not taken from any special Table or assemblage of Tables; but
an Ideal Table, such that all Tables are Tables by participating in
the nature of this Idea. Now the question is, whether there is any
force, or indeed any sense, in this assumption; and this question is
discussed in the _Parmenides_. Socrates is there represented as very
confident in the existence of Ideas of the highest and largest kind,
the Just, the Fair, the Good, and the like. Parmenides asks him how
far he follows his theory. Is there, he asks, an Idea of Man, which is
distinct from us men? an Idea of Fire? of Water? "In truth," replies
Socrates, "I have often hesitated, Parmenides, about these, whether
we are to allow such Ideas." When Plato had proceeded to teach that
there is an Idea of a Table, of course he could not reject such Ideas
as Man, and Fire, and Water. Parmenides, proceeding in the same line,
pushes him further still. "Do you doubt," says he, "whether there
are Ideas of things apparently worthless and vile? Is there an Idea
of a Hair? of Mud? of Filth?" Socrates has not the courage to accept
such an extension of the theory. He says, "By no means. These are not
Ideas. These are nothing more than just what we see them. I have often
been perplexed what to think on this subject. But after standing to
this a while, I have fled the thought, for fear of falling into an
unfathomable abyss of absurdities." On this, Parmenides rebukes him for
his want of consistency. "Ah Socrates," he says, "you are yet young;
and philosophy has not yet taken possession of you as I think she will
one day do--when you will have learned to find nothing despicable in
any of these things. But now your youth inclines you to regard the
opinions of men." It is indeed plain, that if we are to assume an Idea
of a Chair or a Table, we can find no boundary line which will exclude
Ideas of everything for which we have a name, however worthless or
offensive. And this is an argument against the assumption of _such_
Ideas, which will convince most persons of the groundlessness of the
assumption:--the more so, as _for_ the assumption of such Ideas, it
does not appear that Plato offers any argument whatever; nor does
this assumption solve any problem, or remove any difficulty[322].
Parmenides, then, had reason to say that consistency required Socrates,
if he assumed any such Ideas, to assume all. And I conceive his reply
to be to this effect; and to be thus a _reductio ad absurdum_ of the
Theory of Ideas in this sense. According to the opinions of those
who see in the _Parmenides_ an exposition of Platonic doctrines, I
believe that Parmenides is conceived in this passage, to suggest to
Socrates what is necessary for the completion of the Theory of Ideas.
But upon either supposition, I wish especially to draw the attention
of my readers to the position of superiority in the Dialogue in which
Parmenides is here placed with regard to Socrates.

Parmenides then proceeds to propound to Socrates difficulties with
regard to the Ideal Theory, in another of its aspects;--namely, when it
assumes Ideas of Relations of things; and here also, I wish especially
to have it considered how far the answers of Socrates to these
objections are really satisfactory and conclusive.

"Tell me," says he (§ 10, Bekker), "You conceive that there are certain
Ideas, and that things partaking of these Ideas, are called by the
corresponding names;--an Idea of _Likeness_, things partaking of
which are called _Like_;--of _Greatness_, whence they are _Great_: of
_Beauty_, whence they are _Beautiful_?" Socrates assents, naturally:
this being the simple and universal statement of the Theory, in this
case. But then comes one of the real difficulties of the Theory. Since
the special things participate of the General Idea, has each got
the whole of the Idea, which is, of course, One; or has each a part
of the Idea? "For," says Parmenides, "can there be any other way of
participation than these two?" Socrates replies by a similitude: "The
Idea, though One, may be wholly in each object, as the Day, one and the
same, is wholly in each place." The physical illustration, Parmenides
damages by making it more physical still. "You are ingenious,
Socrates," he says, (§ 11) "in making the same thing be in many places
at the same time. If you had a number of persons wrapped up in a sail
or web, would you say that each of them had the whole of it? Is not the
case similar?" Socrates cannot deny that it is. "But in this case, each
person has only a part of the whole; and thus your Ideas are partible."
To this, Socrates is represented as assenting in the briefest possible
phrase; and thus, here again, as I conceive, Parmenides retains his
superiority over Socrates in the Dialogue.

There are many other arguments urged against the Ideal Theory by
Parmenides. The next is a consequence of this partibility of Ideas,
thus supposed to be proved, and is ingenious enough. It is this:

"If the Idea of Greatness be distributed among things that are Great,
so that each has a part of it, each separate thing will be Great in
virtue of a part of Greatness which is less than Greatness itself. Is
not this absurd?" Socrates submissively allows that it is.

And the same argument is applied in the case of the Idea of Equality.

"If each of several things have a part of the Idea of Equality, it
will be Equal to something, in virtue of something which is less than
Equality."

And in the same way with regard to the Idea of Smallness.

"If each thing be small by having a part of the Idea of Smallness,
Smallness itself will be greater than the small thing, since that is a
part of itself."

These ingenious results of the partibility of Ideas remind us of the
ingenuity shown in the Greek geometry, especially the Fifth Book of
Euclid. They are represented as not resisted by Socrates (§ 12): "In
what way, Socrates, can things participate in Ideas, if they cannot
do so either integrally or partibly?" "By my troth," says Socrates,
"it does not seem easy to tell." Parmenides, who completely takes the
conduct of the Dialogue, then turns to another part of the subject and
propounds other arguments. "What do you say to this?" he asks.

"There is an Ideal Greatness, and there are many things, separate from
it, and Great by virtue of it. But now if you look at Greatness and the
Great things together, since they are all Great, they must be Great in
virtue of some higher Idea of Greatness which includes both. And thus
you have a Second Idea of Greatness; and in like manner you will have a
third, and so on indefinitely."

This also, as an argument against the separate existence of Ideas,
Socrates is represented as unable to answer. He replies interrogatively:

"Why, Parmenides, is not each of these Ideas a Thought, which, by its
nature, cannot exist in anything except in the Mind? In that case your
consequences would not follow."

This is an answer which changes the course of the reasoning: but still,
not much to the advantage of the Ideal Theory. Parmenides is still
ready with very perplexing arguments. (§ 13.)

"The Ideas, then," he says, "are Thoughts. They must be Thoughts of
something. They are Thoughts of something, then, which exists in all
the special things; some one thing which the Thought perceives in all
the special things; and this one Thought thus involved in all, is the
_Idea_. But then, if the special things, as you say, participate in the
Idea, they participate in the Thought; and thus, all objects are made
up of Thoughts, and all things think; or else, there are thoughts in
things which do not think."

This argument drives Socrates from the position that Ideas are
Thoughts, and he moves to another, that they are Paradigms, Exemplars
of the qualities of things, to which the things themselves are like,
and their being thus like, is their participating in the Idea. But here
too, he has no better success. Parmenides argues thus:

"If the Object be like the Idea, the Idea must be like the Object.
And since the Object and the Idea are like, they must, according to
your doctrine, participate in the Idea of Likeness. And thus you have
one Idea participating in another Idea, and so on in infinitum."
Socrates is obliged to allow that this demolishes the notion of objects
partaking in their Ideas by likeness: and that he must seek some other
way. "You see then, O Socrates," says Parmenides, "what difficulties
follow, if any one asserts the independent existence of Ideas!"
Socrates allows that this is true. "And yet," says Parmenides, "you
do not half perceive the difficulties which follow from this doctrine
of Ideas." Socrates expresses a wish to know to what Parmenides
refers; and the aged sage replies by explaining that if Ideas exist
independently of us, we can never know anything about them: and that
even the Gods could not know anything about man. This argument, though
somewhat obscure, is evidently stated with perfect earnestness, and
Socrates is represented as giving his assent to it. "And yet," says
Parmenides (end of § 18), "if any one gives up entirely the doctrine of
Ideas, how is any reasoning possible?"

All the way through this discussion, Parmenides appears as vastly
superior to Socrates; as seeing completely the tendency of every line
of reasoning, while Socrates is driven blindly from one position to
another; and as kindly and graciously advising a young man respecting
the proper aims of his philosophical career; as well as clearly
pointing out the consequences of his assumptions. Nothing can be
more complete than the higher position assigned to Parmenides in the
Dialogue.

This has not been overlooked by the Editors and Commentators of Plato.
To take for example one of the latest; in Steinhart's Introduction to
Hieronymus Müller's translation of _Parmenides_ (Leipzig, 1852), p.
261, he says: "It strikes us, at first, as strange, that Plato here
seems to come forward as the assailant of his own doctrine of Ideas.
For the difficulties which he makes Parmenides propound against that
doctrine are by no means sophistical or superficial, but substantial
and to the point. Moreover there is among all these objections, which
are partly derived from the Megarics, scarce one which does not appear
again in the penetrating and comprehensive argumentations of Aristotle
against the Platonic Doctrine of Ideas."

Of course, both this writer and other commentators on Plato offer
something as a solution of this difficulty. But though these
explanations are subtle and ingenious, they appear to leave no
satisfactory or permanent impression on the mind. I must avow that, to
me, they appear insufficient and empty; and I cannot help believing
that the solution is of a more simple and direct kind. It may seem bold
to maintain an opinion different from that of so many eminent scholars;
but I think that the solution which I offer, will derive confirmation
from a consideration of the whole Dialogue; and therefore I shall
venture to propound it in a distinct and positive form. It is this:

I conceive that the _Parmenides_ is not a Platonic Dialogue at all;
but Antiplatonic, or more properly, _Eleatic_: written, not by Plato,
in order to explain and prove his Theory of Ideas, but by some one,
probably an admirer of Parmenides and Zeno, in order to show how strong
were his master's arguments against the Platonists and how weak their
objections to the Eleatic doctrine.

I conceive that this view throws an especial light on every part of the
Dialogue, as a brief survey of it will show. Parmenides and Zeno come
to Athens to the Panathenaic festival: Parmenides already an old man,
with a silver head, dignified and benevolent in his appearance, looking
five and sixty years old: Zeno about forty, tall and handsome. They are
the guests of Pythodorus, outside the Wall, in the Ceramicus; and there
they are visited by Socrates then young, and others who wish to hear
the written discourses of Zeno. These discourses are explanations of
the philosophy of Parmenides, which he had delivered in verse.

Socrates is represented as showing, from the first, a disposition to
criticize Zeno's dissertation very closely; and without any prelude or
preparation, he applies the Doctrine of Ideas to refute the Eleatic
Doctrine that All Things are One. (§ 3.) When he had heard to the
end, he begged to have the first Proposition of the First Book read
again. And then, "How is it, O Zeno, that you say, That if the Things
which exist are Many, and not One, they must be at the same time like
and unlike? Is this your argument? Or do I misunderstand you?" "No,"
says Zeno, "you understand quite rightly." Socrates then turns to
Parmenides, and says, somewhat rudely, as it seems, "Zeno is a great
friend of yours, Parmenides: he shows his friendship not only in
other ways, but also in what he writes. For he says the same things
which you say, though he pretends that he does not. You say, in your
poems, that All Things are One, and give striking proofs: he says that
existences are not many, and he gives many and good proofs. You seem
to soar above us, but you do not really differ." Zeno takes this sally
good-humouredly, and tells him that he pursues the scent with the
keenness of a Laconian hound. "But," says he (§ 6), "there really is
less of ostentation in my writing than you think. My Essay was merely
written as a defence of Parmenides long ago, when I was young; and is
not a piece of display composed now that I am older. And it was stolen
from me by some one; so that I had no choice about publishing it."

Here we have, as I conceive, Socrates already represented as placed
in a disadvantageous position, by his abruptness, rude allusions, and
readiness to put bad interpretations on what is done. For this, Zeno's
gentle pleasantry is a rebuke. Socrates, however, forthwith rushes into
the argument; arguing, as I have said, for his own Theory.

"Tell me," he says, "do you not think there is an Idea of Likeness, and
an Idea of Unlikeness? And that everything partakes of these Ideas? The
things which partake of Unlikeness are unlike. If all things partake of
both Ideas, they are both like and unlike; and where is the wonder? (§
7.) If you could show that Likeness itself was Unlikeness, it would be
a prodigy; but if things which partake of these opposites, have both
the opposite qualities, it appears to me, Zeno, to involve no absurdity.

"So if Oneness itself were to be shown to be Maniness" (I hope I may
use this word, rather than _multiplicity_) "I should be surprised; but
if any one say that _I_ am at the same time one and many, where is the
wonder? For I partake of maniness: my right side is different from my
left side, my upper from my under parts. But I also partake of Oneness,
for I am here One of us seven. So that both are true. And so if any one
say that stocks and stones, and the like, are both one and many,--not
saying that Oneness is Maniness, nor Maniness Oneness, he says nothing
wonderful: he says what all will allow. (§ 8.) If then, as I said
before, any one should take separately the Ideas or Essence of Things,
as Likeness and Unlikeness, Maniness and Oneness, Rest and Motion, and
the like, and then should show that these can mix and separate again,
I should be wonderfully surprised, O Zeno: for I reckon that I have
tolerably well made myself master of these subjects[323]. I should
be much more surprised if any one could show me this contradiction
involved in the Ideas themselves; in the object of the Reason, as well
as in Visible objects."

It may be remarked that Socrates delivers all this argumentation with
the repetitions which it involves, and the vehemence of its manner,
without waiting for a reply to any of his interrogations; instead
of making every step the result of a concession of his opponent, as
is the case in the Dialogues where he is represented as triumphant.
Every reader of Plato will recollect also that in those Dialogues,
the triumph of temper on the part of Socrates is represented as
still more remarkable than the triumph of argument. No vehemence or
rudeness on the part of his adversaries prevents his calmly following
his reasoning; and he parries coarseness by compliment. Now in this
Dialogue, it is remarkable that this kind of triumph is given to the
adversaries of Socrates. "When Socrates had thus delivered himself,"
says Pythodorus, the narrator of the conversation, "we thought that
Parmenides and Zeno would both be angry. But it was not so. They
bestowed entire attention upon him, and often looked at each other,
and smiled, as in admiration of Socrates. And when he had ended,
Parmenides said: 'O Socrates, what an admirable person you are, for the
earnestness with which you reason! Tell me then, Do you then believe
the doctrine to which you have been referring;--that there are certain
Ideas, existing independent of Things; and that there are, separate
from the Ideas, Things which partake of them? And do you think that
there is an Idea of Likeness besides the likeness which we have; and a
Oneness and a Maniness, and the like? And an Idea of the Right, and the
Good, and the Fair, and of other such qualities?'" Socrates says that
he does hold this; Parmenides then asks him, how far he carries this
doctrine of Ideas, and propounds to him the difficulties which I have
already stated; and when Socrates is unable to answer him, lets him off
in the kind but patronizing way which I have already described.

To me, comparing this with the intellectual and moral attitude of
Socrates in the most dramatic of the other Platonic Dialogues, it is
inconceivable, that this representation of Socrates should be Plato's.
It is just what Zeno would have written, if he had wished to bestow
upon his master Parmenides the calm dignity and irresistible argument
which Plato assigns to Socrates. And this character is kept up to the
end of the Dialogue. When Socrates (§ 19) has acknowledged that he is
at loss which way to turn for his philosophy, Parmenides undertakes,
though with kind words, to explain to him by what fundamental error in
the course of his speculative habits he has been misled. He says; "You
try to make a complete Theory of Ideas, before you have gone through
a proper intellectual discipline. The impulse which urges you to such
speculations is admirable--is divine. But you must exercise yourself in
reasoning which many think trifling, while you are yet young; if you
do not, the truth will elude your grasp." Socrates asks submissively
what is the course of such discipline: Parmenides replies, "The course
pointed out by Zeno, as you have heard." And then, gives him some
instructions in what manner he is to test any proposed Theory. Socrates
is frightened at the laboriousness and obscurity of the process. He
says, "You tell me, Parmenides, of an overwhelming course of study; and
I do not well comprehend it. Give me an example of such an examination
of a Theory." "It is too great a labour," says he, "for one so old
as I am." "Well then, you, Zeno," says Socrates, "will you not give
us such an example?" Zeno answers, smiling, that they had better get
it from Parmenides himself; and joins in the petition of Socrates to
him, that he will instruct them. All the company unite in the request.
Parmenides compares himself to an aged racehorse, brought to the course
after long disuse, and trembling at the risk; but finally consents.
And as an example of a Theory to be examined, takes his own Doctrine,
that All Things are One, carrying on the Dialogue thenceforth, not
with Socrates, but with Aristoteles (not the Stagirite, but afterwards
one of the Thirty), whom he chooses as a younger and more manageable
respondent.

The discussion of this Doctrine is of a very subtle kind, and it would
be difficult to make it intelligible to a modern reader. Nor is it
necessary for my purpose to attempt to do so. It is plain that the
discussion is intended seriously, as an example of true philosophy; and
each step of the process is represented as irresistible. The Respondent
has nothing to say but _Yes_; or _No_; _How so_? _Certainly_; _It does
appear_; _It does not appear_. The discussion is carried to a much
greater length than all the rest of the Dialogue; and the result of
the reasoning is summed up by Parmenides thus: "If One exist, it is
Nothing. Whether One exist or do not exist, both It and Other Things
both with regard to Themselves and to Each other, All and Everyway are
and are not, appear and appear not." And this also is fully assented
to; and so the Dialogue ends.

I shall not pretend to explain the Doctrines there examined that One
exists, or One does not exist, nor to trace their consequences. But
these were Formulæ, as familiar in the Eleatic school, as Ideas in the
Platonic; and were undoubtedly regarded by the Megaric contemporaries
of Plato as quite worthy of being discussed, after the Theory of Ideas
had been overthrown. This, accordingly, appears to be the purport of
the Dialogue; and it is pursued, as we see, without any bitterness
toward Socrates or his disciples; but with a persuasion that they were
poor philosophers, conceited talkers, and weak disputants.

The external circumstances of the Dialogue tend, I conceive, to confirm
this opinion, that it is not Plato's. The Dialogue begins, as the
_Republic_ begins, with the mention of a Cephalus, and two brothers,
Glaucon and Adimantus. But this Cephalus is not the old man of the
Piræus, of whom we have so charming a picture in the opening of the
_Republic_. He is from Clazomenæ, and tells us that his fellow-citizens
are great lovers of philosophy; a trait of their character which does
not appear elsewhere. Even the brothers Glaucon and Adimantus are not
the two brothers of Plato who conduct the Dialogue in the later books
of the _Republic_: so at least Ast argues, who holds the genuineness of
the Dialogue. This Glaucon and Adimantus are most wantonly introduced;
for the sole office they have, is to say that they have a half-brother
Antiphon, by a second marriage of their mother. No such half-brother of
Plato, and no such marriage of his mother, are noticed in other remains
of antiquity. Antiphon is represented as having been the friend of
Pythodorus, who was the host of Parmenides and Zeno, as we have seen.
And Antiphon, having often heard from Pythodorus the account of the
conversation of his guests with Socrates, retained it in his memory, or
in his tablets, so as to be able to give the full report of it which we
have in the Dialogue _Parmenides_[324]. To me, all this looks like a
clumsy imitation of the Introductions to the Platonic Dialogues.

I say nothing of the chronological difficulties which arise
from bringing Parmenides and Socrates together, though they are
considerable; for they have been explained more or less satisfactorily;
and certainly in the _Theætetus_, Socrates is represented as saying
that he when very young had seen Parmenides who was very old[325].
Athenæus, however[326], reckons this among Plato's fictions.
Schleiermacher gives up the identification and relation of the persons
mentioned in the Introduction as an unmanageable story.

I may add that I believe Cicero, who refers to so many of Plato's
Dialogues, nowhere refers to the _Parmenides_. Athenæus does refer to
it; and in doing so blames Plato for his coarse imputations on Zeno
and Parmenides. According to our view, these are hostile attempts to
ascribe rudeness to Socrates or to Plato. Stallbaum acknowledges that
Aristotle nowhere refers to this Dialogue.

FOOTNOTES:

[Footnote 321: P. 116. "No amount of human knowledge can be adequate
which does not solve the phenomena of these absolute certainties."]

[Footnote 322: Prof. Butler, Lect. ix. Second Series, p. 136, appears
to think that Plato had sufficient grounds (of a theological kind) for
the assumption of such Ideas; but I see no trace of them.]

[Footnote 323: I am aware that this translation is different from the
common translation. It appears to me to be consistent with the habit
of the Greek language. It slightly leans in favour of my view; but I
do not conceive that the argument would be perceptibly weaker, if the
common interpretation were adopted.]

[Footnote 324: In the _First Alcibiades_, Pythodorus is mentioned as
having paid 100 minæ to Zeno for his instructions (119 A).]

[Footnote 325: P. 183 e.]

[Footnote 326: _Deip._ xi. c. 15, p. 105.]


APPENDIX B.

ON PLATO'S SURVEY OF THE SCIENCES.

(_Cam. Phil. Soc._ APRIL 23, 1855.)


A survey by Plato of the state of the Sciences, as existing in his
time, may be regarded as hardly less interesting than Francis Bacon's
Review of the condition of the Sciences of _his_ time, contained in the
_Advancement of Learning_. Such a survey we have, in the seventh book
of Plato's _Republic_; and it will be instructive to examine what the
Sciences then were, and what Plato aspired to have them become; aiding
ourselves by the light afforded by the subsequent history of Science.

In the first place, it is interesting to note, in the two writers,
Plato and Bacon, the same deep conviction that the large and profound
philosophy which they recommended, had not, in their judgment, been
pursued in an adequate and worthy manner, by those who had pursued it
at all. The reader of Bacon will recollect the passage in the _Novum
Organon_ (Lib. I. Aphorism 80) where he speaks with indignation of
the way in which philosophy had been degraded and perverted, by being
applied as a mere instrument of utility or of early education: "So that
the great mother of the Sciences is thrust down with indignity to the
offices of a handmaid;--is made to minister to the labours of medicine
or mathematics; or again, to give the first preparatory tinge to the
immature minds of youth[327]."

In the like spirit, Plato says (_Rep._ VI. § 11, Bekker's ed.):

"Observe how boldly and fearlessly I set about my explanation of my
assertion that philosophers ought to rule the world. For I begin by
saying, that the State must begin to treat the study of philosophy in a
way opposite to that now practised. Now, those who meddle at all with
this study are put upon it when they are children, between the lessons
which they receive in the farm-yard and in the shop[328]; and as soon
as they have been introduced to the hardest part of the subject, are
taken off from it, even those who get the most of philosophy. By the
hardest part, I mean, the discussion of principles--Dialectic[329].
And in their succeeding years, if they are willing to listen to a
few lectures of those who make philosophy their business, they think
they have done great things, as if it were something foreign to the
business of life. And as they advance towards old age, with a very
few exceptions, philosophy in them is extinguished: extinguished far
more completely than the Heraclitean sun, for theirs is not lighted
up again, as that is every morning:" alluding to the opinion which
was propounded, by way of carrying the doctrine of the _unfixity_ of
sensible objects to an extreme; that the Sun is extinguished every
night and lighted again in the morning. In opposition to this practice,
Plato holds that philosophy should be the especial employment of men's
minds when their bodily strength fails.

What Plato means by _Dialectic_, which he, in the next Book, calls the
highest part of philosophy, and which is, I think, what he here means
by the hardest part of philosophy, I may hereafter consider: but at
present I wish to pass in review the Sciences which he speaks of, as
leading the way to that highest study. These Sciences are Arithmetic,
Plane Geometry, Solid Geometry, Astronomy and Harmonics.

The view in which Plato here regards the Sciences is, as the
instruments of that culture of the philosophical spirit which is
to make the philosopher the fit and natural ruler of the perfect
State--the Platonic Polity. It is held that to answer this purpose, the
mind must be instructed in something more stable than the knowledge
supplied by the senses;--a knowledge of objects which are constantly
changing, and which therefore can be no real permanent Knowledge, but
only Opinion. The real and permanent Knowledge which we thus require is
to be found in certain sciences, which deal with _truths necessary and
universal_, as we should now describe them: and which therefore are,
in Plato's language, a knowledge of that which really _is_[330].

This is the object of the Sciences of which Plato speaks. And hence,
when he introduces Arithmetic, as the first of the Sciences which are
to be employed in this mental discipline, he adds (VII. § 8) that
it must be not mere common Arithmetic, but a science which leads to
speculative truths[331], seen by Intuition[332]; not an Arithmetic
which is studied for the sake of buying and selling, as among tradesmen
and shopkeepers, but for the sake of pure and real Science[333].

I shall not dwell upon the details with which he illustrates this view,
but proceed to the other Sciences which he mentions.

Geometry is then spoken of, as obviously the next Science in order;
and it is asserted that it really does answer the required condition
of drawing the mind from visible, mutable phenomena to a permanent
reality. Geometers indeed speak of their visible diagrams, as if their
problems were certain practical processes; to erect a perpendicular; to
construct a square: and the like. But this language, though necessary,
is really absurd. The figures are mere aids to their reasonings.
Their knowledge is really a knowledge not of visible objects, but of
permanent realities: and thus, Geometry is one of the helps by which
the mind may be drawn to Truth; by which the philosophical spirit may
be formed, which looks upwards instead of downwards.

Astronomy is suggested as the Science next in order, but Socrates, the
leader of the dialogue, remarks that there is an intermediate Science
first to be considered. Geometry treats of plane figures; Astronomy
treats of solids in motion, that is, of spheres in motion; for the
astronomy of Plato's time was mainly the doctrine of the sphere. But
before treating of solids in motion, we must have a science which
treats of solids simply. After taking space of two dimensions, we must
take space of three dimensions, length, breadth and depth, as in cubes
and the like[334]. But such a Science, it is remarked, has not yet
been discovered. Plato "notes as deficient" this branch of knowledge;
to use the expression employed by Bacon on the like occasions in his
Review. Plato goes on to say, that the cultivators of such a science
have not received due encouragement; and that though scorned and
starved by the public, and not recommended by any obvious utility, it
has still made great progress, in virtue of its own attractiveness.

In fact, researches in Solid Geometry had been pursued with great zeal
by Plato and his friends, and with remarkable success. The five Regular
Solids, the Tetrahedron or Pyramid, Cube, Octahedron, Dodecahedron
and Icosahedron, had been discovered; and the curious theorem, that
of Regular Solids there can be just so many, these and no others,
was known. The doctrine of these Solids was already applied in a
way, fanciful and arbitrary, no doubt, but ingenious and lively, to
the theory of the Universe. In the _Timæus_, the elements have these
forms assigned to them respectively. Earth has the Cube: Fire has the
Pyramid: Water has the Octahedron: Air has the Icosahedron: and the
Dodecahedron is the plan of the Universe itself. This application of
the doctrine of the Regular Solids shows that the knowledge of those
figures was already established; and that Plato had a right to speak
of Solid Geometry as a real and interesting Science. And that this
subject was so recondite and profound,--that these five Regular Solids
had so little application in the geometry which has a bearing on man's
ordinary thoughts and actions,--made it all the more natural for Plato
to suppose that these solids had a bearing on the constitution of the
Universe; and we shall find that such a belief in later times found a
ready acceptance in the minds of mathematicians who followed in the
Platonic line of speculation.

Plato next proceeds to consider Astronomy; and here we have an amusing
touch of philosophical drama. Glaucon, the hearer and pupil in the
Dialogue, is desirous of showing that he has profited by what his
instructor had said about the real uses of Science. He says Astronomy
is a very good branch of education. It is such a very useful science
for seamen and husbandmen and the like. Socrates says, with a smile,
as we may suppose: "You are very amusing with your zeal for utility.
I suppose you are afraid of being condemned by the good people of
Athens for diffusing Useless Knowledge." A little afterwards Glaucon
tries to do better, but still with no great success. He says, "You
blamed me for praising Astronomy awkwardly: but now I will follow your
lead. Astronomy is one of the sciences which you require, because it
makes men's minds look upwards, and study things above. Any one can
see that." "Well," says Socrates, "perhaps any one can see it except
me--I cannot see it." Glaucon is surprised, but Socrates goes on: "Your
notice of 'the study of things above' is certainly a very magnificent
one. You seem to think that if a man bends his head back and looks at
the ceiling he 'looks upwards' with his mind as well as his eyes. You
may be right and I may be wrong: but I have no notion of any science
which makes the _mind_ look upwards, except a science which is about
the permanent and the invisible. It makes no difference, as to that
matter, whether a man gapes and looks up or shuts his mouth and looks
down. If a man merely look up and stare at sensible objects, his mind
does not look upwards, even if he were to pursue his studies swimming
on his back in the sea."

The Astronomy, then, which merely looks at phenomena does not satisfy
Plato. He wants something more. What is it? as Glaucon very naturally
asks.

Plato then describes Astronomy as a real science (§ 11). "The
variegated adornments which appear in the sky, the visible luminaries,
we must judge to be the most beautiful and the most perfect things of
their kind: but since they are mere visible figures, we must suppose
them to be far inferior to the true objects; namely, those spheres
which, with their real proportions of quickness and slowness, their
real number, their real figures, revolve and carry luminaries in their
revolutions. These objects are to be apprehended by reason and mental
conception, not by vision." And he then goes on to say that the varied
figures which the skies present to the eye are to be used as _diagrams_
to assist the study of that higher truth; just as if any one were to
study geometry by means of beautiful diagrams constructed by Dædalus or
any other consummate artist.

Here then, Plato points to a kind of astronomical science which goes
beyond the mere arrangement of phenomena: an astronomy which, it
would seem, did not exist at the time when he wrote. It is natural
to inquire, whether we can determine more precisely what kind of
astronomical science he meant, and whether such science has been
brought into existence since his time.

He gives us some further features of the philosophical astronomy which
he requires. "As you do not expect to find in the most exquisite
geometrical diagrams the true evidence of quantities being equal, or
double, or in any other relation: so the true astronomer will not think
that the proportion of the day to the month, or the month to the year,
and the like, are real and immutable things. He will seek a deeper
truth than these. We must treat Astronomy, like Geometry, as a series
of problems suggested by visible things. We must apply the intelligent
portion of our mind to the subject."

Here we really come in view of a class of problems which astronomical
speculators at certain periods have proposed to themselves. What is the
real ground of the proportion of the day to the month, and of the month
to the year, I do not know that any writer of great name has tried to
determine: but to ask the reason of these proportions, namely, that of
the revolution of the earth on its axis, of the moon in its orbit, and
of the earth in its orbit, are questions just of the same kind as to
ask the reason of the proportion of the revolutions of the planets in
their orbits, and of the proportion of the orbits themselves. Now who
has attempted to assign such reasons?

Of course we shall answer, Kepler: not so much in the Laws of the
Planetary motions which bear his name, as in the Law which at an
earlier period he thought he had discovered, determining the proportion
of the distances of the several Planets from the Sun. And, curiously
enough, this solution of a problem which we may conceive Plato to have
had in his mind, Kepler gave by means of the Five Regular Solids which
Plato had brought into notice, and had employed in his theory of the
Universe given in the _Timæus_.

Kepler's speculations on the subject just mentioned were given to the
world in the _Mysterium Cosmographicum_ published in 1596. In his
Preface, he says "In the beginning of the year 1595 I brooded with
the whole energy of my mind on the subject of the Copernican system.
There were three things in particular of which I pertinaciously sought
the causes; why they are not other than they are: the number, the
size, and the motion of the orbits." We see how strongly he had his
mind impressed with the same thought which Plato had so confidently
uttered: that there must be some reason for those proportions in the
scheme of the Universe which appear casual and vague. He was confident
at this period that he had solved two of the three questions which
haunted him;--that he could account for the number and the size of the
planetary orbits. His account was given in this way.--"The orbit of
the Earth is a circle; round the sphere to which this circle belongs
describe a dodecahedron; the sphere including this will give the orbit
of Mars. Round Mars inscribe a tetrahedron; the circle including this
will be the orbit of Jupiter. Describe a cube round Jupiter's orbit;
the circle including this will be the orbit of Saturn. Now inscribe in
the Earth's orbit an icosahedron: the circle inscribed in it will be
the orbit of Venus. Inscribe an octahedron in the orbit of Venus; the
circle inscribed in it will be Mercury's orbit. This is the reason of
the number of the planets;" and also of the magnitudes of their orbits.

