HISTORY
OF
SCIENTIFIC IDEAS.
VOLUME I.
Cambridge;
PRINTED BY C. J. CLAY, M.A.
AT THE UNIVERSITY PRESS.
HISTORY
OF
SCIENTIFIC IDEAS.
BY WILLIAM WHEWELL, D.D.,
MASTER OF TRINITY COLLEGE, CAMBRIDGE, AND
CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE.
BEING THE FIRST PART OF THE PHILOSOPHY
OF THE INDUCTIVE SCIENCES.
_THE THIRD EDITION._
IN TWO VOLUMES.
ΛΑΜΠΑΔIΑ ΕΧΟΝΤΕΣ ΔIΑΔΩΣΟΥΣIΝ ΑΛΛΗΛΟIΣ
VOLUME I.
LONDON:
JOHN W. PARKER AND SON, WEST STRAND.
1858.
{{v}}
PREFACE TO THIS EDITION.
THE Chapters now offered to the Reader were formerly
published as a portion of _The Philosophy of the Inductive
Sciences, founded upon their History_: but the nature and
subject of these Chapters are more exactly described by the
present title, _The History of Scientific Ideas_. For this
part of the work is mainly historical, and was, in fact,
collected from the body of scientific literature, at the
same time that the _History of the Inductive Sciences_ was
so collected. The present work contains the history of
Science so far as it depends on _Ideas_; the former work
contains the same history so far as it is derived from
_Observation_. The leading features in _that_ were Theories
inferred from Facts; the leading features of _this_ are
Discussions of Theories tending to make them consistent with
the conditions of human thought.
The Ideas of which the History is here given are mainly the
following:
_Space_, _Time_, _Number_, _Motion_, _Cause_, _Force_,
_Matter_, _Medium_, _Intensity_, _Scale_, _Polarity_,
_Element_, _Affinity_, _Substance_, _Atom_, _Symmetry_,
_Likeness_, _Natural Classes_, _Species_, _Life_,
_Function_, _Vital Forces_, _Final_ {vi} _Causes_,
_Historical Causation_, _Catastrophe and Uniformity_, _First
Cause_.
The controversies to which the exact fixation of these Ideas
and their properties have given occasion form a large and
essential part of the History of Science: but they also form
an important part of the Philosophy of Science, for no
Philosophy of Science can be complete which does not solve
the difficulties, antitheses, and paradoxes on which such
controversies have turned. I have given a survey of such
controversies, generally carried from their earliest origin
to their latest aspect; and have stated what appeared to me
the best solution of each problem. This has necessarily
involved me in much thorny metaphysics; but such metaphysics
is a necessary part of the progress of Science. The human
mind deriving its knowledge of Truth from the observation of
nature, cannot evade the task of determining at every step
how Truth is consistent with itself. This is the Metaphysics
of Progressive Knowledge, and this is the matter of this
present History.
Of the remaining part of what was formerly published as the
Philosophy of the Inductive Sciences, an additional part,
described in the Introduction to the present work, will
shortly be published.
TRINITY LODGE,
_May_ 24, 1858.
ERRATUM, p. 157, l. 11 from top, _for_ sciences
_read_ science.
CONTENTS
OF
THE FIRST VOLUME.
PAGE
PREFACE v
PART I.
OF IDEAS.
INTRODUCTION 3
BOOK I.
OF IDEAS IN GENERAL.
CHAP. I. OF THE FUNDAMENTAL ANTITHESIS OF PHILOSOPHY 23
_Sect._ 1. _Thoughts and Things_ --
2. _Necessary and Experiential Truths_ 25
3. _Deduction and Induction_ 27
4. _Theories and Facts_ 29
5. _Ideas and Sensations_ 30
6. _Reflexion and Sensation_ 33
7. _Subjective and Objective_ 35
8. _Matter and Form_ 38
9. _Man the Interpreter of Nature_ 41
10. _The Fundamental Antithesis is inseparable_ 43
11. _Successive Generalization_ 49
{viii}
CHAP. II. OF TECHNICAL TERMS 54
_Art._ 1. Examples.
2. Use of Terms.
CHAP. III. OF NECESSARY TRUTHS 57
_Art._ 1. The two Elements of Knowledge,
2. Shown by necessary Truths.
3. Examples of necessary Truths in numbers.
4. The opposite cannot be distinctly conceived.
5. Other Examples.
6. Universal Truths.
CHAP. IV. OF EXPERIENCE 65
_Art._ 1. Experience cannot prove necessary Truths,
2. Except when aided by Ideas.
CHAP. V. OF THE GROUNDS OF NECESSARY TRUTHS 69
_Art._ 1. These Grounds are Fundamental Ideas.
2. These are to be reviewed.
3. Definitions and Axioms.
4. Syllogism,
5. Produces no new Truths.
6. Axioms needed.
7. Axioms depend on Ideas:
8. So do Definitions.
9. Idea not completely expressed.
CHAP. VI. THE FUNDAMENTAL IDEAS ARE NOT DERIVED FROM EXPERIENCE 76
_Art._ 1. No connexion observed.
2. Faculties implied in observation.
3. We are to examine our Faculties.
CHAP. VII. OF THE PHILOSOPHY OF THE SCIENCES 81
Sciences arranged according to Ideas.
{ix}
BOOK II.
THE PHILOSOPHY OF THE PURE SCIENCES.
CHAP. I. OF THE PURE SCIENCES 88
_Art._ 1. Geometry, Arithmetic, Algebra,
2. Are not Inductive Sciences:
3. Are Mathematical Sciences.
4. Mixed Mathematics.
5. Space, Time, Number.
CHAP. II. OF THE IDEA OF SPACE 91
_Art._ 1. Space is an Idea,
2. Not derived from Experience,
3. As Geometrical Truth shows.
4. Space is a Form of Experience.
5. The phrase not essential.
CHAP. III. OF SOME PECULIARITIES OF THE IDEA OF SPACE 95
_Art._ 1. Space is not an Abstract Notion.
2. Space is infinite.
3. Space is real.
4. Space is a Form of Intuition.
5. Figure.
6. Three Dimensions.
CHAP. IV. OF THE DEFINITIONS AND AXIOMS WHICH RELATE TO SPACE 98
_Art._ 1. Geometry.
2. Definitions.
3. Axioms.
4. Not Hypotheses.
5. Axioms necessary.
6. Straight Lines.
7. Planes.
8. Elementary Geometry.
CHAP. V. OF SOME OBJECTIONS WHICH HAVE BEEN MADE TO THE
DOCTRINES STATED IN THE PREVIOUS CHAPTER 107
_Art._ 1. How is Geometry hypothetical?
2. What was Stewart's view?
{x}
3. 'Legitimate filiations' of Definitions.
4. Is a Definition a complete explanation?
5. Are some Axioms Definitions?
6. Axiom concerning Circles.
7. Can Axioms become truisms?
8. Use of such.
CHAP. VI. OF THE PERCEPTION OF SPACE 117
_Art._ 1. Which Senses apprehend Space?
2. Perception of solid figure.
3. Is an interpretation.
4. May be analysed.
5. Outline.
6. Reversed convexity.
7. Do we perceive Space by Touch?
8. Brown's Opinion.
9. The Muscular Sense.
10. Bell's Opinion.
11. Perception includes Activity.
12. Perception of the Skyey Dome.
13. Reid's Idomenians.
14. Motion of the Eye.
15. Searching Motion.
16. Sensible Spot.
17. Expressions implying Motion.
CHAP. VII. OF THE IDEA OF TIME 131
_Art._ 1. Time an Idea not derived from Experience.
2. Time is a Form of Experience.
3. Number.
4. Is Time derived from Motion?
CHAP. VIII. OF SOME PECULIARITIES IN THE IDEA OF TIME 134
_Art._ 1. Time is not an Abstract Notion.
2. Time is infinite.
3. Time is a Form of Intuition.
4. Time is of one Dimension,
5. And no more.
6. Rhythm.
7. Alternation.
8. Arithmetic.
{xi}
CHAP. IX. OF THE AXIOMS WHICH RELATE TO NUMBER 138
_Art._ 1. Grounds of Arithmetic.
2. Intuition.
3. Arithmetical Axioms,
4. Are Conditions of Numerical Reasoning
5. In all Arithmetical Operations.
6. Higher Numbers.
CHAP. X. OF THE PERCEPTION OF TIME AND NUMBER 141
_Art._ 1. Memory.
2. Sense of Successiveness
3. Implies Activity.
4. Number also does so.
5. And apprehension of Rhythm.
Note to Chapter X. 145
CHAP. XI. OF MATHEMATICAL REASONING 147
_Art._ 1. Discursive Reasoning.
2. Technical Terms of Reasoning.
3. Geometrical Analysis and Synthesis.
CHAP. XII. OF THE FOUNDATIONS OF THE HIGHER MATHEMATICS 151
_Art._ 1. The Idea of a Limit.
2. The use of General Symbols.
3. Connexion of Symbols and Analysis.
CHAP. XIII. THE DOCTRINE OF MOTION 156
_Art._ 1. Pure Mechanism.
2. Formal Astronomy.
CHAP. XIV. OF THE APPLICATION OF MATHEMATICS TO THE INDUCTIVE
SCIENCES 159
_Art._ 1. The Ideas of Space and Number are clear from
the first.
2. Their application in Astronomy.
3. Conic Sections, &c.
4. Arabian Numerals.
5. Newton's Lemmas.
6. Tides.
7. Mechanics.
8. Optics.
9. Conclusion.
{xii}
BOOK III.
THE PHILOSOPHY OF THE MECHANICAL SCIENCES.
CHAP. I. OF THE MECHANICAL SCIENCES 171
CHAP. II. OF THE IDEA OF CAUSE 173
_Art._ 1. Not derived from Observation,
2. As appears by its use.
3. Cause cannot be observed.
4. Is Cause only constant succession?
5. Other reasons.
CHAP. III. MODERN OPINIONS RESPECTING THE IDEA OF CAUSE 178
_Art._ 1. Hume's Doctrine.
2. Stewart and Brown.
3. Kant.
4. Relation of Kant and Brown.
5. Axioms flow from the Idea.
6. The Idea implies activity in the Mind.
CHAP. IV. OF THE AXIOMS WHICH RELATE TO THE IDEA OF CAUSE 184
_Art._ 1. Causes are Abstract Conceptions.
2. First Axiom.
3. Second Axiom.
4. Limitation of the Second Axiom.
5. Third Axiom.
6. Extent of the Third Axiom.
CHAP. V. OF THE ORIGIN OF OUR CONCEPTIONS OF FORCE AND MATTER 205
_Art._ 1. Force.
2. Matter.
3. Solidity.
4. Inertia.
5. Application.
{xiii}
CHAP. VI. OF THE ESTABLISHMENT OF THE PRINCIPLES OF STATICS 212
_Art._ 1. Object of the Chapter.
2. Statics and Dynamics.
3. Equilibrium.
4. Measure of Statical Forces.
5. The Center of Gravity.
6. Oblique Forces.
7. Force acts at any point of its Direction.
8. The Parallelogram of Forces
9. Is a necessary Truth.
10. Center of Gravity descends.
11. Stevinus's Proof.
12. Principle of Virtual Velocities.
13. Fluids press equally.
14. Foundation of this Axiom.
CHAP. VII. OF THE ESTABLISHMENT OF THE PRINCIPLES OF DYNAMICS 235
_Art._ 1. History.
2. The First Law of Motion.
3. Gravity is a Uniform Force.
4. The Second Law of Motion.
5. The Third Law of Motion.
6. Action and Reaction in Moving Bodies.
7. D'Alembert's Principle.
8. Connexion of Statics and Dynamics.
9. Mechanical Principles grow more evident.
10. Controversy of the Measure of Force.
CHAP. VIII. OF THE PARADOX OF UNIVERSAL PROPOSITIONS
OBTAINED FROM EXPERIENCE 263
_Art._ 1. Experience cannot establish necessary Truths;
2. But can interpret Axioms.
3. Gives us the Matter of Truths.
4. Exemplifies Truths.
5. Cannot shake Axioms.
6. Is this applicable in other cases?
CHAP. IX. OF THE ESTABLISHMENT OF THE LAW OF UNIVERSAL
GRAVITATION 272
_Art._ 1. General course of the History.