These proportions were only approximations; and the Rule thus asserted
has been shown to be unfounded, by the discovery of new Planets. This
Law of Kepler has been repudiated by succeeding Astronomers. So far,
then, the Astronomy which Plato requires as a part of true philosophy
has not been brought into being. But are we thence to conclude
that the demand for such a kind of Astronomy was a mere Platonic
imagination?--was a mistake which more recent and sounder views have
corrected? We can hardly venture to say that. For the questions which
Kepler thus asked, and which he answered by the assertion of this
erroneous Law, are questions of exactly the same kind as those which
he asked and answered by means of the true Laws which still fasten his
name upon one of the epochs of astronomical history. If he was wrong
in assigning reasons for the number and size of the planetary orbits,
he was right in assigning a reason for the proportion of the motions.
This he did in the _Harmonice Mundi_, published in 1619: where he
established that the squares of the periodic times of the different
Planets are as the cubes of their mean distances from the central Sun.
Of this discovery he speaks with a natural exultation, which succeeding
astronomers have thought well founded. He says: "What I prophesied
two and twenty years ago as soon as I had discovered the five solids
among the heavenly bodies; what I firmly believed before I had seen
the _Harmonics_ of Ptolemy; what I promised my friends in the title of
this book (_On the perfect Harmony of the celestial motions_), which
I named before I was sure of my discovery; what sixteen years ago I
regarded as a thing to be sought; that for which I joined Tycho Brahe,
for which I settled in Prague, for which I devoted the best part of my
life to astronomical contemplations; at length I have brought to light,
and have recognized its truth beyond my most sanguine expectations."
(_Harm. Mundi_, Lib. V.)

Thus the Platonic notion, of an Astronomy which deals with doctrines
of a more exact and determinate kind than the obvious relations of
phænomena, may be found to tend either to error or to truth. Such
aspirations point equally to the five regular solids which Kepler
imagined as determining the planetary orbits, and to the Laws of
Kepler in which Newton detected the effect of universal gravitation.
The realities which Plato looked for, as something incomparably more
real than the visible luminaries, are found, when we find geometrical
figures, epicycles and eccentrics, laws of motion and laws of force,
which explain the appearances. His Realities are Theories which account
for the Phenomena, Ideas which connect the Facts.

But, is Plato right in holding that such Realities as these are _more
real_ than the Phenomena, and constitute an Astronomy of a higher kind
than that of mere Appearances? To this we shall, of course, reply
that Theories and Facts have each their reality, but that these are
realities of different kinds. Kepler's Laws are as real as day and
night; the force of gravity tending to the Sun is as real as the Sun;
but not more so. True Theories and Facts are equally real, for true
Theories _are_ Facts, and Facts are familiar Theories. Astronomy is, as
Plato says, a series of Problems suggested by visible Things; and the
Thoughts in our own minds which bring the solutions of these Problems,
have a reality in the Things which suggest them.

But if we try, as Plato does, to separate and oppose to each other the
Astronomy of Appearances and the Astronomy of Theories, we attempt that
which is impossible. There are no Phenomena which do not exhibit some
Law; no Law can be conceived without Phenomena. The heavens offer a
series of Problems; but however many of these Problems we solve, there
remain still innumerable of them unsolved; and these unsolved Problems
have solutions, and are not different in kind from those of which the
extant solution is most complete.

Nor can we justly distinguish, with Plato, Astronomy into transient
appearances and permanent truths. The theories of Astronomy are
permanent, and are manifested in a series of changes: but the change is
perpetual just _because_ the theory is permanent. The perpetual change
_is_ the permanent theory. The perpetual changes in the positions
and movements of the planets, for instance, manifest the permanent
machinery: the machinery of cycles and epicycles, as Plato would
have said, and as Copernicus would have agreed; while Kepler, with a
profound admiration for both, would have asserted that the motions
might be represented by ellipses, more exactly, if not more truly. The
cycles and epicycles, or the ellipses, are as real as space and time,
_in_ which the motions take place. But we cannot justly say that space
and time and motion are more real than the bodies which move in space
and time, or than the appearances which these bodies present.

Thus Plato, with his tendency to exalt Ideas above Facts,--to find a
Reality which is more real than Phenomena,--to take hold of a permanent
Truth which is more true than truths of observation,--attempts what
is impossible. He tries to separate the poles of the Fundamental
Antithesis, which, however antithetical, are inseparable.

At the same time, we must recollect that this tendency to find a
Reality which is something beyond appearance, a permanence which is
involved in the changes, is the genuine spring of scientific discovery.
Such a tendency has been the cause of all the astronomical science
which we possess. It appeared in Plato himself, in Hipparchus, in
Ptolemy, in Copernicus, and most eminently in Kepler; and in him
perhaps in a manner more accordant with Plato's aspirations when he
found the five Regular Solids in the Universe, than when he found there
the Conic Sections which determine the form of the planetary orbits.
The pursuit of this tendency has been the source of the mighty and
successful labours of succeeding astronomers: and the anticipations of
Plato on this head were more true than he himself could have conceived.

When the above view of the nature of true astronomy has been proposed,
Glaucon says:

"That would be a task much more laborious than the astronomy now
cultivated." Socrates replies: "I believe so: and such tasks must be
undertaken, if our researches are to be good for anything."

After Astronomy, there comes under review another Science, which is
treated in the same manner. It is presented as one of the Sciences
which deal with real abstract truth; and which are therefore suited to
that development of the philosophic insight into the highest truth,
which is here Plato's main object. This Science is _Harmonics_, the
doctrine of the mathematical relations of musical sounds. Perhaps
it may be more difficult to explain to a general audience, Plato's
views on this than on the previous subjects: for though Harmonics is
still acknowledged as a Science including the mathematical truths to
which Plato here refers, these truths are less generally known than
those of geometry or astronomy. Pythagoras is reported to have been
the discoverer of the cardinal proposition in this Mathematics of
Music:--namely, that the musical notes which the ear recognizes as
having that definite and harmonious relation which we call an _octave_,
a _fifth_, a _fourth_, a _third_, have also, in some way or other, the
numerical relation of 2 to 1, 3 to 2, 4 to 3, 5 to 4. I say "some way
or other," because the statements of ancient writers on this subject
are physically inexact, but are right in the essential point, that
those simple numerical ratios are characteristic of the most marked
harmonic relations. The numerical ratios really represent the rate of
vibration of the air when those harmonics are produced. This perhaps
Plato did not know: but he knew or assumed that those numerical ratios
were cardinal truths in harmony: and he conceived that the exactness
of the ratios rested on grounds deeper and more intellectual than any
testimony which the ear could give. This is the main point in his mode
of applying the subject, which will be best understood by translating
(with some abridgement) what he says. Socrates proceeds:

(§ 11 near the end.) "Motion appears in many aspects. It would take a
very wise man to enumerate them all: but there are two obvious kinds.
One which appears in astronomy, (the revolutions of the heavenly
bodies,) and another which is the echo of that[335]. As the eyes are
made for Astronomy, so are the ears made for the motion which produces
Harmony[336]: and thus we have two sister sciences, as the Pythagoreans
teach, and we assent.

(§ 12.) "To avoid unnecessary labour, let us first learn what _they_
can tell us, and see whether anything is to be added to it; retaining
our own view on such subjects: namely this:--that those whose education
we are to superintend--real philosophers--are never to learn any
imperfect truths:--anything which does not tend to that point (exact
and permanent truth) to which all our knowledge ought to tend, as we
said concerning astronomy. Now those who cultivate music take a very
different course from this. You may see them taking immense pains in
measuring musical notes and intervals by the ear, as the astronomers
measure the heavenly motions by the eye.

"Yes, says Glaucon, they apply their ears close to the instrument, as
if they could catch the note by getting near to it, and talk of some
kind of recurrences[337]. Some say they can distinguish an interval,
and that this is the smallest possible interval, by which others are to
be measured; while others say that the two notes are identical: both
parties alike judging by the ear, not by the intellect.

"You mean, says Socrates, those fine musicians who torture their
notes, and screw their pegs, and pinch their strings, and speak of the
resulting sounds in grand terms of art. We will leave them, and address
our inquiries to our other teachers, the Pythagoreans."

The expressions about the small interval in Glaucon's speech appear to
me to refer to a curious question, which we know was discussed among
the Greek mathematicians. If we take a keyed instrument, and ascend
from a key note by two _octaves_ and a _third_, (say from _A__{1} to
_C__{3}) we arrive at the _same nominal note_, as if we ascend four
times by a _fifth_ (_A__{1} to _E__{1}, _E__{1} to _B__{2}, _B__{2}
to _F__{2}, _F__{2} to _C__{3}). Hence one party might call this the
_same_ note. But if the Octaves, Fifths, and Third be perfectly true
intervals, the notes arrived at in the two ways will not be really
the same. (In the one case, the note is ½ × ½ × ⅘; in the other
⅔ × ⅔ × ⅔ × ⅔; which are ⅕ and 16/81, or in the ratio of
81 to 80). This small interval by which the two notes really differ,
the Greeks called a _Comma_, and it was the smallest musical interval
which they recognized. Plato disdains to see anything important in this
controversy; though the controversy itself is really a curious proof
of his doctrine, that there is a mathematical truth in Harmony, higher
than instrumental exactness can reach. He goes on to say:

 "The musical teachers are defective in the same way as the
 astronomical. They do indeed seek numbers in the harmonic notes, which
 the ear perceives: but they do not ascend from them to the Problem,
 What are harmonic numbers and what are not, and what is the reason of
 each[338]?" "That", says Glaucon, "would be a sublime inquiry."

Have we in Harmonics, as in Astronomy, anything in the succeeding
History of the Science which illustrates the tendency of Plato's
thoughts, and the value of such a tendency?

It is plain that the tendency was of the same nature as that which
induced Kepler to call his work on Astronomy _Harmonice Mundi_; and
which led to many of the speculations of that work, in which harmonical
are mixed with geometrical doctrines. And if we are disposed to judge
severely of such speculations, as too fanciful for sound philosophy, we
may recollect that Newton himself seems to have been willing to find an
analogy between harmonic numbers and the different coloured spaces in
the spectrum.

But I will say frankly, that I do not believe there really exists any
harmonical relation in either of these cases. Nor can the problem
proposed by Plato be considered as having been solved since his
time, any further than the recurrence of vibrations, when their
ratios are so simple, may be easily conceived as affecting the ear
in a peculiar manner. The imperfection of musical scales, which the
_comma_ indicates, has not been removed; but we may say that, in the
case of this problem, as in the other ultimate Platonic problems,
the duplication of the cube and the quadrature of the circle, the
impossibility of a solution has been already established. The problem
of a perfect musical scale is impossible, because no power of 2 can
be equal to a power of 3; and if we further take the multiplier 5, of
course it also cannot bring about an exact equality. This impossibility
of a perfect scale being recognized, the practical problem is what is
the system of _temperament_ which will make the scale best suited for
musical purposes; and this problem has been very fully discussed by
modern writers.


FOOTNOTES:

[Footnote 327: Accedit et illud quod naturalis philosophia in iis ipsis
viris, qui ei incubuerunt, vacantem et integrum hominem, præsertim
his recentioribus temporibus, vix nacta sit; nisi forte quis monachi
alicujus in cellula, aut nobilis in villula lucubrantis, exemplum
adduxerit; sed facta est demum naturalis philosophia instar transitus
cujusdam et pontisternii ad alia. Atque magna ista scientiarum mater
ad officia ancillæ detrusa est; quæ medicinæ aut mathematicis operibus
ministrat, et rursus quæ adolescentium immatura ingenia lavat et imbuat
velut tinctura quadam prima, ut aliam postea felicius et commodius
excipiant.]

[Footnote 328: μεταξὺ οἰκονομίας καὶ χρεματισμοῦ, between house-keeping
and money-getting.]

[Footnote 329: τὸ  περὶ τοὺς λόγους.]

[Footnote 330: The Sciences are to draw the mind from that which grows
and perishes to that which really is: μάθημα ψυχῆς ὁλκὸν ἀπὸ τοῦ
γιγνομένου ἐπι τὸ ὅν.]

[Footnote 331: ἐπὶ θέαν τῆς τῶν ἀριθμῶν φύσεως.]

[Footnote 332: τῇ νοηήσει αὐτῇ.]

[Footnote 333: He adds "and for the sake of war;" this point I have
passed by. Plato does not really ascribe much weight to this use of
Science, as we see in what he says of Geometry and Astronomy.]

[Footnote 334: ἀρθῶς ἕχει ἑξῆς μετὰ δευτέραν αὕξην τρίτην λαμβάνειν,
ἕστι δέ  που τοῦτο περὶ τὴν τῶν κύβων αύξην καὶ τὸ βάθους μέτεχον.]

[Footnote 335: ἀντίστροφον αὐτοῦ.]

[Footnote 336: πρὸς ἐναρμόνιον φορὰν ὦτα παγῆναι.]

[Footnote 337: πυκνώματα ἄ ττα.]

[Footnote 338: τίνες ξύμφωνοι ἀριθμοὶ, &c.]


APPENDIX BB.

ON PLATO'S NOTION OF DIALECTIC.

(_Cam. Phil. Soc._ MAY 7, 1855.)


The survey of the sciences, arithmetic, plane geometry, solid geometry,
astronomy and harmonics--which is contained in the seventh Book of
the Republic (§ 6-12), and which has been discussed in the preceding
paper, represents them as instruments in an education, of which the
end is something much higher--as steps in a progression which is to go
further. "Do you not know," says Socrates (§ 12), "that all this is
merely a prelude to the strain which we have to learn?" And what that
strain is, he forthwith proceeds to indicate. "That these sciences
do not suffice, you must be aware: for--those who are masters of
such sciences--do they seem to you to be good in dialectic? δεινοὶ
διαλεκτικοὶ εἷναι;"

"In truth, says Glaucon, they are not, with very few exceptions, so far
as I have fallen in with them."

"And yet, said I, if persons cannot give and receive a reason, they
cannot attain that knowledge which, as we have said, men ought to have."

Here it is evident that "to give and to receive a reason," is a
phrase employed as coinciding, in a general way at least, with being
"good in dialectic;" and accordingly, this is soon after asserted in
another form, the verb being now used instead of the adjective. "It is
dialectic discussion τὸ διαλέγεσθαι, which executes the strain which we
have been preparing." It is further said that it is a progress to clear
intellectual light, which corresponds to the progress of bodily vision
in proceeding from the darkened cave described in the beginning of the
Book to the light of day. This progress, it is added, of course you
call _Dialectic_ διαλεκτικήν.

Plato further says, that other sciences cannot properly be called
sciences. They begin from certain assumptions, and give us only the
consequences which follow from reasoning on such assumptions. But these
assumptions they cannot prove. To do so is not in the province of
each science. It belongs to a higher science: to the science of Real
Existences. You call the man Dialectical, who requires a reason of the
essence of each thing[339].

And as Dialectic gives an account of other real existences, so does
it of that most important reality, the true guide of Life and of
Philosophy, the Real Good. He who cannot follow this through all the
windings of the battle of Life, knows nothing to any purpose. And
thus Dialectic is the pinnacle, the top stone of the edifice of the
sciences[340].

Dialectic is here defined or described by Plato according to the
_subject_ with which it treats, and the _object_ with which it is to
be pursued: but in other parts of the Platonic Dialogues, Dialectic
appears rather to imply a certain _method_ of investigation;--to
describe the _form_ rather than the _matter_ of discussion; and it will
perhaps be worth while to compare these different accounts of Dialectic.

(_Phædrus._) One of the cardinal passages on this Point is in the
Phædrus, and may be briefly quoted. Phædrus, in the Dialogue which
bears his name, appears at first as an admirer of Lysias, a celebrated
writer of orations, the contemporary of Plato. In order to expose this
writer's style of composition as frigid and shallow, a specimen of it
is given, and Socrates not only criticises this, but delivers, as rival
compositions, two discourses on the same subject. Of these discourses,
given as the inspiration of the moment, the first is animated and
vigorous; the second goes still further, and clothes its meaning in a
gorgeous dress of poetical and mythical images. Phædrus acknowledges
that his favourite is outshone; and Socrates then proceeds to point
out that the real superiority of his own discourse consists in its
having a dialectical structure, beneath its outward aspect of imagery
and enthusiasm. He says: (§ 109, Bekker. It is to be remembered that
the subject of all the discourses was _Love_, under certain supposed
conditions.)

"The rest of the performance may be taken as play: but there were, in
what was thus thrown out by a random impulse, two features, of which,
if any one could reduce the effect to an art, it would be a very
agreeable and useful task.

"What are they? Phædrus asks.

"In the first place, Socrates replies, the taking a connected view of
the scattered elements of a subject, so as to bring them into one
Idea; and thus to give a definition of the subject, so as to make it
clear what we are speaking of; as was then done in regard to _Love_.
A definition was given of it, what it is: whether the definition was
good or bad, at any rate there was a definition. And hence, in what
followed, we were able to say what was clear and consistent with itself.

"And what, Phædrus asks, was the other feature?

"The dividing the subject into kinds or elements, according to the
nature of the thing itself:--not breaking its natural members, like a
bad carver who cannot hit the joint. So the two discourses which we
have delivered, took the irrational part of the mind, as their common
subject; and as the body has two different sides, the right and the
left, with the same names for its parts; so the two discourses took
the irrational portion of man; and the one took the left-hand portion,
and divided this again, and again subdivided it, till, among the
subdivisions, it found a left-handed kind of Love, of which nothing
but ill was to be said. While the discourse that followed out the
right-hand side of phrenzy, (the irrational portion of man's nature,)
was led to something which bore the name of _Love_ like the other,
but which is divine, and was praised as the source of the greatest
blessing."

"Now I," Socrates goes on to say, "am a great admirer of these
processes of division and comprehension, by which I endeavour to speak
and to think correctly. And if I can find any one who is able to see
clearly what is by nature reducible to one and manifested in many
elements, I follow his footsteps as a divine guide. Those who can do
this, I call--whether rightly or not, God knows--but I have hitherto
been in the habit of calling them _dialectical_ men."

It is of no consequence to our present purpose whether either of the
discourses of Socrates in the Phædrus, or the two together, as is here
assumed, do contain a just division and subdivision of that part of the
human soul which is distinguishable from Reason, and do thus exhibit,
in its true relations, the affection of Love. It is evident that
division and subdivision of this kind is here presented as, in Plato's
opinion, a most valuable method; and those who could successfully
practise this method are those whom he admires as dialectical men. This
is here his _Dialectic_.

(_Sophistes._) We are naturally led to ask whether this method of
dividing a subject as the best way of examining it, be in any other
part of the Platonic Dialogues more fully explained than it is in the
Phædrus; or whether any rules are given for this kind of Dialectic.

To this we may reply, that in the Dialogue entitled _The Sophist_, a
method of dividing a subject, in order to examine it, is explained
and exemplified with extraordinary copiousness and ingenuity. The
object proposed in that Dialogue is, to define what a Sophist is;
and with that view, the principal speaker, (who is represented as an
Eleatic stranger,) begins by first exemplifying what is his method of
framing a definition, and by applying it to define an _Angler_. The
course followed, though it now reads like a burlesque of philosophical
methods, appears to have been at that time a _bona fide_ attempt to be
philosophical and methodical. It proceeds thus:

"We have to inquire concerning _Angling_. Is it an Art? It is. Now
what kind of art? All art is an art of making or an art of getting:
(_Poietic_ or _Ktetic_.) It is Ktetic. Now the art of getting, is
the art of getting by exchange or by capture: (_Metabletic_ or
_Chirotic_.) Getting by capture is by contest or by chase: (_Agonistic_
or _Thereutic_.) Getting by chase is a chase of lifeless or of living
things: (the first has no name, the second is _Zootheric_.) The chase
of living things is the chase of land animals or of water animals:
(_Pezotheric_ or _Enygrotheric_.) Chase of water animals is of birds
or of fish: (_Ornithothereutic_ and _Halieutic_.) Chase of fish is by
inclosing or by striking them: (_Hercotheric_ or _Plectic_.) We strike
them by day with pointed instruments, or by night, using torches:
(hence the division _Ankistreutic_ and _Pyreutic_.) Of Ankistreutic,
one kind consists in spearing the fish downwards from above, the other
in twitching them upwards from below: (these two arts are _Triodontic_
and _Aspalieutic_.) And thus we have, what we sought, the notion and
the description of angling: namely that it is a Ktetic, Chirotic,
Thereutic, Zootheric, Enygrotheric, Halieutic, Plectic, Ankistreutic,
Aspalieutic Art."

Several other examples are given of this ingenious mode of definition,
but they are all introduced with reference to the definition of the
Sophist. And it will further illustrate this method to show how,
according to it, the Sophist is related to the Angler.

The Sophistical Art is an art of getting, by capture, living things,
namely men. It is thus a Ktetic, Chirotic, Thereutic art, and so far
agrees with that of the Angler. But here the two arts diverge, since
that of the Sophist is Pezotheric, that of the Angler Enygrotheric.
To determine the Sophist still more exactly, observe that the chase
of land animals is either of tame animals (including man) or of
wild animals: (_Hemerotheric_ and _Agriotheric_.) The chase of tame
animals is either by violence, (as kidnapping, tyranny, and war in
general,) or by persuasion, (as by the arts of speech;) that is, it
is _Biaiotheric_ or _Pithanurgic_. The art of persuasion is a private
or a public proceeding: (_Idiothereutic_ or _Demosiothereutic_.)
The art of private persuasion is accompanied with the giving of
presents, (as lovers do,) or with the receiving of pay: (thus it is
_Dorophoric_ or _Mistharneutic_.) To receive pay as the result of
persuasion, is the course, either of those who merely earn their bread
by supplying pleasure, namely flatterers, whose art is _Hedyntic_;
or of those who profess for pay to teach virtue. And who are they?
Plainly the Sophists. And thus _Sophistic_ is that kind of Ktetic,
Chirotic, Thereutic, Zootheric, Pezotheric, Hemerotheric, Pithanurgic,
Idiothereutic, Mistharneutic art, which professes to teach virtue, and
takes money on that account.

The same process is pursued along several other lines of inquiry: and
at the end of each of them the Sophist is detected, involved in a
number of somewhat obnoxious characteristics. This process of division
it will be observed, is at every step bifurcate, or as it is called,
_dichotomous_. Applied as it is in these examples, it is rather the
vehicle of satire than of philosophy. Yet, I have no doubt that this
bifurcate method was admired by some of the philosophers of Plato's
time, as a clever and effective philosophical invention. We may the
more readily believe this, inasmuch as one of the most acute persons
of our own time, who has come nearer than any other to the ancient
heads of sects in the submission with which his followers have accepted
his doctrines, has taken up this Dichotomous Method, and praised it
as the only philosophical mode of dividing a subject. I refer to Mr.
Jeremy Bentham's _Chrestomathia_ (published originally in 1816), in
which this exhaustive bifurcate method, as he calls it, was applied
to classify sciences and arts, with a view to a scheme of education.
How exactly the method, as recommended by him, agrees with the method
illustrated in the _Sophist_, an examination of any of his examples
will show. Thus to take Mineralogy as an example: according to Bentham,
Ontology is Cœnoscopic or Idioscopic: the Idioscopic is Somatoscopic
or Pneumatoscopic; the Somatoscopic is Pososcopic or Poioscopic:
Poioscopic is Physiurgoscopic or Anthropurgoscopic: Physiurgoscopic is
Uranoscopic or Epigeoscopic: Epigeoscopic is Abioscopic or Embioscopic.
And thus Mineralogy is the Science Idioscopic, Somatoscopic,
Poioscopic, Physiurgoscopic, Epigeoscopic, Abioscopic: inasmuch as
it is the science which regards bodies, with reference to their
qualities,--bodies, namely, the works of nature, terrestrial, lifeless.

I conceive that this bifurcate method is not really philosophical or
valuable: but that is not our business here. What we have to consider
is whether this is what Plato meant by the term _Dialectic_.

The general description of Dialectic in the _Sophistes_ agrees very
closely with that quoted from the _Phædrus_, that it is the separation
of a subject according to its natural divisions.

Thus, see in the Sophist the passage § 83: "To divide a subject
according to the kinds of things, so as neither to make the same
kind different nor different kinds identical, is the office of the
Dialectical Science." And this is illustrated by observing that it is
the office of the science of Grammar to determine what letters may be
combined and what may not; it is the office of the science of Music to
determine what sounds differing as acute and grave, may be combined,
and what may not: and in like manner it is the office of the science of
Dialectic to determine what _kinds_ may be combined in one subject and
what may not. And the proof is still further explained.

In many of the Platonic Dialogues, the Dialectic which Socrates is thus
represented as approving, appears to include the form of Dialogue,
as well as the subdivision of the subject into its various branches.
Socrates is presented as attaching so much importance to this form,
that in the Protagoras (§ 65) he rises to depart, because his opponent
will not conform to this practice. And generally in Plato, Dialectic is
opposed to Rhetoric, as a string of short questions and answers to a
continuous dissertation.

Xenophon also seems to imply (_Mem._ IV. 5, 11) that Socrates included
in his notion of Dialectic the form of Dialogue as well as the division
of the subject.

But that the method of close Dialogue was not called _Dialectic_ by
the author of the _Sophist_, we have good evidence in the work itself.
Among other notions which are analysed by the bifurcate division here
exhibited, is that of getting by contest (_Agonistic_, previously given
as a division of _Ktetic_). Now getting by contest may be by peaceful
trial of superiority, or by fight: (_Hamilletic_ or _Machelic_). The
fight may be of body against body, or of words against words: these
may be called _Biastic_ and _Amphisbetic_. The fight of words about
right and wrong, may be by long discourses opposed to each other, as
in judicial cases; or by short questions and answers: the former may
be called _Dicanic_, the latter _Antilogic_. Of these colloquies,
about right and wrong, some are natural and spontaneous, others
artificial and studied: the former need no special name; the latter are
commonly called _Eristic_. Of Eristic colloquies, some are a source
of expense to those who hold them, some of gain: that is, they are
_Chrematophthoric_ or _Chrematistic_: the former, the occupation of
those who talk for pleasure's and for company's sake, is _Adoleschic_,
wasteful garrulity; the latter, that of those who talk for the sake
of gain, is _Sophistic_. And thus Sophistic is an art Eristic, which
is part of Antilogic, which is part of Amphisbetic, which is part of
Agonistic, which is part of Chirotic, which is a part of Ktetic. (§ 23.)

We may notice here an indication that satire rather than exact reason
directs these analyses; in that Sophistic, which was before a part of
the _thereutic_ branch of _chirotic_ and _ktetic_, is here a part of
the other branch, _agonistic_.

But the remark which I especially wish to make here is, that the art of
discussing points of right and wrong by short questions and answers,
being here brought into view, is not called _Dialectic_, which we
might have expected; but _Antilogic_. It would seem therefore that the
Author of the Sophist did not understand by _Dialectic_ such a process
as Socrates describes in Xenophon; (_Mem._ IV. 5, 11, 12;) where he
says it was called _Dialectic_, because it was followed by persons
_dividing things into their kinds in conversation_: (κοινῇ βουλεύεσθαι
διαλέγοντας:)or such as the Socrates of Plato insisted upon in the
Protagoras and the Gorgias. Of the two elements which the Dialectical
Process of Socrates implied, Division of the subject and Dialogue, the
author of the _Sophistes_ does not claim the name of _Dialectic_ for
either, and seems to reject it for the second.

But without insisting upon the name, are we to suppose that the
Dichotomous Method of the _Sophistes_ Dialogue, (I may add of the
_Politicus_, for the method is the same in this Dialogue also,) is the
method of division of a subject according to its natural members, of
which Plato speaks in the _Phædrus_?

If the _Sophistes_ be the work of Plato, the answer is difficult either
way. If this method be Plato's _Dialectic_, how came he to omit to say
so there? how came he even to seem to deny it? But on the other hand,
if this dichotomous division be a different process from the division
called _Dialectic_ in the Phædrus, had Plato two methods of division of
a subject? and yet has he never spoken of them as two, or marked their
distinction?

This difficulty would be removed if we were to adopt the opinion, to
which others, on other grounds, have been led, that the Sophistes,
though of Plato's time, is not Plato's work. The grounds of this
opinion are,--that the doctrines of the Sophistes are not Platonic:
(the doctrine of Ideas is strongly impugned and weakly defended:)
Socrates is not the principal speaker, but an Eleatic stranger: and
there is, in the Dialogue, none of the dramatic character which we
generally have in Plato. The Dialogue seems to be the work of some
Eleatic opponent of Plato, rather than his.

(_Rep._ B. VII.) But we can have no doubt that the _Phædrus_ contains
Plato's real view of the nature of Dialectic, as to its form; let us
see how this agrees with the view of Dialectic, as to its matter and
object, given in the seventh Book of the _Republic_.

According to Plato, Real Existences are the objects of the exact
sciences (as number and figure, of Arithmetic and Geometry). The things
which are the objects of sense transitory phenomena, which have no
reality, because no permanence. Dialectic deals with Realities in a
more general manner. This doctrine is everywhere inculcated by Plato,
and particularly in this part of the _Republic_. He does not tell us
how we are to obtain a view of the higher realities, which are the
objects of Dialectic: only he here assumes that it will result from
the education which he enjoins. He says (§ 13) that the Dialectic
Process (ἡ διαλεκτικὴ μέθοδος) alone leads to true science: it makes
no assumptions, but goes to First Principles, that its doctrines may
be firmly grounded: and thus it purges the eye of the soul, which was
immersed in barbaric mud, and turns it upward; using for this purpose
the aid of the sciences which have been mentioned. But when Glaucon
inquires about the details of this Dialectic, Socrates says he will not
then answer the inquiry. We may venture to say, that it does not appear
that he had any answer ready.

Let us consider for a moment what is said about a philosophy rendering
a reason for the First Principles of each Science, which the Science
itself cannot do. That there is room for such a branch of philosophy
in some sciences, we easily see. Geometry, for instance, proceeds
from Axioms, Definitions and Postulates; but by the very nature of
these terms, does not prove these First Principles. These--the Axioms,
Definitions and Postulates,--are, I conceive, what Plato here calls the
_Hypotheses_ upon which Geometry proceeds, and for which it is not the
business of Geometry to render a reason. According to him, it is the
business of "Dialectic" to give a just account of these "Hypotheses."
What then is _Dialectic?_

(_Aristotle._) It is, I think, well worthy of remark, that Aristotle,
giving an account in many respects different from that of Plato, of
the nature of Dialectic, is still led in the same manner to consider
Dialectic as the branch of philosophy which renders a reason for First
Principles. In the _Topics_, we have a distinction drawn between
reasoning demonstrative, and reasoning dialectical: and the distinction
is this:--(_Top_. I. 1) that demonstration is by syllogisms from true
first principles, or from true deductions from such principles; and
that the Dialectical Syllogism is that which syllogizes from probable
propositions (ἠξ ἠνδόξων). And he adds that probable propositions are
those which are accepted by all, or by the greatest part, or by the
wise. In the next chapter, he speaks of the uses of Dialectic, which,
he says, are three, mental discipline, debates, and philosophical
science. And he adds (_Top_. I. 2, 6) that it is also useful with
reference to the First Principles in each Science: for from the
appropriate Principles of each science we cannot deduce anything
concerning First Principles, since these principles are the beginning
of reasoning. But from the probable principles in each province of
science we must reason concerning First Principles: and this is either
the peculiar office of Dialectic, or the office most appropriate to it;
for it is a process of investigation, and must lead to the Principles
of all methods.

That a demonstrative science, as such, does not explain the origin
of its own First Principles, is undoubtedly true. Geometry does not
undertake to give a reason for the Axioms, Definitions, and Postulates.
This has been attempted, both in ancient and in modern times, by the
Metaphysicians. But the Metaphysics employed on such subjects has not
commonly been called Dialectic. The term has certainly been usually
employed rather as describing a Method, than as determining the subject
of investigation. Of the Faculty which apprehends First Principles,
both according to Plato and to Aristotle, I will hereafter say a few
words.

The object of the dichotomous process pursued in the Sophistes, and
its result in each case, is a Definition. Definition also was one of
the main features of the inquiries pursued by Socrates, Induction
being the other; and indeed in many cases Induction was a series of
steps which ended in Definition. And Aristotle also taught a peculiar
method, the object and result of which was the construction of
Definitions:--namely his _Categories_. This method is one of division,
but very different from the divisions of the Sophistes. His method
begins by dividing the whole subject of possible inquiry into ten heads
or _Categories_--Substance, Quantity, Quality, Relation, Place, Time,
Position, Habit, Action, Passion. These again are subdivided: thus
Quality is Habit or Disposition, Power, Affection, Form. And we have
an example of the application of this method to the construction of a
Definition in the Ethics; where he determines Virtue to be a Habit with
certain additional limitations.

Thus the Induction of Socrates, the Dichotomy of the Eleatics, the
Categories of Aristotle, may all be considered as methods by which we
proceed to the construction of Definitions. If, by any method, Plato
could proceed to the construction of a Definition, or rather of an
Idea, of the Absolute Realities on which First Principles depend,
such a method would correspond with the notion of Dialectic in the
_Republic_. And if it was a method of division like the Eleatic or
Aristotelic, it would correspond with the notion of Dialectic in the
_Phædrus_.

That Plato's notion, however, cannot have been exactly either of these
is, I think, plain. The colloquial method of stimulating and testing
the progress of the student in Dialectic is implied, in the sequel
of this discussion of the effect of scientific study. And the method
of Dialogue, as the instrument of instruction, being thus supposed,
the continuation of the account in the _Republic_, implies that Plato
expected persons to be made dialectical by the study of the exact
sciences in a comprehensive spirit. After insisting on Geometry and
other sciences, he says (_Rep._ VII. § 16): "The synoptical man is
dialectical; and he who is not the one, is not the other."

But, we may ask, does a knowledge of sciences lead naturally to a
knowledge of Ideas, as absolute realities from which First Principles
flow? And supposing this to be true, as the Platonic Philosophy
supposes, is the Idea of the Good, as the source of moral truths, to
be thus attained to? That it is, is the teaching of Plato, here and
elsewhere; but have the speculations of subsequent philosophers in the
same direction given any confirmation of this lofty assumption?

In reply to this inquiry, I should venture to say, that this assumption
appears to be a remnant of the Socratic doctrine from which Plato
began his speculations, that Virtue is a kind of knowledge; and that
all attempts to verify the assumption have failed. What Plato added to
the Socratic notion was, that the inquiry after The Good, the Supreme
Good, was to be aided by the analogy or suggestions of those sciences
which deal with necessary and eternal truths; the supreme good being
of the nature of those necessary and eternal truths. This notion is a
striking one, as a suggestion, but it has always failed, I think, in
the attempts to work it out. Those who in modern times, as Cudworth
and Samuel Clarke, have supposed an analogy between the necessary
truths of Geometry and the truths of Morality, though they have used
the like expressions concerning the one and the other class of truths,
have failed to convey clear doctrines and steady convictions to their
readers; and have now, I believe, few or no followers.

The result of our investigation appears to be, that though Plato added
much to the matter by means of which the mind was to be improved and
disciplined in its research after Principles and Definitions, he did
not establish any form of Method according to which the inquiry
must be conducted, and by which it might be aided. The most definite
notion of Dialectic still remained the same with the original informal
view which Socrates had taken of it, as Xenophon tells us, (_Mem._
IV. 5, 11) when he says: "He said that Dialectic (τὸ διαλέγεσθαι)
was so called because it is an inquiry pursued by persons who take
counsel together, separating the subjects considered according to
their kinds (διαλέγοντας). He held accordingly that men should try
to be well prepared for such a process, and should pursue it with
diligence: by this means, he thought, they would become good men,
fitted for responsible offices of command, and truly dialectical"
(διαλέκτικωτάτους). And this is, I conceive, the answer to Mr. Grote's
interrogatory exclamation (Vol. VIII. p. 577): "Surely the Etymology
here given by Xenophon or Socrates of the word (διαλέγεσθαι) cannot
be considered as satisfactory." The two notions, of investigatory
Dialogue, and Distribution of notions according to their kinds, which
are thus asserted to be connected in etymology, were, among the
followers of Socrates, connected in fact; the dialectic dialogue was
supposed to involve of course the dialectic division of the subject.


FOOTNOTES:

[Footnote 339: Η καὶ διαλεκτικὸν καλεῖς τὸν λόγον ἐκάστου λαμβάνοντα
τῆς οὐσίας; (§ 14).]

[Footnote 340: ὥσπερ θριγγὸς τοῖς μαθήμασιν ἡ διαλεκτικὴ ἦμιν ἐπάνω
κεῖσθαι. (§ 14).]


APPENDIX C.

OF THE INTELLECTUAL POWERS ACCORDING TO PLATO.

(_Cam. Phil. Soc._ NOV. 10, 1856.)


In the Seventh Book of Plato's _Republic_, we have certain sciences
described as the instruments of a philosophical and intellectual
education; and we have a certain other intellectual employment spoken
of, namely, Dialectic, as the means of carrying the mind beyond these
sciences, and of enabling it to see the sources of those truths which
the sciences assume as their first principles. These points have been
discussed in the two preceding papers. But this scheme of the highest
kind of philosophical education proceeds upon a certain view of the
nature and degrees of knowledge, and of the powers by which we know;
which view had been presented in a great measure in the Sixth Book;
this view I shall now attempt to illustrate.

To analyse the knowing powers of man is a task so difficult, that we
need not be surprised if there is much obscurity in this portion of
Plato's writings. But as a reason for examining what he has said, we
must recollect that if there be in it anything on this subject which
was true then, it is true still; and also, that if we know any truth on
that subject now, we shall find something corresponding to that truth
in the best speculations of sagacious ancient writers, like Plato.
It may therefore be worth while to discuss the Platonic doctrines on
this matter, and to inquire how they are to be expressed in modern
phraseology.

Plato's doctrine will perhaps be most clearly understood, if we begin
by considering the _diagram_ by which he illustrates the different
degrees of knowledge[341]. He sets out from the distinction of
_visible_ and _intelligible_ things. There are visible objects,
squares and triangles, for instance; but these are not the squares
and triangles about which the Geometer reasons. The exactness of
his reasoning does not depend on the exactness of his diagrams. He
reasons from certain mental squares and triangles, as he conceives and
understands them. "Thus there are visible and there are intelligible
things. There is a visible and an intelligible world[342]: and there
are two different regions about which our knowledge is concerned.
Now take a line divided into two unequal segments to represent these
two regions: and again, divide each segment in the same ratio. The
parts of each segment are to represent differences of clearness and
distinctness, and in the visible world these parts are _things_ and
_images_. By _images_ I mean shadows, and reflections in water, and in
polished bodies; and by _things_, I mean that of which these images
are the resemblances; as animals, plants, things made by man. This
difference corresponds to the difference of _Knowledge_ and mere
_Opinion_; and the _Opinable_ is to the _Knowable_ as the Image to the
Reality."

This analogy is assented to by Glaucon; and thus there is assumed a
ground for a further construction of the diagram.

"Now," he says, "we have to divide the segment which represents
Intelligible Things in the same way in which we have divided that which
represents Visible Things. The one part must represent the knowledge
which the mind gets by dealing as it were with images, and by reasoning
downwards _from_ Principles; the other that which it has by dealing
with the Ideas themselves, and going _to_ First Principles.

"The one part depends upon assumptions or hypotheses[343], the other is
unhypothetical or absolute truth.

"One kind of Intelligible Things, then, is Conceptions; for instance,
geometrical conceptions of figures, by means of which we reason
downwards, assuming certain First Principles.

"Now the other kind of Intelligible Things is this:--that which the
Reason includes in virtue of its power of reasoning, when it regards
the assumptions of the Sciences as, what they are, assumptions only;
and uses them as occasions and starting points, that from these it may
ascend to the _absolute_, (ἀνυπόθετον, unhypothetical,) which does
not depend upon assumption, but is the origin of scientific truth.
The Reason takes hold of this first principle of truth; and availing
itself of all the connections and relations of this principle, it
proceeds to the conclusion; using no sensible image in doing this, but
contemplating the Ideas alone; and with these Ideas the process begins,
goes on, and terminates."

This account of the matter will probably seem to require at least
further explanation; and that accordingly is acknowledged in the
Dialogue itself. Glaucon says:

"I apprehend your meaning in a certain degree, but not very clearly,
for the matter is somewhat abstruse. You wish to prove that the
knowledge which, by the Reason, we acquire, of Real Existence and
Intelligible Things, is of a higher degree of certainty than the
knowledge which belongs to what are commonly called Sciences. Such
sciences, you say, have certain assumptions for their bases; and these
assumptions are, by the students of such sciences, apprehended, not
by Sense (that is, the Bodily Senses), but by a Mental Operation,--by
Conception. But inasmuch as such students ascend no higher than the
assumptions, and do not go to the First Principles of Truth, they do
not seem to you to have true knowledge--intuitive insight--_Nous_--on
the subject of their reasonings, though the subjects are intelligible,
along with their principle. And you call this habit and practice of the
Geometers and others by the name _Conception_, not _Intuition_[344];
taking Conception to be something between Opinion on the one side, and
Intuitive Insight on the other."

"You have explained it well, said I. And now consider the four sections
(of the line) of which we have spoken, as corresponding to four
affections in the mind. Intuition, the highest; Conception, the next;
the third, Belief; and the fourth, Conjecture (from likenesses); and
arrange them in order, so that they may have more or less of certainty,
as their objects have more or less of truth[345].

"I understand, said he. I agree to what you say, and I arrange them as
you direct."

And so the Sixth Book ends: and the Seventh Book opens with the
celebrated image of the Cave, in which men are confined, and see all
external objects only by the shadows which they cast on the walls of
their prison. And this imperfect knowledge of things is to the true
vision of them, which is attained by those who ascend to the light of
day, as the ordinary knowledge of men is to the knowledge attainable by
those whose minds are purged and illuminated by a true philosophy.

Confining ourselves at present to the part of Plato's speculations
which we have mentioned, namely, the degrees of knowledge, and the
division of our knowing faculties, we may understand, and may in a
great degree accept, Plato's scheme. We have already (in the preceding
papers) seen that, by the knowledge of real things, he means, in the
first place, the knowledge of universal and necessary truths, such
as Geometry and the other exact sciences deal with. These _we_ call
sciences of Demonstration; and we are in the habit of contrasting the
knowledge which constitutes such sciences with the knowledge obtained
by the Senses, by Experience or mere Observation. This distinction of
Demonstrative and Empirical knowledge is a cardinal point in Plato's
scheme also; the former alone being allowed to deserve the name of
_Knowledge_, and the latter being only _Opinion_. The Objects with
which Demonstration deals may be termed _Conceptions_, and the objects
with which Observation or Sense has to do, however much speculation may
reduce them to mere Sensations, are commonly described as _Things_. Of
these Things, there may be Shadows or Images, as Plato says; and as we
may obtain a certain kind of knowledge, namely Opinion or Belief, by
seeing the Things themselves, we may obtain an inferior kind of Opinion
or Belief by seeing their Images, which kind of opinion we may for the
moment call _Conjecture_. Whether then we regard the distinctions of
knowledge itself or of the objects of it, we have three terms before us.

  If we consider the kinds of knowledge, they are
  Demonstration: Belief: Conjecture.
  If the objects of this knowledge, they are
  Conceptions: Things: Images.

But in each of these Series, the first term is evidently wanting: for
Demonstration supposes Principles to reason from. Conceptions suppose
some basis in the mind which gives them their evidence. What then is
the first term in each of these two Series?

The Principles of Demonstration must be seen by _Intuition_.

Conceptions derive their properties from certain powers or attributes
of the mind which we may term _Ideas_.

Therefore the two series are

  Intuition: Demonstration: Belief: Conjecture.
  Ideas: Conceptions: Things: Images.

Plato further teaches that the two former terms in each Series belong
to the Intelligible, the two latter to the Visible World: and he
supposes that the ratio of these two primary segments of the line is
the same as the ratio in which each segment is divided[346].

In using the term _Ideas_ to describe the mental sources from which
Conceptions derive their validity in demonstration, I am employing a
phraseology which I have already introduced in the _Philosophy of the
Inductive Sciences_. But independently altogether of this, I do not
see what other term could be employed to denote the mental objects,
attributes, or powers, whatever they be, from which Conceptions derive
their evidence, as Demonstrative Truths derive their evidence from
Intuitive Truths.

That the Scheme just presented is Plato's doctrine on this subject,
I do not conceive there can be any doubt. There is a little want of
precision in his phraseology, arising from his mixing together the two
series. In fact, his final series

  _Noësis_: _Dianoia_: _Pistis_: _Eikasia_;

is made by putting in the second place, instead of _Demonstration_,
which is the _process_ pursued, or _Science_, which is the _knowledge_
obtained, _Conception_, which is the _object_ with which the mind
deals. Such deviations from exact symmetry and correlation in speaking
of the faculties of the mind, are almost unavoidable in every language.
And there is yet another source of such inaccuracies of language; for
we have to speak, not only of the process of acquiring knowledge, and
of the objects with which the mind deals, but of the Faculties of the
mind which are thus employed. Thus _Intuition_ is the Process; _Ideas_
are the Object, in the first term of our series. The Faculty also we
may call _Intuition_; but the Greek offers a distinction. _Noësis_ is
the _Process_ of Intuition; but the _Faculty_ is _Nous_. If we wish to
preserve this distinction in English, what must we call the Faculty?
I conceive we must call it _the Intuitive Reason_, a term well known
to our older philosophical writers[347]. Again: taking the second
term of the series, _Demonstration_ is the process, _Science_, the
result; and _Conceptions_ are the objects with which the mind deals.
But what is the _Faculty_ thus employed? What is the Faculty employed
in Demonstration? The same philosophical writers of whom I spoke would
have answered at once, _the Discursive Reason_; and I do not know
that, even now, we can suggest any better term. The Faculty employed
in acquiring the two lower kinds of knowledge, the Faculty which deals
with Things and their Images is, of course, _Sense_, or _Sensation_.

The assertion of a Faculty of the mind by which it apprehends Truth,
which Faculty is higher than the Discursive Reason, as the Truth
apprehended by it is higher than mere Demonstrative Truth, agrees (as
it will at once occur to several of my readers) with the doctrine
taught and insisted upon by the late Samuel Taylor Coleridge. And so
far as he was the means of inculcating this doctrine, which, as we
see, is the doctrine of Plato, and I might add, of Aristotle, and of
many other philosophers, let him have due honour. But in his desire
to impress the doctrine upon men's minds, he combined it with several
other tenets, which will not bear examination. He held that the two
Faculties by which these two kinds of truth are apprehended, and which,
as I have said, our philosophical writers call _the Intuitive Reason_
and _the Discursive Reason_, may be called, and ought to be called,
respectively, _The Reason_ and _The Understanding_; and that the second
of these is of the nature of the _Instinct_ of animals, so as to be
something intermediate between Reason and Instinct. These opinions,
I may venture to say, are altogether erroneous. The Intuitive Reason
and the Discursive Reason are not, by any English writers, called the
Reason and the Understanding; and accordingly, Coleridge has had to
alter all the passages, namely, those taken from Leighton, Harrington,
and Bacon, from which his exposition proceeds. The Understanding is so
far from being especially the Discursive or Reasoning Faculty, that
it is, in universal usage, and by our best writers, _opposed_ to the
Discursive or Reasoning Faculty. Thus this is expressly declared by Sir
John Davis in his poem _On the Immortality of the Soul_. He says, of
the soul,

    When she _rates_ things, and moves from ground to ground,
        The name of _Reason_ (_Ratio_) she acquires from this:
    But when by reason she truth hath found,
        And standeth fixt, she _Understanding_ is.

Instead of the Reason being fixed, and the Understanding discursive,
as Mr. Coleridge says, the Reason is distinctively discursive; that
is, it obtains conclusions by running from one point to another. This
is what is meant by _Discursus_; or, taking the full term, _Discursus
Rationis_, _Discourse of Reason_. Understanding is fixed, that is, it
dwells upon one view of a subject, and not upon the steps by which that
view is obtained. The verb _to reason_, implies the substantive, _the
Reason_, though it is not coextensive with it: for as I have said,
there is the Intuitive Reason as well as the Discursive Reason. But it
is by the Faculty of Reason that we are capable of reasoning; though
undoubtedly the practice or the pretence of reasoning may be carried so
far as to seem at variance with reason in the more familiar sense of
the term; as is the case also in French. Moliere's Crisale says (in the
_Femmes Savantes_),

  Raisonner est l'emploi de toute ma maison,
  Et le raisonnement en bannit la Raison.

If Mr. Coleridge's assertion were true, that the Understanding is the
discursive and the Reason the fixed faculty, we should be justified in
saying that _The Understanding is the faculty by which we reason, and
the Reason is the faculty by which we understand_. But this is not so.

Nor is the Understanding of the nature of Instinct, nor does it
approach nearer than the Reason to the nature of Instinct, but the
contrary. The Instincts of animals bear a very obscure resemblance
to any of man's speculative Faculties; but so far as there is any
such resemblance, Instinct is an obscure image of Reason, not of
Understanding. Animals are said to act as if they reasoned, rather than
as if they understood. The verb _understand_ is especially applied to
man as distinguished from animals. Mr. Coleridge tells a tale from
Huber, of certain bees which, to prevent a piece of honey from falling,
balanced it by their weight, while they built a pillar to support it.
They did this by Instinct, not _understanding_ what they did; men,
doing the same, would have _understood_ what they were doing. Our
Translation of the Scriptures, in making it the special distinction of
man and animals, that _he has Understanding_ and they have not, speaks
quite consistently with good philosophy and good English.

Mr. Coleridge's object in his speculations is nearly the same as
Plato's; namely, to declare that there is a truth of a higher kind than
can be obtained by mere reasoning; and also to claim, as portions of
this higher truth, certain fundamental doctrines of Morality. Among
these, Mr. Coleridge places the Authority of Conscience, and Plato, the
Supreme Good. Mr. Coleridge also holds, as Plato held, that the Reason
of man, in its highest and most comprehensive form, is a portion of a
Supreme and Universal Reason; and leads to Truth, not in virtue of its
special attributes in each person, but by its own nature.

Many of the opinions which are combined with these doctrines, both
in Plato and in Coleridge, are such as we should, I think, find it
impossible to accept, upon a careful philosophical examination of them;
but on these I shall not here dwell.

I will only further observe, that if any one were to doubt whether the
term Νοῦς is rightly rendered _Intuitive Reason_, we may find proof
of the propriety of such a rendering in the remarkable discussion
concerning the Intellectual Virtues, which we have in the Sixth Book
of the Nicomachean Ethics. It can hardly be questioned that Aristotle
had in his mind, in writing that passage, the doctrines of Plato, as
expounded in the passage just examined, and similar passages. Aristotle
there says that there are five Intellectual Virtues, or Faculties
by which the Mind aims at Truth in asserting or denying:--namely,
_Art_, _Science_, _Prudence_, _Wisdom_, _Nous_. In this enumeration,
passing over Art, Prudence, and Wisdom, as virtues which are mainly
concerned from practical life, we have, in the region of speculative
Truth, a distinction propounded between _Science_ and _Nous_: and this
distinction is further explained (c. 6) by the remarks that Science
reasons with Principles; and that these Principles cannot be given
_by_ Science, because Science reasons _from_ them; nor by Art, nor
Prudence, for these are conversant with matters contingent, not with
matters demonstrable; nor can the First Principles of the Reasonings
of Science be given by Wisdom, for Wisdom herself has often to reason
from Principles. Therefore the First Principles of Demonstrative
Reasoning must be given by a peculiar Faculty, _Nous_. As we have
said, _Intuitive Reason_ is the most appropriate English term for this
Faculty.

The view thus given of that higher kind of Knowledge which Plato and
Aristotle place above ordinary Science, as being the Knowledge of and
Faculty of learning First Principles, will enable us to explain some
expressions which might otherwise be misunderstood. Socrates, in the
concluding part of this Sixth Book of the _Republic_, says, that this
kind of knowledge is "that of which the Reason (λόγος) takes hold,
_in virtue of its power of reasoning_[348]." Here we are plainly not
to understand that we arrive at First Principles _by reasoning_: for
the very opposite is true, and is here taught;--namely, that First
Principles are not what we reason _to_, but what we reason _from_.
The meaning of this passage plainly is, that First Principles are
those of which the Reason takes hold _in virtue of its power of
reasoning_;--they are the conditions which must exist in order to make
any reasoning possible:--they are the propositions which the Reason
must involve implicitly, in order that we may reason explicitly;--they
are the intuitive roots of the dialectical power.

In accordance with the views now explained, Plato's Diagram may be
thus further expanded. The term ιδέα is not used in this part of the
_Republic_; but, as is well known, occurs in its peculiar Platonic
sense in the Tenth Book.

 +---------+------------------------------------+-----------------------+
 |         |    Intelligible World. νοήτον.     | Visible World. ὁρατον.|
 +---------+-----------------+------------------+-----------------------+
 |_Object_ |     Ideas       |    Conceptions   |  Things   |   Images  |
 |         |     ἰδέαι       |      διάνοια     | ζῶα κ.τ.λ.|   εἰκἰνες |
 +---------+-----------------+------------------+-----------------------+
 |_Process_|   Intuition     |   Demonstration  |  Belief   | Conjecture|
 |         |    νἰησις       |     ἐπιστήμη     |  πίστις   |  είκασία  |
 +---------+-----------------+------------------+-----------------------+
 |_Faculty_|Intuitive Reason | Discursive Reason|        Sensation      |
 |         |      νοῦς       |       λόγος      |        αἴσθησις       |
 +---------+-----------------+------------------+-----------------------+


FOOTNOTES:

[Footnote 341: _Pol_. vi. § 19.]

[Footnote 342: He adds, "This _oraton_, this visible world, I will not
say has any connexion with _ouranon_, heaven, that I may not be accused
of playing upon words."]

[Footnote 343: It is plain that Plato, by _Hypotheses_, in this place,
means the usual foundations of Arithmetic and Geometry; namely,
Definitions and Postulates. He says that "the arithmeticians and
geometers take as hypotheses (hυποθεμενοι) odd and even, and the
three kinds of angles (right, acute, and obtuse); and figures, (as
a triangle, a square,) and the like." I say his "hypotheses" are
the Definitions and Postulates, not the Axioms: for the Axioms of
Arithmetic and Geometry belong to the Higher Faculty, which ascends
to First Principles. But this Faculty operates rather in using these
axioms than in enunciating them. It knows them implicitly rather than
expresses them explicitly.]

[Footnote 344: διάνοιαν άλλ' οὐ νοῦν.]

[Footnote 345: The Diagram, as here described, would be this:

  +---------------------------+---------------------------+
  |   _Intelligible World._   |      _Visible World._     |
  |-------------+-------------+-------------+-------------+
  | Intuition.  | Conception. |   Things.   |   Images.   |
  +-------------+-------------+-------------+-------------+

Plato supposes the whole, and each of the two parts, to be divided in
the same ratio, in order that the _analogy_ of the division in each
case may be represented.]

[Footnote 346: The four segments might be as 4: 2: 2: 1; or as 9: 6: 6:
4; or generally, as _a_: _ar_: _ar_: _ar_^2.]

[Footnote 347:

           Hence the mind Reason receives
  Intuitive or Discursive.

  MILTON.]

[Footnote 348: τῇ τοῦ διαλέγεσθαι δυνόμει.]


APPENDIX D.

CRITICISM OF ARISTOTLE'S ACCOUNT OF INDUCTION.

(_Cam. Phil. Soc._ FEB. 11, 1850.)


The Cambridge Philosophical Society has willingly admitted among
its proceedings not only contributions to science, but also to the
philosophy of science; and it is to be presumed that this willingness
will not be less if the speculations concerning the philosophy of
science which are offered to the Society involve a reference to ancient
authors. Induction, the process by which general truths are collected
from particular examples, is one main point in such philosophy: and the
comparison of the views of Induction entertained by ancient and modern
writers has already attracted much notice. I do not intend now to go
into this subject at any length; but there is a cardinal passage on the
subject in Aristotle's _Analytics_, (_Analyt. Prior._ II. 25) which I
wish to explain and discuss. I will first translate it, making such
emendations as are requisite to render it intelligible and consistent,
of which I shall afterwards give an account.

I will number the sentences of this chapter of Aristotle in order that
I may afterwards be able to refer to them readily.

§ 1. "We must now proceed to observe that we have to examine not only
syllogisms according to the aforesaid _figures_,--syllogisms logical
and demonstrative,--but also rhetorical syllogisms,--and, speaking
generally, any kind of proof by which belief is influenced, following
any method.

§ 2. "All belief arises either from Syllogism or from Induction: [we
must now therefore treat of Induction.]

§ 3. "Induction, and the Inductive Syllogism, is when by means of one
extreme term we infer the other extreme term to be true of the middle
term.

§ 4. "Thus if _A_, _C_, be the extremes, and _B_ the mean, we have to
show, by means of _C_, that _A_ is true of _B_.

§ 5. "Thus let _A_ be _long-lived_; _B_, _that which has no
gall-bladder;_ and _C_, particular long-lived animals, as _elephant_,
_horse_, _mule_.

§ 6. "Then every _C_ is _A_, for all the animals above named are
long-lived.

§ 7. "Also every _C_ is _B_, for all those animals are destitute of
gall-bladder.

§ 8. "If then _B_ and _C_ are convertible, and the mean (_B_) does not
extend further than extreme (_C_), it necessarily follows that every
_B_ is _A_.

§ 9. "For it was shown before, that, if any two things be true of the
same, and if either of them be convertible with the extreme, the other
of the things predicated is true of the convertible (extreme).

§ 10. "But we must conceive that _C_ consists of a collection of all
the particular cases; for Induction is applied to all the cases.

§ 11. "But such a syllogism is an inference of a first truth and
immediate proposition.

§ 12. "For when there is a mean term, there is a demonstrative
syllogism through the mean; but when there is not a mean, there is
proof by Induction.

§ 13. "And in a certain way, Induction is contrary to Syllogism; for
Syllogism proves, by the middle term, that the extreme is true of the
third thing: but Induction proves, by means of the third thing, that
the extreme is true of the mean.

§ 14. "And Syllogism concluding by means of a middle term is prior
by nature and more usual to us; but the proof by Induction, is more
luminous."

I think that the chapter, thus interpreted, is quite coherent and
intelligible; although at first there seems to be some confusion, from
the author sometimes saying that Induction is a kind of Syllogism, and
at other times that it is not. The amount of the doctrine is this.

When we collect a general proposition by Induction from particular
cases, as for instance, that all animals destitute of gall-bladder
(_acholous_), are long-lived, (if this proposition were true, of which
hereafter,) we may express the process in the form of a Syllogism, if
we will agree to make a collection of particular cases our middle term,
and assume that the proposition in which the second extreme term occurs
is convertible. Thus the known propositions are

  Elephant, horse, mule, &c., are long-lived.
  Elephant, horse, mule, &c., are _acholous_.

But if we suppose that the latter proposition is convertible, we shall
have these propositions:

  Elephant, horse, mule, &c., are long-lived.
  All acholous animals are elephant, horse, mule, &c.,

from whence we infer, quite rigorously as to _form_,

  All acholous animals are long-lived.

This mode of putting the Inductive inference shows both the strong and
the weak point of the illustration of Induction by means of Syllogism.
The strong point is this, that we make the inference perfect as to
form, by including an indefinite collection of particular cases,
elephant, horse, mule, &c., in a single term, _C_. The Syllogism then is

  All _C_ are long-lived.
  All acholous animals are _C_.
  Therefore all acholous animals are long-lived.

The weak point of this illustration is, that, at least in some
instances, when the number of actual cases is necessarily indefinite,
the representation of them as a single thing involves an unauthorized
step. In order to give the reasoning which really passes in the mind,
we must say

  Elephant, horse, &c., are long-lived.
  All acholous animals are _as_ elephant, horse, &c.,
  Therefore all acholous animals are long-lived.

This "_as_" must be introduced in order that the "all _C_" of the first
proposition may be justified by the "_C_" of the second.

This step is, I say, necessarily unauthorized, where the number of
particular cases is indefinite; as in the instance before us, the
species of acholous animals. We do not know how many such species
there are, yet we wish to be able to assert that _all_ acholous
animals are long-lived. In the proof of such a proposition, put in a
syllogistic form, there must necessarily be a logical defect; and the
above discussion shows that this defect is the substitution of the
proposition, "All acholous animals are _as_ elephant, &c.," for the
converse of the experimentally proved proposition, "elephant, &c., are
acholous."

In instances in which the number of particular cases is limited, the
necessary existence of a logical flaw in the syllogistic translation
of the process is not so evident. But in truth, such a flaw exists in
all cases of Induction _proper_: (for Induction by _mere enumeration_
can hardly be called _Induction_). I will, however, consider for a
moment the instance of a celebrated proposition which has often been
taken as an example of Induction, and in which the number of particular
cases is, or at least is at present supposed to be, limited. Kepler's
laws, for instance the law that the planets describe ellipses, may
be regarded as examples of Induction. The law was inferred, we will
suppose, from an examination of the orbits of Mars, Earth, Venus. And
the syllogistic illustration which Aristotle gives, will, with the
necessary addition to it, stand thus,

  Mars, Earth, Venus describe ellipses.
  Mars, Earth, Venus are planets.

Assuming the convertibility of this last proposition, _and its
universality_, (which is the necessary addition in order to make
Aristotle's syllogism valid) we say

  All the planets are as Mars, Earth, Venus.

Whence it follows that all the planets describe ellipses.

If, instead of this assumed universality, the astronomer had made a
real enumeration, and had established the fact of each particular, he
would be able to say

 Saturn, Jupiter, Mars, Earth, Venus, Mercury, describe ellipses.

 Saturn, Jupiter, Mars, Earth, Venus, Mercury are all the planets.

And he would obviously be entitled to convert the second proposition,
and then to conclude that

  All the planets describe ellipses.

But then, if this were given as an illustration of Induction by means
of syllogism, we should have to remark, in the first place, that the
conclusion that "all the planets describe ellipses," adds nothing to
the major proposition, that "S., J., M., E., V., m., do so." It is
merely the same proposition expressed in other words, so long as S.,
J., M., E., V., m., are supposed to be all the planets. And in the
next place we have to make a remark which is more important; that the
minor, in such an example, must generally be either a very precarious
truth, or, as appears in this case, a transitory error. For that the
planets known at any time are _all_ the planets, must always be a
doubtful assertion, liable to be overthrown to-night by an astronomical
observation. And the assertion, as received in Kepler's time, has been
overthrown. For Saturn, Jupiter, Mars, Earth, Venus, Mercury, are
not all the planets. Not only have several new ones been discovered
at intervals, as Uranus, Ceres, Juno, Pallas, Vesta, but we have new
ones discovered every day; and any conclusion depending upon this
premiss that _A_, _B_, _C_, _D_, _E_, _F_, _G_, _H_, to _Z_ are all the
planets, is likely to be falsified in a few years by the discovery of
_A´_, _B´_, _C´_, &c. If, therefore, this were the syllogistic analysis
of Induction, Kepler's discovery rested upon a false proposition;
and even if the analysis were now made conformable to our present
knowledge, that induction, analysed as above, would still involve a
proposition which to-morrow may show to be false. But yet no one, I
suppose, doubts that Kepler's discovery was really a discovery--the
establishment of a scientific truth on solid grounds; or, that it is
a scientific truth for us, notwithstanding that we are constantly
discovering new planets. Therefore the syllogistic analysis of it now
discussed (namely, that which introduces simple enumeration as a step)
is not the right analysis, and does not represent the grounds of the
Inductive Truth, that all the planets describe ellipses.