{xiv}
2. Particulars as to the Law.
3. As to the Gravity of Matter.
4. Universality of the Law.
5. Is Gravity an essential quality?
6. Newton's Rule of Philosophizing.
7. Hypotheses respecting Gravity.
8. Do Bodies act at a distance?
CHAP. X. OF THE GENERAL DIFFUSION OF CLEAR MECHANICAL IDEAS 279
_Art._ 1. Nature of the Process
2. Among the Ancients.
3. Kepler, &c.
4. Lord Monboddo, &c.
5. Schelling, &c.
6. Common usage.
7. Effect of Phrases.
8. Contempt of Predecessors.
9. Less detail hereafter.
10. Mechanico-Chemical Sciences.
11. Secondary Mechanical Sciences.
BOOK IV.
THE PHILOSOPHY OF THE SECONDARY MECHANICAL SCIENCES.
CHAP. I. OF THE IDEA OF A MEDIUM AS COMMONLY EMPLOYED 293
_Art._ 1. Of Primary and Secondary Qualities.
2. The Idea of Externality.
3. Sensation by a Medium.
4. Process of Perception of Secondary Qualities.
CHAP. II. ON PECULIARITIES IN THE PERCEPTIONS OF THE
DIFFERENT SENSES 302
_Art._ 1. Difference of Senses.
_Sect._ I. _Prerogatives of Sight._
_Art._ 2. Position.
3. Distance.
{xv}
_Sect._ II. _Prerogatives of Hearing._
_Art._ 4. Musical Intervals.
5. Chords.
6. Rhythm.
_Sect._ III. _The Paradoxes of Vision._
_Art._ 7. First Paradox.
8. Second Paradox.
9. The same for near Objects.
10. Objections answered.
_Sect._ IV. _The Perception of Visible Figures._
_Art._ 11. Brown's Opinion.
CHAP. III. SUCCESSIVE ATTEMPTS AT THE SCIENTIFIC
APPLICATION OF THE IDEA OF A MEDIUM 322
_Art._ 1. Introduction.
2. Sound.
3. Light.
4. Heat.
CHAP. IV. OF THE MEASURE OF SECONDARY QUALITIES 333
_Sect._ I. _Scales of Qualities in General._
_Art._ 1. Intensity.
2. Quantity and Quality.
_Sect._ II. _The Musical Scale._
_Art._ 3. Musical Relations.
4. Musical Standard.
_Sect._ III. _Scales of Colour._
_Art._ 5. The Prismatic Scale.
6. Newton's Scale.
7. Scales of Impure Colours.
8. Chromatometer.
_Sect._ IV. _Scales of Light._
_Art._ 9. Photometer.
10. Cyanometer.
_Sect._ V. _Scales of Heat._
_Art._ 11. Thermometers.
12. Their progress.
13. Fixed Points.
14. Concordance of Thermometers.
15. Natural Measure.
16. Law of Cooling.
{xvi}
17. Theory of Exchanges.
18. Air Thermometer.
19. Theory of Heat.
20. Other Instruments.
_Sect._ VI. _Scales of other Quantities._
_Art._ 21. Tastes and Smells.
22. Quality of Sounds.
23. Articulate Sounds.
24. Transition.
BOOK V.
OF THE PHILOSOPHY OF THE MECHANICO-CHEMICAL SCIENCES.
CHAP. I. ATTEMPTS AT THE SCIENTIFIC APPLICATION OF THE IDEA
OF POLARITY 359
_Art._ 1. Introduction of the Idea.
2. Magnetism.
3. Electricity.
4. Voltaic Electricity.
5. Light.
6. Crystallization.
7. Chemical Affinity.
8. General Remarks.
9. Like _repels_ like.
CHAP. II. OF THE CONNEXION OF POLARITIES 371
_Art._ 1. Different Polar Phenomena from one Cause.
2. Connexion of Magnetic and Electric Polarity.
3. Ampère's Theory.
4. Faraday's views.
5. Connexion of Electrical and Chemical Polarity.
6. Davy's and Faraday's views
7. Depend upon Ideas as well as Experiments.
8. Faraday's Anticipations.
9. Connexion of Chemical and Crystalline Polarities.
10. Connexion of Crystalline and Optical Polarities.
11. Connexion of Polarities in general.
12. Schelling's Speculations.
13. Hegel's vague notions.
14. Ideas must guide Experiment.
{{1}}
THE
PHILOSOPHY
OF THE
INDUCTIVE SCIENCES.
INTRODUCTION.
{{3}}
INTRODUCTION.
THE PHILOSOPHY OF SCIENCE, if the phrase were to be
understood in the comprehensive sense which most naturally
offers itself to our thoughts, would imply nothing less than
a complete insight into the essence and conditions of all
real knowledge, and an exposition of the best methods for
the discovery of new truths. We must narrow and lower this
conception, in order to mould it into a form in which we may
make it the immediate object of our labours with a good hope
of success; yet still it may be a rational and useful
undertaking, to endeavour to make some advance towards such
a Philosophy, even according to the most ample conception of
it which we can form. The present work has been written with
a view of contributing, in some measure, however small it
may be, towards such an undertaking.
But in this, as in every attempt to advance beyond the
position which we at present occupy, our hope of success
must depend mainly upon our being able to profit, to the
fullest extent, by the progress already made. We may best
hope to understand the nature and conditions of real
knowledge, by studying the nature and conditions of the most
certain and stable portions of knowledge which we already
possess: and we are most likely to learn the best methods of
discovering truth, by examining how truths, now universally
recognized, have really been discovered. Now there do exist
among us doctrines of solid and acknowledged certainty, and
truths of which the discovery has been received with
universal applause. These constitute what we commonly term
_Sciences_; and of these bodies of exact and enduring
knowledge, we have within our {4} reach so large and varied
a collection, that we may examine them, and the history of
their formation, with a good prospect of deriving from the
study such instruction as we seek. We may best hope to make
some progress towards the Philosophy of Science, by
employing ourselves upon THE PHILOSOPHY OF THE SCIENCES.
The _Sciences_ to which the name is most commonly and
unhesitatingly given, are those which are concerned about
the material world; whether they deal with the celestial
bodies, as the sun and stars, or the earth and its products,
or the elements; whether they consider the differences which
prevail among such objects, or their origin, or their mutual
operation. And in all these Sciences it is familiarly
understood and assumed, that their doctrines are obtained by
a common process of collecting general truths from
particular observed facts, which process is termed
_Induction_. It is further assumed that both in these and in
other provinces of knowledge, so long as this process is
duly and legitimately performed, the results will be real
substantial truth. And although this process, with the
conditions under which it is legitimate, and the general
laws of the formation of Sciences, will hereafter be
subjects of discussion in this work, I shall at present so
far adopt the assumption of which I speak, as to give to the
Sciences from which our lessons are to be collected the name
of _Inductive Sciences_. And thus it is that I am led to
designate my work as THE PHILOSOPHY OF THE INDUCTIVE
SCIENCES.
The views respecting the nature and progress of knowledge,
towards which we shall be directed by such a course of
inquiry as I have pointed out, though derived from those
portions of human knowledge which are more peculiarly and
technically termed _Sciences_, will by no means be confined,
in their bearing, to the domain of such Sciences as deal
with the material world, nor even to the whole range of
Sciences now existing. On the contrary, we shall be led to
believe that the nature of truth is in all subjects the
same, and that its discovery involves, in all cases, the
like {5} conditions. On one subject of human speculation
after another, man's knowledge assumes that exact and
substantial character which leads us to term it _Science_;
and in all these cases, whether inert matter or living
bodies, whether permanent relations or successive
occurrences, be the subject of our attention, we can point
out certain universal characters which belong to truth,
certain general laws which have regulated its progress among
men. And we naturally expect that, even when we extend our
range of speculation wider still, when we contemplate the
world within us as well as the world without us, when we
consider the thoughts and actions of men as well as the
motions and operations of unintelligent bodies, we shall
still find some general analogies which belong to the
essence of truth, and run through the whole intellectual
universe. Hence we have reason to trust that a just
Philosophy of the Sciences may throw light upon the nature
and extent of our knowledge in every department of human
speculation. By considering what is the real import of our
acquisitions, where they are certain and definite, we may
learn something respecting the difference between true
knowledge and its precarious or illusory semblances; by
examining the steps by which such acquisitions have been
made, we may discover the conditions under which truth is to
be obtained; by tracing the boundary-line between our
knowledge and our ignorance, we may ascertain in some
measure the extent of the powers of man's understanding.
But it may be said, in such a design there is nothing new;
these are objects at which inquiring men have often before
aimed. To determine the difference between real and
imaginary knowledge, the conditions under which we arrive at
truth, the range of the powers of the human mind, has been a
favourite employment of speculative men from the earliest to
the most recent times. To inquire into the original,
certainty, and compass of man's knowledge, the limits of his
capacity, the strength and weakness of his reason, has been
the professed purpose of many of the most conspicuous and
valued labours of the philosophers of {6} all periods up to
our own day. It may appear, therefore, that there is little
necessity to add one more to these numerous essays; and
little hope that any new attempt will make any very
important addition to the stores of thought upon such
questions, which have been accumulated by the profoundest
and acutest thinkers of all ages.
To this I reply, that without at all disparaging the value
or importance of the labours of those who have previously
written respecting the foundations and conditions of human
knowledge, it may still be possible to add something to what
they have done. The writings of all great philosophers, up
to our own time, form a series which is not yet terminated.
The books and systems of philosophy which have, each in its
own time, won the admiration of men, and exercised a
powerful influence upon their thoughts, have had each its
own part and functions in the intellectual history of the
world; and other labours which shall succeed these may also
have their proper office and useful effect. We may not be
able to do much, and yet still it may be in our power to
effect something. Perhaps the very advances made by former
inquirers may have made it possible for us, at present, to
advance still further. In the discovery of truth, in the
development of man's mental powers and privileges, each
generation has its assigned part; and it is for us to
endeavour to perform our portion of this perpetual task of
our species. Although the terms which describe our
undertaking may be the same which have often been employed
by previous writers to express their purpose, yet our
position is different from theirs, and thus the result may
be different too. We have, as they had, to run our
appropriate course of speculation with the exertion of our
best powers; but our course lies in a more advanced part of
the great line along which Philosophy travels from age to
age. However familiar and old, therefore, be the design of
such a work as this, the execution may have, and if it be
performed in a manner suitable to the time, will have,
something that is new and not unimportant. {7}
Indeed, it appears to be absolutely necessary, in order to
check the prevalence of grave and pernicious errour, that
the doctrines which are taught concerning the foundations of
human knowledge and the powers of the human mind, should be
from time to time revised and corrected or extended.
Erroneous and partial views are promulgated and accepted;
one portion of the truth is insisted upon to the undue
exclusion of another; or principles true in themselves are
exaggerated till they produce on men's minds the effect of
falsehood. When evils of this kind have grown to a serious
height, a _Reform_ is requisite. The faults of the existing
systems must be remedied by correcting what is wrong, and
supplying what is wanting. In such cases, all the merits and
excellencies of the labours of the preceding times do not
supersede the necessity of putting forth new views suited to
the emergency which has arrived. The new form which errour
has assumed makes it proper to endeavour to give a new and
corresponding form to truth. Thus the mere progress of time,
and the natural growth of opinion from one stage to another,
leads to the production of new systems and forms of
philosophy. It will be found, I think, that some of the
doctrines now most widely prevalent respecting the
foundations and nature of truth are of such a kind that a
Reform is needed. The present age seems, by many
indications, to be called upon to seek a sounder Philosophy
of Knowledge than is now current among us. To contribute
towards such a Philosophy is the object of the present work.
The work is, therefore, like all works which take into
account the most recent forms of speculative doctrine,
invested with a certain degree of novelty in its aspect and
import, by the mere time and circumstances of its
appearance.
But, moreover, we can point out a very important peculiarity
by which this work is, in its design, distinguished from
preceding essays on like subjects; and this difference
appears to be of such a kind as may well entitle us to
expect some substantial addition to our knowledge as the
result of our labours. The peculiarity {8} of which I speak
has already been announced;--it is this: that we purpose to
collect our doctrines concerning the nature of knowledge,
and the best mode of acquiring it, from a contemplation of
the Structure and History of those Sciences (the Material
Sciences), which are universally recognized as the clearest
and surest examples of knowledge and of discovery. It is by
surveying and studying the whole mass of such Sciences, and
the various steps of their progress, that we now hope to
approach to the true Philosophy of Science.