It may be said that all the planets discovered since Kepler's time
conform to his law, and thus confirm his discovery. This we grant:
but they only _confirm_ the discovery, they do not make it; they are
not its groundwork. It was a discovery before these new cases were
known; it was an inductive truth without them. Still, an objector might
urge, if any one of these new planets had contradicted the law, it
would have overturned the discovery. But this is too boldly said. A
discovery which is so precise, so complex (in the phenomena which it
explains), so supported by innumerable observations extending through
space and time, is not so easily overturned. If we find that Uranus,
or that Encke's comet, deviates from Kepler's and Newton's laws, we
do not infer that these laws must be false; we say that there must
be some disturbing cause in these cases. We seek, and we find these
disturbing causes: in the case of Uranus, a new planet; in the case
of Encke's comet, a resisting medium. Even in this case therefore,
though the number of particulars is limited, the Induction was not
made by a simple enumeration of all the particulars. It was made from
a few cases, and when the law was discerned to be true in these, it
was extended to all; the conversion and assumed universality of the
proposition that "these are planets," giving us the proposition which
we need for the syllogistic exhibition of Induction, "all the planets
are as these."

I venture to say further, that it is plain, that Aristotle did not
regard Induction as the result of simple enumeration. This is plain,
in the first place, from his example. Any proposition with regard to
a special class of animals, cannot be proved by simple enumeration:
for the number of particular cases, that is, of animal species in
the class, is indefinite at any period of zoological discovery, and
must be regarded as infinite. In the next place, Aristotle says (§
10 of the above extract), "We must conceive that _C_ consists of a
collection of all the particular cases; for induction is applied to
all the cases." We must _conceive_ (νοεῖν) that _C_ in the major,
consists of all the cases, in order that the conclusion may be true
of all the cases; but we cannot _observe_ all the cases. But the
evident proof that Aristotle does not contemplate in this chapter an
Induction by simple enumeration, is the contrast in which he places
Induction and Syllogism. For Induction by simple enumeration stands
in no contrast to Syllogism. The Syllogism of such Induction is quite
logical and conclusive. But Induction from a comparatively small
number of particular cases to a general law, does stand in opposition
to Syllogism. It gives us a truth,--a truth which, as Aristotle
says (§ 14), is more luminous than a truth proved syllogistically,
though Syllogism may be _more natural and usual_. It gives us (§ 11)
immediate propositions, obtained directly from observation, and not
by a chain of reasoning: "first truths," the principles from which
syllogistic reasonings may be deduced. The Syllogism proves by means of
a middle term (§ 13) that the extreme is true of a third thing: thus,
(_acholous_ being the middle term):

  Acholous animals are long-lived:
  All elephants are acholous animals:
  Therefore all elephants are long-lived.

But Induction proves by means of a third thing (namely, particular
cases) that the extreme is true of the mean; thus (_acholous_, still
being the middle term)

  Elephants are long-lived:
  Elephants are acholous animals:
  Therefore acholous animals are long-lived.

It may be objected, such reasoning as this is quite inconclusive:
and the answer is, that this is precisely what we, and as I believe,
Aristotle, are here pointing out. Induction _is_ inconclusive _as
reasoning_. It is not reasoning: it is another way of getting at
truth. As we have seen, no reasoning can prove such an inductive
truth as this, that all planets describe ellipses. It is _known_ from
observation, but it is not _demonstrated_. Nevertheless, no one doubts
its universal truth, (except, as aforesaid, when disturbing causes
intervene). And thence, Induction is, as Aristotle says, opposed to
syllogistic reasoning, and yet is a means of discovering truth: not
only so, but a means of discovering primary truths, immediately derived
from observation.

I have elsewhere taught that all Induction involves a _Conception_ of
the mind applied to facts. It may be asked whether this applies in
such a case as that given by Aristotle. And I reply, that Aristotle's
instance is a very instructive example of what I mean. The Conception
which is applied to the facts in order to make the induction possible
is the want of the gall-bladder;--and Aristotle supplies us with a
special term for this conception; _acholous_[349]. But, it may be
said, that the animals observed, the elephant, horse, mule, &c., are
acholous, is a mere fact of observation, not a Conception. I reply
that it is a _Selected_ Fact, a fact selected and compared in several
cases, which is what we mean by a _Conception_. That there is needed
for such selection and comparison a certain activity of the mind, is
evident; but this also may become more clear by dwelling a little
further on the subject. Suppose that Aristotle, having a desire to know
what class of animals are long-lived, had dissected for that purpose
many animals; elephants, horses, cows, sheep, goats, deer and the like.
How many resemblances, how many differences, must he have observed
in their anatomy! He was very likely long in fixing upon any one
resemblance which was common to all the long-lived. Probably he tried
several other characters, before he tried the presence and absence
of the gall-bladder:--perhaps, trying such characters, he found them
succeed for a few cases, and then fail in others, so that he had to
reject them as useless for his purpose. All the while, the absence of
the gall-bladder in the long-lived animals was a fact: but it was of
no use to him, because he had not selected it and drawn it forth from
the mass of other facts. He was looking for a mean term to connect his
first extreme, _long-lived_, with his second, the special cases. He
sought this middle term in the entrails of the many animals which he
used as extremes: it _was_ there, but he could not find it. The fact
existed, but it was of no use for the purpose of Induction, because
it did not become a special Conception in his mind. He considered the
animals in various points of view, it may be, as ruminant, as horned,
as hoofed, and the contrary; but not as _acholous_ and the contrary.
When he looked at animals in that point of view,--when he took up that
character as the ground of distinction, he forthwith imagined that he
found a separation of long-lived and short-lived animals. When that
Fact became a Conception, he obtained an inductive truth, or, at any
rate, an inductive proposition.

He obtained an inductive proposition by applying the Conception
_acholous_ to his observation of animals. This Conception divided
them into two classes; and these classes were, he fancied, long-lived
and short-lived respectively. That it was the Conception, and not
the Fact which enabled him to obtain his inductive proposition, is
further plain from this, that the supposed Fact is not a fact. Acholous
animals are not longer-lived than others. The presence or absence of
the gall-bladder is no character of longevity. It is true, that in one
familiar class of animals, the herbivorous kind, there is a sort of
first seeming of the truth of Aristotle's asserted rule: for the horse
and mule which have not the gall-bladder are longer-lived than the
cow, sheep, and goat, which have it. But if we pursue the investigation
further, the rule soon fails. The deer-tribe that want the gall-bladder
are not longer-lived than the other ruminating animals which have it.
And as a conspicuous evidence of the falsity of the rule, man and the
elephant are perhaps, for their size, the longest-lived animals, and
of these, man has, and the elephant has not, the organ in question.
The inductive proposition, then, is false; but what we have mainly
to consider is, where the fallacy enters, according to Aristotle's
analysis of Induction into Syllogism. For the two premisses are still
true; that elephants, &c., are long-lived; and that elephants, &c.,
are acholous. And it is plain that the fallacy comes in with that
conversion and generalization of the latter proposition, which we have
noted as necessary to Aristotle's illustration of Induction. When we
say "All acholous animals are as elephants, &c.," that is, as those
in their biological conditions, we say what is not true. Aristotle's
condition (§ 8) is not complied with, that the middle term shall not
extend beyond the extreme. For the character _acholous_ does extend
beyond the elephant and the animals biologically resembling it; it
extends to deer, &c., which are not like elephants and horses, in the
point in question. And thus, we see that the assumed conversion and
generalization of the minor proposition, is the seat of the fallacy of
false Inductions, as it is the seat of the peculiar logical character
of true Inductions.

As true Inductive Propositions cannot be logically demonstrated by
syllogistic rules, so they cannot be discovered by any rule. There
is no formula for the discovery of inductive truth. It is caught by
a peculiar sagacity, or power of divination, for which no precepts
can be given. But from what has been said, we see that this sagacity
shows itself in the discovery of propositions which are both _true_,
and _convertible_ in the sense above explained. Both these steps may
be difficult. The former is often very laborious: and when the labour
has been expended, and a true proposition obtained, it may turn out
useless, because the proposition is not convertible. It was a matter
of great labour to Kepler to prove (from calculation of observations)
that Mars moves elliptically. Before he proved this, he had tried
to prove many similar propositions:--that Mars moved according to
the "bisection of the eccentricity,"--according to the "vicarious
hypothesis,"--according to the "physical hypothesis,"--and the like;
but none of these was found to be exactly true. The proposition that
Mars moves elliptically was proved to be true. But still, there was
the question, Is it convertible? Do all the planets move as Mars
moves? This was proved, (suppose,) to be true, for the Earth and
Venus. But still the question remains, Do all the planets move as
Mars, Earth, Venus, do? The inductive generalizing impulse boldly
answers, Yes, to this question; though the rules of Syllogism do not
authorize the answer, and though there remain untried cases. The
inductive Philosopher tries the cases as fast as they occur, in order
to confirm his previous conviction; but if he had to wait for belief
and conviction till he had tried every case, he never could have belief
or conviction of such a proposition at all. He is prepared to modify or
add to his inductive truth according as new cases and new observations
instruct him; but he does not fear that new cases or new observations
will overturn an inductive proposition established by exact comparison
of many complex and various phenomena.

Aristotle's example offers somewhat similar reflections. He had to
establish a proposition concerning long-lived animals, which should
be true, and should be susceptible of generalized conversion. To
prove that the elephant, horse and mule are destitute of gall-bladder
required, at least, the labour of anatomizing those animals in the
seat of that organ. But this labour was not enough; for he would find
those animals to agree in many other things besides in being acholous.
He must have selected that character somewhat at a venture. And the
guess was wrong, as a little more labour would have shown him; if
for instance he had dissected deer: for they are acholous, and yet
short-lived. A trial of this kind would have shown him that the extreme
term, _acholous_, did extend beyond the mean, namely, animals such
as elephant, horse, mule; and therefore, that the conversion was not
allowable, and that the Induction was untenable. In truth, there is no
relation between bile and longevity[350], and this example given by
Aristotle of generalization from induction is an unfortunate one.

       *       *       *       *       *

In discussing this passage of Aristotle, I have made two alterations in
the text, one of which is necessary on account of the fact; the other
on account of the sense. In the received text, the particular examples
of long-lived animals given are _man_, horse, and mule (ἐφ' ᾧ δὲ Γ, τὸ
καθέκαστον μακρόβιον, οἷον ἄνθρωπος, καὶ ἵππος, καὶ ἡμίονος). And it is
afterwards said that all these are _acholous_: (ἀλλὰ καὶ τὸ Β, τὸ μὴ
ἔχον χολὴν, παντὶ ὑπάρχει τῷ Γ). But man _has_ a gall-bladder: and the
fact was well known in Aristotle's time, for instance, to Hippocrates;
so that it is not likely that Aristotle would have made the mistake
which the text contains. But at any rate, it is a mistake; if not of
the transcriber, of Aristotle; and it is impossible to reason about the
passage, without correcting the mistake. The substitution of ἔλεφας
for ἄνθρωπος makes the reasoning coherent; but of course, any other
acholous long-lived animal would do so equally well.

The other emendation which I have made is in § 6. In the received text
§ 6 and 7 stand thus:

 6. Then every _C_ is _A_, for _every acholous animal is long-lived_

 (τῷ δὴ Γ ὅλω ὑπάρχει τὸ Α, πᾶν γὰρ τὸ ἄχολον μακρόβιον).

 7. Also every _C_ is _B_, for all _C_ is destitute of bile.

Whence it may be inferred, says Aristotle, under certain conditions,
that every _B_ is _A_ (τὸ Α τῷ Β ὑπάρχειν) that is, that _every
acholous animal is long-lived_. But this conclusion is, according
to the common reading, identical with the major premiss; so that
the passage is manifestly corrupt. I correct it by substituting for
ἄχολον, Γ; and thus reading πᾶν γὰρ τὸ Γ μακρόβιον "for every _C_ is
long-lived:" just as in the parallel sentence, 7, we have ἀλλὰ καὶ τὸ
Β, τὸ μὴ ἔχον χολην, παντὶ ὑπάρχει τῷ Γ. In this way the reasoning
becomes quite clear. The corrupt substitution of ἄχολον for Γ may have
been made in various ways; which I need not suggest. As my business is
with the sense of the passage, and as it makes no sense without the
change, and very good sense with it, I cannot hesitate to make the
emendation. And these emendations being made, Aristotle's view of the
nature and force of Induction becomes, I think, perfectly clear and
very instructive.

       *       *       *       *       *

ADDITIONAL NOTE.

I take the liberty of adding to this Memoir the following remarks, for
which I am indebted to Mr. Edleston, Fellow of Trinity College.

Several of the earlier editions of Aristotle have γ instead of ἄχολον
in the passage referred to in the above paper: ex. gr.

(1) The edition printed at Basle, 1539 (after Erasmus): "τὸ γ."

(2) Basil (Erasmus) 1550. "τὸ γ."

(3) Burana's Latin version, Venet. 1552, has "omne enim _C_ longævum."

(4) Sylburg, Francf. 1587 "τὸ γ" is printed in brackets thus: "[τὸ γ]
τὸ ἄχολον."

(5) So also in Casaubon's edition, 1590.

(6) Casaub. 1605 "τὸ γ," (though the Latin version has "vacans bile;")
not "[τὸ γ] τὸ ἄχολον," as the edition of 1590.

(7) In the edition printed Aurel. Allobr. 1607, "[τὸ γ] τὸ ἄχολον," as
in (4) and (5).

(8) Du Val's editions, Paris, 1619, 1629, 1654 "τὸ γ," though in
Pacius's translation in the adjacent column we find "vacans bile."

(9) In the critical notes to Waitz's edition of the _Organon_ (Lips.
1844) it is stated that "post ἄχολον del. γ. _n_," implying apparently,
that in the MS. marked _n_, the letter γ, which had been originally
written after ἄχολον, had been erased.

       *       *       *       *       *

The following passages throw light upon the question whether ἄνθρωπος
ought or ought not to be retained in the passage discussed in the
Memoir.

(A) Aristot. _De Animalibus Histor._ II. 15, 9 (Bekk.), τῶν μὲν
ζωοτόκων καὶ τετραπόδων ἔλαφος οὐκ ἔχει [χολήν] οὐδὲ πρόξ, ἕτι δὲ
ἵππος, ὀρεύς, ὄνος, φώκη καὶ τῶν ὑῶν ἔνιοι.... Ἔχει δὲ καὶ ὁ ἐλέφας τὸ
ῆπαρ ἄχολον μέν, κ.τ.λ.

(B) Conf. Ib. I. 17, 10, 11. (In the beginning of Chap. 16, he says
that the external μορια of man are γνώριμα, "τὰ δ' ἐντὸς τοὐναντίον.
Ἄγνωστα γάρ ἐστι μάλιστα τὰ τῶν ἀνθρώπων, ὡστε δεῖ πρὸς τὰ τῶν ἄλλων μόρια
ζώων ἀνάγοντας σκοπεῖν," ...)

(C) Id _De Part. Animal._ IV. 2, 2. τὰ μὲν γὰρ ὅλως οὐκ ἕχει χολήν,
οἷον ἱππος και ὀρεύς καὶ ονος καὶ ἔλαφος καὶ πρόξ..... Ἐν δὲ τοῖς
γένεσι τοῖς αὐτοῖς τὰ μὲν ἔχειν φαίνεται, τὰ δ' οὐκ ἔχειν, οἷον ἐν
τῷ τῶν μυῶν. Τούτων δ' ἐστὶ καὶ ὁ ἄνθρωπος· ἔνιοι μὲν γὰρ φαίνονται
ἔχοντες χολὴν ἐπὶ του ἥπατος, ἔνιοι δ' οὐκ ἔχοντες. Διο καὶ γίνεται
ἀμφισβήτησις περὶ ὁλου τοῦ γένους· οἱ γὰρ ἐντυχόντες ὁποτερωσοῦν ἔχουσι
περὶ πάντων ὑπολαμβάνουσιν ὡς ἁπάντων ἐχόντων.....

(D) Ib. § 11. Διὸ καὶ χαριέστατα λέγουσι τῶν ῶρχαίων ὁι φάσκοντες
αἴτιον εῖναι τοῦ πλείω ζῆν χρόνον το μὴ ἔχειν χολήν, βλέψαντες ἐπὶ τὰ
μωνυχα και τὰς ελαφους· ταῦτα γὰρ ἄχολά τε καὶ ζῇ πολὺν χρόνον. Ἔτι
δὲ καὶ τὰ μὴ ἑωραμένα ὑπ' ἐκείνων ὁτι οὐκ ἔχει χολήν, οἷον δελφις καὶ
κάμηλος, καὶ ταῦτα τυγχάνει μακρόβια ὄντα. Εὔλογον γάρ, κ.τ.λ.

(E) The elephant and man are mentioned together as long-lived animals
(_De Long. et Brev. Vitæ_, IV. 2, and _De Generat. Animal._ IV. 10, 2.)

       *       *       *       *       *

The following is the import of these passages:

(_A_) "Of viviparous quadrupeds, the deer, roe, horse, mule, ass, seal,
and some of the swine have not the gall-bladder....

The elephant also has the liver without gall-bladder, &c."

(_B_) "The external parts of man are well known: the internal parts are
far from being so. The parts of man are in a great measure unknown; so
that we must judge concerning them by reference to the analogy of other
animals...."

(_C_) "Some animals are altogether destitute of gall-bladder, as the
horse, the mule, the ass, the deer, the roe.... But in some kinds it
appears that some have it, and some have it not, as the mice kind. And
among these is man; for some men appear to have a gall-bladder on the
liver, and some not to have one. And thus there is a doubt as to the
species in general; for those who have happened to examine examples of
either kind, hold that all the cases are of that kind."

(_D_) Those of the ancients speak most plausibly, who say that the
absence of the gall-bladder is the cause of long life; looking at
animals with uncloven hoof, and deer: for these are destitute of
gall-bladder, and live a long time. And further, those animals in which
the ancients had not the opportunity of ascertaining that they have not
the gall-bladder, as the dolphin, and the camel, are also long-lived
animals."

It appears, from these passages, that Aristotle was aware that some
persons had asserted man to have a gall-bladder, but that he also
conceived this not to be universally true. He may have inclined to
the opinion, that the opposite case was the more usual, and may have
written ἄνθρωπος in the passage which I have been discussing. Another
mistake of his is the reckoning deer among long-lived animals.

It appears probable, from the context of the passages (_C_) and (_D_),
that the conjecture of a connexion between absence of the gall-bladder
and length of life was suggested by some such notion as this:--that
the gall, from its bitterness, is the cause of irritation, mental and
bodily, and that irritation is adverse to longevity. The opinion is
ascribed to "the ancients," not claimed by Aristotle as his own.


FOOTNOTES:

[Footnote 350: Mr. Owen, to whom I am indebted for the physiological
part of this criticism, tells me, "All mammalia have bile, the
carnivora in greater proportion than the herbivora: the gall-bladder
is a comparatively unimportant accessory to the biliary apparatus;
adjusting it to certain modifications of stomach and intestine: there
is no relation between natural longevity and bile. Neither has the
presence or absence of the gall-bladder any connexion with age. Man and
the elephant are perhaps for their size the longest lived animals, and
the latest at coming to maturity: one has the gall-bladder, and the
other not."]


APPENDIX E.

ON THE FUNDAMENTAL ANTITHESIS OF PHILOSOPHY.

(_Cam. Phil. Soc._ FEB. 5, 1844.)


1. All persons who have attended in any degree to the views generally
current of the nature of reasoning are familiar with the distinction
of _necessary_ truths and _truths of experience_; and few such
persons, or at least few students of mathematics, require to have this
distinction explained or enforced. All geometricians are satisfied that
the geometrical truths with which they are conversant are necessarily
true: they not only are true, but they must be true. The meaning of the
terms being understood, and the proof being gone through, the truth
of the proposition must be assented to. That parallelograms upon the
same base and between the same parallels are equal;--that angles in the
same segment are equal;--these are propositions which we learn to be
true by demonstrations deduced from definitions and axioms; and which,
when we have thus learnt them, we see could not be otherwise. On the
other hand, there are other truths which we learn from experience;
as for instance, that the stars revolve round the pole in one day;
and that the moon goes through her phases from full to full again in
thirty days. These truths we see to be true; but we know them only
by experience. Men never could have discovered them without looking
at the stars and the moon; and having so learnt them, still no one
will pretend to say that they are necessarily true. For aught we can
see, things might have been otherwise; and if we had been placed in
another part of the solar system, then, according to the opinions of
astronomers, experience would have presented them otherwise.

2. I take the astronomical truths of experience to contrast with the
geometrical necessary truths, as being both of a familiar definite
sort; we may easily find other examples of both kinds of truth. The
truths which regard numbers are necessary truths. It is a necessary
truth, that 27 and 38 are equal to 65; that half the sum of two
numbers added to half their difference is equal to the greater
number. On the other hand, that sugar will dissolve in water; that
plants cannot live without light; and in short, the whole body of our
knowledge in chemistry, physiology, and the other inductive sciences,
consists of truths of experience. If there be any science which offer
to us truths of an ambiguous kind, with regard to which we may for a
moment doubt whether they are necessary or experiential, we will defer
the consideration of them till we have marked the distinction of the
two kinds more clearly.

3. One mode in which we may express the difference of necessary truths
and truths of experience, is, that necessary truths are those _of
which we cannot distinctly conceive the contrary_. We can very readily
conceive the contrary of experiential truths. We can conceive the stars
moving about the pole or across the sky in any kind of curves with any
velocities; we can conceive the moon always appearing during the whole
month as a luminous disk, as she might do if her light were inherent
and not borrowed. But we cannot conceive one of the parallelograms on
the same base and between the same parallels larger than the other;
for we find that, if we attempt to do this, when we separate the
parallelograms into parts, we have to conceive one triangle larger
than another, both having all their parts equal; which we cannot
conceive at all, if we conceive the triangles distinctly. We make this
impossibility more clear by conceiving the triangles to be placed so
that two sides of the one coincide with two sides of the other; and it
is then seen, that in order to conceive the triangles unequal, we must
conceive the two bases which have the same extremities both ways, to
be different lines, though both straight lines. This it is impossible
to conceive: we assent to the impossibility as an axiom, when it is
expressed by saying, that two straight lines cannot inclose a space;
and thus we cannot distinctly conceive the contrary of the proposition
just mentioned respecting parallelograms.

4. But it is necessary, in applying this distinction, to bear in mind
the terms of it;--that we cannot _distinctly_ conceive the contrary
of a necessary truth. For in a certain loose, indistinct way, persons
conceive the contrary of necessary geometrical truths, when they
erroneously conceive false propositions to be true. Thus, Hobbes
erroneously held that he had discovered a means of geometrically
doubling the cube, as it is called, that is, finding two mean
proportionals between two given lines; a problem which cannot be solved
by plane geometry. Hobbes not only proposed a construction for this
purpose, but obstinately maintained that it was right, when it had
been proved to be wrong. But then, the discussion showed how indistinct
the geometrical conceptions of Hobbes were; for when his critics had
proved that one of the lines in his diagram would not meet the other
in the point which his reasoning supposed, but in another point near
to it; he maintained, in reply, that one of these points was large
enough to include the other, so that they might be considered as the
same point. Such a mode of conceiving the opposite of a geometrical
truth, forms no exception to the assertion, that this opposite cannot
be distinctly conceived.

5. In like manner, the indistinct conceptions of children and of rude
savages do not invalidate the distinction of necessary and experiential
truths. Children and savages make mistakes even with regard to numbers;
and might easily happen to assert that 27 and 38 are equal to 63 or
64. But such mistakes cannot make such arithmetical truths cease to be
necessary truths. When any person conceives these numbers and their
addition distinctly, by resolving them into parts, or in any other way,
he sees that their sum is necessarily 65. If, on the ground of the
possibility of children and savages conceiving something different, it
be held that this is not a necessary truth, it must be held on the same
ground, that it is not a necessary truth that 7 and 4 are equal to 11;
for children and savages might be found so unfamiliar with numbers as
not to reject the assertion that 7 and 4 are 10, or even that 4 and 3
are 6, or 8. But I suppose that no persons would on such grounds hold
that these arithmetical truths are truths known only by experience.

6. Necessary truths are established, as has already been said, by
demonstration, proceeding from definitions and axioms, according to
exact and rigorous inferences of reason. Truths of experience are
collected from what we see, also according to inferences of reason,
but proceeding in a less exact and rigorous mode of proof. The former
depend upon the relations of the ideas which we have in our minds:
the latter depend upon the appearances or phenomena, which present
themselves to our senses. Necessary truths are formed from our
thoughts, the elements of the world within us; experiential truths are
collected from things, the elements of the world without us. The truths
of experience, as they appear to us in the external world, we call
Facts; and when we are able to find among our ideas a train which will
conform themselves to the apparent facts, we call this a Theory.

7. This distinction and opposition, thus expressed in various forms;
as Necessary and Experiential Truth, Ideas and Senses, Thoughts and
Things, Theory and Fact, may be termed the _Fundamental Antithesis
of Philosophy_; for almost all the discussions of philosophers have
been employed in asserting or denying, explaining or obscuring this
antithesis. It may be expressed in many other ways; but is not
difficult, under all these different forms, to recognize the same
opposition: and the same remarks apply to it under its various forms,
with corresponding modifications. Thus, as we have already seen, the
antithesis agrees with that of Reasoning and Observation: again, it
is identical with the opposition of Reflection and Sensation: again,
sensation deals with Objects; facts involve Objects, and generally all
things without us are Objects:--Objects of sensation, of observation.
On the other hand, we ourselves who thus observe objects, and in whom
sensation is, may be called the Subjects of sensation and observation.
And this distinction of Subject and Object is one of the most general
ways of expressing the fundamental antithesis, although not yet perhaps
quite familiar in English. I shall not scruple however to speak of
the Subjective and Objective element of this antithesis, where the
expressions are convenient.

8. All these forms of antithesis, and the familiar references to them
which men make in all discussions, show the fundamental and necessary
character of the antithesis. We can have no knowledge without the
union, no philosophy without the separation, of the two elements. We
can have no knowledge, except we have both impressions on our senses
from the world without, and thoughts from our minds within:--except we
attend to things, and to our ideas;--except we are passive to receive
impressions, and active to compare, combine, and mould them. But on
the other hand, philosophy seeks to distinguish the impressions of our
senses from the thoughts of our minds;--to point out the difference of
ideas and things;--to separate the active from the passive faculties
of our being. The two elements, sensations and ideas, are both
requisite to the existence of our knowledge, as both matter and form
are requisite to the existence of a body. But philosophy considers the
matter and the form separately. The properties of the form are the
subject of geometry, the properties of the matter are the subject of
chemistry or mechanics.

9. But though philosophy considers these elements of knowledge
separately, they cannot really be separated, any more than can matter
and form. "We cannot exhibit matter without form, or form without
matter; and just as little can we exhibit sensations without ideas, or
ideas without sensations;--the passive or the active faculties of the
mind detached from each other.

In every act of my knowledge, there must be concerned the things
whereof I know, and thoughts of me who know: I must both passively
receive or have received impressions, and I must actively combine
them and reason on them. No apprehension of things is purely ideal:
no experience of external things is purely sensational. If they
be conceived as _things_, the mind must have been awakened to the
conviction of things by sensation: if they be _conceived_ as things,
the expressions of the senses must have been bound together by
conceptions. If we _think_ of any _thing_, we must recognize the
existence both of thoughts and of things. _The fundamental antithesis
of philosophy is an antithesis of inseparable elements._

10. Not only cannot these elements be separately exhibited, but they
cannot be separately conceived and described. The description of them
must always imply their relation; and the names by which they are
denoted will consequently always bear a relative significance. And thus
_the terms which denote the fundamental antithesis of philosophy cannot
be applied absolutely and exclusively in any case_. We may illustrate
this by a consideration of some of the common modes of expressing the
antithesis of which we speak. The terms Theory and Fact are often
emphatically used as opposed to each other: and they are rightly so
used. But yet it is impossible to say absolutely in any case, This is
a Fact and not a Theory; this is a Theory and not a Fact, meaning by
Theory, true Theory. Is it a fact or a theory that the stars appear
to revolve round the pole? Is it a fact or a theory that the earth is
a globe revolving round its axis? Is it a fact or a theory that the
earth revolves round the sun? Is it a fact or a theory that the sun
attracts the earth? Is it a fact or a theory that a loadstone attracts
a needle? In all these cases, some persons would answer one way and
some persons another. A person who has never watched the stars, and has
only seen them from time to time, considers their circular motion round
the pole as a theory, just as he considers the motion of the sun in the
ecliptic as a theory, or the apparent motion of the inferior planets
round the sun in the zodiac. A person who has compared the measures of
different parts of the earth, and who knows that these measures cannot
be conceived distinctly without supposing the earth a globe, considers
its globular form a fact, just as much as the square form of his
chamber. A person to whom the grounds of believing the earth to revolve
round its axis and round the sun, are as familiar as the grounds for
believing the movements of the mail-coaches in this country, conceives
the former events to be facts, just as steadily as the latter. And a
person who, believing the fact of the earth's annual motion, refers it
distinctly to its mechanical course, conceives the sun's attraction as
a fact, just as he conceives as a fact the action of the wind which
turns the sails of a mill. We see then, that in these cases we cannot
apply absolutely and exclusively either of the terms, Fact or Theory.
Theory and Fact are the elements which correspond to our Ideas and our
Senses. The Facts are facts so far as the Ideas have been combined with
the sensations and absorbed in them: the Theories are Theories so far
as the Ideas are kept distinct from the sensations, and so far as it is
considered as still a question whether they can be made to agree with
them. A true Theory is a fact, a Fact is a familiar theory.

In like manner, if we take the terms Reasoning and Observation; at
first sight they appear to be very distinct. Our observation of the
world without us, our reasonings in our own minds, appear to be clearly
separated and opposed. But yet we shall find that we cannot apply
these terms absolutely and exclusively. I see a book lying a few feet
from me: is this a matter of observation? At first, perhaps, we might
be inclined to say that it clearly is so. But yet, all of us, who
have paid any attention to the process of vision, and to the mode in
which we are enabled to judge of the distance of objects, and to judge
them to be distant objects at all, know that this judgment involves
inferences drawn from various sensations;--from the impressions on
our two eyes;--from our muscular sensations; and the like. These
inferences are of the nature of reasoning, as much as when we judge of
the distance of an object on the other side of a river by looking at
it from different points, and stepping the distance between them. Or
again: we observe the setting sun illuminate a gilded weathercock; but
this is as much a matter of reasoning as when we observe the phases of
the moon, and infer that she is illuminated by the sun. All observation
involves inferences, and inference is reasoning.

11. Even the simplest terms by which the antithesis is expressed cannot
be applied: ideas and sensations, thoughts and things, subject and
object, cannot in any case be applied absolutely and exclusively. Our
sensations require ideas to bind them together, namely, ideas of space,
time, number, and the like. If not so bound together, sensations do not
give us any apprehension of things or objects. All things, all objects,
must exist in space and in time--must be one or many. Now space, time,
number, are not sensations or things. They are something different
from, and opposed to sensations and things. We have termed them ideas.
It may be said they are _relations_ of things, or of sensations. But
granting this form of expression, still a _relation_ is not a thing
or a sensation; and therefore we must still have another and opposite
element, along with our sensations. And yet, though we have thus these
two elements in every act of perception, we cannot designate any
portion of the act as absolutely and exclusively belonging to one of
the elements. Perception involves sensation, along with ideas of time,
space, and the like; or, if any one prefers the expression, involves
sensations along with the apprehension of relations. Perception is
sensation, along with such ideas as make sensation into an apprehension
of things or objects.

12. And as perception of objects implies ideas, as observation implies
reasoning; so, on the other hand, ideas cannot exist where sensation
has not been: reasoning cannot go on when there has not been previous
observation. This is evident from the necessary order of development
of the human faculties. Sensation necessarily exists from the first
moments of our existence, and is constantly at work. Observation
begins before we can suppose the existence of any reasoning which is
not involved in observation. Hence, at whatever period we consider
our ideas, we must consider them as having been already engaged in
connecting our sensations, and as modified by this employment. By being
so employed, our ideas are unfolded and defined, and such development
and definition cannot be separated from the ideas themselves. We
cannot conceive space without boundaries or forms; now forms involve
sensations. We cannot conceive time without events which mark the
course of time; but events involve sensations. We cannot conceive
number without conceiving things which are numbered; and things imply
sensations. And the forms, things, events, which are thus implied in
our ideas, having been the objects of sensation constantly in every
part of our life, have modified, unfolded and fixed our ideas, to
an extent which we cannot estimate, but which we must suppose to be
essential to the processes which at present go on in our minds. We
cannot say that objects create ideas; for to perceive objects we must
already have ideas. But we may say, that objects and the constant
perception of objects have so far modified our ideas, that we cannot,
even in thought, separate our ideas from the perception of objects.

We cannot say of any ideas, as of the idea of space, or time, or
number, that they are absolutely and exclusively ideas. We cannot
conceive what space, or time, or number would be in our minds, if we
had never perceived any thing or things in space or time. We cannot
conceive ourselves in such a condition as never to have perceived any
thing or things in space or time. But, on the other hand, just as
little can we conceive ourselves becoming acquainted with space and
time or numbers as objects of sensation. We cannot reason without
having the operations of our minds affected by previous sensations; but
we cannot conceive reasoning to be merely a series of sensations. In
order to be used in reasoning, sensation must become observation; and,
as we have seen, observation already involves reasoning. In order to
be connected by our ideas, sensations must be things or objects, and
things or objects already include ideas. And thus, as we have said,
none of the terms by which the fundamental antithesis is expressed can
be absolutely and exclusively applied.

13. I now proceed to make one or two remarks suggested by the views
which have thus been presented. And first I remark, that since, as
we have just seen, none of the terms which express the fundamental
antithesis can be applied absolutely and exclusively, the absolute
application of the antithesis in any particular case can never be a
conclusive or immoveable principle. This remark is the more necessary
to be borne in mind, as the terms of this antithesis are often used
in a vehement and peremptory manner. Thus we are often told that such
a thing is a _Fact_ and not a Theory, with all the emphasis which, in
speaking or writing, tone or italics or capitals can give. "We see from
what has been said, that when this is urged, before we can estimate the
truth, or the value of the assertion, we must ask to whom is it a fact?
what habits of thought, what previous information, what ideas does
it imply, to conceive the fact as a fact? Does not the apprehension
of the fact imply assumptions which may with equal justice be called
theory, and which are perhaps false theory? in which case, the fact is
no fact. Did not the ancients assert it as a fact, that the earth stood
still, and the stars moved? and can any fact have stronger apparent
evidence to justify persons in asserting it emphatically than this
had? These remarks are by no means urged in order to show that no fact
can be certainly known to be true; but only to show that no fact can
be certainly shown to be a fact merely by calling it a fact, however
emphatically. There is by no means any ground of general skepticism
with regard to truth involved in the doctrine of the necessary
combination of two elements in all our knowledge. On the contrary,
ideas are requisite to the essence, and things to the reality of our
knowledge in every case. The proportions of geometry and arithmetic are
examples of knowledge respecting our ideas of space and number, with
regard to which there is no room for doubt. The doctrines of astronomy
are examples of truths not less certain respecting the external world.

14. I remark further, that since in every act of knowledge, observation
or perception, both the elements of the fundamental antithesis are
involved, and involved in a manner inseparable even in our conceptions,
it must always be possible to derive one of these elements from the
other, if we are satisfied to accept, as proof of such derivation,
that one always co-exists with and implies the other. Thus an
opponent may say, that our ideas of space, time, and number, are
derived from our sensations or perceptions, because we never were
in a condition in which we had the ideas of space and time, and had
not sensations or perceptions. But then, we may reply to this, that
we no sooner perceive objects than we perceive them as existing in
space and time, and therefore the ideas of space and time are not
derived from the perceptions. In the same manner, an opponent may
say, that all knowledge which is involved in our reasonings is the
result of experience; for instance, our knowledge of geometry. For
every geometrical principle is presented to us by experience as true;
beginning with the simplest, from which all others are derived by
processes of exact reasoning. But to this we reply, that experience
cannot be the origin of such knowledge; for though experience shows
that such principles are true, it cannot show that they _must be_ true,
which we also know. We never have seen, as a matter of observation,
two straight lines inclosing a space; but we venture to say further,
without the smallest hesitation, that we never shall see it; and if any
one were to tell us that, according to his experience, such a form was
often seen, we should only suppose that he did not know what he was
talking of. No number of acts of experience can add to the certainty
of our knowledge in this respect; which shows that our knowledge is
not made up of acts of experience. We cannot test such knowledge by
experience; for if we were to try to do so, we must first know that the
lines with which we make the trial _are_ straight; and we have no test
of straightness better than this, that two such lines cannot inclose a
space. Since then, experience can neither destroy, add to, nor test our
axiomatic knowledge, such knowledge cannot be derived from experience.
Since no one act of experience can affect our knowledge, no numbers of
acts of experience can make it.

15. To this a reply has been offered, that it is a characteristic
property of geometric forms that the ideas of them exactly resemble the
sensations; so that these ideas are as fit subjects of experimentation
as the realities themselves; and that by such experimentation we learn
the truth of the axioms of geometry. I might very reasonably ask those
who use this language to explain how a particular class of ideas can
be said to resemble sensations; how, if they do, we can know it to be
so; how we can prove this resemblance to belong to geometrical ideas
and sensations; and how it comes to be an especial characteristic of
those. But I will put the argument in another way. Experiment can only
show what is, not what must be. If experimentation on ideas shows what
must be, it is different from what is commonly called experience.

I may add, that not only the mere use of our senses cannot show that
the axioms of geometry _must be_ true, but that, without the light
of our ideas, it cannot even show that they _are_ true. If we had a
segment of a circle a mile long and an inch wide, we should have two
lines inclosing a space; but we could not, by seeing or touching any
part of either of them, discover that it was a bent line.

16. That mathematical truths are not derived from experience is perhaps
still more evident, if greater evidence be possible, in the case of
numbers. We assert that 7 and 8 are 15. We find it so, if we try with
counters, or in any other way. But we do not, on that account, say that
the knowledge is derived from experience. We refer to our conceptions
of seven, of eight, and of addition, and as soon as we possess these
conceptions distinctly, we see that the sum must be fifteen. We cannot
be said to make a trial, for we should not believe the apparent result
of the trial if it were different. If any one were to say that the
multiplication table is a table of the results of experience, we should
know that he could not be able to go along with us in our researches
into the foundations of human knowledge; nor, indeed, to pursue with
success any speculations on the subject.

17. Attempts have also been made to explain the origin of axiomatic
truths by referring them to the association of ideas. But this is
one of the cases in which the word _association_ has been applied so
widely and loosely, that no sense can be attached to it. Those who
have written with any degree of distinctness on the subject, have
truly taught, that the habitual association of the ideas leads us to
believe a connexion of the things: but they have never told us that
this association gave us the power of forming the ideas. Association
may determine belief, but it cannot determine the possibility of our
conceptions. The African king did not believe that water could become
solid, because he had never seen it in that state. But that accident
did not make it impossible to conceive it so, any more than it is
impossible for us to conceive frozen quicksilver, or melted diamond,
or liquefied air; which we may never have seen, but have no difficulty
in conceiving. If there were a tropical philosopher really incapable
of conceiving water solidified, he must have been brought into that
mental condition by abstruse speculations on the necessary relations of
solidity and fluidity, not by the association of ideas.

18. To return to the results of the nature of the Fundamental
Antithesis. As by assuming universal and indissoluble connexion of
ideas with perceptions, of knowledge with experience, as an evidence
of derivation, we may assert the former to be derived from the latter,
so might we, on the same ground, assert the latter to be derived from
the former. We see all forms in space; and we might hence assert all
forms to be mere modifications of our idea of space. We see all events
happen in time; and we might hence assert all events to be merely
limitations and boundary-marks of our idea of time. We conceive all
collections of things as two or three, or some other number: it might
hence be asserted that we have an original idea of number, which is
reflected in external things. In this case, as in the other, we are met
at once by the impossibility of this being a complete account of our
knowledge. Our ideas of space, of time, of number, however distinctly
reflected to us with limitations and modifications, must be reflected,
limited and modified by something different from themselves. We must
have visible or tangible forms to limit space, perceived events to mark
time, distinguishable objects to exemplify number. But still, in forms,
and events, and objects, we have a knowledge which they themselves
cannot give us. For we know, without attending to them, that whatever
they are, they will conform and must conform to the truths of geometry
and arithmetic. There is an ideal portion in all our knowledge of the
external world; and if we were resolved to reduce all our knowledge
to one of its two antithetical elements, we might say that all our
knowledge consists in the relation of our ideas. Wherever there is
necessary truth, there must be something more than sensation can
supply: and the necessary truths of geometry and arithmetic show us
that our knowledge of objects in space and time depends upon necessary
relations of ideas, whatever other element it may involve.

19. This remark may be carried much further than the domain of geometry
and arithmetic. Our knowledge of matter may at first sight appear
to be altogether derived from the senses. Yet we cannot derive from
the senses our knowledge of a truth which we accept as universally
certain;--namely, that we cannot by any process add to or diminish
the quantity of matter in the world. This truth neither is nor can be
derived from experience; for the experiments which we make to verify
it pre-suppose its truth. When the philosopher was asked what was
the weight of smoke, he bade the inquirer subtract the weight of
the ashes from the weight of the fuel. Every one who thinks clearly
of the changes which take place in matter, assents to the justice of
this reply: and this, not because any one had found by trial that such
was the weight of the smoke produced in combustion, but because the
weight lost was assumed to have gone into some other form of matter,
not to have been destroyed. When men began to use the balance in
chemical analysis, they did not prove by trial, but took for granted,
as self-evident, that the weight of the whole must be found in the
aggregate weight of the elements. Thus it is involved in the idea of
matter that its amount continues unchanged in all changes which take
place in its consistence. This is a necessary truth: and thus our
knowledge of matter, as collected from chemical experiments, is also
a modification of our idea of matter as the material of the world
incapable of addition or diminution.

20. A similar remark may be made with regard to the mechanical
properties of matter. Our knowledge of these is reduced, in our
reasonings, to principles which we call the laws of motion. These laws
of motion, as I have endeavoured to show[351], depend upon the idea
of Cause, and involve necessary truths, which are necessarily implied
in the idea of cause;--namely, that every change of motion must have
a cause--that the effect is measured by the cause;--that reaction
is equal and opposite to action. These principles are not derived
from experience. No one, I suppose, would derive from experience the
principle, that every event must have a cause. Every attempt to see
the traces of cause in the world assumes this principle. I do not say
that these principles are anterior to experience; for I have already,
I hope, shown, that neither of the two elements of our knowledge is,
or can be, anterior to the other. But the two elements are co-ordinate
in the development of the human mind; and the ideal element may be
said to be the origin of our knowledge with the more propriety of the
two, inasmuch as our knowledge is the relation of ideas. The other
element of knowledge, in which sensation is concerned, and which
embodies, limits, and defines the necessary truths which express the
relations of our ideas, may be properly termed experience; and I have,
in the discussion just quoted, endeavoured to show how the principles
concerning mechanical causation, which I have just stated, are, by
observation and experiment, limited and defined, so that they become
the laws of motion. And thus we see that such knowledge is derived
from ideas, in a sense quite as general and rigorous, to say the least,
as that in which it is derived from experience.

21. I will take another example of this; although it is one less
familiar, and the consideration of it perhaps a little more difficult
and obscure. The objects which we find in the world, for instance,
minerals and plants, are of different kinds; and according to their
kinds, they are called by various names, by means of which we know
what we mean when we speak of them. The discrimination of these kinds
of objects, according to their different forms and other properties,
is the business of chemistry and botany. And this business of
discrimination, and of consequent classification, has been carried on
from the first periods of the development of the human mind, by an
industrious and comprehensive series of observations and experiments;
the only way in which any portion of the task could have been effected.
But as the foundation of all this labour, and as a necessary assumption
during every part of its progress, there has been in men's minds
the principle, that objects are so distinguishable by resemblances
and differences, that they may be named, and known by their names.
This principle is involved in the idea of a Name; and without it no
progress could have been made. The principle may be briefly stated
thus:--Intelligible Names of kinds are possible. If we suppose this
not to be so, language can no longer exist, nor could the business
of human life go on. If instead of having certain definite kinds of
minerals, gold, iron, copper and the like, of which the external forms
and characters are constantly connected with the same properties and
qualities, there were no connexion between the appearance and the
properties of the object;--if what seemed externally iron might turn
out to resemble lead in its hardness; and what seemed to be gold during
many trials, might at the next trial be found to be like copper; not
only all the uses of these minerals would fail, but they would not be
distinguishable kinds of things, and the names would be unmeaning. And
if this entire uncertainty as to kind and properties prevailed for all
objects, the world would no longer be a world to which language was
applicable. To man, thus unable to distinguish objects into kinds, and
call them by names, all knowledge would be impossible, and all definite
apprehension of external objects would fade away into an inconceivable
confusion. In the very apprehension of objects as intelligibly sorted,
there is involved a principle which springs within us, contemporaneous,
in its efficacy, with our first intelligent perception of the kinds
of things of which the world consists. We assume, as a necessary
basis of our knowledge, that things are of definite kinds; and the aim
of chemistry, botany, and other sciences is to find marks of these
kinds; and along with these, to learn their definitely-distinguished
properties. Even here, therefore, where so large a portion of our
knowledge comes from experience and observation, we cannot proceed
without a necessary truth derived from our ideas, as our fundamental
principle of knowledge.

22. What the marks are, which distinguish the constant differences of
kinds of things (definite marks, selected from among many unessential
appearances), and what their definite properties are, when they
are so distinguished, are parts of our knowledge to be learnt from
observation, by various processes; for instance, among others, by
chemical analysis. We find the differences of bodies, as shown by such
analysis, to be of this nature:--that there are various elementary
bodies, which, combining in different definite proportions, form kinds
of bodies definitely different. But, in arriving at this conclusion,
we introduce a new idea, that of Elementary Composition, which is not
extracted from the phenomena, but supplied by the mind, and introduced
in order to make the phenomena intelligible. That this notion of
elementary composition is not supplied by the chemical phenomena of
combustion, mixture, &c. as merely an observed fact, we see from this;
that men had in ancient times performed many experiments in which
elementary composition was concerned, and had not seen the fact. It
never was truly seen till modern times; and when seen, it gave a new
aspect to the whole body of known facts. This idea of elementary
composition, then, is supplied by the mind, in order to make the
facts of chemical analysis and synthesis intelligible _as_ analysis
and synthesis. And this idea being so supplied, there enters into our
knowledge along with it a corresponding necessary principle;--That the
elementary composition of a body determines its kind and properties.
This is, I say, a principle assumed, as a consequence of the idea of
composition, not a result of experience; for when bodies have been
divided into their kinds, we take for granted that the analysis of a
single specimen may serve to determine the analysis of all bodies of
the same kind: and without this assumption, chemical knowledge with
regard to the kinds of bodies would not be possible. It has been said
that we take only one experiment to determine the composition of any
particular kind of body, because we have a thousand experiments to
determine that bodies of the same kind have the same composition. But
this is not so. Our belief in the principle that bodies of the same
kind have the same composition is not established by experiments,
but is assumed as a necessary consequence of the ideas of Kind and of
Composition. If, in our experiments, we found that bodies supposed
to be of the same kind had not the same composition, we should not
at all doubt of the principle just stated, but conclude at once that
the bodies were _not_ of the same kind;--that the marks by which the
kinds are distinguished had been wrongly stated. This is what has very
frequently happened in the course of the investigations of chemists and
mineralogists. And thus we have it, not as an experiential fact, but
as a necessary principle of chemical philosophy, that the Elementary
Composition of a body determines its Kind and Properties.

23. How bodies differ in their elementary composition, experiment must
teach us, as we have already said, that experiment has taught us. But
as we have also said, whatever be the nature of this difference, kinds
must be definite, in order that language may be possible: and hence,
whatever be the terms in which we are taught by experiment to express
the elementary composition of bodies, the result must be conformable
to this principle, That the differences of elementary composition
are definite. The law to which we are led by experiment is, that the
elements of bodies continue in definite proportions according to
weight. Experiments add other laws; as for instance, that of multiple
proportions in different kinds of bodies composed of the same elements;
but of these we do not here speak.

24. We are thus led to see that in our knowledge of mechanics,
chemistry, and the like, there are involved certain necessary
principles, derived from our ideas, and not from experience. But to
this it may be objected, that the parts of our knowledge in which these
principles are involved has, in historical fact, all been acquired by
experience. The laws of motion, the doctrine of definite proportions,
and the like, have all become known by experiment and observation; and
so far from being seen as necessary truths, have been discovered by
long-continued labours and trials, and through innumerable vicissitudes
of confusion, error, and imperfect truth. This is perfectly true: but
does not at all disprove what has been said. Perception of external
objects and experience, experiment and observation are needed,
not only, as we have said, to supply the objective element of all
knowledge--to embody, limit, define, and modify our ideas; but this
intercourse with objects is also requisite to unfold and fix our ideas
themselves. As we have already said, ideas and facts can never be
separated. Our ideas cannot be exercised and developed in any other
form than in their combination with facts, and therefore the trials,
corrections, controversies, by which the matter of our knowledge is
collected, is also the only way in which the form of it can be rightly
fashioned. Experience is requisite to the clearness and distinctness of
our ideas, not because they are derived from experience, but because
they can only be exercised upon experience. And this consideration
sufficiently explains how it is that experiment and observation have
been the means, and the only means, by which men have been led to a
knowledge of the laws of nature. In reality, however, the necessary
principles which flow from our ideas, and which are the basis of such
knowledge, have not only been inevitably assumed in the course of such
investigations, but have been often expressly promulgated in words
by clear-minded philosophers, long before their true interpretation
was assigned by experiment. This has happened with regard to such
principles as those above mentioned; That every event must have a
cause; That reaction is equal and opposite to action; That the quantity
of matter in the world cannot be increased or diminished: and there
would be no difficulty in finding similar enunciations of the other
principles above mentioned;--That the kinds of things have definite
differences, and that these differences depend upon their elementary
composition. In general, however, it may be allowed, that the necessary
principles which are involved in those laws of nature of which we have
a knowledge become then only clearly known, when the laws of nature are
discovered which thus involve the necessary ideal element.

25. But since this is allowed, it may be further asked, how we are to
distinguish between the necessary principle which is derived from our
ideas, and the law of nature which is learnt by experience. And to this
we reply, that the necessary principle may be known by the condition
which we have already mentioned as belonging to such principles: ...
that it is impossible distinctly to conceive the contrary. We cannot
conceive an event without a cause, except we abandon all distinct idea
of cause; we cannot distinctly conceive two straight lines inclosing
space; and if we seem to conceive this, it is only because we conceive
indistinctly. We cannot conceive 5 and 3 making 7 or 9; if a person
were to say that he could conceive this, we should know that he was a
person of immature or rude or bewildered ideas, whose conceptions had
no distinctness. And thus we may take it as the mark of a necessary
truth, that we cannot conceive the contrary distinctly.

26. If it be asked what is the test of distinct conception (since it
is upon the distinctness of conception that the matter depends), we
may consider what answer we should give to this question if it were
asked with regard to the truths of geometry. If we doubted whether
anyone had these distinct conceptions which enable him to see the
necessary nature of geometrical truth, we should inquire if he could
understand the axioms as axioms, and could follow, as demonstrative,
the reasonings which are founded upon them. If this were so, we should
be ready to pronounce that he had distinct ideas of space, in the sense
now supposed. And the same answer may be given in any other case. That
reasoner has distinct conceptions of mechanical causes who can see
the axioms of mechanics as axioms, and can follow the demonstrations
derived from them as demonstrations. If it be said that the science,
as presented to him, may be erroneously constructed; that the axioms
may not be axioms, and therefore the demonstrations may be futile, we
still reply, that the same might be said with regard to geometry: and
yet that the possibility of this does not lead us to doubt either of
the truth or of the necessary nature of the propositions contained
in Euclid's Elements. We may add further, that although, no doubt,
the authors of elementary books maybe persons of confused minds, who
present as axioms what are not axiomatic truths; yet that in general,
what is presented as an axiom by a thoughtful man, though it may
include some false interpretation or application of our ideas, will
also generally include some principle which really is necessarily true,
and which would still be involved in the axiom, if it were corrected
so as to be true instead of false. And thus we still say, that if in
any department of science a man can conceive distinctly at all, there
are principles the contrary of which he cannot distinctly conceive, and
which are therefore necessary truths.

27. But on this it may be asked, whether truth can thus depend upon
the particular state of mind of the person who contemplates it; and
whether that can be a necessary truth which is not so to all men. And
to this we again reply, by referring to geometry and arithmetic. It
is plain that truths may be necessary truths which are not so to all
men, when we include men of confused and perplexed intellects; for to
such men it is not a necessary truth that two straight lines cannot
inclose a space, or that 14 and 17 are 31. It need not be wondered
at, therefore, if to such men it does not appear a necessary truth
that reaction is equal and opposite to action, or that the quantity of
matter in the world cannot be increased or diminished. And this view of
knowledge and truth does not make it depend upon the state of mind of
the student, any more than geometrical knowledge and geometrical truth,
by the confession of all, depend upon that state. We know that a man
cannot have any knowledge of geometry without so much of attention to
the matter of the science, and so much of care in the management of
his own thoughts, as is requisite to keep his ideas distinct and clear.
But we do not, on that account, think of maintaining that geometrical
truth depends merely upon the state of the student's mind. We conceive
that he knows it because it is true, not that it is true because he
knows it. We are not surprised that attention and care and repeated
thought should be requisite to the clear apprehension of truth. For
such care and such repetition are requisite to the distinctness and
clearness of our ideas: and yet the relations of these ideas, and
their consequences, are not produced by the efforts of attention or
repetition which we exert. They are in themselves something which
we may discover, but cannot make or change. The idea of space, for
instance, which is the basis of geometry, cannot give rise to any
doubtful propositions. What is inconsistent with the idea of space
cannot be truly obtained from our ideas by any efforts of thought or
curiosity; if we blunder into any conclusion inconsistent with the idea
of space, our knowledge, so far as this goes, is no knowledge: any more
than our observation of the external world would be knowledge, if, from
haste or inattention, or imperfection of sense, we were to mistake the
object which we see before us.

28. But further: not only has truth this reality, which makes it
independent of our mistakes, that it must be what is really consistent
with our ideas; but also, a further reality, to which the term
is more obviously applicable, arising from the principle already
explained, that ideas and perceptions are inseparable. For since,
when we contemplate our ideas, they have been frequently embodied and
exemplified in objects, and thus have been fixed and modified; and
since this compound aspect is that under which we constantly have
them before us, and free from which they cannot be exhibited; our
attempts to make our ideas clear and distinct will constantly lead us
to contemplate them as they are manifested in those external forms
in which they are involved. Thus in studying geometrical truth, we
shall be led to contemplate it as exhibited in visible and tangible
figures;--not as if these could be sources of truth, but as enabling
us more readily to compare the aspects which our ideas, applied to the
world of objects, may assume. And thus we have an additional indication
of the reality of geometrical truth, in the necessary possibility of
its being capable of being exhibited in a visible or tangible form. And
yet even this test by no means supersedes the necessity of distinct
ideas, in order to a knowledge of geometrical truth. For in the case
of the duplication of the cube by Hobbes, mentioned above, the diagram
which he drew made two points appear to coincide, which did not
really, and by the nature of our idea of space, coincide; and thus
confirmed him in his error.

_Thus the inseparable nature of the Fundamental Antithesis of Ideas and
Things gives reality to our knowledge, and makes objective reality a
corrective of our subjective imperfections in the pursuit of knowledge.
But this objective exhibition of knowledge can by no means supersede a
complete development of the subjective condition, namely, distinctness
of ideas. And that there is a subjective condition, by no means makes
knowledge altogether subjective, and thus deprives it of reality;
because, as we have said, the subjective and the objective elements are
inseparably bound together in the fundamental antithesis._

29. It would be easy to apply these remarks to other cases, for
instance, to the case of the principle we have just mentioned, that
the differences of elementary composition of different kinds of bodies
must be definite. We have stated that this principle is necessarily
true;--that the contrary proposition cannot be distinctly conceived.
But by whom? Evidently, according to the preceding reasoning, by a
person who distinctly conceives Kinds, as marked by intelligible
names, and Composition, as determining the kinds of bodies. Persons
new to chemical and classificatory science may not possess these ideas
distinctly; or rather, cannot possess them distinctly; and therefore
cannot apprehend the impossibility of conceiving the opposite of
the above principle; just as the schoolboy cannot apprehend the
impossibility of the numbers in his multiplication table being other
than they are. But this inaptitude to conceive, in either case, does
not alter the necessary character of the truth: although, in one case,
the truth is obvious to all except schoolboys and the like, and the
other is probably not clear to any except those who have attentively
studied the philosophy of elementary compositions. At the same time,
this difference of apprehension of the truth in different persons does
not make the truth doubtful or dependent upon personal qualifications;
for in proportion as persons attain to distinct ideas, they will see
the truth; and cannot, with such ideas, see anything as truth which
is not truth. When the relations of elements in a compound become as
familiar to a person as the relations of factors in a multiplication
table, he will then see what are the necessary axioms of chemistry, as
he now sees the necessary axioms of arithmetic.

30. There is also one other remark which I will here make. In the
progress of science, both the elements of our knowledge are constantly
expanded and augmented. By the exercise of observation and experiment,
we have a perpetual accumulation of facts, the materials of knowledge,
the objective element. By thought and discussion, we have a perpetual
development of man's ideas going on: theories are framed, the materials
of knowledge are shaped into form; the subjective element is evolved;
and by the necessary coincidence of the objective and subjective
elements, the matter and the form, the theory and the facts, each of
these processes furthers and corrects the other: each element moulds
and unfolds the other. Now it follows, from this constant development
of the ideal portion of our knowledge, that we shall constantly be
brought in view of new Necessary Principles, the expression of the
conditions belonging to the Ideas which enter into our expanding
knowledge. These principles, at first dimly seen and hesitatingly
asserted, at last become clearly and plainly self-evident. Such is the
case with the principles which are the basis of the laws of motion.
Such may soon be the case with the principles which are the basis
of the philosophy of chemistry. Such may hereafter be the case with
the principles which are to be the basis of the philosophy of the
connected and related polarities of chemistry, electricity, galvanism,
magnetism. That knowledge is possible in these cases, we know; that
our knowledge may be reduced to principles, gradually more simple,
we also know; that we have reached the last stage of simplicity of
our principles, few cultivators of the subject will be disposed to
maintain; and that the additional steps which lead towards very simple
and general principles will also lead to principles which recommend
themselves by a kind of axiomatic character, those who judge from the
analogy of the past history of science will hardly doubt. That the
principles thus axiomatic in their form, do also express some relation
of our ideas, of which experiment and observation have given a true
and real interpretation, is the doctrine which I have here attempted
to establish and illustrate in the most clear and undoubted of the
existing sciences; and the evidence of this doctrine in those cases
seems to be unexceptionable, and to leave no room to doubt that such is
the universal type of the progress of science. Such a doctrine, as we
have now seen, is closely connected with the views here presented of
the nature of the Fundamental Antithesis of Philosophy, which I have
endeavoured to illustrate.


FOOTNOTES:

[Footnote 351: _Hist. Sc. Ind._ b. iii.]


APPENDIX F.

REMARKS ON A REVIEW OF THE PHILOSOPHY OF THE INDUCTIVE SCIENCES.


  _Trinity Lodge, April 11th, 1844._

  MY DEAR HERSCHEL,

Being about to send you a copy of a paper on a philosophical question
just printed in the Transactions of our Cambridge Society, I am tempted
to add, as a private communication, a few Remarks on another aspect of
the same question. These Remarks I think I may properly address to you.
They will refer to an Article in the _Quarterly Review_ for June, 1841,
respecting my _History_ and _Philosophy_ of the Inductive Sciences; and
without assigning any other reason, I may say that the interest I know
you to take in speculations on such subjects makes me confident that
you will give a reasonable attention to what I may have to say on the
subject of that Article. With the Reviewal itself, I am so far from
having any quarrel, that when it appeared I received it as affording
all that I hoped from Public Criticism. The degree and the kind of
admiration bestowed upon my works by a writer so familiar with science,
so comprehensive in his views, and so equitable in his decisions, as
the Reviewer manifestly was, I accepted as giving my work a stamp of
acknowledged value which few other hands could have bestowed.

You may perhaps recollect, however, that the Reviewer dissented
altogether from some of the general views which I had maintained,
and especially from a general view which is also, in the main, that
presented in the accompanying Memoir, namely, that, besides Facts,
Ideas are an indispensable source of our knowledge; that Ideas are
the ground of necessary truth; that the Idea of Space, in particular,
is the ground of the necessary truths of geometry. This question,
and especially as limited to the last form, will be the subject of
my Remarks in the first place; and I wish to consider the Reviewer's
objections with the respect which their subtlety and depth of thought
well deserve.

The Reviewer makes objections to the account which I have given of
the source whence geometrical truth derives its characters of being
necessary and universal; but he is not one of those metaphysicians
who deny those characters to the truths of geometry. He allows in the
most ample manner that the truths of geometry _are_ necessary. The
question between us therefore is from what this character is derived.
The Reviewer prefers, indeed, to have it considered that the question
is not concerning the necessity, but, as he says, the universality of
these truths; or rather, the nature and grounds of our conviction of
their universality. He might have said, with equal justice, the nature
and grounds of our conviction of their necessity. For his objection to
the term _necessity_ in this case--"that all the propositions about
realities are necessarily true, since every reality must be consistent
with itself," (p. 206)--does not apply to our conviction of necessity,
since we may not be able to see what are the properties of real things;
and therefore may have no conviction of their necessity. It may be a
necessary property of salt to be soluble, but we see no such necessity;
and therefore the assertion of such a property is not one of the
necessary truths with which we are here concerned. But to turn back to
the necessary or universal truths of geometry, and the ground of those
attributes: The main difference between the Author and the Reviewer is
brought into view, when the Reviewer discusses the general argument
which I had used, in order to show that truths which we see to be
necessary and universal cannot be derived from experience. The argument
is this,--

"Experience must always consist of a limited number of observations;
and however numerous these may be, they can show nothing with regard
to the infinite number of cases in which the experiment has not been
made.... Truths can only be known to be general, not universal, if
they depend upon experience alone. Experience cannot bestow that
universality which she herself cannot have; nor that necessity of which
she has no comprehension." (_Phil._ _i._ pp. 60, 61.)

Here is that which must be considered as the cardinal argument on this
subject. It is therefore important to attend to the answer which the
Reviewer makes to it. He says,--

"We conceive that a full answer to this argument is afforded by the
nature of the inductive propensity,--by the irresistible impulse of
the mind to generalize _ad infinitum_, when nothing in the nature of
limitation or opposition offers itself to the imagination; and by our
involuntary application of the law of continuity to fill up, by the
same ideal substance of truth, every interval which uncontradicted
experience may have left blank in our inductive conclusion." (p. 207.)