Now this, I venture to say, is a new method of pursuing the
philosophy of human knowledge. Those who have hitherto
endeavoured to explain the nature of knowledge, and the
process of discovery, have, it is true, often illustrated
their views by adducing special examples of truths which
they conceived to be established, and by referring to the
mode of their establishment. But these examples have, for
the most part, been taken at random, not selected according
to any principle or system. Often they have involved
doctrines so precarious or so vague that they confused
rather than elucidated the subject; and instead of a single
difficulty,--What is the nature of Knowledge? these attempts
at illustration introduced two,--What was the true analysis
of the Doctrines thus adduced? and,--Whether they might
safely be taken as types of real Knowledge?
This has usually been the case when there have been adduced,
as standard examples of the formation of human knowledge,
doctrines belonging to supposed sciences other than the
material sciences; doctrines, for example, of Political
Economy, or Philology, or Morals, or the Philosophy of the
Fine Arts. I am very far from thinking that, in regard to
such subjects, there are no important truths hitherto
established: but it would seem that those truths which have
been obtained in these provinces of knowledge, have not yet
been fixed by means of distinct and permanent phraseology,
and sanctioned by universal reception, and formed into a
connected system, and traced through the steps of their
gradual discovery and establishment, so as to make {9} them
instructive examples of the nature and progress of truth in
general. Hereafter we trust to be able to show that the
progress of moral, and political, and philological, and
other knowledge, is governed by the same laws as that of
physical science. But since, at present, the former class of
subjects are full of controversy, doubt, and obscurity,
while the latter consist of undisputed truths clearly
understood and expressed, it may be considered a wise
procedure to make the latter class of doctrines the basis of
our speculations. And on the having taken this course, is,
in a great measure, my hope founded, of obtaining valuable
truths which have escaped preceding inquirers.
But it may be said that many preceding writers on the nature
and progress of knowledge have taken their examples
abundantly from the Physical Sciences. It would be easy to
point out admirable works, which have appeared during the
present and former generations, in which instances of
discovery, borrowed from the Physical Sciences, are
introduced in a manner most happily instructive. And to the
works in which this has been done, I gladly give my most
cordial admiration. But at the same time I may venture to
remark that there still remains a difference between my
design and theirs: and that I use the Physical Sciences as
exemplifications of the general progress of knowledge in a
manner very materially different from the course which is
followed in works such as are now referred to. For the
conclusions stated in the present work, respecting knowledge
and discovery, are drawn from _a connected and systematic
survey of the whole range of Physical Science and its
History_; whereas, hitherto, philosophers have contented
themselves with adducing detached examples of scientific
doctrines, drawn from one or two departments of science. So
long as we select our examples in this arbitrary and limited
manner, we lose the best part of that philosophical
instruction, which the sciences are fitted to afford when we
consider them as all members of one series, and as governed
by rules which are the same for all. Mathematical and
chemical truths, physical and physiological doctrines, the
sciences of {10} classification and of causation, must alike
be taken into our account, in order that we may learn what
are the general characters of real knowledge. When our
conclusions assume so comprehensive a shape that they apply
to a range of subjects so vast and varied as these, we may
feel some confidence that they represent the genuine form of
universal and permanent truth. But if our exemplification is
of a narrower kind, it may easily cramp and disturb our
philosophy. We may, for instance, render our views of truth
and its evidence so rigid and confined as to be quite
worthless, by founding them too much on the contemplation of
mathematical truth. We may overlook some of the most
important steps in the general course of discovery, by
fixing our attention too exclusively upon some one
conspicuous group of discoveries, as, for instance, those of
Newton. We may misunderstand the nature of physiological
discoveries, by attempting to force an analogy between them
and discoveries of mechanical laws, and by not attending to
the intermediate sciences which fill up the vast interval
between these extreme terms in the series of material
sciences. In these and in many other ways, a partial and
arbitrary reference to the material sciences in our inquiry
into human knowledge may mislead us; or at least may fail to
give us those wider views, and that deeper insight, which
should result from a systematic study of the whole range of
sciences with this particular object.
The design of the following work, then, is to form a
Philosophy of Science, by analyzing the substance and
examining the progress of the existing body of the sciences.
As a preliminary to this undertaking, a survey of the
history of the sciences was necessary. This, accordingly, I
have already performed; and the result of the labour thus
undertaken has been laid before the public as a _History of
the Inductive Sciences_.
In that work I have endeavoured to trace the steps by which
men acquired each main portion of that knowledge on which
they now look with so much confidence and satisfaction. The
events which that History relates, the speculations and
controversies {11} which are there described, and
discussions of the same kind, far more extensive, which are
there omitted, must all be taken into our account at
present, as the prominent and standard examples of the
circumstances which attend the progress of knowledge. With
so much of real historical fact before us, we may hope to
avoid such views of the processes of the human mind as are
too partial and limited, or too vague and loose, or too
abstract and unsubstantial, to represent fitly the real
forms of discovery and of truth.
Of former attempts, made with the same view of tracing the
conditions of the progress of knowledge, that of Bacon is
perhaps the most conspicuous: and his labours on this
subject were opened by his book on the _Advancement of
Learning_, which contains, among other matter, a survey of
the then existing state of knowledge. But this review was
undertaken rather with the object of ascertaining in what
quarters future advances were to be hoped for, than of
learning by what means they were to be made. His examination
of the domain of human knowledge was conducted rather with
the view of discovering what remained undone, than of
finding out how so much had been done. Bacon's survey was
made for the purpose of tracing the boundaries, rather than
of detecting the principles of knowledge. 'I will now
attempt,' he says[1\I], 'to make a general and faithful
perambulation of learning, with an inquiry what parts
thereof lie fresh and waste, and not improved and converted
by the industry of man; to the end that such a plot made and
recorded to memory, may both minister light to any public
designation, and also serve to excite voluntary endeavours.'
Nor will it be foreign to our scheme also hereafter to
examine with a like purpose the frontier-line of man's
intellectual estate. But the object of our perambulation in
the first place, is not so much to determine the extent of
the field, as the sources of its fertility. We would learn
by what plan and rules {12} of culture, conspiring with the
native forces of the bounteous soil, those rich harvests
have been produced which fill our garners. Bacon's maxims,
on the other hand, respecting the mode in which he conceived
that knowledge was thenceforth to be cultivated, have little
reference to the failures, still less to the successes,
which are recorded in his Review of the learning of his
time. His precepts are connected with his historical views
in a slight and unessential manner. His Philosophy of the
Sciences is not collected from the Sciences which are
noticed in his survey. Nor, in truth, could this, at the
time when he wrote, have easily been otherwise. At that
period, scarce any branch of physics existed as a science,
except Astronomy. The rules which Bacon gives for the
conduct of scientific researches are obtained, as it were,
by divination, from the contemplation of subjects with
regard to which no sciences as yet were. His instances of
steps rightly or wrongly made in this path, are in a great
measure cases of his own devising. He could not have
exemplified his Aphorisms by references to treatises then
extant, on the laws of nature; for the constant burden of
his exhortation is, that men up to his time had almost
universally followed an erroneous course. And however we may
admire the sagacity with which he pointed the way along a
better path, we have this great advantage over him;--that we
can interrogate the many travellers who since his time have
journeyed on this road. At the present day, when we have
under our notice so many sciences, of such wide extent, so
well established; a Philosophy of the Sciences ought, it
must seem, to be founded, not upon conjecture, but upon an
examination of many instances;--should not consist of a few
vague and unconnected maxims, difficult and doubtful in
their application, but should form a system of which every
part has been repeatedly confirmed and verified.
[Note 1\I: _Advancement of Learning_, b. i. p. 74.]
This accordingly it is the purpose of the present work to
attempt. But I may further observe, that as my hope of
making any progress in this undertaking is {13} founded upon
the design of keeping constantly in view the whole result of
the past history and present condition of science, I have
also been led to draw my lessons from my examples in a
manner more systematic and regular, as appears to me, than
has been done by preceding writers. Bacon, as I have just
said, was led to his maxims for the promotion of knowledge
by the sagacity of his own mind, with little or no aid from
previous examples. Succeeding philosophers may often have
gathered useful instruction from the instances of scientific
truths and discoveries which they adduced, but their
conclusions were drawn from their instances casually and
arbitrarily. They took for their moral any which the story
might suggest. But such a proceeding as this cannot suffice
for us, whose aim is to obtain a consistent body of
philosophy from a contemplation of the whole of Science and
its History. For our purpose it is necessary to resolve
scientific truths into their conditions and ingredients, in
order that we may see in what manner each of these has been
and is to be provided, in the cases which we may have to
consider. This accordingly is necessarily the first part of
our task:--_to analyse Scientific Truth into its Elements_.
This attempt will occupy the earlier portion of the present
work; and will necessarily be somewhat long, and perhaps, in
many parts, abstruse and uninviting. The risk of such an
inconvenience is inevitable; for the inquiry brings before
us many of the most dark and entangled questions in which
men have at any time busied themselves. And even if these
can now be made clearer and plainer than of yore, still they
can be made so only by means of mental discipline and mental
effort. Moreover this analysis of scientific truth into its
elements contains much, both in its principles and in its
results, different from the doctrines most generally
prevalent among us in recent times: but on that very account
this analysis is an essential part of the doctrines which I
have now to lay before the reader: and I must therefore
crave his indulgence towards any portion of it which may
appear to him obscure or repulsive. {14}
There is another circumstance which may tend to make the
present work less pleasing than others on the same subject,
in the nature of the examples of human knowledge to which I
confine myself; all my instances being, as I have said,
taken from the material sciences. For the truths belonging
to these sciences are, for the most part, neither so
familiar nor so interesting to the bulk of readers as those
doctrines which belong to some other subjects. Every general
proposition concerning politics or morals at once stirs up
an interest in men's bosoms, which makes them listen with
curiosity to the attempts to trace it to its origin and
foundation. Every rule of art or language brings before the
mind of cultivated men subjects of familiar and agreeable
thought, and is dwelt upon with pleasure for its own sake,
as well as on account of the philosophical lessons which it
may convey. But the curiosity which regards the truths of
physics or chemistry, or even of physiology or astronomy, is
of a more limited and less animated kind. Hence, in the mode
of inquiry which I have prescribed to myself, the examples
which I have to adduce will not amuse and relieve the
reader's mind as much as they might do, if I could allow
myself to collect them from the whole field of human
knowledge. They will have in them nothing to engage his
fancy, or to warm his heart. I am compelled to detain the
listener in the chilly air of the external world, in order
that we may have the advantage of full daylight.
But although I cannot avoid this inconvenience, so far as it
is one, I hope it will be recollected how great are the
advantages which we obtain by this restriction. We are thus
enabled to draw all our conclusions from doctrines which are
universally allowed to be eminently certain, clear, and
definite. The portions of knowledge to which I refer are
well known, and well established among men. Their names are
familiar, their assertions uncontested. Astronomy and
Geology, Mechanics and Chemistry, Optics and Acoustics,
Botany and Physiology, are each recognized as large and
substantial collections of undoubted truths. Men are {15}
wont to dwell with pride and triumph on the acquisitions of
knowledge which have been made in each of these provinces;
and to speak with confidence of the certainty of their
results. And all can easily learn in what repositories these
treasures of human knowledge are to be found. When,
therefore, we begin our inquiry from such examples, we
proceed upon a solid foundation. With such a clear ground of
confidence, we shall not be met with general assertions of
the vagueness and uncertainty of human knowledge; with the
question, What truth is, and How we are to recognize it;
with complaints concerning the hopelessness and
unprofitableness of such researches. We have, at least, a
definite problem before us. We have to examine the structure
and scheme, not of a shapeless mass of incoherent materials,
of which we doubt whether it be a ruin or a natural
wilderness, but of a fair and lofty palace, still erect and
tenanted, where hundreds of different apartments belong to a
common plan, where every generation adds something to the
extent and magnificence of the pile. The certainty and the
constant progress of science are things so unquestioned,
that we are at least engaged in an intelligible inquiry,
when we are examining the grounds and nature of that
certainty, the causes and laws of that progress.
To this inquiry, then, we now proceed. And in entering upon
this task, however our plan or our principles may differ
from those of the eminent philosophers who have endeavoured,
in our own or in former times, to illustrate or enforce the
philosophy of science, we most willingly acknowledge them as
in many things our leaders and teachers. Each reform must
involve its own peculiar principles, and the result of our
attempts, so far as they lead to a result, must be, in some
respects, different from those of former works. But we may
still share with the great writers who have treated this
subject before us, their spirit of hope and trust, their
reverence for the dignity of the subject, their belief in
the vast powers and boundless destiny of man. And we may
once more venture to use the {16} words of hopeful
exhortation, with which the greatest of those who have
trodden this path encouraged himself and his followers when
he set out upon his way.
'Concerning ourselves we speak not; but as touching the
matter which we have in hand, this we ask;--that men deem it
not to be the setting up an Opinion, but the performing of a
Work: and that they receive this as a certainty; that we are
not laying the foundations of any sect or doctrine, but of
the profit and dignity of mankind. Furthermore, that being
well disposed to what shall advantage themselves, and
putting off factions and prejudices, they take common
counsel with us, to the end that being by these our aids and
appliances freed and defended from wanderings and
impediments, they may lend their hands also to the labours
which remain to be performed: and yet further, that they be
of good hope; neither 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 errour; 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
one single age, but assigning it as a task to a succession
of generations.'
[The Philosophy of the Inductive Sciences, according to our
view, must be founded upon the History of such Sciences;
which history we have attempted in a former work. The events
of that history may be described generally as the rise of
Theories out of Facts. But besides this, which we may term
the _external_ history of Theories, there is an internal
history of Theories, namely, the series of steps by which
the human mind becomes capable of forming each Theory. Hence
to complete the History of the Sciences as derived from
Facts, we require a history of the Ideas by which such
derivation has been made possible: and thus, the _First
Part_ of our Philosophy must be a _History of Scientific
Ideas_;--a labour no less historical than our former work,
and concerned with the same events; but which has been
purposely kept separate during the {17} composition, in
order that it might be afterwards presented in a more
systematic form, which I have here attempted to do.
Scientific Ideas are the Conditions of the derivation of
Sciences from Facts: but can any method or methods be given
by which such a Derivation can be ensured, or at least,
aided? Many such methods have been proposed; of which the
most celebrated is the _Novum Organon_ of Bacon, of which
the title was intended to imply that its scope goes much
beyond the _Organon_ of Aristotle. With the experience of
the formation of Science which the world has had since
Bacon's time, it does not appear presumptuous to suppose
that we can now improve or correct his methods; nor to term
such an attempt _Novum Organon Renovatum_.
The Philosophy of the Inductive Sciences, then, contains
these two parts, _The History of Scientific Ideas_, and the
_Novum Organon Renovatum_.]
{{19}}
THE
PHILOSOPHY
OF THE
INDUCTIVE SCIENCES.
PART I.
HISTORY OF SCIENTIFIC IDEAS.
[We have just spoken of _Theories_ and _Facts_, of _Ideas_
and _Facts_, and of _Inductive_ Sciences, which imply the
opposition of _Induction_ and _Deduction_. The explanation
of these antitheses must be the starting point of our
Philosophy.]
[Knowledge grows, and] through the ages one increasing purpose runs,
And the thoughts of men are widen'd with the process of the Suns.
BOOK I.
OF IDEAS IN GENERAL.
Quæ adhuc inventa sunt in Scientiis, ea hujusmodi sunt ut
Notionibus Vulgaribus fere subjaceant: ut vero ad interiora
et remotiora Naturæ penetretur, necesse est ut tam NOTIONES
quam AXIOMATA magis certâ et munitâ viâ a particularibus
abstrahantur; atque omnino melior et certior intellectûs
adoperatio in usum veniat.
BACON, _Nov. Org._, Lib. 1. Aphor. xviii.
{{23}}
BOOK I.
OF IDEAS IN GENERAL.
CHAPTER I.
OF THE FUNDAMENTAL ANTITHESIS OF PHILOSOPHY.
_Sect._ 1.--_Thoughts and Things._
IN order that we may do something towards determining the
nature and conditions of human knowledge, (which I have
already stated as the purpose of this work,) I shall have to
refer to an antithesis or opposition, which is familiar and
generally recognized, and in which the distinction of the
things opposed to each other is commonly considered very
clear and plain. I shall have to attempt to make this
opposition sharper and stronger than it is usually
conceived, and yet to shew that the distinction is far from
being so clear and definite as it is usually assumed to be:
I shall have to point the contrast, yet shew that the things
which are contrasted cannot be separated:--I must explain
that the antithesis is constant and essential, but yet that
there is no fixed and permanent line dividing its members. I
may thus appear, in different parts of my discussion, to be
proceeding in opposite directions, but I hope that the
reader who gives me a patient attention will see that both
steps lead to the point of view to which I wish to lead him.
The antithesis or opposition of which I speak is denoted,
with various modifications, by various pairs of terms: I
shall endeavour to shew the connexion of these different
modes of expression, and I will begin with that form which
is the simplest and most idiomatic. {24}
The simplest and most idiomatic expression of the antithesis
to which I refer is that in which we oppose to each other
THINGS and THOUGHTS. The opposition is familiar and plain.
Our thoughts are something which belongs to ourselves;
something which takes place within us; they are what we
think; they are actions of our minds. Things, on the
contrary, are something different from ourselves and
independent of us; something which is without us; they
_are_; we see them, touch them, and thus know that they
exist; but we do not make them by seeing or touching them,
as we make our _Thoughts_ by thinking them; we are passive,
and _Things_ act upon our organs of perception.
Now what I wish especially to remark is this: that in all
human KNOWLEDGE both Thoughts and Things are concerned. In
every part of my knowledge there must be some _thing_ about
which I know, and an internal act of _me_ who know. Thus, to
take simple yet definite parts of our knowledge, if I know
that a solar year consists of 365 days, or a lunar month of
30 days, I know something about the sun or the moon; namely,
that those objects perform certain revolutions and go
through certain changes, in those numbers of days; but I
count such numbers and conceive such revolutions and changes
by acts of my own thoughts. And both these elements of my
knowledge are indispensable. If there were not such external
Things as the sun and the moon I could not have any
knowledge of the progress of time as marked by them. And
however regular were the motions of the sun and moon, if I
could not count their appearances and combine their changes
into a cycle, or if I could not understand this when done by
other men, I could not know anything about a year or a
month. In the former case I might be conceived as a human
being, possessing the human powers of thinking and
reckoning, but kept in a dark world with nothing to mark the
progress of existence. The latter is the case of brute
animals, which see the sun and moon, but do not know how
many days make a month or a year, because they have not
human powers of thinking and reckoning. {25}
The two elements which are essential to our knowledge in the
above cases, are necessary to human knowledge in all cases.
In all cases, Knowledge implies a combination of Thoughts
and Things. Without this combination, it would not be
Knowledge. Without Thoughts, there could be no connexion;
without Things, there could be no reality. Thoughts and
Things are so intimately combined in our Knowledge, that we
do not look upon them as distinct. One single act of the
mind involves them both; and their contrast disappears in
their union.
But though Knowledge requires the union of these two
elements, Philosophy requires the separation of them, in
order that the nature and structure of Knowledge may be
seen. Therefore I begin by considering this separation. And
I now proceed to speak of another way of looking at the
antithesis of which I have spoken; and which I may, for the
reasons which I have just mentioned, call the FUNDAMENTAL
ANTITHESIS OF PHILOSOPHY.
_Sect._ 2.--_Necessary and Experiential Truths._
MOST persons are familiar with the distinction of
_necessary_ and _contingent_ truths. The former kind are
Truths which cannot but be true; as that 19 and 11 make
30;--that parallelograms upon the same base and between the
same parallels are equal;--that all the angles in the same
segment of a circle are equal. The latter are Truths which
_it happens_ (_contingit_) are true; but which, for anything
which we can see, might have been otherwise; as that a lunar
month contains 30 days, or that the stars revolve in circles
round the pole. The latter kind of Truths are learnt by
experience, and hence we may call them _Truths of
Experience_, or, for the sake of convenience, _Experiential_
Truths, in contrast with Necessary Truths.
Geometrical propositions are the most manifest examples of
Necessary Truths. All persons who have read and understood
the elements of geometry, know that the propositions above
stated (that parallelograms {26} upon the same base and
between the same parallels are equal; that all the angles in
the same segment of a circle are equal,) are necessarily
true; not only they are true, but they _must be_ true. The
meaning of the terms being understood, and the proof being
gone through, the truth of the propositions must be assented
to. We learn these propositions to be true by demonstrations
deduced from definitions and axioms; and when we have thus
learnt them, we see that they could not be otherwise. In the
same manner, the truths which concern numbers are necessary
truths: 19 and 11 not only _do_ make 30, but _must_ make
that number, and cannot make anything else. In the same
manner, it is a necessary truth that half the sum of two
numbers added to half their difference is equal to the
greater number.
It is easy to find examples of Experiential Truths;--
propositions which we know to be true, but know by
experience only. We know, in this way, that salt will
dissolve in water; that plants cannot live without light;--
in short, we know in this way all that we do know in
chemistry, physiology, and the material sciences in general.
I take the _Sciences_ as my examples of human knowledge,
rather than the common truths of daily life, or moral or
political truths; because, though the latter are more
generally interesting, the former are much more definite and
certain, and therefore better starting-points for our
speculations, as I have already said. And we may take
elementary astronomical truths as the most familiar examples
of Experiential Truths in the domain of science.
With these examples, the distinction of Necessary and
Experiential Truths is, I hope, clear. The former kind, we
see to be true by thinking about them, and see that they
could not be otherwise. The latter kind, men could never
have discovered to be true without looking at them; and
having so discovered them, still no one will pretend to say
they might not have been otherwise. For aught we can see,
the astronomical truths which express the motions and
periods of the sun, moon and stars, might have been
otherwise. If we had been placed in another part of the
solar system, our {27} experiential truths respecting days,
years, and the motions of the heavenly bodies, would have
been other than they are, as we know from astronomy itself.
It is evident that this distinction of Necessary and
Experiential Truths involves the same antithesis which we
have already considered;--the antithesis of Thoughts and
Things. Necessary Truths are derived from our own Thoughts:
Experiential truths are derived from our observation of
Things about us. The opposition of Necessary and
Experiential Truths is another aspect of the Fundamental
Antithesis of Philosophy.
_Sect._ 3.--_Deduction and Induction._
I HAVE already stated that geometrical truths are
established by demonstrations _deduced_ from definitions and
axioms. The term _Deduction_ is specially applied to such a
course of demonstration of truths from definitions and
axioms. In the case of the parallelograms upon the same base
and between the same parallels, we prove certain triangles
to be equal, by supposing them placed so that their two
bases have the same extremities; and hence, referring to an
Axiom respecting straight lines, we infer that the bases
coincide. We combine these equal triangles with other equal
spaces, and in this way make up both the one and the other
of the parallelograms, in such a manner as to shew that they
are equal. In this manner, going on step by step, deducing
the equality of the triangles from the axiom, and the
equality of the parallelograms from that of the triangles,
we travel to the conclusion. And this process of successive
deduction is the scheme of all geometrical proof. We begin
with Definitions of the notions which we reason about, and
with Axioms, or self-evident truths, respecting these
notions; and we get, by reasoning from these, other truths
which are demonstratively evident; and from these truths
again, others of the same kind, and so on. We begin with our
own Thoughts, which supply us with Axioms to start from; and
we reason from these, till we come to propositions {28}
which are applicable to the Things about us; as for
instance, the propositions respecting circles and spheres
applicable to the motions of the heavenly bodies. This is
_Deduction_, or _Deductive Reasoning_.