Now here we have two rival explanations of the same thing,--the
conviction of the universality of geometrical truths. The one
explanation is, that this universality is imposed upon such truths by
their involving a certain element, derived from the universal mode of
activity of the mind when apprehending such truths, which element I
have termed an Idea. The other explanation is, that this universality
arises from the _inductive propensity_--from the _irresistible impulse
to generalize ad infinitum_--from the _involuntary application of the
law of continuity_--from the _filling up all intervals with the same
ideal substance of truth_.

With regard to these two explanations, I may observe, that so far as
they are thus stated they do not necessarily differ. They both agree
in expressing this; that the ground of the universality of geometrical
truths is a certain law of the mind's activity, which determines its
procedure when it is concerned in apprehending the external world.
One explanation says, that we impress upon the external world the
relations of our ideas, and thus believe more than we see,--the
other says, that we have an irresistible impulse to introduce into
our conviction a relation between what we do observe and what we do
not, namely, to generalize _ad infinitum_ from what we do see. One
explanation says, that we perceive all external objects as included
in absolute ideal space,--the other, that we fill up the intervals of
the objects which we perceive with the same ideal substance of truth.
Both sets of expressions may perhaps be admissible; and if admitted,
may be understood as expressing the same opinions, or opinions which
have much in common. The Author's expressions have the advantage, which
ought to belong to them, as the expressions employed in a systematic
work, of being fixed expressions, technical phrases, intentionally
selected, uniformly and steadily employed whenever the occasion recurs.
The Reviewer's expressions are more lively and figurative, and such
as well become an occasional composition; but hardly such as could
be systematically applied to the subject in a regular treatise. We
could not, as a standard and technical phrase, talk of filling up
the intervals of observation with the same ideal substance of truth;
and the inevitable impulse to generalize would hardly sufficiently
express that we generalize according to a certain idea, namely, the
idea of space. Perhaps that which is suggested to us as the common
import of the two sets of expressions may be conveyed by some other
phrase, in a manner free from the objections which lie against both the
Author's and the Critic's terms. Perhaps the mental idea governing
our experience, and the irresistible impulse to generalize our
observation, may both be superseded by our speaking of a law of the
mind's _activity_, which is really implied in both. There operates, in
observing the external world, a law of the mind's activity, by which it
connects its observations; and this law of the mind's activity may be
spoken of either as the idea of space, or as the irresistible impulse
to generalize the relations of space which it observes. And this
expression--_the laws of the mind's activity_--thus opposed to that
merely passive function by which the mind receives the impressions of
sense, may be applied to other ideas as well as to the idea of space,
and to the impulse to generalize in other truths as well as those of
geometry.

So far, it would seem, that the Author and the Critic may be brought
into much nearer agreement than at first seemed likely, with regard
to the grounds of the necessity and universality in our knowledge.
But even if we adopt this conciliatory suggestion, and speak of the
necessity and universality of certain truths as arising from the laws
of the mind's activity, we cannot, without producing great confusion,
allow ourselves to say, as the Critic says, that these truths are thus
derived from _experience_, or from _observation_. It will, I say, be
found fatal to all philosophical precision of thought and language,
to say that the fundamental truths of geometry, the axioms, with the
conviction of their necessary truth, are derived from experience. Let
us take any axiomatic truth of geometry, and ask ourselves if this is
not so.

It is, for example, an axiom in geometry that if a straight line cut
one of two parallel straight lines, it must cut the other also. Is this
truth derived or derivable from observation of actual parallel lines,
and a line cutting them, exhibited to our senses? Let those who say
that we do acquire this truth by observation, imagine to themselves
the mode in which the observation must be made. We have before us two
parallel straight lines, and we see that a straight line which cuts
the one cuts the other also. We see this again in another case, it
may be the angles and the distances being different, and in a third,
and in a fourth; and so on; and generalizing, we are irresistibly
led to believe the assertion to be universally true. But can any one
really imagine this to be the mode in which we arrive at this truth?
"We see," says this explanation, "two parallel straight lines, cut by
a third." But how do we know that the observed lines are parallel?
If we apply any test of parallelism, we must assume some property of
parallels, and thus involve some axiom on the subject, which we have no
more right to assume than the one now under consideration. We should
thus destroy our explanation as an account of the mode of arriving
at independent geometrical axioms. But probably those who would give
such an explanation would not do this. They would not suppose that in
observing this property of parallels we try by measurement whether the
lines are parallel. They would say, I conceive, that we suppose lines
to be parallel, and that then we see that the straight line which cuts
the one must cut the other. That when we make this supposition, we are
persuaded of the truth of the conclusion, is certain. But what I have
to remark is, that this being so, the conclusion is the result, not of
observation, but of the hypothesis. The geometrical truth here spoken
of, after this admission, no longer flows from experience, but from
supposition. It is not that we _ascertain_ the lines to be parallel,
and then _find_ that they have this property: but we _suppose_ the
lines to be parallel, and _therefore_ they have this property. This is
not a truth of experience.

This, it may be said, is so evident that it cannot have been overlooked
by a very acute reasoner, such as you describe your Critic to be.
What, it may be asked, is the answer which he gives to so palpable an
objection as this? How does he understand his assertion that we learn
the truth of geometrical axioms from experience (p. 208), so as to make
it tenable on his own principles? What account does he give of the
origin of such axioms which makes them in any sense to be derived from
experience?

In justice to the Reviewer's fairness (which is unimpeachable
throughout his argumentation) it must be stated that he does give an
account in which he professes to show how this is done. And the main
step of his explanation consists in introducing the conception of
_direction_, and _unity of direction_. He says (p. 208), "The _unity of
direction_, or that we cannot march from a given point by more than one
path _direct to the same object_, is a matter of practical experience,
long before it can by possibility become matter of abstract thought."
We might ask here, as in the former case, how this can be a matter of
experience, except we have some independent test of directness? and we
might demand to know what this test is. Or do we not rather, here as
in the other case, _suppose_ the directness of the path; and is not
the singleness of the direct path a consequence, not of its observed
form, but of its hypothetical directness; and thus by no means a
result of experience? But we may put our remark upon this deduction
of the geometrical axiom in another form. We generalize, it is said,
the observations which we have made ever since we were born. But this
term "generalize" is far too vague to pass for an explanation, without
being itself explained. We are impelled to believe that to be true in
general which we see to be true in particular. But how do we see any
truth? How do we pick out any proposition with respect to a diagram
which we see before us? We see in particular, and state in general,
some truth respecting straight lines, or parallel lines, or concerning
direction. But where do we find the conception of straightness, or
parallelism, or direction? These conceptions are not upon the surface
of things. The child does not, from his birth, see straightness
and parallelism so as to know that he sees them. How then does his
experience bear upon a proposition in which these conceptions are
involved? It is said that it is a matter of experience long before it
is a matter of abstract thought. But how can there be any experience
by which we learn these properties of a straight line, till our
thoughts are at least so abstract as to conceive what straightness is?
If it be said that this conception grows with our experience, and is
gradually unfolded with our unfolding materials of knowledge, so as
to give import and significance to them: I need make no objection to
such a statement, except this--that this power of unfolding out of the
mind conceptions which give meaning to our experience, is something
in addition to the mere employment of our senses upon the external
world. It is what I have called the ideal part of our knowledge. It
implies, not only an impulse to generalize from experience, but also
an impulse to form conceptions by which generalization is possible. It
requires, not only that nothing should oppose the tendency, but that
the direction in which the tendency is to operate should be determined
by the laws of the mind's activity; by an internal, not by an external
agency.

One main ground on which the Reviewer is disposed to quarrel with and
reject several of the expressions used in the _Philosophy_;--such as
that space is an idea, a form of our perception, and the like,--is
this; that such expressions appear to deprive the external world of its
reality; to make it, or at least most of its properties, a creation of
the observing mind. He quotes the following argument which is urged in
the _Philosophy_, in order to prove that space is not a notion obtained
from experience: "Experience gives us information concerning things
without us, but our apprehending them as without us takes for granted
their existence in space. Experience acquaints us with the form,
position, magnitude, &c. of particular objects, but that they _have_
form, position, magnitude, pre-supposes that they are in space." From
this statement he altogether dissents. No, says he, "the reason why we
apprehend things as without us is that they _are_ without us. We take
for granted that they exist in space, because they _do_ so exist, and
because such their existence is a matter of direct perception, which
can neither be explained in words nor contravened in imagination:
because, in short, space is a _reality_, and not a mere matter of
convention or imagination."

Now, if by calling space an idea, we suggest any doubt of its reality
and of the reality of the external world, we certainly run the risk
of misleading our readers; for the external world is real if anything
be real: the bodies which exist in space are things, if things are
anywhere to be found. That bodies do exist in space, and that _that_ is
the reason why we apprehend them as existing in space, I readily grant.
But I conceive that the term Idea ought not to suggest any such doubt
of the reality of the knowledge in which it is involved. Ideas are
always, in our knowledge, conjoined with facts. Our real knowledge is
knowledge, because it involves ideas, real, because it involves facts.
We apprehend things as existing in space because they do so exist: and
our idea of space enables us so to observe them, and so to conceive
them.

But we want, further, a reason why, apprehending them as they are, we
also apprehend, that in certain relations they could not be otherwise
(that two straight linear objects could not inclose a space, for
instance). This circumstance is no way accounted for by saying that we
apprehend them as they are; and is, I presume to say, inexplicable,
except by supposing that it arises from some property of the observing
mind:--an Idea, as I have termed it,--an irresistible Impulse to
generalize, as the Reviewer expresses it. Or, as I have suggested, we
may adopt a third phrase, a Law of the mind's activity: and in order
that no question may remain, whether we ascribe reality to the objects
and relations which we observe, we may describe it as "a Law of the
mind's activity in apprehending what is." And thus the real existence
of the object, and the ideal element which our apprehension of it
introduces, would both be clearly asserted.

I am ready to use expressions which recognize the reality of space
and other external things more emphatically than those expressions
which I have employed in the _Philosophy_, if expressions can be
found which, while they do this, enable us to explain the possibility
of knowledge, and to analyze the structure of truth. It is, indeed,
extremely difficult to find, in speaking of this subject, expressions
which are satisfactory. The reality of the objects which we perceive
is a profound, apparently an insoluble problem[352]. We cannot but
suppose that existence is something different from our knowledge of
existence:--that which exists, does not exist merely in our knowing
that it does:--truth is truth whether we know it or not. Yet how can we
conceive truth, otherwise than as something known? How can we conceive
things as existing, without conceiving them as objects of perception?
Ideas and Things are constantly opposed, yet necessarily co-existent.
How they are thus opposite and yet identical, is the ultimate problem
of all philosophy. The successive phases of philosophy have consisted
in separating and again uniting these two opposite elements; in
dwelling sometimes upon the one and sometimes upon the other, as the
principal or original or only element; and then in discovering that
such an account of the state of the case was insufficient. Knowledge
requires ideas. Reality requires things. Ideas and things co-exist.
Truth _is_, and is known. But the complete explanation of these points
appears to be beyond our reach. At least it is not necessary for the
purposes of our philosophy. The separation of ideas and sensations
in order to discover the conditions of knowledge is our main task.
How ideas and sensations are united so as to form things, does not so
immediately concern us.

I have stated that we may, without giving up any material portion
of the Philosophy of Science to which I have been led, express the
conclusions in other phraseology; and that instead of saying that all
our knowledge involves certain Fundamental Ideas, the sources from
which all universal truth is derived, we may say that there are certain
Laws of Mental Activity according to which alone all the real relations
of things are apprehended. If this alteration in the phraseology will
make the doctrines more generally intelligible or acceptable, there is
no reason why it should not be adopted. But I may remark, that a main
purpose of the _Philosophy_ was not merely to prove that there _are_
such Fundamental Ideas or Laws of mental activity, but to enumerate
those of them which are involved in the existing sciences; and to state
the fundamental truths to which the fundamental ideas lead. This was
the task which was attempted; and if this have been executed with any
tolerable success, it may perhaps be received as a contribution to the
philosophy of science, of which the value is not small, in whatever
terms it be expressed. And this enumeration of fundamental ideas, and
of truths derived from them, must have something to correspond to it,
in any other mode of expressing that view of the nature of knowledge
which we are led to adopt. If instead of _Fundamental Ideas_, we speak
of Impulses of generalization, or of _Laws of mental activity_, we
must still distinguish such Impulses, or such Laws, according to the
distinctions of ideas to which the survey of science led us. We shall
thus have a series of groups of Laws, or of classes of generalizing
Impulses, corresponding to the series of Fundamental Ideas already
given. If we employ the language of the Reviewer, we shall have one
generalizing Impulse which suggests relations of Space; another which
directs us to properties of Numbers; another which deals with Time;
another with Cause: another which groups objects according to Likeness;
another which suggests a purpose as a necessary relation among
them; to which may be added, even while we confine ourselves to the
physical sciences, several others, as may be seen in the _Philosophy_.
Now when the fundamental conditions and elements of truth are thus
arranged into groups, it is not a matter of so much consequence to
decide whether each group shall be said to be bound together by an
idea or by an impulse of generalization; as it is to see that, if
this happen in virtue of ideas, here are so many distinct ideas which
enter into the structure of science, and give universality to its
matter; and again, if this happen in virtue of an irresistible impulse
of generalization in each case, we have so many different kinds of
impulses of generalization. The main purpose in the _Philosophy_ was to
analyze scientific truth into its conditions and elements; and I did
not content myself with saying that those elements are Sensations and
Ideas; the Ideas being that element which makes universal knowledge
conceivable and possible. I went further: I enumerated the Ideas
which thus enter into science. I showed that in the sciences which
I passed in review, the most acute and profound inquirers had taken
for granted that certain truths in each science are of universal and
necessary validity, and I endeavoured to select the idea in which this
universality and necessity resided, and to separate it from all other
ideas involved in other sciences. If therefore it be thought better
to say that those principles in each science upon which, as upon the
axioms in geometry, the universality and necessity of scientific truth
depends, are arrived at, not by ideas, but by an irresistible impulse
of generalization, those who employ such phraseology, if they make a
classification of such impulses corresponding to my classification of
ideas, will still adopt the greater part of my philosophy, altering
only the phraseology. Or if, as I suggested, instead of "Fundamental
Ideas," we use the phrase "Laws of Mental Activity," then our primary
intellectual Code--the Constitution of our minds, as it may be
termed--will consist of a Body of Laws of which the Titles correspond
with the Fundamental Ideas of the _Philosophy_.

My object was, from the writings of the most sagacious and profound
philosophers who have laboured on each science, to extract such a
code, such a constitution. If I have in any degree succeeded in this,
the result must have a reality and a value independently of all forms
of expression. Still I do not think that any language can ever serve
for such legislation, in which the two elements of truth are not
distinguished. Even if we adopt the phraseology which I have just
employed, we shall have to recollect that Law and Fact must be kept
distinct, and that the Constitution has its Principles as well as its
History.

But I will not longer detain you by seeking other modes of expressing
the Fundamental Antithesis to which the accompanying Memoir refers.
The Remarks which I here send you were written three years ago, on the
appearance of the Review which I have quoted. If I succeed in obtaining
for them a few minutes' attention from you and a few other friends, I
shall be glad that they have been preserved.

  I am, my dear Herschel,
  always truly yours,
  W. WHEWELL.

P.S. I have abstained from sending you a large portion of my Remarks
as originally written. I had gone on to show that, in my _Philosophy_,
I had not only enumerated and analyzed a great number of different
Fundamental Ideas which belong to the different existing sciences,
but that I had also shown in what manner these ideas enter into their
respective sciences; namely, by the statement or use of Axioms, which
involve the ideas, and which form the basis of each science when
systematically exhibited. A number of these Axioms belonging to most
of the physical sciences, are stated in the _Philosophy_. I might have
added also that I have attempted to classify the historical steps
by which such Axioms are brought into view and applied. But it is
not necessary to dwell upon these points, in order to illustrate the
difference and the agreement between the Reviewer and me.

  _Sir John F. W. Herschel, Bart. &c._


APPENDIX G.

ON THE TRANSFORMATION OF HYPOTHESES IN THE HISTORY OF SCIENCE.

(_Cam. Phil. Soc._ MAY 19, 1851.)


1. The history of science suggests the reflection that it is very
difficult for the same person at the same time to do justice to two
conflicting theories. Take for example the Cartesian hypothesis of
vortices and the Newtonian doctrine of universal gravitation. The
adherents of the earlier opinion resisted the evidence of the Newtonian
theory with a degree of obstinacy and captiousness which now appears
to us quite marvellous: while on the other hand, since the complete
triumph of the Newtonians, _they_ have been unwilling to allow any
merit at all to the doctrine of vortices. It cannot but seem strange,
to a calm observer of such changes, that in a matter which depends
upon mathematical proofs, the whole body of the mathematical world
should pass over, as in this and similar cases they seem to have done,
from an opinion confidently held, to its opposite. No doubt this must
be, in part, ascribed to the lasting effects of education and early
prejudice. The old opinion passes away with the old generation: the new
theory grows to its full vigour when its congenital disciples grow to
be masters. John Bernoulli continues a Cartesian to the last; Daniel,
his son, is a Newtonian from the first. Newton's doctrines are adopted
at once in England, for they are the solution of a problem at which his
contemporaries have been labouring for years. They find no adherents
in France, where Descartes is supposed to have already explained
the constitution of the world; and Fontenelle, the secretary of the
Academy of Sciences at Paris, dies a Cartesian seventy years after
the publication of Newton's _Principia_. This is, no doubt, a part
of the explanation of the pertinacity with which opinions are held,
both before and after a scientific revolution: but this is not the
whole, nor perhaps the most instructive aspect of the subject. There
is another feature in the change, which explains, in some degree, how
it is possible that, in subjects, mainly at least mathematical, and
therefore claiming demonstrative evidence, mathematicians should hold
different and even opposite opinions. And the object of the present
paper is to point out this feature in the successions of theories, and
to illustrate it by some prominent examples drawn from the history of
science.

2. The feature to which I refer is this; that when a prevalent
theory is found to be untenable, and consequently, is succeeded by a
different, or even by an opposite one, the change is not made suddenly,
or completed at once, at least in the minds of the most tenacious
adherents of the earlier doctrine; but is effected by a transformation,
or series of transformations, of the earlier hypothesis, by means of
which it is gradually brought nearer and nearer to the second; and
thus, the defenders of the ancient doctrine are able to go on as if
still asserting their first opinions, and to continue to press their
points of advantage, if they have any, against the new theory. They
borrow, or imitate, and in some way accommodate to their original
hypothesis, the new explanations which the new theory gives, of the
observed facts; and thus they maintain a sort of verbal consistency;
till the original hypothesis becomes inextricably confused, or breaks
down under the weight of the auxiliary hypotheses thus fastened upon
it, in order to make it consistent with the facts.

This often-occurring course of events might be illustrated from the
history of the astronomical theory of epicycles and eccentrics, as
is well known. But my present purpose is to give one or two brief
illustrations of a somewhat similar tendency from other parts of
scientific history; and in the first place, from that part which has
already been referred to, the battle of the Cartesian and Newtonian
systems.

3. The part of the Cartesian system of vortices which is most
familiarly known to general readers is the explanation of the motions
of the planets by supposing them carried round the sun by a kind
of whirlpool of fluid matter in which they are immersed: and the
explanation of the motions of the satellites round their primaries by
similar subordinate whirlpools, turning round the primary, and carried,
along with it, by the primary vortex. But it should be borne in mind
that a part of the Cartesian hypothesis which was considered quite as
important as the cosmical explanation, was the explanation which it
was held to afford of terrestrial gravity. Terrestrial gravity was
asserted to arise from the motion of the vortex of subtle matter which
revolved round the earth's axis and filled the surrounding space. It
was maintained that by the rotation of such a vortex, the particles
of the subtle matter would exert a centrifugal force, and by virtue of
that force, tend to recede from the center: and it was held that all
bodies which were near the earth, and therefore immersed in the vortex,
would be pressed towards the center by the effort of the subtle matter
to recede from the center[353].

These two assumed effects of the Cartesian vortices--to carry bodies
in their stream, as straws are carried round by a whirlpool, and to
press bodies to the center by the centrifugal effort of the whirling
matter--must be considered separately, because they were modified
separately, as the progress of discussion drove the Cartesians from
point to point. The former effect indeed, the _dragging_ force
of the vortex, as we may call it, would not bear working out on
mechanical principles at all; for as soon as the law of motion was
acknowledged (which Descartes himself was one of the loudest in
proclaiming), that a body in motion keeps all the motion which it has,
and receives in addition all that is impressed upon it; as soon, in
short, as philosophers rejected the notion of an inertness in matter
which constantly retards its movements,--it was plain that a planet
perpetually dragged onwards in its orbit by a fluid moving quicker than
itself, must be perpetually accelerated; and therefore could not follow
those constantly-recurring cycles of quicker and slower motion which
the planets exhibit to us.

The Cartesian mathematicians, then, left untouched the calculation of
the progressive motion of the planets; and, clinging to the assumption
that a vortex would produce a tendency of bodies to the center, made
various successive efforts to construct their vortices in such a manner
that the centripetal forces produced by them should coincide with those
which the phenomena required, and therefore of course, in the end, with
those which the Newtonian theory asserted.

In truth, the Cartesian vortex was a bad piece of machinery for
producing a central force: from the first, objections were made to the
sufficiency of its mechanism, and most of these objections were very
unsatisfactorily answered, even granting the additional machinery which
its defenders demanded. One formidable objection was soon started,
and continued to the last to be the torment of the Cartesians. If
terrestrial gravity, it was urged, arise from the centrifugal force of
a vortex which revolves about the earth's axis, terrestrial gravity
ought to act in planes perpendicular to the earth's axis, instead
of tending to the earth's center. This objection was taken by James
Bernoulli[354], and by Huyghens[355] not long after the publication of
Descartes's _Principia_. Huyghens (who adopted the theory of vortices
with modifications of his own) supposes that there are particles of the
fluid matter which move about the earth in every possible direction,
within the spherical space which includes terrestrial objects; and
that the greater part of these motions being in spherical surfaces
concentric with the earth, produces a tendency towards the earth's
center.

This was a procedure tolerably arbitrary, but it was the best which
could be done. Saurin, a little later[356], gave nearly the same
solution of this difficulty. The solution, identifying a vortex of some
kind with a central force, made the hypothesis of vortices applicable
wherever central forces existed; but then, in return, it deprived the
image of a vortex of all that clearness and simplicity which had been
its first great recommendation.

But still there remained difficulties not less formidable. According
to this explanation of gravity, since the tendency of bodies to the
earth's center arose from the superior centrifugal force of the
whirling matter which pushed them inward as water pushes a light body
upward, bodies ought to tend more strongly to the center in proportion
as they are less dense. The rarest bodies should be the heaviest;
contrary to what we find.

Descartes's original solution of this difficulty has a certain degree
of ingenuity. According to him (_Princip._ IV. 23) a terrestrial body
consists of particles of the _third element_, and the more it has
of such particles, the more it excludes the parts of the _celestial
matter_, from the revolution of which matter gravity arises; and
therefore the denser is the terrestrial body, and the heavier it will
be.

But though this might satisfy him, it could not satisfy the
mathematicians who followed him, and tried to reduce his system to
calculation on mechanical principles. For how could they do this,
if the celestial matter, by the operation of which the phenomena
of force and motion were produced, was so entirely different from
ordinary matter, which alone had supplied men with experimental
illustrations of mechanical principles? In order that the celestial
matter, by its whirling, might produce the gravity of heavy bodies,
it was mechanically necessary that it must be very dense; and _dense_
in the ordinary sense of the term; for it was by regarding density in
the ordinary sense of the term that the mechanical necessity had been
established.

The Cartesians tried to escape this result (Huyghens, _Pesanteur_, p.
161, and John Bernoulli, _Nouvelles Pensées_, Art. 31) by saying that
there were two meanings of _density_ and _rarity_; that some fluids
might be rare by having their particles far asunder, others, by having
their particles very small though in contact. But it is difficult to
think that they could, as persons well acquainted with mechanical
principles, satisfy themselves with this distinction; for they could
hardly fail to see that the mechanical effect of any portion of fluid
depends upon the total mass moved, not on the size of its particles.

Attempts made to exemplify the vortices experimentally only showed more
clearly the force of this difficulty. Huyghens had found that certain
bodies immersed in a whirling fluid tended to the center of the vortex.
But when Saulmon[357] a little later made similar experiments, he had
the mortification of finding that the heaviest bodies had the greatest
tendency to recede from the axis of the vortex. "The result is," as
the Secretary of the Academy (Fontenelle) says, "exactly the opposite
of what we could have wished, for the [Cartesian] system of gravity:
but we are not to despair; sometimes in such researches disappointment
leads to ultimate success."

But, passing by this difficulty, and assuming that in some way or
other a centripetal force arises from the centrifugal force of the
vortex, the Cartesian mathematicians were naturally led to calculate
the circumstances of the vortex on mechanical principles; especially
Huyghens, who had successfully studied the subject of centrifugal
force. Accordingly, in his little treatise on the _Cause of
Gravitation_ (p. 143), he calculates the velocity of the fluid matter
of the vortex, and finds that, at a point in the equator, it is 17
times the velocity of the earth's rotation.

It may naturally be asked, how it comes to pass that a stream of fluid,
dense enough to produce the gravity of bodies by its centrifugal force,
moving with a velocity 17 times that of the earth (and therefore
moving round the earth in 85 minutes), does not sweep all terrestrial
objects before it. But to this Huyghens had already replied (p. 137),
that there are particles of the fluid moving _in all directions_, and
therefore that they neutralize each other's action, so far as lateral
motion is concerned.

And thus, as early as this treatise of Huyghens, that is, in three
years from the publication of Newton's _Principia_, a vortex is made
to mean nothing more than some machinery or other for producing a
central force. And this is so much the case, that Huyghens commends
(p. 165), as confirming his own calculation of the velocity of his
vortex, Newton's proof that at the Moon's orbit the centripetal force
is equal to the centrifugal; and that thus, this force is less than the
centripetal force at the earth's surface in the inverse proportion of
the squares of the distances.

John Bernoulli, in the same manner, but with far less clearness
and less candour, has treated the hypothesis of vortices as being
principally a hypothetical cause of central force. He had repeated
occasions given him of propounding his inventions for propping up the
Cartesian doctrine, by the subjects proposed for prizes by the Paris
Academy of Sciences; in which competition Cartesian speculations were
favourably received. Thus the subject of the Prize Essays for 1730
was, the explanation of the Elliptical Form of the planetary orbits
and of the Motion of their Aphelia, and the prize was assigned to
John Bernoulli, who gave the explanation on Cartesian principles. He
explains the elliptical figure, not as Descartes himself had done,
by supposing the vortex which carries the planet round the sun to be
itself squeezed into an elliptical form by the pressure of contiguous
vortices; but he supposes the planet, while it is carried round by the
vortex, to have a limited oscillatory motion to and from the center,
produced by its being originally, not at the distance at which it would
float in equilibrium in the vortex, but above or below that point. On
this supposition, the planet would oscillate to and from the center,
Bernoulli says, like the mercury when deranged in a barometer: and
it is evident that such an oscillation, combined with a motion round
the center, might produce an oval curve, either with a fixed or with
a moveable aphelion. All this however merely amounts to a possibility
that the oval _may_ be an ellipse, not to a proof that it will be so;
nor does Bernoulli advance further.

It was necessary that the vortices should be adjusted in such a manner
as to account for Kepler's laws; and this was to be done by making
the velocity of each stratum of the vortex depend in a suitable
manner on its radius. The Abbé de Molières attempted this on the
supposition of elliptical vortices, but could not reconcile Kepler's
first two laws, of equal elliptical areas in equal times, with his
third law, that the squares of the periodic times are as the cubes
of the mean distances[358]. Bernoulli, with his circular vortices,
could accommodate the velocities at different distances so that they
should explain Kepler's laws. He pretended to prove that Newton's
investigations respecting vortices (in the ninth Section of the Second
Book of the _Principia_) were mechanically erroneous; and in truth,
it must be allowed that, besides several arbitrary assumptions, there
are some errors of reasoning in them. But for the most part, the more
enlightened Cartesians were content to accept Newton's account of the
motions and forces of the solar system as part of their scheme; and to
say only that the hypothesis of vortices explained the origin of the
Newtonian forces; and that thus theirs was a philosophy of a higher
kind. Thus it is asserted (_Mém. Acad._ 1734), that M. de Molières
retains the beautiful theory of Newton entire, only he renders it
in a sort less Newtonian, by disentangling it from attraction, and
transferring it from a vacuum into a plenum. This plenum, though
not its native region, frees it from the need of attraction, which
is all the better for it. These points were the main charms of the
Cartesian doctrine in the eyes of its followers;--the getting rid of
attractions, which were represented as a revival of the Aristotelian
"occult qualities," "substantial forms," or whatever else was the
most disparaging way of describing the bad philosophy of the dark
ages[359];--and the providing some material intermedium, by means of
which a body may affect another at a distance; and thus avoid the
reproach urged against the Newtonians, that they made a body act where
it was not. And we are the less called upon to deny that this last
feature in the Newtonian theory was a difficulty, inasmuch as Newton
himself was never unwilling to allow that gravity might be merely an
effect produced by some ulterior cause.

With such admissions on the two sides, it is plain that the Newtonian
and Cartesian systems would coincide, if the hypothesis of vortices
could be modified in such a way as to produce the force of gravitation.
All attempts to do this, however, failed: and even John Bernoulli,
the most obstinate of the mathematical champions of the vortices,
was obliged to give them up. In his Prize Essay for 1734, (on the
Inclinations of the Planetary Orbits[360],) he says (Art. VIII.), "The
gravitation of the Planets towards the center of the Sun and the weight
of bodies towards the center of the earth has not, for its cause,
either the attraction of M. Newton, or the centrifugal force of the
matter of the vortex according to M. Descartes;" and he then goes on to
assert that these forces are produced by a perpetual torrent of matter
tending to the center on all sides, and carrying all bodies with it.
Such a hypothesis is very difficult to refute. It has been taken up in
more modern times by Le Sage[361], with some modifications; and may be
made to account for the principal facts of the universal gravitation
of matter. The great difficulty in the way of such a hypothesis is,
the overwhelming thought of the whole universe filled with torrents
of an invisible but material and tangible substance, rushing in every
direction in infinitely prolonged straight lines and with immense
velocity. Whence can such matter come, and whither can it go? Where
can be its perpetual and infinitely distant fountain, and where the
ocean into which it pours itself when its infinite course is ended?
A revolving whirlpool is easily conceived and easily supplied; but
the central torrent of Bernoulli, the infinite streams of particles
of Le Sage, are an explanation far more inconceivable than the thing
explained.

But however the hypothesis of vortices, or some hypothesis substituted
for it, was adjusted to explain the facts of attraction to a
center, this was really nearly all that was meant by a vortex or a
"tourbillon," when the system was applied. Thus in the case of the last
act of homage to the Cartesian theory which the French Academy rendered
in the distribution of its prizes, the designation of a Cartesian
Essay in 1741 (along with three Newtonian ones) as worthy of a prize
for an explanation of the Tides; the difference of high and low water
was not explained, as Descartes has explained it, by the pressure, on
the ocean, of the terrestrial vortex, forced into a strait where it
passes under the Moon; but the waters were supposed to rise towards the
Moon, the terrestrial vortex being disturbed and broken by the Moon,
and therefore less effective in forcing them down. And in giving an
account of a Tourmaline from Ceylon (Acad. Sc. 1717), when it has been
ascertained that it attracts and repels substances, the writer adds, as
a matter of course, "It would seem that it has a vortex." As another
example, the elasticity of a body was ascribed to vortices between its
particles: and in general, as I have said, a vortex implied what we now
imply by speaking of a central force.

4. In the same manner vortices were ascribed to the Magnet, in order
to account for its attractions and repulsions. But we may note a
circumstance which gave a special turn to the hypothesis of vortices as
applied to this subject, and which may serve as a further illustration
of the manner in which a transition may be made from one to the other
of two rival hypotheses.

If iron filings be brought near a magnet, in such a manner as to be
at liberty to assume the position which its polar action assigns to
them; (for instance, by strewing them upon a sheet of paper while
the two poles of the magnet are close below the paper;) they will
arrange themselves in certain curves, each proceeding from the N. to
the S. pole of the magnet, like the meridians in a map of the globe.
It is easily shown, on the supposition of magnetic attraction and
repulsion, that these _magnetic curves_, as they are termed, are each
a curve whose tangent at every point is the direction of a small line
or particle, as determined by the attraction and repulsion of the two
poles. But if we suppose a _magnetic vortex_ constantly to flow out
of one pole and into the other, in streams which follow such curves,
it is evident that such a vortex, being supposed to exercise material
pressure and impulse, would arrange the iron filings in corresponding
streams, and would thus produce the phenomenon which I have described.
And the hypothesis of _central torrents_ of Bernoulli or Le Sage which
I have referred to, would, in its application to magnets, really become
this hypothesis of a magnetic vortex, if we further suppose that the
matter of the torrents which proceed to one pole and from the other,
mingles its streams, so as at each point to produce a stream in the
resulting direction. Of course we shall have to suppose two sets of
magnetic torrents;--a boreal torrent, proceeding to the north pole,
and from the south pole of a magnet; and an austral torrent proceeding
to the south and from the north pole:--and with these suppositions,
we make a transition from the hypothesis of attraction and repulsion,
to the Cartesian hypothesis of vortices, or at least, torrents, which
determine bodies to their magnetic positions by impulse.

Of course it is to be expected that, in this as in the other case,
when we follow the hypothesis of impulse into detail, it will need to
be loaded with so many subsidiary hypotheses, in order to accommodate
it to the phenomena, that it will no longer seem tenable. But the
plausibility of the hypothesis in its first application cannot be
denied:--for, it may be observed, the two _opposite_ streams would
counteract each other so as to produce no local _motion_, only
_direction_. And this case may put us on our guard against other
suggestions of forces acting in curve lines, which may at first sight
appear to be discerned in magnetic and electric phenomena. Probably
such curve lines will all be found to be only resulting lines, arising
from the direct action and combination of elementary attraction and
repulsion.

5. There is another case in which it would not be difficult to devise
a mode of transition from one to the other of two rival theories;
namely, in the case of the emission theory and the undulation theory
of Light. Indeed several steps of such a transition have already
appeared in the history of optical speculation; and the conclusive
objection to the emission theory of light, as to the Cartesian theory
of vortices, is, that no amount of additional hypotheses will reconcile
it to the phenomena. Its defenders had to go on adding one piece of
machinery after another, as new classes of facts came into view, till
it became more complex and unmechanical than the theory of epicycles
and eccentrics at its worst period. Otherwise, as I have said, there
was nothing to prevent the emission theory from migrating into the
undulatory theory, and as the theory of vortices did into the theory
of attraction. For the emissionists allow that rays may _interfere_;
and that these interferences may be modified by alternate _fits_ in the
rays; now these fits are already a kind of _undulation_. Then again the
phenomena of polarized light show that the fits or undulations must
have a _transverse_ character: and there is no reason why emitted rays
should not be subject to _fits_ of _transverse_ modification as well
as to any other fits. In short, we may add to the emitted rays of the
one theory, all the properties which belong to the undulations of the
other, and thus account for all the phenomena on the emission theory;
with this limitation only, that the emission will have no share in the
explanation, and the undulations will have the whole. If, instead of
conceiving the universe full of a _stationary_ ether, we suppose it
to be full of etherial particles moving in every direction; and if we
suppose, in the one case and in the other, this ether to be susceptible
of undulations proceeding from every luminous point; the results of the
two hypotheses will be the same; and all we shall have to say is, that
the supposition of the emissive motion of the particles is superfluous
and useless.

6. This view of the manner in which rival theories pass into one
another appears to be so unfamiliar to those who have only slightly
attended to the history of science, that I have thought it might be
worth while to illustrate it by a few examples.

It might be said, for instance, by such persons[362], "Either the
planets are not moved by vortices, or they do not move by the law by
which heavy bodies fall. It is impossible that both opinions can be
true." But it appears, by what has been said above, that the Cartesians
did hold both opinions to be true; and one with just as much reason as
the other, on their assumptions. It might be said in the same manner,
"Either it is false that the planets are made to describe their orbits
by the above quasi-Cartesian theory of Bernoulli, or it is false that
they obey the Newtonian theory of gravitation." But this would be
said quite erroneously; for if the hypothesis of Bernoulli be true,
it is so because it agrees in its result with the theory of Newton.
It is not only possible that both opinions may be true, but it is
certain that if the first be so, the second is. It might be said again,
"Either the planets describe their orbits by an inherent virtue, or
according to the Newton theory." But this again would be erroneous,
for the Newtonian doctrine decided nothing as to whether the force of
gravitation was inherent or not. Cotes held that it was, though Newton
strongly protested against being supposed to hold such an opinion.
The word _inherent_ is no part of the physical theory, and will be
asserted or denied according to our metaphysical views of the essential
attributes of matter and force.

Of course, the possibility of two rival hypotheses being true, one
of which takes the explanation a step higher than the other, is
not affected by the impossibility of two contradictory assertions
of the _same order_ of generality being both true. If there be a
new-discovered comet, and if one astronomer asserts that it will return
once in _every_ twenty years, and another, that it will return once in
every thirty years, both cannot be right. But if an astronomer says
that though its interval was in the last instance 30 years, it will
only be 20 years to the next return, in consequence of perturbation and
resistance, he may be perfectly right.

And thus, when different and rival explanations of the same phenomena
are held, till one of them, though long defended by ingenious men, is
at last driven out of the field by the pressure of facts, the defeated
hypothesis is transformed before it is extinguished. Before it has
disappeared, it has been modified so as to have all palpable falsities
squeezed out of it, and subsidiary provisions added, in order to
reconcile it with the phenomena. It has, in short, been penetrated,
infiltrated, and metamorphosed by the surrounding medium of truth,
before the merely arbitrary and erroneous residuum has been finally
ejected out of the body of permanent and certain knowledge.


FOOTNOTES:

[Footnote 352: These remarks were written in 1841. The accompanying
Memoir contains a further discussion of this problem.]


APPENDIX H.

ON HEGEL'S CRITICISM OF NEWTON'S PRINCIPIA.

(_Cam. Phil. Soc._ MAY 21, 1849.)


The Newtonian doctrine of universal gravitation, as the cause of
the motions which take place in the solar system, is so entirely
established in our minds, and the fallacy of all the ordinary arguments
against it is so clearly understood among us, that it would undoubtedly
be deemed a waste of time to argue such questions in this place, so far
as physical truth is concerned. But since in other parts of Europe,
there are teachers of philosophy whose reputation and influence are
very great, and who are sometimes referred to among our own countrymen
as the authors of new and valuable views of truth, and who yet reject
the Newtonian opinions, and deny the validity of the proofs commonly
given of them, it may be worth while to attend for a few minutes to the
declarations of such teachers, as a feature in the present condition
of European philosophy. I the more readily assume that the Cambridge
Philosophical Society will not think a communication on such a subject
devoid of interest, in consequence of the favourable reception which it
has given to philosophical speculations still more abstract, which I
have on previous occasions offered to it. I will therefore proceed to
make some remarks on the opinions concerning the Newtonian doctrine of
gravitation, delivered by the celebrated Hegel, of Berlin, than whom no
philosopher in modern, and perhaps hardly any even in ancient times,
has had his teaching received with more reverential submission by his
disciples, or been followed by a more numerous and zealous band of
scholars bent upon diffusing and applying his principles.

The passages to which I shall principally refer are taken from one of
his works which is called the _Encyclopædia_ (Encyklopädie), of which
the First Part is _the Science of Logic_, the Second, the _Philosophy
of Nature_, the Third, the _Philosophy of Spirit_. The Second Part,
with which I am here concerned, has for an _aliter_ title, _Lectures
on Natural Philosophy_ (Vorlesungen über Natur-philosophie), and would
through its whole extent offer abundant material for criticism, by
referring it to principles with which we are here familiar: but I
shall for the present confine myself to that part which refers to the
subject which I have mentioned, the Newtonian Doctrine of Gravitation,
§ 269, 270, of the work. Nor shall I, with regard to this part, think
it necessary to give a continuous and complete criticism of all the
passages bearing upon the subject; but only such specimens, and such
remarks thereon, as may suffice to show in a general manner the value
and the character of Hegel's declarations on such questions. I do not
pretend to offer here any opinion upon the value and character of
Hegel's philosophy in general: but I think it not unlikely that some
impression on that head may be suggested by the examination, here
offered, of some points in which we can have no doubt where the truth
lies; and I am not at all persuaded that a like examination of many
other parts of the Hegelian _Encyclopædia_, would not confirm the
impression which we shall receive from the parts now to be considered.

Hegel both criticises the Newtonian doctrines, or what he states as
such; and also, not denying the truth of the laws of phenomena which he
refers to, for instance Kepler's laws, offers his own proof of these
laws. I shall make a few brief remarks on each of these portions of the
pages before me. And I would beg it to be understood that where I may
happen to put my remarks in a short, and what may seem a peremptory
form, I do so for the sake of saving time; knowing that among us, upon
subjects so familiar, a few words will suffice. For the same reason, I
shall take passages from Hegel, not in the order in which they occur,
but in the order in which they best illustrate what I have to say. I
shall do Hegel no injustice by this mode of proceeding: for I will
annex a faithful translation, so far as I can make one, of the whole of
the passages referred to, with the context.

No one will be surprised that a German, or indeed any lover of science,
should speak with admiration of the discovery of Kepler's laws, as a
great event in the history of Astronomy, and a glorious distinction to
the discoverer. But to say that the glory of the discovery of the proof
of these laws has been unjustly transferred from Kepler to Newton, is
quite another matter. This is what Hegel says (_a_)[363]. And we have
to consider the reasons which he assigns for saying so.

He says (_b_) that "it is allowed by mathematicians that the Newtonian
Formula maybe derived from the Keplerian laws," and hence he seems to
infer that the Newtonian law is not an additional truth. That is, he
does not allow that the discovery of the cause which produces a certain
phenomenal law is anything additional to the discovery of the law
itself.

"The Newtonian formula may be derived from the Keplerian law." It was
professedly so derived; but derived by introducing the Idea of _Force_,
which Idea and its consequences were not introduced and developed till
after Kepler's time.

"The Newtonian formula may be derived from the Keplerian law." And the
Keplerian law may be derived, and was derived, from the observations of
the Greek astronomers and their successors; but was not the less a new
and great discovery on that account.

But let us see what he says further of this derivation of the Newtonian
"formula" from the Keplerian Law. It is evident that by calling it a
_formula_, he means to imply, what he also asserts, that it is no new
law, but only a new form (and a bad one) of a previously known truth.

How is the Newtonian "formula," that is, the law of the inverse squares
of the central force, derived from the Keplerian law of the cubes of
the distances proportional to the squares of the times? This, says
Hegel, is the "immediate derivation." (_c_).--By Kepler's law, _A_
being the distance and _T_ the periodic time, _A_^3/_T_^2 is constant.
But Newton _calls_ _A_/_T_^2 universal gravitation; whence it easily
follows that gravitation is inversely as _A_^2.

This is Hegel's way of representing Newton's proof. Reading it, any one
who had never read the _Principia_ might suppose that Newton _defined_
gravitation to be _A_/_T_^2. We, who have read the _Principia_, know
that Newton _proves_ that in circles, the _central force_ (not the
_universal gravitation_) is as _A_/_T_^2: that he proves this, by
setting out from the idea of force, as that which deflects a body from
the tangent, and makes it describe a curved line: and that in this way,
he passes from Kepler's laws of mere motion to his own law of Force.

But Hegel does not see any value in this. Such a mode of treating the
subject he says (_i_) "offers to us a tangled web, formed of the Lines
of the mere geometrical construction, to which a physical meaning of
independent forces is given." That a _measure_ of forces is _found_ in
such lines as the sagitta of the arc described in a given time, (not
such a _meaning_ arbitrarily _given_ to them,) is certainly true, and
is very distinctly proved in Newton, and in all our elementary books.

But, says Hegel, as further showing the artificial nature of the
Newtonian formulæ, (_h_) "Analysis has long been able to derive the
Newtonian expression and the laws therewith connected out of the Form
of the Keplerian Laws;" an assertion, to verify which he refers to
Francœur's _Mécanique_. This is apparently in order to show that the
"lines" of the Newtonian construction are superfluous. We know very
well that analysis does not always refer to visible representations of
such lines: but we know too, (and Francœur would testify to this also,)
that the analytical proofs contain equivalents to the Newtonian lines.
We, in this place, are too familiar with the substitution of analytical
for geometrical proofs, to be led to suppose that such a substitution
affects the substance of the truth proved. The conversion of Newton's
geometrical proofs of his discoveries into analytical processes by
succeeding writers, has not made them cease to be discoveries: and
accordingly, those who have taken the most prominent share in such a
conversion, have been the most ardent admirers of Newton's genius and
good fortune.

So much for Newton's comparison of the Forces in different circular
orbits, and for Hegel's power of understanding and criticising it. Now
let us look at the motion in different parts of the same elliptical
orbit, as a further illustration of the value of Hegel's criticism. In
an elliptical orbit the velocity alternately increases and diminishes.
This follows necessarily from Kepler's law of the equal description
of the areas, and so Newton explains it. Hegel, however, treats of
this acceleration and retardation as a separate fact, and talks of
another explanation of it, founded upon Centripetal and Centrifugal
Force (_o_). Where he finds this explanation, I know not; certainly
not in Newton, who in the second and third section of the _Principia_
explains the variation of the velocity in a quite different manner, as
I have said; and nowhere, I think, employs centrifugal force in his
explanations. However, the notion of centrifugal as acting along with
centripetal force is introduced in some treatises, and may undoubtedly
be used with perfect truth and propriety. How far Hegel can judge
when it is so used, we may see from what he says of the confusion
produced by such an explanation, which is, he says, a maximum. In the
first place, he speaks of the motion being _uniformly_ accelerated and
retarded in an elliptical orbit, which, in any exact use of the word
_uniformly_, it is not. But passing by this, he proceeds to criticise
an explanation, not of the variable velocity of the body in its orbit,
but of the alternate access and recess of the body to and from the
center. Let us overlook this confusion also, and see what is the value
of his criticism on the explanation. He says (_p_), "according to
this explanation, in the motion of a planet from the aphelion to the
perihelion, the centrifugal is less than the centripetal force; and
in the perihelion itself the centripetal force is supposed suddenly
to become greater than the centrifugal;" and so, of course, the body
re-ascends to the aphelion.

Now I will not say that this explanation has never been given in a book
professing to be scientific; but I have never seen it given; and it
never can have been given but by a very ignorant and foolish person.
It goes upon the utterly unmechanical supposition that the approach
of a body to the center at any moment depends solely upon the excess
of the centripetal over the centrifugal force; and reversely. But the
most elementary knowledge of mechanics shows us that when a body is
moving _obliquely_ to the distance from the center, it approaches to
or recedes from the center in virtue of this obliquity, even if no
force at all act. And the total approach to the center is the approach
due to this cause, _plus_ the approach due to the centripetal force,
_minus_ the recess due to the centrifugal force. At the aphelion, the
centripetal is greater than the centrifugal force; and _hence_ the
motion becomes oblique; and _then_, the body approaches to the center
on _both_ accounts, and approaches on account of the obliquity of the
path even when the centrifugal has become greater than the centripetal
force, which it becomes before the body reaches the perihelion. This
reasoning is so elementary, that when a person who cannot see this,
writes on the subject with an air of authority, I do not see what can
be done but to point out the oversight and leave it.

But there is, says Hegel (_q_), another way of explaining the motion
by means of centripetal and centrifugal forces. The two forces are
supposed to increase and decrease gradually, according to different
laws. In this case, there must be a point where they are equal, and in
equilibrio; and this being the case, they will always continue equal,
for there will be no reason for their going out of equilibrium.

This, which is put as _another_ mode of explanation, is, in fact, the
same mode; for, as I have already said, the centrifugal force, which is
less than the centripetal at the aphelion, becomes the greater of the
two before the perihelion; and there is an intermediate position, at
which the two forces are equal. But at this point, is there no reason
why, being equal, the forces should become unequal? Reason abundant:
for the body, being there, moves in a line oblique to the distance, and
so changes its distance; and the centripetal and centrifugal force,
depending upon the distance by different laws, they forthwith become
unequal.

But these modes of explanation, by means of the centripetal and
centrifugal forces and their relation, are not necessary to Newton's
doctrine, and are nowhere used by Newton; and undoubtedly much
confusion has been produced in other minds, as well as Hegel's,
by speaking of the centrifugal force, which is a mere intrinsic
geometrical result of a body's curvilinear motion round a center, in
conjunction with centripetal force, which is an extrinsic force, acting
upon the body and urging it to the center. Neither Newton, nor any
intelligent Newtonian, ever spoke of the centripetal and centrifugal
force as two distinct forces both extrinsic to the motion, which Hegel
accuses them of doing. (_n_)

I have spoken of the third and second of Kepler's laws; of Newton's
explanations of them, and of Hegel's criticism. Let us now, in the same
manner, consider the first law, that the planets move in ellipses.
Newton's proof that this was the result of a central force varying
inversely as the square of the distance, was the solution of a problem
at which his contemporaries had laboured in vain, and is commonly
looked upon as an important step. "But," says Hegel, (_d_) "the proof
gives a conic section generally, whereas the main point which ought
to be proved is, that the path of the body is an ellipse only, not a
circle or any other conic section." Certainly if Newton _had_ proved
that a planet cannot move in a circle, (which Hegel says he ought to
have done), his system would have perplexed astronomers, since there
are planets which move in orbits hardly distinguishable from circles,
and the variation of the extremity from planet to planet shows that
there is nothing to prevent the excentricity vanishing and the orbit
becoming a circle.

"But," says Hegel again, (_e_) "the conditions which make the path to
be an ellipse rather than any other conic section, are empirical and
extraneous;--the supposed casual strength of the impulsion originally
received." Certainly the circumstances which determine the amount
of excentricity of a planet's orbit are derived from experience, or
rather, observation. It is not a part of Newton's system to determine
_à priori_ what the excentricity of a planet's orbit must be. A system
that professes to do this will undoubtedly be one very different
from his. And as our knowledge of the excentricity is derived from
observation, it is, in that sense, empirical and casual. The strength
of the original impulsion is a hypothetical and impartial way of
expressing this result of observation. And as we see no reason why the
excentricity should be of any certain magnitude, we see none why the
fraction which expresses the excentricity should not become as large
as unity, that is, why the orbit should not become a parabola; and
accordingly, some of the bodies which revolve about the same appear to
move in orbits of this form: so little is the motion in an ellipse, as
Hegel says, (_f_) "the only thing to be proved."

But Hegel himself has offered proof of Kepler's laws, to which,
considering his objections to Newton's proofs, we cannot help turning
with some curiosity.

And first, let us look at the proof of the Proposition which we have
been considering, that the path of a planet is necessarily an ellipse.
I will translate Hegel's language as well as I can; but without
answering for the correctness of my translation, since it does not
appear to me to conform to the first condition of translation, of
being intelligible. The translation however, such as it is, may help
us to form some opinion of the validity and value of Hegel's proofs as
compared with Newton's. (_r_)

"For absolutely uniform motion, the circle is the only path.... The
circle is the line returning into itself in which all the radii are
equal; there is, for it, only one determining quantity, the radius.

"But in free motion, the determination according to space and to
time come into view with differences. There must be a difference in
the spatial aspect in itself, and therefore the form requires two
determining quantities. Hence the form of the path returning into
itself is an ellipse."

Now even if we could regard this as reasoning, the conclusion does
not in the smallest degree follow. A curve returning into itself and
determined by two quantities, may have innumerable forms besides the
ellipse; for instance, any _oval_ form whatever, besides that of the
conic section.

But why must the curve be a curve returning into itself? Hegel has
professed to prove this previously (_m_) from "the determination of
particularity and individuality of the bodies in general, so that
they have partly a center in themselves, and partly at the same time
their center in another." Without seeking to find any precise meaning
in this, we may ask whether it proves the impossibility of the orbits
with moveable apses, (which do not return into themselves,) such as the
planets (affected by perturbations) really do describe, and such as
we know that bodies must describe in all cases, except when the force
varies exactly as the square of the distance? It appears to do so:
and it proves this impossibility of known facts at least as much as it
proves anything.

Let us now look at Hegel's proof of Kepler's second law, that the
elliptical sectors swept by the radius vector are proportional to the
time. It is this: (_s_).

"In the circle, the arc or angle which is included by the two radii is
independent of them. But in the motion [of a planet] as determined by
the conception, the distance from the center and the arc run over in a
certain time must be compounded in one determination, and must make out
a whole. This whole is the sector, a space of two dimensions. And hence
the arc is essentially a Function of the radius vector; and the former
(the arc) being unequal, brings with it the inequality of the radii."

As was said in the former case, if we could regard this as reasoning,
it would not prove the conclusion, but only, that the arc is _some
function or other_ of the radii.

Hegel indeed offers (_t_) a reason why there must be an arc involved.
This arises, he says, from "the determinateness [of the nature of
motion], at one while as time in the root, at another while as space in
the square. But here the quadratic character of the space is, by the
returning of the line of motion into itself, limited to a sector."

Probably my readers have had a sufficient specimen of Hegel's mode of
dealing with these matters. I will however add his proof of Kepler's
third law, that the cubes of the distances are as the squares of the
times.

Hegel's proof in this case (_u_) has a reference to a previous doctrine
concerning falling bodies, in which time and space have, he says, a
relation to each other as root and square. Falling bodies however
are the case of only _half-free_ motion, and the determination is
incomplete.

"But in the case of absolute motion, the domain of _free_ masses, the
determination attains its totality. The time as the root is a mere
empirical magnitude: but as a component of the developed Totality,
it is a Totality in itself: it produces itself, and therein has a
reference to itself. And in this process, Time, being itself the
dimensionless element, only comes to a formal identity with itself and
reaches the square: Space, on the other hand, as a positive external
relation, comes to the full dimensions of the conception of space,
that is, the cube. The Realization of the two conceptions (space and
time) preserves their original difference. This is the third Keplerian
law, the relation of the Cubes of the distances to the squares of the
times."

"And this," he adds, (_v_) with remarkable complacency, "represents
simply and immediately _the reason of the thing_:--while on the
contrary, the Newtonian Formula, by means of which the Law is changed
into a Law for the Force of Gravity, shows the distortion and inversion
of _Reflexion_, which stops half-way."

I am not able to assign any precise meaning to the _Reflexion_, which
is here used as a term of condemnation, applicable especially to the
Newtonian doctrine. It is repeatedly applied in the same manner by
Hegel. Thus he says, (_g_) "that what Kepler expresses in a simple and
sublime manner in the form of Laws of the Celestial Motions, Newton has
metamorphosed into the _Reflexion-Form_ of the Force of Gravitation."

Though Hegel thus denies Newton all merit with regard to the
explanation of Kepler's laws by means of the gravitation of the
planets to the sun, he allows that to the Keplerian Laws Newton added
the Principle of Perturbations (_k_). This Principle he accepts to a
certain extent, transforming the expression of it after his peculiar
fashion. "It lies," he says, (_l_) "in this: that matter in general
assigns a center for itself: the collective bodies of the system
recognise a reference to their sun, and all the individual bodies,
according to the relative positions into which they are brought by
their motions, form a momentary relation of their gravity towards each
other."

This must appear to us a very loose and insufficient way of stating the
Principle of Perturbations, but loose as it is, it recognises that the
Perturbations depend upon the gravity of the planets one to another,
and to the sun. And if the Perturbations depend upon these forces,
one can hardly suppose that any one who allows this will deny that
the primary undisturbed motions depend upon these forces, and must be
explained by means of them; yet this is what Hegel denies.

It is evident, on looking at Hegel's mode of reasoning on such
subjects, that his views approach towards those of Aristotle and the
Aristotelians; according to which motions were divided into _natural_
and _unnatural_;--the _celestial motions_ were circular and uniform in
their nature;--and the like. Perhaps it may be worth while to show how
completely Hegel adheres to these ancient views, by an extract from
the additions to the Articles on Celestial Motions, made in the last
edition of the _Encyclopædia_. He says (_w_),

"The motion of the heavenly bodies is not a being pulled this way
and that, as is imagined (by the Newtonians). _They go along, as the
ancients said, like blessed gods._ The celestial conformity is not
such a one as has the principle of rest or motion external to itself.
It is not right to say because a stone is inert, and the whole earth
consists of stones, and the other heavenly bodies are of the same
nature as the earth, therefore the heavenly bodies are inert. This
conclusion makes the properties of the whole the same as those of the
part. Impulse, Pressure, Resistance, Friction, Pulling, and the like,
are valid only for other than celestial matter."

There can be no doubt that this is a very different doctrine from that
of Newton.

I will only add to these specimens of Hegel's physics, a specimen of
the logic by which he refutes the Newtonian argument which has just
been adduced; namely, that the celestial bodies are matter, and that
matter, as we see in terrestrial matter, is inert. He says (_x_),

"Doubtless both are matter, as a good thought and a bad thought are
both thoughts; but the bad one is not therefore good, because it is a
thought."


APPENDIX TO THE MEMOIR ON HEGEL'S CRITICISM OF NEWTON'S PRINCIPIA.

HEGEL. _Encyclopædia_ (2nd Ed. 1827), Part XI. p. 250.

C. _Absolute Mechanics._

§ 269.

Gravitation is the true and determinate conception of material
Corporeity, which (Conception) is realized to the Idea (zur Idee).
_General_ Corporeity is separable essentially into _particular_
Bodies, and connects itself with the Element of _Individuality_ or
subjectivity, as apparent (phenomenal) presence in the _Motion_, which
by this means is immediately a system of _several Bodies_.

Universal gravitation must, as to itself, be recognised as a profound
thought, although it was principally as apprehended in the sphere
of Reflexion that it eminently attracted notice and confidence on
account of the quantitative determinations therewith connected, and
was supposed to find its confirmation in _Experiments_ (Erfahrung)
pursued from the Solar System down to the phenomena of Capillary
Tubes.--But Gravitation contradicts immediately the Law of Inertia,
for in virtue of it (Gravitation) matter tends _out of itself_ to the
other (matter).--In the _Conception of Weight_, there are, as has been
shown, involved the two elements--Self-existence, and Continuity,
which takes away self-existence. These elements of the Conception,
however, experience a fate, as particular forces, corresponding to
Attractive and Repulsive Force, and are thereby apprehended in nearer
determination, as _Centripetal_ and _Centrifugal Force_, which (Forces)
like weight, _act upon Bodies_, independent of each other, and are
supposed to come in contact accidentally in a third thing, Body. By
this means, what there is of profound in the thought of universal
weight is again reduced to nothing; and Conception and Reason cannot
make their way into the doctrine of absolute motion, so long as the
so highly-prized discoveries of Forces are dominant there. In the
conclusion which contains the _Idea_ of Weight, namely, [contains
this Idea] as the Conception which, in the case of motion, enters
into external Reality through the particularity of the Bodies, and
at the same time into this [Reality] and into their Ideality and
self-regarding Reflexion, (Reflexion-in-sich), the rational identity
and inseparability of the elements is involved, which at other times
are represented as independent. Motion itself, as such, has only its
meaning and existence in a system of _several_ bodies, and those,
such as stand in relation to each other according to different
determinations.

§ 270.

As to what concerns bodies in which the conception of gravity
(weight) is realized free by itself, we say that they have for the
determinations of their different nature the elements (momente) of
their conception. One [conception of this kind] is the _universal_
center of the abstract reference [of a body] to itself. Opposite
to this [conception] stands the immediate, extrinsic, centerless
_Individuality_, appearing as _Corporeity_ similarly independent. Those
[Bodies] however which are particular, which stand in the determination
of extrinsic, and at the same time of intrinsic relation, are centers
for themselves, and [also] have a reference to the first as to their
essential unity.

    The Planetary Bodies, as the immediately concrete, are in their
    existence the most complete. Men are accustomed to take the Sun
    as the most excellent, inasmuch as the understanding prefers the
    abstract to the concrete, and in like manner the fixed stars are
    esteemed higher than the Bodies of the Solar System. Centerless
    Corporeity, as belonging to externality, naturally separates itself
    into the opposition of the lunar and the cometary Body. The laws
    of absolutely free motion, as is well known, were discovered by
    Kepler;--a discovery of immortal fame. Kepler has proved these
    laws in this sense, that for the empirical data he found their
(_a_) general expression. Since then, (_a_) it has become a common way
    of speaking to say that Newton first found out the proof of these
    Laws. It has rarely happened that fame has been more unjustly
    transferred from the first discoverer to another person. On this
    subject I make the following remarks.

    1. That it is allowed by Mathematicians that the Newtonian
(_b_) Formulæ may be derived from the Keplerian Laws. The
    completely immediate derivation is this: In the third Keplerian
(_c_) Law, _A_^3/_T_^2 is the constant quantity. This being put
    as _A.A_^2/_T_^2 and calling, with Newton, _A_/_T_^2 universal
    Gravitation, his expression of the effect of gravity in the
    reciprocal ratio of the square of the distances is obvious.

(_d_) 2. That the Newtonian proof of the Proposition that a body
    subjected to the Law of Gravitation moves about the central body
    in an _Ellipse_, gives a _Conic Section_ generally, while the
    main Proposition which ought to be proved is that the fall of
    such a Body is _not_ a _Circle or any other Conic Section_, but
    an _Ellipse only_. Moreover, there are objections which may be
    made against this proof in itself (_Princ. Math._ I. 1. Sect. II.
(_e_) Prop. 1); and although it is the foundation of the Newtonian
    Theory, analysis has no longer any need of it. The conditions which
    in the sequel make the path of the Body to a determinate Conic
    Section, are referred to an _empirical_ circumstance, namely, a
    particular position of the Body at a determined moment of time, and
(_f_) the _casual_ strength of an _impulsion_ which it is supposed
    to have received originally; so that the circumstance which makes
    the Curve be an Ellipse, which alone ought to be the thing proved,
    is extraneous to the Formula.

    3. That the Newtonian Law of the so-called Force of Gravitation is
    in like manner only proved from experience by Induction.

(_g_) The sum of the difference is this, that what Kepler
    expressed in a simple and sublime manner in the Form of _Laws_
    _of the Celestial Motions_, Newton has metamorphosed into the
    _Reflection-Form_ of the _Force of Gravitation_. If the Newtonian
    Form has not only its convenience but its necessity in reference
(_h_) to the analytical method, this is only a difference of the
    mathematical formulæ; Analysis has long been able to derive the
    Newtonian expression, and the Propositions therewith connected,
    out of the Form of the Keplerian Laws; (on this subject I refer
(_i_) to the elegant exposition in _Francœur's Traité Elém. de
    Mécanique_, Liv. II. Ch. xi. n. 4.)--The old method of so-called
    proof is conspicuous as offering to us a tangled web, formed of
    the _Lines_ of the mere geometrical construction, to which a
    physical meaning of _independent Forces_ is given; and of empty
    Reflexion-determinations of the already mentioned _Accelerating
    Force_ and _Vis Inertiæ_, and especially of the relation of
    the so-called gravitation itself to the centripetal force and
    centrifugal force, and so on.

    The remarks which are here made would undoubtedly have need of
    a further explication to show how well founded they are: in a
    Compendium, propositions of this kind which do not agree with
    that which is assumed, can only have the shape of assertions.
    Indeed, since they contradict such high authorities, they must
    appear as something worse, as presumptuous assertions. I will not,
    on this subject, support myself by saying, by the bye, that an
    interest in these subjects has occupied me for 25 years; but it
    is more precisely to the purpose to remark, that the distinctions
    and determinations which Mathematical Analysis introduces,
    and the course which it must take according to its method, is
    altogether different from that which a physical reality must
    have. The Presuppositions, the Course, and the Results, which
    the Analysis necessarily has and gives, remain quite extraneous
    to the considerations which determine the physical value and the
    signification of those determinations and of that course. To this
    it is that attention should be directed. We have to do with a
    consciousness relative to the deluging of physical Mechanics with
    an _inconceivable_ (unsäglichen) _Metaphysic_, which--contrary to
    experience and conception--has those mathematical determinations
    alone for its source.