Experiential truths are acquired in a very different way. In
order to obtain such truths, we begin with Things. In order
to learn how many days there are in a year, or in a lunar
month, we must begin by observing the sun and the moon. We
must observe their changes day by day, and try to make the
cycle of change fit into some notion of number which we
supply from our own Thoughts. We shall find that a cycle of
30 days nearly will fit the changes of phase of the
moon;--that a cycle of 365 days nearly will fit the changes
of daily motion of the sun. Or, to go on to experiential
truths of which the discovery comes within the limits of the
history of science--we shall find (as Hipparchus found) that
the unequal motion of the sun among the stars, such as
observation shews it to be, may be fitly represented by the
notion of an _eccentric_;--a circle in which the sun has an
equable annual motion, the spectator not being in the center
of the circle. Again, in the same manner, at a later period,
Kepler started from more exact observations of the sun, and
compared them with a supposed motion in a certain ellipse;
and was able to shew that, not a circle about an eccentric
point, but an ellipse, supplied the mode of conception which
truly agreed with the motion of the sun about the earth; or
rather, as Copernicus had already shewn, of the earth about
the sun. In such cases, in which truths are obtained by
beginning from observation of external things and by finding
some notion with which the Things, as observed, agree, the
truths are said to be obtained by _Induction_. The process
is an _Inductive Process_.
The contrast of the Deductive and Inductive process is
obvious. In the former, we proceed at each step from general
truths to particular applications of them; in the latter,
from particular observations to a general truth which
includes them. In the former case we may be said to reason
_downwards_, in the latter case, {29} _upwards_; for general
notions are conceived as standing above particulars.
Necessary truths are proved, like arithmetical sums, by
adding together the portions of which they consist. An
inductive truth is proved, like the guess which answers a
riddle, by its agreeing with the facts described.
Demonstration is irresistible in its effect on the belief,
but does not produce surprize, because all the steps to the
conclusion are exhibited, before we arrive at the
conclusion. Inductive inference is not demonstrative, but it
is often more striking than demonstrative reasoning, because
the intermediate links between the particulars and the
inference are not shewn. Deductive truths are the results of
relations among our own Thoughts. Inductive truths are
relations which we discern among existing Things; and thus,
this opposition of Deduction and Induction is again an
aspect of the Fundamental Antithesis already spoken of.
_Sect._ 4.--_Theories and Facts._
GENERAL experiential Truths, such as we have just spoken of,
are called _Theories_, and the particular observations from
which they are collected, and which they include and
explain, are called _Facts_. Thus Hipparchus's doctrine,
that the sun moves in an eccentric about the earth, is _his
Theory_ of the Sun, or the _Eccentric Theory_. The doctrine
of Kepler, that the Earth moves in an Ellipse about the Sun,
is _Kepler's Theory_ of the Earth, the Elliptical Theory.
Newton's doctrine that this elliptical motion of the Earth
about the Sun is produced and governed by the Sun's
attraction upon the Earth, is the _Newtonian_ theory, the
_Theory of Attraction_. Each of these Theories was accepted,
because it included, connected and explained the _Facts_;
the Facts being, in the two former cases, the motions of the
Sun as observed; and in the other case, the elliptical
motion of the Earth as known by Kepler's Theory. This
antithesis of _Theory_ and _Fact_ is included in what has
just been said of Inductive Propositions. A Theory is an
Inductive Proposition, and the Facts {30} are the particular
observations from which, as I have said, such Propositions
are inferred by Induction. The Antithesis of Theory and Fact
implies the fundamental Antithesis of Thoughts and Things;
for a Theory (that is, a true Theory) may be described as a
Thought which is contemplated distinct from Things and seen
to agree with them; while a Fact is a combination of our
Thoughts with Things in so complete agreement that we do not
regard them as separate.
Thus the antithesis of Theory and Fact involves the
antithesis of Thoughts and Things, but is not identical with
it. Facts involve Thoughts, for we know Facts only by
thinking about them. The Fact that the year consists of 365
days; the Fact that the month consists of 30 days, cannot be
known to us, except we have the Thoughts of Time, Number and
Recurrence. But these Thoughts are so familiar, that we have
the fact in our mind as a simple Thing without attending to
the Thought which it involves. When we mould our Thoughts
into a Theory, we consider the thought as distinct from the
Facts; but yet, though distinct, not independent of them;
for it is a true Theory, only by including and agreeing with
the Facts.
_Sect._ 5.--_Ideas and Sensations._
WE have just seen that the antithesis of Theory and Fact,
although it involves the antithesis of Thoughts and Things,
is not identical with it. There are other modes of
expression also, which involve the same Fundamental
Antithesis, more or less modified. Of these, the pair of
words which in their relations appear to separate the
members of the antithesis most distinctly are _Ideas_ and
_Sensations_. We see and hear and touch external things, and
thus perceive them by our senses; but in perceiving them, we
connect the impressions of sense according to relations of
space, time, number, likeness, cause, &c. Now some at least
of these kinds of connexion, as space, time, number, may be
contemplated distinct from the things to which they are
applied; and so contemplated, I term them _Ideas_. And {31}
the other element, the impressions upon our senses which
they connect, are called _Sensations_.
I term space, time, cause, &c., _Ideas_, because they are
general relations among our sensations, apprehended by an
act of the mind, not by the senses simply. These relations
involve something beyond what the senses alone could
furnish. By the sense of sight we see various shades and
colours and shapes before us, but the _outlines_ by which
they are separated into distinct objects of definite forms,
are the work of the mind itself. And again, when we conceive
visible things, not only as surfaces of a certain form, but
as _solid bodies_, placed at various distances in space, we
again exert an act of the mind upon them. When we see a body
move, we see it move in a path or _orbit_, but this orbit is
not itself seen; it is constructed by the mind. In like
manner when we see the motions of a needle towards a magnet,
we do not _see_ the attraction or force which produces the
effects; but we infer the force, by having in our minds the
Idea of Cause. Such acts of thought, such _Ideas_, enter
into our perceptions of external things.
But though our perceptions of external things involve some
act of the mind, they must involve something else besides an
act of the mind. If we must exercise an act of thought in
order to see force exerted, or orbits described by bodies in
motion, or even in order to see bodies existing in space,
and to distinguish one kind of object from another, still
the act of thought alone does not make the Bodies. There
must be something besides, _on which_ the thought is
exerted. A colour, a form, a sound, are not produced by the
mind, however they may be moulded, combined, and interpreted
by our mental acts. A philosophical poet has spoken of
All the world
Of eye and ear, both what they half create,
And what perceive.
But it is clear, that though they _half_ create, they do not
wholly create: there must be an external world of colour and
sound to give impressions to the eye and ear, as well as internal
powers by which we perceive {32} what is offered to our organs.
The mind is in some way passive as well as active: there are
objects without as well as faculties within;--Sensations,
as well as acts of Thought.
Indeed this is so far generally acknowledged, that according
to common apprehension, the mind is passive _rather_ than
active in acquiring the knowledge which it receives
concerning the material world. Its sensations are generally
considered more distinct than its operations. The world
without is held to be more clearly real than the faculties
within. That there is something different from ourselves,
something external to us, something independent of us,
something which no act of our minds can make or can destroy,
is held by all men to be at least as evident, as that our
minds can exert any effectual process in modifying and
appreciating the impressions made upon them. Most persons
are more likely to doubt whether the mind be always actively
applying Ideas to the objects which it perceives, than
whether it perceive them passively by means of Sensations.
But yet a little consideration will show us that an activity
of the mind, and an activity according to certain Ideas, is
requisite in all our knowledge of external objects. We see
objects, of various solid forms, and at various distances
from us. But we do not thus perceive them by sensation
alone. Our visual impressions cannot, of themselves, convey
to us a knowledge of solid form, or of distance from us.
Such knowledge is inferred from what we see:--inferred by
conceiving the objects as existing in space, and by applying
to them the Idea of Space. Again:--day after day passes,
till they make up a year: but we do not know that the days
are 365, except we count them; and thus apply to them our
Idea of Number. Again:--we see a needle drawn to a magnet:
but, in truth, the _drawing_ is what we cannot see. We see
the needle move, and infer the attraction, by applying to
the fact our Idea of Force, as the cause of motion.
Again:--we see two trees of different kinds; but we cannot
know that they are so, except by applying to them our Idea
of the resemblance {33} and difference which makes kinds.
And thus Ideas, as well as Sensations, necessarily enter
into all our knowledge of objects: and these two words
express, perhaps more exactly than any of the pairs before
mentioned, that Fundamental Antithesis, in the union of
which, as I have said, all knowledge consists.
_Sect._ 6.--_Reflexion and Sensation._
IT will hereafter be my business to show what the Ideas are,
which thus enter into our knowledge; and how each Idea has
been, as a matter of historical fact, introduced into the
Science to which it especially belongs. But before I proceed
to do this, I will notice some other terms, besides the
phrases already noticed, which have a reference, more or
less direct, to the Fundamental Antithesis of Ideas and
Sensations. I will mention some of these, in order that if
they should come under the reader's notice, he may not be
perplexed as to their bearing upon the view here presented
to him.
The celebrated doctrine of Locke, that all our 'Ideas,'
(that is, in his use of the word, all our objects of
thinking,) come from Sensation or Reflexion, will naturally
occur to the reader as connected with the antithesis of
which I have been speaking. But there is a great difference
between Locke's account of Sensation and Reflexion, and our
view of Sensation and Ideas. He is speaking of the origin of
our knowledge;--we, of its nature and composition. He is
content to say that all the knowledge which we do not
receive directly by Sensation, we obtain by Reflex Acts of
the mind, which make up his Reflexion. But we hold that
there is no Sensation without an act of the mind, and that
the mind's activity is not only reflexly exerted upon
itself, but directly upon objects, so as to perceive in them
connexions and relations which are not Sensations. He is
content to put together, under the name of Reflexion,
everything in our knowledge which is not Sensation: we are
to attempt to analyze all that is not Sensation; not only to
say it consists of Ideas, but {34} to point out what those
Ideas are, and to show the mode in which each of them enters
into our knowledge. His purpose was, to prove that there are
no Ideas, except the reflex acts of the mind: our endeavour
will be to show that the acts of the mind, both direct and
reflex, are governed by certain Laws, which may be
conveniently termed Ideas. His procedure was, to deny that
any knowledge could be derived from the mind alone: our
course will be, to show that in every part of our most
certain and exact knowledge, those who have added to our
knowledge in every age have referred to principles which the
mind itself supplies. I do not say that my view is contrary
to his: but it is altogether different from his. If I grant
that all our knowledge comes from Sensation and Reflexion,
still my task then is only begun; for I want further to
determine, in each science, what portion comes, not from
mere Sensation, but from those Ideas by the aid of which
either Sensation or Reflexion can lead to Science.
Locke's use of the word 'idea' is, as the reader will
perceive, different from ours. He uses the word, as he says,
which 'serves best to stand for whatsoever is the object of
the understanding when a man thinks.' 'I have used it,' he
adds, 'to express whatever is meant by _phantasm_, _notion_,
_species_, or whatever it is to which the mind can be
employed about in thinking.' It might be shown that this
separation of the _mind itself_ from the ideal _objects_
about which it is employed in thinking, may lead to very
erroneous results. But it may suffice to observe that we use
the word _Ideas_, in the manner already explained, to
express that element, supplied by the mind itself, which
must be combined with Sensation in order to produce
knowledge. For us, Ideas are not Objects of Thought, but
rather Laws of Thought. Ideas are not synonymous with
Notions; they are Principles which give to our Notions
whatever they contain of truth. But our use of the term
_Idea_ will be more fully explained hereafter. {35}
_Sect._ 7.--_Subjective and Objective._
THE Fundamental Antithesis of Philosophy of which I have to
speak has been brought into great prominence in the writings
of modern German philosophers, and has conspicuously formed
the basis of their systems. They have indicated this
antithesis by the terms _subjective_ and _objective_.
According to the technical language of old writers, a thing
and its qualities are described as _subject_ and
_attributes_; and thus a man's faculties and acts are
attributes of which he is the _subject_. The mind is the
_subject_ in which ideas inhere. Moreover, the man's
faculties and acts are employed upon external _objects_; and
from objects all his sensations arise. Hence the part of a
man's knowledge which belongs to his own mind, is
_subjective_: that which flows in upon him from the world
external to him, is _objective_. And as in man's
contemplation of nature, there is always some act of thought
which depends upon himself, and some matter of thought which
is independent of him, there is, in every part of his
knowledge, a subjective and an objective element. The
combination of the two elements, the subjective or ideal,
and the objective or observed, is necessary, in order to
give us any insight into the laws of nature. But different
persons, according to their mental habits and constitution,
may be inclined to dwell by preference upon the one or the
other of these two elements. It may perhaps interest the
reader to see this difference of intellectual character
illustrated in two eminent men of genius of modern times,
Göthe and Schiller.
Göthe himself gives us the account to which I refer, in his
history of the progress of his speculations concerning the
Metamorphosis of Plants; a mode of viewing their structure
by which he explained, in a very striking and beautiful
manner, the relations of the different parts of a plant to
each other; as has been narrated in the _History of the
Inductive Sciences_. Göthe felt a delight in the passive
contemplation of nature, unmingled with the desire of
reasoning and theorizing; a delight such as naturally
belongs to those poets who {36} merely embody the images
which a fertile genius suggests, and do not mix with these
pictures, judgments and reflexions of their own. Schiller,
on the other hand, both by his own strong feeling of the
value of a moral purpose in poetry, and by his adoption of a
system of metaphysics in which the subjective element was
made very prominent, was well disposed to recognize fully
the authority of ideas over external impressions.
Göthe for a time felt a degree of estrangement towards
Schiller, arising from this contrariety in their views and
characters. But on one occasion they fell into discussion on
the study of natural history; and Göthe endeavoured to
impress upon his companion his persuasion that nature was to
be considered, not as composed of detached and incoherent
parts, but as active and alive, and unfolding herself in
each portion, in virtue of principles which pervade the
whole. Schiller objected that no such view of the objects of
natural history had been pointed out by observation, the
only guide which the natural historians recommended; and was
disposed on this account to think the whole of their study
narrow and shallow. 'Upon this,' says Göthe, 'I expounded to
him, in as lively a way as I could, the metamorphosis of
plants, drawing on paper for him, as I proceeded, a diagram
to represent that general form of a plant which shows itself
in so many and so various transformations. Schiller attended
and understood; and, accepting the explanation, he said,
"This is not observation, but an idea." I replied,' adds
Göthe, 'with some degree of irritation; for the point which
separated us was most luminously marked by this expression:
but I smothered my vexation, and merely said, "I was happy
to find that I had got ideas without knowing it; nay, that I
saw them before my eyes."' Göthe then goes on to say, that
he had been grieved to the very soul by maxims promulgated
by Schiller, that no observed fact ever could correspond
with an idea. Since he himself loved best to wander in the
domain of external observation, he had been led to look with
repugnance and hostility upon anything which professed to
depend upon ideas. 'Yet,' he {37} observes, 'it occurred to
me that if my Observation was identical with his Idea, there
must be some common ground on which we might meet.' They
went on with their mutual explanations, and became intimate
and lasting friends. 'And thus,' adds the poet, by means of
that mighty and interminable controversy between _object_
and _subject_, we two concluded an alliance which remained
unbroken, and produced much benefit to ourselves and others.'
The general diagram of a plant, of which Göthe here speaks,
must have been a combination of lines and marks expressing
the relations of position and equivalence among the elements
of vegetable forms, by which so many of their resemblances
and differences may be explained. Such a symbol is not an
Idea in that general sense in which we propose to use the
term, but is a particular modification of the general Ideas
of symmetry, developement, and the like; and we shall
hereafter see, according to the phraseology which we shall
explain in the next chapter, how such a diagram might
express the _ideal conception_ of a plant.
The antithesis of _subjective_ and _objective_ is very
familiar in the philosophical literature of Germany and
France; nor is it uncommon in any age of our own literature.
But though efforts have recently been made to give currency
among us to this phraseology, it has not been cordially
received, and has been much complained of as not of obvious
meaning. Nor is the complaint without ground: for when we
regard the mind as the _subject_ in which ideas inhere, it
becomes for us an _object_, and the antithesis vanishes. We
are not so much accustomed to use _subject_ in this sense,
as to make it a proper contrast to _object_. The combination
'_ideal_ and _objective_,' would more readily convey to a
modern reader the opposition which is intended between the
ideas of the mind itself, and the objects which it
contemplates around it.
To the antitheses already noticed--Thoughts and Things;
Necessary and Experiential Truths; Deduction and Induction;
Theory and Fact; Ideas and Sensations; Reflexion and
Sensation; Subjective and {38} Objective; we may add others,
by which distinctions depending more or less upon the
fundamental antithesis have been denoted. Thus we speak of
the _internal_ and _external_ sources of our knowledge; of
the world _within_ and the world _without_ us; of _Man_ and
_Nature_. Some of the more recent metaphysical writers of
Germany have divided the universe into the _Me_ and _Not-me_
(Ich and Nicht-ich). Upon such phraseology we may observe,
that to have the fundamental antithesis of which we speak
really understood, is of the highest consequence to
philosophy, but that little appears to be gained by
expressing it in any novel manner. The most weighty part of
the philosopher's task is to analyze the operations of the
mind; and in this task, it can aid us but little to call it,
instead of the _mind_, the _subject_, or the _me_.
_Sect._ 8.--_Matter and Form._
THERE are some other ways of expressing, or rather of
illustrating, the fundamental antithesis, which I may
briefly notice. The antithesis has been at different times
presented by means of various images. One of the most
ancient of these, and one which is still very instructive,
is that which speaks of Sensations as the _Matter_, and
Ideas as the _Form_, of our knowledge; just as ivory is the
matter, and a cube the form, of a die. This comparison has
the advantage of showing that two elements of an antithesis
which cannot be separated in fact, may yet be advantageously
separated in our reasonings. For Matter and Form cannot by
any means be detached from each other. All matter must have
some form; all form must be the form of some material thing.
If the ivory be not a cube, it must have a spherical or some
other form. And the cube, in order to be a cube, must be of
some material;--if not of ivory, of wood, or stone, for
instance, A figure without matter is merely a geometrical
conception;--a modification of the idea of space. Matter
without figure is a mere abstract term;--a supposed union of
certain sensible qualities which, so insulated {39} from
others, cannot exist. Yet the distinction of Matter and Form
is real; and, as a subject of contemplation, clear and
plain. Nor is the distinction by any means useless. The
speculations which treat of the two subjects, Matter and
Figure, are very different. Matter is the subject of the
sciences of Mechanics and Chemistry; Figure, of Geometry.
These two classes of Sciences have quite different sets of
principles. If we refuse to consider the Matter and the Form
of bodies separately, because we cannot exhibit Matter and
Form separately, we shut the door to all philosophy on such
subjects. In like manner, though Sensations and Ideas are
necessarily united in all our knowledge, they can be
considered as distinct; and this distinction is the basis of
all philosophy concerning knowledge.
This illustration of the relation of Ideas and Sensations
may enable us to estimate a doctrine which has been put
forwards at various times. In a certain school of
speculators there has existed a disposition to derive all
our Ideas from our Sensations, the term _Idea_, being, in
this school, used in its wider sense, so as to include all
modifications and limitations of our Fundamental Ideas. The
doctrines of this school have been summarily expressed by
saying that 'Every Idea is a transformed Sensation.' Now,
even supposing this assertion to be exactly true, we easily
see, from what has been said, how little we are likely to
answer the ends of philosophy by putting forward such a
maxim as one of primary importance. For we might say, in
like manner, that every statue is but a transformed block of
marble, or every edifice but a collection of transformed
stones. But what would these assertions avail us, if our
object were to trace the rules of art by which beautiful
statues were formed, or great works of architecture erected?
The question naturally occurs, What is the nature, the
principle, the law of this Transformation? In what faculty
resides the transforming power? What train of ideas of
beauty, and symmetry, and stability, in the mind of the
statuary or the architect, has produced those great works
which {40} mankind look upon as among their most valuable
possessions;--the Apollo of the Belvidere, the Parthenon,
the Cathedral of Cologne? When this is what we want to know,
how are we helped by learning that the Apollo is of Parian
marble, or the Cathedral of basaltic stone? We must know
much more than this, in order to acquire any insight into
the principles of statuary or of architecture. In like
manner, in order that we may make any progress in the
philosophy of knowledge, which is our purpose, we must
endeavour to learn something further respecting ideas than
that they are transformed sensations, even if they were this.
But, in reality, the assertion that our ideas are
transformed sensations, is erroneous as well as frivolous.
For it conveys, and is intended to convey, the opinion that
our sensations have one form which properly belongs to them;
and that, in order to become ideas, they are converted into
some other form. But the truth is, that our sensations, of
themselves, without some act of the mind, such as involves
what we have termed an Idea, have no form. We cannot see one
object without the idea of space; we cannot see two without
the idea of resemblance or difference; and space and
difference are not sensations. Thus, if we are to employ the
metaphor of Matter and Form, which is implied in the
expression to which I have referred, our sensations, from
their first reception, have their Form not _changed_, but
_given_ by our Ideas. Without the relations of thought which
we here term _Ideas_, the sensations are matter without
form. Matter without form cannot exist: and in like manner
sensations cannot become perceptions of objects, without
some formative power of the mind. By the very act of being
received as perceptions, they have a formative power
exercised upon them, the operation of which might be
expressed, by speaking of them, not as _transformed_, but
simply as _formed_;--as invested with form, instead of being
the mere formless material of perception. The word _inform_,
according to its Latin etymology, at first implied this
process by which matter is {41} invested with form. Thus
Virgil[1\1] speaks of the thunderbolt as _informed_ by the
hands of Brontes, and Steropes, and Pyracmon. And Dryden
introduces the word in another place:--
Let others better mould the running mass
Of metals, or _inform_ the breathing brass.
Even in this use of the word, the form is something superior
to the brute manner, and gives it a new significance and
purpose. And hence the term is again used to denote the
effect produced by an intelligent principle of a still
higher kind:--
. . . . He _informed_
This ill-shaped body with a daring soul.
And finally even the soul itself, in its original condition,
is looked upon as matter, when viewed with reference to
education and knowledge, by which it is afterwards moulded;
and hence these are, in our language, termed _information_.
If we confine ourselves to the first of these three uses of
the term, we may correct the erroneous opinion of which we
have just been speaking, and retain the metaphor by which it
is expressed, by saying, that ideas are not _transformed_,
but _informed_ sensations.
[Note 1\1: Ferrum exercebant vasto Cyclopes in Antro
Brontesque Steropesque et nudus membra Pyracmon;
His informatum manibus, jam parte polita
Fulmen erat.--_Æn._ viii. 424.]
_Sect._ 9.--_Man the Interpreter of Nature._
THERE is another image by which writers have represented the
acts of thought through which knowledge is obtained from the
observation of the external world. Nature is the Book, and
Man is the _Interpreter_. The facts of the external world
are marks, in which man discovers a meaning, and so reads
them. Man is the Interpreter of Nature, and Science is the
right Interpretation. And this image also is, in many
respects, {42} instructive. It exhibits to us the necessity
of both elements;--the marks which man has to look at, and
the knowledge of the alphabet and language which he must
possess and apply before he can find any meaning in what he
sees. Moreover this image presents to us, as the ideal
element, an activity of the mind of that very kind which we
wish to point out. Indeed the illustration is rather an
example than a comparison of the composition of our
knowledge. The letters and symbols which are presented to
the Interpreter are really objects of sensation: the notion
of letters as signs of words, the notion of connexions among
words by which they have meaning, really are among our
Ideas;--_Signs_ and _Meaning_ are Ideas, supplied by the
mind, and added to all that sensation can disclose in any
collection of visible marks. The Sciences are not
figuratively, but really, Interpretations of Nature. But
this image, whether taken as example or comparison, may
serve to show both the opposite character of the two
elements of knowledge, and their necessary combination, in
order that there may be knowledge.
This illustration may also serve to explain another point in
the conditions of human knowledge which we shall have to
notice:--namely, the very different degrees in which, in
different cases, we are conscious of the mental act by which
our sensations are converted into knowledge. For the same
difference occurs in reading an inscription. If the
inscription were entire and plain, in a language with which
we were familiar, we should be unconscious of any mental act
in reading it. We should seem to collect its meaning by the
sight alone. But if we had to decipher an ancient
inscription, of which only imperfect marks remained, with a
few entire letters among them, we should probably make
several suppositions as to the mode of reading it, before we
found any mode which was quite successful; and thus, our
guesses, being separate from the observed facts, and at
first not fully in agreement with them, we should be clearly
aware that the conjectured meaning, on the one hand, and the
observed marks on the other, were distinct things, though
these {43} two things would become united as elements of one
act of knowledge when we had hit upon the right conjecture.