    It is recognized that what Newton--besides the foundation of the
    analytical treatment, the development of which, by the bye, has
    of itself rendered superfluous, or indeed rejected much which
    belonged to Newton's essential Principles and glory--has added
    to the Keplerian Laws is the Principle of _Perturbations_,--a
    Principle whose importance we may here accept thus far (hier in
(_k_) sofern anzuführen ist); namely, so far as it rests upon the
    Proposition that the so-called attraction is an operation of all
(_l_) the individual parts of bodies, as being material. It lies
    in this, that matter in general assigns a center for itself (sich
    das centrum setzt), and the figure of the body is an element in the
    determination of its place; that collective bodies of the system
    recognize a reference to their Sun (sich ihre Sonne setzen), but
    also the individual bodies themselves, according to the relative
    position with regard to each other into which they come by their
    general motion, form a momentary relation of their gravity
    (schwere) _towards each other_, and are related to each other not
    only in abstract spatial relations, but at the same time assign to
    themselves a joint center, which however is again resolved [into
    the general center] in the universal system.

(_m_) As to what concerns the features of the path, to show how
    the fundamental determinations of Free Motion are connected _with
    the Conception_, cannot here be undertaken in a satisfactory and
    detailed manner, and must therefore be left to its fate. The proof
    from reason of the quantitative determinations of free motion can
    only rest upon the _determinations_ of _Conceptions_ of space and
    time, the elements whose relation (intrinsic not extrinsic) motion
    is.

    That, _in the first place_, the motion in general is a motion
    _returning into itself_, is founded on the determination of
    particularity and individuality of the bodies in general (§ 269),
    so that partly they have a center in themselves, and partly at the
    same time their center in another. These are the determinations of
    Conceptions which form the basis of the false representatives of
(_n_) Centripetal Force and Centrifugal Force, as if each of these
    were self-existing, extraneous to the other, and independent of
    it; and as if they only came in contact in their operations and
    consequently _externally_. They are, as has already been mentioned,
    the Lines which must be drawn for the mathematical determinations,
    transformed into physical realities.

    Further, this motion is _uniformly accelerated_, (and--as returning
    into itself--in turn uniformly retarded). In motion as _free_,
    Time and Space enter as _different_ things which are to make
(_o_) themselves effective in the determination of the motion
    (§ 266, note). In the so-called _Explanation_ of the uniformly
    accelerated and retarded motion, by means of the alternate
    decrease and increase of the magnitude of the Centripetal Force
    and Centrifugal Force, the _confusion_ which the assumption of
(_p_) such independent Forces produces is at its greatest height.
    According to this explanation, in the motion of a Planet from the
    Aphelion to the Perihelion, the centrifugal is _less_ than the
    centripetal force, and on the contrary, in the Perihelion itself,
    the centrifugal force is supposed to become greater than the
    centripetal. For the motion from the Perihelion to the Aphelion,
    this representation makes the forces pass into the opposite
    relation in the same manner. It is apparent that such a sudden
    conversion of the preponderance which a force has obtained over
    another, into an inferiority to the other, cannot be anything taken
    out of the nature of Forces. On the contrary it must be concluded,
    that a preponderance which one Force has obtained over another
    must not only be preserved, but must go onwards to the complete
    annihilation of the other Force, and the motion must either, by
    the Preponderance of the Centripetal Force, proceed till it ends
    in rest, that is, in the Collision of the Planet with the Central
(_q_) Body, or till by the Preponderance of the Centrifugal Force
    it ends in a straight line. But now, if in place of the suddenness
    of the conversion, we suppose a gradual increase of the Force in
    question, then, since rather the other Force ought to be assumed as
    increasing, we lose the opposition which is assumed for the sake
    of the explanation; and if the increase of the one is assumed to
    be different from that of the other, (which is the case in some
    representations,) then there is found at the mean distance between
    the apsides a point in which the Forces are _in equilibrio_. And
    the transition of the Forces out of Equilibrium is a thing just as
    little without any sufficient reason as the aforesaid suddenness
    of inversion. And in the whole of this kind of explanation, we see
    that the mode of remedying a bad mode of dealing with a subject
    leads to newer and greater confusion.--A similar confusion makes
    its appearance in the explanation of the phænomenon that the
    pendulum oscillates more slowly at the equator. This phænomenon is
    ascribed to the Centrifugal Force, which it is asserted must then
    be greater; but it is easy to see that we may just as well ascribe
    it to the augmented gravity, inasmuch as that holds the pendulum
    more strongly to the perpendicular line of rest.


    § 240.

(_r_) And now first, as to what concerns the _Form of the Path_,
    the _Circle_ only can be conceived as the path of an _absolutely
    uniform_ motion. _Conceivable_, as people express it, no doubt it
    is, that an increasing and diminishing motion should take place in
    a circle. But this conceivableness or possibility means only an
    abstract capability of being represented, which leaves out of sight
    that Determinate Thing on which the question turns.

    The Circle is the line returning into itself in which all the radii
    are _equal_, that is, it is completely determined by means of the
    radius. There is only _one_ Determination, and that is the _whole_
    Determination.

    But in free motion, in which the Determinations according to
    space and according to time come into view with Differences, in a
    qualitative relation to each other, this Relation appears in the
    spatial aspect as a _Difference_ thereof in itself, which therefore
    requires two Determinations. Hereby the Form of the path returning
    into itself is essentially an _Ellipse_.

(_s_) The abstract Determinations which produces the circle
    appears also in this way, that the arc or angle which is included
    by two Radii is independent of them, a magnitude with regard to
    them completely empirical. But since in the motion as determined
    by the Conception, the distance from the center, and the arc
    which is run over in a certain time, must be comprehended in one
    determinateness, [_and_] make out a whole, this is the sector, a
    space-determination of two dimensions: in this way, the arc is
    essentially a Function of the Radius Vector; and the former (the
    arc) being unequal, brings with it the inequality of the Radii.
    That the determination with regard to the space by means of the
(_t_) time appears as a Determination of two Dimensions,--as a
    Superficies-Determination,--agrees with what was said before (§
    266) respecting Falling Bodies, with regard to the exposition of
    the same Determinateness, at one while as Time in the root, at
    another while as Space in the Square. Here, however, the Quadratic
    character of the space is, by the returning of the Line of motion
    into itself, limited to a Sector. These are, as may be seen, the
    general principles on which the Keplerian Law, that in equal times
    equal sectors are cut off, rests.

    This Law becomes, as is clear, only the relation of the arc to
    the Radius Vector, and the Time enters there as the abstract
    Unity, in which the different Sectors are compared, because as
    Unity it is the Determining Element. But the further relation is
    that of the Time, not as Unity, but as a Quantity in general,--as
    the time of Revolution--to the magnitude of the Path, or, what is
    the same thing, the distance from the center. As Root and Square,
    we saw that Time and Space had a relation to each other, in the
    case of Falling Bodies, the case of half-free motion--because
    that [_motion_] is determined on one side by the conception, on
(_u_) the other by external [_conditions_]. But in the case of
    absolute motion--the domain of _free_ masses--the determination
    attains its Totality. The Time as the Root is a mere empirical
    magnitude; but as a component (moment) of the developed Totality,
    it is a Totality in itself,--it produces itself, and therein has
    a reference to itself; as the Dimensionless Element in itself, it
    only comes to a formal identity with itself, the Square; Space,
    on the other hand, as the positive Distribution (aussereinander)
    [_comes_] to the Dimension of the Conception, _the_ CUBE. Their
(_v_) Realization preserves their original difference. This is the
    third Keplerian Law, the relation of the _Cubes_ of the _Distances_
    to the _Squares_ of the _Times_;--a Law which is so great on this
    account, that it represents so simply and immediately _Reason
    as belonging to the thing_: while on the contrary the Newtonian
    Formula, by means of which the Law is changed into a Law for the
    Force of Gravity, shows the Distortion, Perversion and Inversion of
    _Reflexion_ which stops half-way.

    Additions to new Edition. § 269.

    The center has no sense without the circumference, nor the
    circumference without the center. This makes all physical
    hypotheses vanish which sometimes proceed from the center,
    sometimes from the particular bodies, and sometimes assign this,
    sometimes that, as the original [cause of motion] ... It is silly
    (läppisch) to suppose that the centrifugal force, as a tendency to
    fly off in a Tangent, has been produced by a lateral projection, a
    projectile force, an impulse which they have retained ever since
    they set out on their journey (von Haus aus). Such casualty of the
    motion produced by external causes belongs to inert matter; as when
    a stone fastened to a thread which is thrown transversely tries to
    fly from the thread. We are not to talk in this way of Forces. If
    we will speak of Force, there is one Force, whose elements do not
(_w_) draw bodies to different sides as if they were two Forces.
    The motion of the heavenly bodies is not a being pulled this way or
    that, such as is thus imagined; it is free motion: they go along,
    as the ancients said, as blessed Gods (sie gehen als selige Götter
    einher). The celestial corporeity is not such a one as has the
    principle of rest or motion external to itself. Because stone is
    inert, and all the earth consists of stones, and the other heavenly
    bodies are of the same nature,--is a conclusion which makes the
    properties of the whole the same as those of the part. Impulse,
    Pressure, Resistance, Friction, Pulling, and the like, are valid
(_x_) only for an existence of matter other than the celestial.
    Doubtless that which is common to the two is matter, as a good
    thought and a bad thought are both thoughts; but the bad one is not
    therefore good, because it is a thought.


FOOTNOTES:

[Footnote 353: Cartes. _Princip._ iv. 23.]

[Footnote 354: Jac. Bernoulli, _Nouvelles Pensées sur le Système de M.
Descartes_, op. t. i. p. 239 (1686).]

[Footnote 355: _De la Cause de la Pesanteur_ (1689), p. 135.]

[Footnote 356: _Journal des Savans_, 1703. Mém. Acad. Par. 1709.

Bulfinger, in 1726 (Acad. Petrop.), conceived that by making a sphere
revolve at the same time about two axes at right angles to each other,
every particle would describe a great circle; but this is not so.]

[Footnote 357: Acad. Par. 1714, _Hist._ p. 106.]

[Footnote 358: Acad. Par. 1733.]

[Footnote 359: Acad. Sc. 1709. If we abandon the clear principles of
mechanics, the writer says, "toute la lumière que nous pouvons avoir
est éteinte, et nous voilà replongés de nouveau dans les anciennes
ténèbres du Peripatetisme, dont le Ciel nous veuille preserver!"

It was also objected to the Newtonian system, that it did not account
for the remarkable facts, that all the motions of the primary planets,
all the motions of the satellites, and all the motions of rotation,
including that of the sun, are in the same direction, and nearly in
the same plane; facts which have been urged by Laplace as so strongly
recommending the Nebular Hypothesis; and that hypothesis is, in truth,
a hypothesis of vortices respecting the _origin_ of the system of the
world.]

[Footnote 360: _Nouvelle Physique Céleste_, Op. t. iii. p. 163.

The deviation of the orbits of the planets from the plane of the
sun's equator was of course a difficulty in the system which supposed
that they were carried round by the vortices which the sun's rotation
caused, or at least rendered evident. Bernoulli's explanation consists
in supposing the planets to have a sort of _leeway_ (_dérive des
vaisseaux_) in the stream of the vortex.]

[Footnote 361: See _Hist. Sc. Ideas_, b. iii. c. ix. Art. 7.]

[Footnote 362: See Mill's _Logic_, vol. i. p. 311, 2nd ed.]

[Footnote 363: These letters refer to passages in the Translation
annexed to this Memoir.]


APPENDIX K.

DEMONSTRATION THAT ALL MATTER IS HEAVY.

(_Cam. Phil. Soc._ FEB. 22, 1841.)


The discussion of the nature of the grounds and proofs of the most
general propositions which the physical sciences include, belongs
rather to Metaphysics than to that course of experimental and
mathematical investigation by which the sciences are formed. But such
discussions seem by no means unfitted to occupy the attention of the
cultivators of physical science. The ideal, as well as the experimental
side of our knowledge must be carefully studied and scrutinized,
in order that its true import may be seen; and this province of
human speculation has been perhaps of late unjustly depreciated and
neglected by men of science. Yet it can be prosecuted in the most
advantageous manner by them only: for no one can speculate securely
and rightly respecting the nature and proofs of the truths of science
without a steady possession of some large and solid portions of such
truths. A man must be a mathematician, a mechanical philosopher, a
natural historian, in order that he may philosophize well concerning
mathematics, and mechanics, and natural history; and the mere
metaphysician who without such preparation and fitness sets himself
to determine the grounds of mathematical or mechanical truths, or the
principles of classification, will be liable to be led into error at
every step. He must speculate by means of general terms, which he
will not be able to use as instruments of discovering and conveying
philosophical truth, because he cannot, in his own mind, habitually and
familiarly, embody their import in special examples.

Acting upon such views, I have already laid before the Philosophical
Society of Cambridge essays on such subjects as I here refer to;
especially a memoir "On the Nature of the Truth of the Laws of Motion,"
which was printed by the Society in its Transactions. This memoir
appears to have excited in other places, notice of such a kind as to
show that the minds of many speculative persons are ready for and
inclined towards the discussion of such questions. I am therefore the
more willing to bring under consideration another subject of a kind
closely related to the one just mentioned.

The general questions which all such discussions suggest, are (in
the existing phase of English philosophy) whether certain proposed
scientific truths, (as the laws of motion,) be _necessary_ truths;
and if they are necessary, (which I have attempted to show that in a
certain sense they are,) _on what ground_ their necessity rests. These
questions may be discussed in a general form, as I have elsewhere
attempted to show. But it may be instructive also to follow the general
arguments into the form which they assume in special cases; and to
exhibit, in a distinct shape, the incongruities into which the opposite
false doctrine leads us, when applied to particular examples. This
accordingly is what I propose to do in the present memoir, with regard
to the proposition stated at the head of this paper, namely, that _all
matter is heavy_.

At first sight it may appear a doctrine altogether untenable to assert
that this proposition is a necessary truth: for, it may be urged, we
have no difficulty in conceiving matter which is not heavy; so that
matter without weight is a conception not inconsistent with itself;
which it must be if the reverse were a necessary truth. It may be
added, that the possibility of conceiving matter without weight
was shown in the controversy which ended in the downfall of the
phlogiston theory of chemical composition; for some of the reasoners
on this subject asserted phlogiston to be a body with positive levity
instead of gravity, which hypothesis, however false, shows that such
a supposition is possible. Again, it may be said that _weight_ and
_inertia_ are two separate properties of matter: that mathematicians
measure the quantity of matter by the inertia, and that we learn
by experiment only that the weight is proportional to the inertia;
Newton's experiments with pendulums of different materials having been
made with this very object.

I proceed to reply to these arguments. And first, as to the possibility
of conceiving matter without weight, and the argument thence
deduced, that the universal gravity of matter is not a necessary
truth, I remark, that it is indeed just, to say that we cannot even
distinctly conceive the contrary of a necessary truth to be true;
but that this impossibility can be asserted only of those perfectly
distinct conceptions which result from a complete development of
the fundamental idea and its consequences. Till we reach this stage
of development, the obscurity and indistinctness may prevent our
perceiving absolute contradictions, though they exist. We have abundant
store of examples of this, even in geometry and arithmetic; where the
truths are universally allowed to be necessary, and where the relations
which are impossible, are also inconceivable, that is, not conceivable
distinctly. Such relations, though not distinctly conceivable, still
often appear conceivable and possible, owing to the indistinctness
of our ideas. Who, at the first outset of his geometrical studies,
sees any impossibility in supposing the side and the diagonal of a
square to have a common measure? Yet they can be rigorously proved to
be incommensurable, and therefore the attempt distinctly to conceive
a common measure of them must fail. The attempts at the geometrical
duplication of the cube, and the supposed solutions, (as that of
Hobbes,) have involved absolute contradictions; yet this has not
prevented their being long and obstinately entertained by men, even of
minds acute and clear in other respects. And the same might be shewn to
be the case in arithmetic. It is plain, therefore, that we cannot, from
the supposed possibility of conceiving matter without weight, infer
that the contrary may not be a necessary truth.

Our power of judging, from the compatibility or incompatibility of our
conceptions, whether certain propositions respecting the relations of
ideas are true or not, must depend entirely, as I have said, upon the
degree of development which such ideas have undergone in our minds.
Some of the relations of our conceptions on any subject are evident
upon the first steady contemplation of the fundamental idea by a sound
mind: these are the _axioms_ of the subject. Other propositions may be
deduced from the axioms by strict logical reasoning. These propositions
are no less _necessary_ than the axioms, though to common minds their
_evidence_ is very different. Yet as we become familiar with the steps
by which these ulterior truths are deduced from the axioms, _their_
truth also becomes evident, and the contrary becomes inconceivable.
When a person has familiarized himself with the first twenty-six
propositions of Euclid, and not till then, it becomes evident to him,
that parallelograms on the same base and between the same parallels
are equal; and he cannot even conceive the contrary. When he has a
little further cultivated his geometrical powers, the equality of the
square on the hypothenuse of a right-angled triangle to the squares on
the sides, becomes also evident; the steps by which it is demonstrated
being so familiar to the mind as to be apprehended without a conscious
act. And thus, the contrary of a necessary truth cannot be distinctly
conceived; but the incapacity of forming such a conception is a
condition which depends upon cultivation, being intimately connected
with the power of rapidly and clearly perceiving the connection of the
necessary truth under consideration with the elementary principles on
which it depends. And thus, again, it may be that there is an absolute
impossibility of conceiving matter without weight; but then, this
impossibility may not be apparent, till we have traced our fundamental
conceptions of matter into some of their consequences.

The question then occurs, whether we can, by any steps of reasoning,
point out an inconsistency in the conception of matter without weight.
This I conceive we may do, and this I shall attempt to show.

The general mode of stating the argument is this:--the quantity of
matter is measured by those sensible properties of matter which undergo
quantitative addition, subtraction and division, as the matter is
added, subtracted and divided. The quantity of matter cannot be known
in any other way. But this mode of measuring the quantity of matter,
in order to be true at all, must be universally true. If it were only
partially true, the limits within which it is to be applied would be
arbitrary; and therefore the whole procedure would be arbitrary, and,
as a method of obtaining philosophical truth, altogether futile.

We may unfold this argument further. Let the contrary be supposed, of
that which we assert to be true: namely, let it be supposed that while
all other kinds of matter are heavy (and of course heavy in proportion
to the quantity of matter), there is one kind of matter which is
absolutely destitute of weight; as, for instance, phlogiston, or any
other element. Then where this _weightless_ element (as we may term
it) is mixed with _weighty_ elements, we shall have a compound, in
which the weight is no longer proportional to the quantity of matter.
If, for example, 2 measures of heavy matter unite with one measure
of phlogiston, the weight is as 2, and the quantity of matter as 3.
In all such cases, therefore, the weight ceases to be the measure of
the quantity of matter. And as the proportion of the weighty and the
weightless matter may vary in innumerable degrees in such compounds,
the weight affords no criterion at all of the quantity of matter
in them. And the smallest admixture of the weightless element is
sufficient to prevent the weight from being taken as the measure of the
quantity of matter.

But on this hypothesis, how are we to distinguish such compounds from
bodies consisting purely of heavy matter? How are we to satisfy
ourselves that there is not, in every body, some admixture, small or
great, of the weightless element? If we call this element _phlogiston_,
how shall we know that the bodies with which we have to do are, any of
them, absolutely free from phlogiston?

We cannot refer to the weight for any such assurance; for by
supposition the presence and absence of phlogiston makes no difference
in the weight. Nor can any other properties secure us at least from
a very small admixture; for to assert that a mixture of 1 in 100 or
1 in 10 of phlogiston would always manifest itself in the properties
of the body, must be an arbitrary procedure, till we have proved this
assertion by experiment: and we cannot do this till we have learnt
some mode of measuring the quantities of matter in bodies and parts of
bodies; which is exactly what we question the possibility of, in the
present hypothesis.

Thus, if we assume the existence of an element, _phlogiston_, devoid of
weight, we cannot be sure that every body does not contain some portion
of this element; while we see that if there be an admixture of such
an element, the weight is no longer any criterion of the quantity of
matter. And thus we have proved, that if there be any kind of matter
which is not heavy, the weight can no longer avail us, _in any case or
to any extent_, as a measure of the quantity of matter.

I may remark, that the same conclusion is easily extended to the case
in which phlogiston is supposed to have absolute levity; for in that
case, a certain mixture of phlogiston and of heavy matter would have
no weight, and might be substituted for phlogiston in the preceding
reasoning.

I may remark, also, that the same conclusion would follow by the same
reasoning, if any kind of matter, instead of being void of weight, were
heavy, indeed, but not _so_ heavy, in proportion to its quantity of
matter, as other kinds.

On all these hypotheses there would be no possibility of measuring
quantity of matter by weight at all, in any case, or to any extent.

But it may be urged, that we have not yet reduced the hypothesis of
matter without weight to a contradiction; for that mathematicians
measure quantity of matter, not by weight, but by the other property,
of which we have spoken, inertia.

To this I reply, that, practically speaking, quantity of matter is
always measured by weight, both by mechanicians and chemists: and as
we have proved that this procedure is utterly insecure in all cases,
on the hypothesis of weightless matter, the practice rests upon a
conviction that the hypothesis is false. And yet the practice is
universal. Every experimenter measures quantity of matter by the
balance. No one has ever thought of measuring quantity of matter by
its inertia practically: no one has constructed a measure of quantity
of matter in which the matter produces its indications of quantity by
its motion. When we have to take into account the inertia of a body,
we inquire what its weight is, and assume this as the measure of the
inertia; but we never take the contrary course, and ascertain the
inertia first in order to determine by that means the weight.

But it may be asked, Is it not then true, and an important scientific
truth, that the _quantity of matter_ is measured by the _inertia_?
Is it not true, and proved by experiment, that the _weight_ is
_proportional_ to the _inertia_? If this be not the result of Newton's
experiments mentioned above, what, it may be demanded, do they prove?

To these questions I reply: It is true that quantity of matter is
measured by the inertia, for it is true that inertia is as the quantity
of matter. This truth is indeed one of the laws of motion. That weight
is proportional to inertia is proved by experiment, as far as the laws
of motion are so proved: and Newton's experiments prove one of the laws
of motion, so far as any experiments can prove them, or are needed to
prove them.

That inertia is proportional to weight, is a law equivalent to that
law which asserts, that when pressure produces motion in a given body,
the velocity produced in a given time is as the pressure. For if the
velocity be as the pressure, when the body is given, the velocity will
be constant if the inertia also be as the pressure. For the inertia is
understood to be that property of bodies to which, _ceteris paribus_,
the velocity impressed is _inversely_ proportional. One body has
twice as much inertia as another, if, when the same force acts upon
it for the same time, it acquires but half the velocity. This is the
fundamental conception of _inertia_.

In Newton's pendulum experiments, the pressure producing motion was
a certain resolved part of the weight, and was proportional to the
weight. It appeared by the experiments, that whatever were the material
of which the pendulum was formed, the rate of oscillation was the same;
that is, the velocity acquired was the same. Hence the inertia of the
different bodies must have been in each case as the weight: and thus
this assertion is true of all different kinds of bodies.

Thus it appears that the assertion, that inertia is universally
proportional to weight, is equivalent to the law of motion, that the
velocity is as the pressure. The conception of inertia (of which,
as we have said, the fundamental conception is, that the velocity
impressed is inversely proportional to the inertia,) connects the two
propositions so as to make them identical.

Hence our argument with regard to the universal gravity of matter
brings us to the above law of motion, and is proved by Newton's
experiments in the same sense in which that law of motion is so proved.

Perhaps some persons might conceive that the identity of weight
and inertia is obvious at once; for both are merely resistance
to motion;--inertia, resistance to all motion (or change of
motion)--weight, resistance to motion upwards.

But there is a difference in these two kinds of resistance to motion.
Inertia is instantaneous, weight is continuous resistance. Any
momentary impulse which acts upon a free body overcomes its inertia,
for it changes its motion; and this change once effected, the inertia
opposes any return to the former condition, as well as any additional
change. The inertia is thus overcome by a momentary force. But the
weight can only be overcome by a continuous force like itself. If an
impulse act in opposition to the weight, it may for a moment neutralize
or overcome the weight; but if it be not continued, the weight resumes
its effect, and restores the condition which existed before the impulse
acted.

But weight not only produces rest, when it is resisted, but motion,
when it is not resisted. Weight is measured by the reaction which would
balance it; but when unbalanced, it produces motion, and the velocity
of this motion increases constantly. Now what determines the velocity
thus produced in a given time, or its rate of increase? What determines
it to have one magnitude rather than another? To this we must evidently
reply, _the inertia_. When weight produces motion, the inertia is the
reaction which makes the motion determinate. The accumulated motion
produced by the action of unbalanced weight is as determinate a
condition as the equilibrium produced by balanced weight. In both cases
the condition of the body acted on is determined by the opposition of
the action and reaction.

Hence inertia is the reaction which opposes the weight, when
unbalanced. But by the conception of action and reaction, (as mutually
determining and determined,) they are measured by each other: and hence
the inertia is necessarily proportional to the weight.

But when we have reached this conclusion, the original objection may be
again urged against it. It may be said, that there must be some fallacy
in this reasoning, for it proves a state of things to be necessary when
we can so easily conceive a contrary state of things. Is it denied,
the opponent may ask, that we can readily imagine a state of things in
which bodies have no weight? Is not the uniform tendency of all bodies
in the same direction not only not necessary, but not even true? For
they do in reality tend, not with equal forces in parallel lines, but
to a center with unequal forces, according to their position: and we
can conceive these differences of intensity and direction in the force
to be greater than they really are; and can with equal ease suppose the
force to disappear altogether.

To this I reply, that certainly we may conceive the weight of bodies
to vary in intensity and direction, and by an additional effort of
imagination, may conceive the weight to vanish: but that in all these
suppositions, even in the extreme one, we must suppose the rule to be
universal. If _any_ bodies have weight, _all_ bodies must have weight.
If the direction of weight be different in different points, this
direction must still vary according to the _law of continuity_; and the
same is true of the intensity of the weight. For if this were not so,
the rest and motion, the velocity and direction, the permanence and
change of bodies, as to their mechanical condition, would be arbitrary
and incoherent: they would not be subject to mechanical ideas; that
is, not to ideas at all: and hence these conditions of objects would
in fact be inconceivable. In order that the universe may be possible,
that is, may fall under the conditions of intelligible conceptions, we
must be able to conceive a body at rest. But the rest of bodies (except
in the absolute negation of all force) implies the equilibrium of
opposite forces. And one of these opposite forces must be a _general_
force, as weight, in order that the universe may be governed by general
conditions. And this general force, by the conception of force, may
produce motion, as well as equilibrium; and this motion again must
be determined, and determined by general conditions; which cannot
be, except the communication of motion be regulated by an inertia
proportional to the weight.

But it will be asked, Is it then pretended that Newton's experiment,
by which it was intended to prove inertia proportional to weight,
does really prove nothing but what may be demonstrated _à priori_?
Could we know, without experiment, that all bodies,--gold, iron, wood,
cork,--have inertia proportional to their weight? And to this we reply,
that experiment holds the same place in the establishment of this, as
of the other fundamental doctrines of mechanics. Intercourse with the
external world is requisite for developing our ideas; measurement of
phenomena is needed to fix our conceptions and to render them precise:
but the result of our experimental studies is, that we reach a
position in which our convictions do not rest upon experiment. We learn
by observation truths of which we afterwards see the necessity. This is
the case with the laws of motion, as I have repeatedly endeavoured to
show. The same will appear to be the case with the proposition, that
bodies of different kinds have their inertia proportional to their
weight.

For bodies _of the same kind_ have their inertia proportional to their
weight, both quantities being proportional to the quantity of matter.
And if we compress the same quantity of matter into half the space,
neither the weight nor the inertia is altered, because these depend
on the quantity of matter alone. But in this way we obtain a body
of _twice the density_; and in the same manner we obtain a body of
any other density. Therefore whatever be the density, the inertia is
proportional to the quantity of matter. But the mechanical relations
of bodies cannot depend upon any difference of _kind_, _except_ a
difference of density. For if we suppose any fundamental difference of
mechanical nature in the particles or component elements of bodies, we
are led to the same conclusion, of arbitrary, and therefore impossible,
results, which we deduced from this supposition with regard to weight.
Therefore all bodies of different density, and hence, all bodies
whatever, must have their inertia proportional to their weight.

Hence we see, that the propositions, that all bodies are heavy, and
that inertia is proportional to weight, necessarily follow from those
fundamental ideas which we unavoidably employ in all attempts to
reason concerning the mechanical relations of bodies. This conclusion
may perhaps appear the more startling to many, because they have
been accustomed to expect that fundamental ideas and their relations
should be self-evident at our first contemplation of them. This,
however, is far from being the case, as I have already shown. It is
not the _first_, but the most complete and developed condition of our
conceptions which enables us to see what are axiomatic truths in each
province of human speculation. Our fundamental ideas are necessary
conditions of knowledge, universal forms of intuition, inherent types
of mental development; they may even be termed, if any one chooses,
results of connate intellectual tendencies; but we cannot term them
_innate_ ideas, without calling up a large array of false opinions. For
innate ideas were considered as capable of composition, but by no means
of simplification: as most perfect in their original condition; as to
be found, if any where, in the most uneducated and most uncultivated
minds; as the same in all ages, nations, and stages of intellectual
culture; as capable of being referred to at once, and made the basis
of our reasonings, without any special acuteness or effort: in all
which circumstances the Fundamental Ideas of which we have spoken, are
opposed to Innate Ideas so understood.

I shall not, however, here prosecute this subject. I will only remark,
that Fundamental Ideas, as we view them, are not only not innate, in
any usual or useful sense, but they are not necessarily _ultimate_
elements of our knowledge. They are the results of our analysis so far
as we have yet prosecuted it; but they may themselves subsequently
be analysed. It may hereafter appear, that what we have treated as
different Fundamental Ideas have, in fact, a connexion, at some point
below the structure which we erect upon them. For instance, we treat of
the mechanical ideas of force, matter, and the like, as distinct from
the idea of substance. Yet the principle of measuring the quantity of
matter by its weight, which we have deduced from mechanical ideas, is
applied to determine the substances which enter into the composition
of bodies. The idea of substance supplies the axiom, that the whole
quantity of matter of a compound body is equal to the sum of the
quantities of matter of its elements. The mechanical ideas of force
and matter lead us to infer that the quantity both of the whole and
its parts must be measured by their weights. _Substance_ may, for some
purposes, be described as that to which properties belong; _matter_
in like manner may be described as that which resists force. The
former involves the Idea of permanent Being; the latter, the Idea of
Causation. There may be some elevated point of view from which these
ideas may be seen to run together. But even if this be so, it will by
no means affect the validity of reasonings founded upon these notions,
when duly determined and developed. If we once adopt a view of the
nature of knowledge which makes necessary truth possible at all, we
need be little embarrassed by finding how closely connected different
necessary truths are; and how often, in exploring towards their roots,
different branches appear to spring from the same stem.


END OF THE APPENDIX.




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Transcriber's Notes

Obvious typographical errors have been silently corrected. Other
variations in spelling, punctuation and hyphenation remain unchanged.

In the Table of Contents Chap. XV. item 3. is not listed.

In the Table of Contents Chap. XXVIII.  item 5.
Italics are represented thus _italics_.

The identification of the appendices skips I and J.







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