_Sect._ 10.--_The Fundamental Antithesis inseparable._
THE illustration just referred to, as well as other ways of
considering the subject, may help us to get over a
difficulty which at first sight appears perplexing. We have
spoken of the common opposition of _Theory_ and _Fact_ as
important, and as involving what we have called the
Fundamental Antithesis of Philosophy. But after all, it may
be asked, Is this distinction of Theory and Fact really
tenable? Is it not often difficult to say whether a special
part of our knowledge is a Fact or a Theory? Is it a Fact or
a Theory that the stars revolve round the pole? Is it a Fact
or a Theory that the earth is a globe revolving on its axis?
Is it a Fact or a Theory that the earth travels in an
ellipse round the sun? Is it a Fact or a Theory that the sun
attracts the earth? Is it a Fact or a Theory that the
loadstone attracts the needle? In all these cases, probably
some persons would answer one way, and some persons the
other. There are many persons by whom the doctrine of the
globular form of the earth, the doctrine of the earth's
elliptical orbit, the doctrine of the sun's attraction on
the earth, would be called _theories_, even if they allowed
them to be true theories. But yet if each of these
propositions be true, is it not a _fact_? And even with
regard to the simpler facts, as the motion of the stars
round the pole, although this may be a Fact to one who has
watched and measured the motions of the stars, one who has
not done this, and who has only carelessly looked at these
stars from time to time, may naturally speak of the circles
which the astronomer makes them describe as Theories. It
would seem, then, that we cannot in such cases expect
general assent, if we say, _This is a Fact and not a
Theory_, or _This is a Theory and not a Fact_. And the same
is true in a vast range of cases. It would seem, therefore,
that we cannot rest any reasoning upon this distinction of
Theory {44} and Fact; and we cannot avoid asking whether
there is any real distinction in this antithesis, and if so,
what it is.
To this I reply: the distinction between Theory (that is,
true Theory) and Fact, is this: that in Theory the Ideas are
considered as distinct from the Facts: in Facts, though
Ideas may be involved, they are not, in our apprehension,
separated from the sensations. In a Fact, the Ideas are
applied so readily and familiarly, and incorporated with the
sensations so entirely, that we do not see _them_, we see
_through them_. A person who carefully notes the motion of a
star all night, sees the circle which it describes, as he
sees the star, though the circle is, really, a result of his
own Ideas. A person who has in his mind the measures of
different lines and countries on the earth's surface, and
who can put them, together into one conception, finds that
they can make no figure but a globular one: to him, the
earth's globular form is a Fact, as much as the square form
of his chamber. A person to whom the grounds of believing
the earth to travel round the sun are as familiar as the
grounds for believing the movements of the mail-coaches in
this country, looks upon the former event as a Fact, just as
he looks upon the latter events as Facts. And a person who,
knowing the Fact of the earth's annual motion, refers it
distinctly to its mechanical cause, 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. He
cannot _see_ the force in either case; he supplies it out of
his own Ideas. And thus, a true Theory is a Fact; a Fact is
a familiar Theory. That which is a Fact under one aspect, is
a Theory under another. The most recondite Theories when
firmly established are Facts: the simplest Facts involve
something of the nature of Theory. Theory and Fact
correspond, in a certain degree, with Ideas and Sensations,
as to the nature of their opposition. But 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 {45} considered still a question whether
those can be made to agree with these.
We may, as I have said, illustrate this matter by
considering man as _interpreting_ the phenomena which he
sees. He often interprets without being aware that he does
so. Thus when we see the needle move towards the magnet, we
assert that the magnet exercises an attractive force on the
needle. But it is only by an interpretative act of our own
minds that we ascribe this motion to attraction. That, in
this case, a force is exerted--something of the nature of
the pull which we could apply by our own volition--is our
interpretation of the phenomena; although we may be
conscious of the act of interpretation, and may then regard
the attraction as a Fact.
Nor is it in such cases only that we interpret phenomena in
our own way, without being conscious of what we do. We see a
tree at a distance, and judge it to be a chestnut or a lime;
yet this is only an inference from the colour or form of the
mass according to preconceived classifications of our own.
Our lives are full of such unconscious interpretations. The
farmer recognizes a good or a bad soil; the artist a picture
of a favourite master; the geologist a rock of a known
locality, as we recognize the faces and voices of our
friends; that is, by judgments formed on what we see and
hear; but judgments in which we do not analyze the steps, or
distinguish the inference from the appearance. And in these
mixtures of observation and inference, we speak of the
judgment thus formed, as a Fact directly observed.
Even in the case in which our perceptions appear to be most
direct, and least to involve any interpretations of our
own,--in the simple process of seeing,--who does not know
how much we, by an act of the mind, add to that which our
senses receive? Does any one fancy that he sees a solid
cube? It is easy to show that the solidity of the figure,
the relative position of its faces and edges to each other,
are inferences of the spectator; no more conveyed to his
conviction by the eye alone, than they would be if he were
looking at {46} a painted representation of a cube. The
scene of nature is a picture without depth of substance, no
less than the scene of art; and in the one case as in the
other, it is the mind which, by an act of its own, discovers
that colour and shape denote distance and solidity. Most men
are unconscious of this perpetual habit of reading the
language of the external world, and translating as they
read. The draughtsman, indeed, is compelled, for his
purposes, to return back in thought from the solid bodies
which he has inferred, to the shapes of surface which he
really sees. He knows that there is a mask of theory over
the whole face of nature, if it be _theory_ to infer more
than we _see_. But other men, unaware of this masquerade,
hold it to be a fact that they see cubes and spheres,
spacious apartments and winding avenues. And these things
are facts to them, because they are unconscious of the
mental operation by which they have penetrated nature's
disguise.
And thus, we still have an intelligible distinction of Fact
and Theory, if we consider Theory as a conscious, and Fact
as an unconscious inference, from the phenomena which are
presented to our senses.
But still, Theory and Fact, Inference and Perception,
Reasoning and Observation, are antitheses in none of which
can we separate the two members by any fixed and definite line.
Even the simplest terms by which the antithesis is expressed
cannot be separated. 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 {47} 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,
we may say, Perception 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.
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 developement 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 having been modified by this employment.
By being so employed, our Ideas are unfolded and defined;
and such developement 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 {48}
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, none of the terms by which the fundamental antithesis
is expressed can be absolutely and exclusively applied.
I will make a remark suggested by the views which have thus
been presented. 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_; 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? {49} 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 Facts of the external world.
_Sect._ 11.--_Successive Generalization._
IN the preceding pages we have been led to the doctrine,
that though, in the Antithesis of Theory and Fact, there is
involved an essential opposition; namely the opposition of
the thoughts within us and the phenomena without us; yet
that we cannot distinguish and define the members of this
antithesis separately. Theories become Facts, by becoming
certain and familiar: and thus, as our knowledge becomes
more sure and more extensive, we are constantly transferring
to the class of facts, opinions which were at first regarded
as theories.
Now we have further to remark, that in the progress of human
knowledge respecting any branch of speculation, there may be
several such steps in succession, each depending upon and
including the preceding. {50} The theoretical views which
one generation of discoverers establishes, become the facts
from which the next generation advances to new theories. As
men rise from the particular to the general, so, in the same
manner, they rise from what is general to what is more
general. Each induction supplies the materials of fresh
inductions; each generalization, with all that it embraces
in its circle, may be found to be but one of many circles,
comprehended within the circuit of some wider
generalization.
This remark has already been made, and illustrated, in the
_History of the Inductive Sciences_[2\1]; and, in truth, the
whole of the history of science is full of suggestions and
exemplifications of this course of things. It may be
convenient, however, to select a few instances which may
further explain and confirm this view of the progress of
scientific knowledge.
[Note 2\1: _Hist. Inductive Sciences_, b. vii. c. ii. sect. 5.]
The most conspicuous instance of this succession is to be
found in that science which has been progressive from the
beginning of the world to our own times, and which exhibits
by far the richest collection of successive discoveries: I
mean Astronomy. It is easy to see that each of these
successive discoveries depended on those antecedently made,
and that in each, the truths which were the highest point of
the knowledge of one age were the fundamental basis of the
efforts of the age which came next. Thus we find, in the
days of Greek discovery, Hipparchus and Ptolemy combining
and explaining the particular _facts_ of the motion of the
sun, moon, and planets, by means of the _theory_ of
epicycles and eccentrics;--a highly important step, which
gave an intelligible connexion and rule to the motions of
each of these luminaries. When these cycles and epicycles,
thus truly representing the apparent motions of the heavenly
bodies, had accumulated to an inconvenient amount, by the
discovery of many inequalities in the observed motions,
Copernicus showed that their effects might all be more
simply included, by making the sun the center of motion of
the planets, instead of {51} the earth. But in this new
view, he still retained the epicycles and eccentrics which
governed the motion of each body. Tycho Brahe's
observations, and Kepler's calculations, showed that,
besides the vast number of facts which the epicyclical
theory could account for, there were some which it would not
exactly include, and Kepler was led to the persuasion that
the planets move in ellipses. But this view of motion was at
first conceived by Kepler as a modification of the
conception of epicycles. On one occasion he blames himself
for not sooner seeing that such a modification was possible.
'What an absurdity on my part!' he cries[3\1]; 'as if
libration in the diameter of the epicycle might not come to
the same thing as motion in the ellipse.' But again;
Kepler's _laws_ of the elliptical motion of the planets were
established; and these laws immediately became the _facts_
on which the mathematicians had to found their mechanical
theories. From these facts, Newton, as we have related,
proved that the central force of the sun retains the planets
in their orbits, according to the law of the inverse square
of the distance. The same _law_ was shown to prevail in the
gravitation of the earth. It was shown, too, by induction
from the motions of Jupiter and Saturn, that the planets
attract each other; by calculations from the figure of the
earth, that the parts of the earth attract each other; and,
by considering the course of the tides, that the sun and
moon attract the waters of the ocean. And all these curious
discoveries being established as _facts_, the subject was
ready for another step of generalization. By an unparalleled
rapidity in the progress of discovery in this case, not only
were all the inductions which we have first mentioned made
by one individual, but the new advance, the higher flight,
the closing victory, fell to the lot of the same
extraordinary person.
[Note 3\1: _Hist. Inductive Sciences_, b. v. c. iv. sect. 3.]
The attraction of the sun upon the planets, of the moon upon
the earth, of the planets on each other, of the parts of the
earth on themselves, of the sun and {52} moon upon the
ocean;--all these truths, each of itself a great discovery,
were included by Newton in the higher _generalization_, of
the universal gravitation of matter, by which each particle
is drawn to every other according to the law of the inverse
square: and thus this long advance from discovery to
discovery, from truths to truths, each justly admired when
new, and then rightly used as old, was closed in a worthy
and consistent manner, by a truth which is the most worthy
admiration, because it includes all the researches of
preceding ages of Astronomy.
We may take another example of a succession of this kind
from the history of a science, which, though it has made
wonderful advances, has not yet reached its goal, as
physical astronomy appears to have done, but seems to have
before it a long prospect of future progress. I now refer to
Chemistry, in which I shall try to point out how the
preceding discoveries afforded the materials of the
succeeding; although this subordination and connexion is, in
this case, less familiar to men's minds than in Astronomy,
and is, perhaps, more difficult to present in a clear and
definite shape. Sylvius saw, in the facts which occur, when
an acid and an alkali are brought together, the evidence
that they neutralize each other. But cases of
neutralization, and acidification, and many other effects of
mixture of the ingredients of bodies, being thus viewed as
_facts_, had an aspect of unity and law given them by
Geoffroy and Bergman[4\1], who introduced the _conception_
of the Chemical Affinity or Elective Attraction, by which
certain elements select other elements, as if by preference.
That combustion, whether a chemical union or a chemical
separation of ingredients, is of the same nature with
acidification, was the doctrine of Beccher and Stahl, and
was soon established as a truth which must form a part of
every succeeding physical theory. That the rules of affinity
and chemical composition may include gaseous elements, was
established by Black and Cavendish. And all these truths,
thus brought to light by {53} chemical
discoverers,--affinity, the identity of acidification and
combustion, the importance of gaseous elements,--along with
all the facts respecting the weight of ingredients and
compounds which the balance disclosed,--were taken up,
connected, and included as _particulars_ in the oxygen
_theory_ of Lavoisier. Again, the results of this theory,
and the quantity of the several ingredients which entered
into each compound--(such results, for the most part, being
now no longer mere theoretical speculations, but recognized
facts)--were the _particulars_ from which Dalton derived
that wide law of chemical combination which we term the
Atomic _Theory_. And this law, soon generally accepted among
chemists, is already in its turn become one of the _facts_
included in Faraday's _Theory_ of the identity of Chemical
Affinity and Electric Attraction.
[Note 4\1: _Hist. Inductive Sciences_, b. xiv. c. iii.]
It is unnecessary to give further exemplifications of this
constant ascent from one step to a higher; this perpetual
conversion of true theories into the materials of other and
wider theories. It will hereafter be our business to
exhibit, in a more full and formal manner, the mode in which
this principle determines the whole scheme and structure of
all the most exact sciences. And thus, beginning with the
facts of sense, we gradually climb to the highest forms of
human knowledge, and obtain from experience and observation
a vast collection of the most wide and elevated truths.
There are, however, truths of a very different kind, to
which we must turn our attention, in order to pursue our
researches respecting the nature and grounds of our
knowledge. But before we do this, we must notice one more
feature in that progress of science which we have already in
part described.
{{54}}
CHAPTER II.
OF TECHNICAL TERMS.
1. IT has already been stated that we gather knowledge from
the external world, when we are able to apply, to the facts
which we observe, some ideal conception, which gives unity
and connexion to multiplied and separate perceptions. We
have also shown that our conceptions, thus verified by
facts, may themselves be united and connected by a new bond
of the same nature; and that man may thus have to pursue his
way from truth to truth through a long progression of
discoveries, each resting on the preceding, and rising above it.
Each of these steps, in succession, is recorded, fixed, and
made available, by some peculiar form of words; and such
words, thus rendered precise in their meaning, and
appropriated to the service of science, we may call
_Technical Terms_. It is in a great measure by inventing
such Terms that men not only best express the discoveries
they have made, but also enable their followers to become so
familiar with these discoveries, and to possess them so
thoroughly, that they can readily use them in advancing to
ulterior generalizations.
Most of our ideal conceptions are described by exact and
constant words or phrases, such as those of which we here
speak. We have already had occasion to employ many of these.
Thus we have had instances of technical Terms expressing
geometrical conceptions, as _Ellipsis_, _Radius Vector_,
_Axis_, _Plane_, the Proportion of the _Inverse Square_, and
the like. Other Terms have described mechanical conceptions,
as _Accelerating Force_ and _Attraction_. Again, chemistry
exhibits (as do all sciences) a series of Terms which mark
the steps of our {55} progress. The views of the first real
founders of the science are recorded by the Terms which are
still in use, _Neutral Salts_, _Affinity_, and the like. The
establishment of Dalton's theory has produced the use of the
word _Atom_ in a peculiar sense, or of some other word, as
_Proportion_, in a sense equally technical. And Mr. Faraday
has found it necessary, in order to expound his
electro-chemical theory, to introduce such terms as _Anode_
and _Cathode_, _Anïon_ and _Cathïon_.
2. I need not adduce any further examples, for my object at
present is only to point out the use and influence of such
language: its rules and principles I shall hereafter try, in
some measure, to fix. But what we have here to remark is,
the extraordinary degree in which the progress of science is
facilitated, by thus investing each new discovery with a
compendious and steady form of expression. These terms soon
become part of the current language of all who take an
interest in speculation. However strange they may sound at
first, they soon grow familiar in our ears, and are used
without any effort, or any recollection of the difficulty
they once involved. They become as common as the phrases
which express our most frequent feelings and interests,
while yet they have incomparably more precision than belongs
to any terms which express feelings; and they carry with
them, in their import, the results of deep and laborious
trains of research. They convey the mental treasures of one
period to the generations that follow; and laden with this,
their precious freight, they sail safely across gulfs of
time in which empires have suffered shipwreck, and the
languages of common life have sunk into oblivion. We have
still in constant circulation among us the Terms which
belong to the geometry, the astronomy, the zoology, the
medicine of the Greeks, and the algebra and chemistry of the
Arabians. And we can in an instant, by means of a few words,
call to our own recollection, or convey to the apprehension
of another person, phenomena and relations of phenomena in
optics, mineralogy, chemistry, which are so complex and
abstruse, that it might seem to require the utmost subtlety
of the human mind to {56} grasp them, even if that were made
the sole object of its efforts. By this remarkable effect of
Technical Language, we have the results of all the labours
of past times not only always accessible, but so prepared
that we may (provided we are careful in the use of our
instrument) employ what is really useful and efficacious for
the purpose of further success, without being in any way
impeded or perplexed by the length and weight of the chain
of past connexions which we drag along with us.
By such means,--by the use of the Inductive Process, and by
the aid of Technical Terms,--man has been constantly
advancing in the path of scientific truth. In a succeeding
part of this work we shall endeavour to trace the general
rules of this advance, and to lay down the maxims by which
it may be most successfully guided and forwarded. But in
order that we may do this to the best advantage, we must
pursue still further the analysis of knowledge into its
elements; and this will be our employment in the first part
of the work.
{{57}}
CHAPTER III.
OF NECESSARY TRUTHS.
1. EVERY advance in human knowledge consists, as we have
seen, in adapting new ideal conceptions to ascertained
facts, and thus in superinducing the Form upon the Matter,
the active upon the passive processes of our minds. Every
such step introduces into our knowledge an additional
portion of the ideal element, and of those relations which
flow from the nature of Ideas. It is, therefore, important
for our purpose to examine more closely this element, and to
learn what the relations are which may thus come to form
part of our knowledge. An inquiry into those Ideas which
form the foundations of our sciences;--into the reality,
independence, extent, and principal heads of the knowledge
which we thus acquire; is a task on which we must now enter,
and which will employ us for several of the succeeding Books.
In this inquiry our object will be to pass in review all the
most important Fundamental Ideas which our sciences involve;
and to prove more distinctly in reference to each, what we
have already asserted with regard to all, that there are
everywhere involved in our knowledge acts of the mind as
well as impressions of sense; and that our knowledge
derives, from these acts, a generality, certainty, and
evidence which the senses could in no degree have supplied.
But before I proceed to do this in particular cases, I will
give some account of the argument in its general form.
We have already considered the separation of our knowledge
into its two elements,--Impressions of Sense and Ideas,--as
evidently indicated by this; that all knowledge possesses
characters which neither of these {58} elements alone could
bestow. Without our ideas, our sensations could have no
connexion; without external impressions, our ideas would
have no reality; and thus both ingredients of our knowledge
must exist.
2. There is another mode in which the distinction of the two
elements of knowledge appears, as I have already said (c. i.
sect. 2): namely in the distinction of _necessary_, and
_contingent_ or _experiential_, truths. For of these two
classes of truths, the difference arises from this;--that
the one class derives its nature from the one, and the other
from the other, of the two elements of knowledge. I have
already stated briefly the difference of these two kinds of
truths:--namely, that the former are truths which, we see,
must be true:--the latter are true, but so far as we can
see, might be otherwise. The former are true necessarily and
universally: the latter are learnt from experience and
limited by experience. Now with regard to the former kind of
truths, I wish to show that the universality and necessity
which distinguish them can by no means be derived from
experience; that these characters do in reality flow from
the ideas which these truths involve; and that when the
necessity of the truth is exhibited in the way of logical
demonstration, it is found to depend upon certain
fundamental principles, (Definitions and Axioms,) which may
thus be considered as expressing, in some measure, the
essential characters of our ideas. These fundamental
principles I shall afterwards proceed to discuss and to
exhibit in each of the principal departments of science.
I shall begin by considering Necessary Truths more fully
than I have yet done. As I have already said, necessary
truths are those in which we not only learn, that the
proposition _is_ true, but see that it _must be_ true; in
which the negation of the truth is not only false, but
impossible; in which we cannot, even by an effort of
imagination, or in a supposition, conceive the reverse of
that which is asserted.
3. That there are such truths cannot be doubted. We may
take, for example, all relations of number. Three and Two
added together make Five. We cannot {59} conceive it to be
otherwise. We cannot, by any freak of thought, imagine Three
and Two to make Seven.
It may be said that this assertion merely expresses what we
mean by our words; that it is a matter of definition; that
the proposition is an identical one.
But this is by no means so. The definition of Five is not
Three and Two, but Four and One. How does it appear that
Three and Two is the same number as Four and One? It is
evident that it is so; but _why_ is it evident?--not because
the proposition is identical; for if that were the reason,
all numerical propositions must be evident for the same
reason. If it be a matter of definition that 3 and 2 make 5,
it must be a matter of definition that 39 and 27 make 66.
But who will say that the definition of 66 is 39 and 27? Yet
the magnitude of the numbers can make no difference in the
ground of the truth. How do we know that the product of 13
and 17 is 4 less than the product of 15 and 15? We see that
it is so, if we perform certain operations by the rules of
arithmetic; but how do we know the truth of the rules of
arithmetic? If we divide 123375 by 987 according to the
process taught us at school, how are we assured that the
result is correct, and that the number 125 thus obtained is
really the number of times one number is contained in the
other?
The correctness of the rule, it may be replied, can be
rigorously demonstrated. It can be shown that the process
must inevitably give the true quotient.
Certainly this can be shown to be the case. And precisely
because it _can_ be shown that the result must be true, we
have here an example of a necessary truth; and this truth,
it appears, is not _therefore_ necessary because it is
itself evidently identical, however it may be possible to
prove it by reducing it to evidently identical propositions.
And the same is the case with all other numerical
propositions; for, as we have said, the nature of all of
them is the same.
Here, then, we have instances of truths which are not only
true, but demonstrably and necessarily true. Now such truths
are, in this respect at least, altogether {60} different
from truths, which, however certain they may be, are learnt
to be so only by the evidence of observation, interpreted,
as observation must be interpreted, by our own mental
faculties. There is no difficulty in finding examples of
these merely observed truths. We find that sugar dissolves
in water, and forms a transparent fluid, but no one will say
that we can see any reason beforehand why the result _must_
be so. We find that all animals which chew the cud have also
the divided hoof; but could any one have predicted that this
would be universally the case? or supposing the truth of the
rule to be known, can any one say that he cannot conceive
the facts as occurring otherwise? Water expands when it
crystallizes, some other substances contract in the same
circumstances; but can any one know that this will be so
otherwise than by observation? We have here propositions
_rigorously_ true, (we will assume,) but can any one say
they are _necessarily_ true? These, and the great mass of
the doctrines established by induction, are actual, but so
far as we can see, accidental laws; results determined by
some unknown selection, not demonstrable consequences of the
essence of things, inevitable and perceived to be
inevitable. According to the phraseology which has been
frequently used by philosophical writers, they are
_contingent_, not necessary truths.
It is requisite to insist upon this opposition, because no
insight can be obtained into the true nature of knowledge,
and the mode of arriving at it, by any one who does not
clearly appreciate the distinction. The separation of truths
which are learnt by observation, and truths which can be
seen to be true by a pure act of thought, is one of the
first and most essential steps in our examination of the
nature of truth, and the mode of its discovery. If any one
does not clearly comprehend this distinction of necessary
and contingent truths, he will not be able to go along with
us in our researches into the foundations of human
knowledge; nor, indeed, to pursue with success any
speculation on the subject. But, in fact, this distinction
is one that can hardly fail to be at once understood. It
{61} is insisted upon by almost all the best modern, as well
as ancient, metaphysicians[5\1], as of primary importance.
And if any person does not fully apprehend, at first, the
different kinds of truth thus pointed out, let him study, to
some extent, those sciences which have necessary truth for
their subject, as geometry, or the properties of numbers, so
as to obtain a familiar acquaintance with such truth; and he
will then hardly fail to see how different the evidence of
the propositions which occur in these sciences, is from the
evidence of the facts which are merely learnt from
experience. That the year goes through its course in 365
days, can only be known by observation of the sun or stars:
that 365 days is 52 weeks and a day, it requires no
experience, but only a little thought to perceive. That bees
build their cells in the form of hexagons, we cannot know
without looking at them; that regular hexagons may be
arranged so as to fill space, may be proved with the utmost
rigour, even if there were not in existence such a thing as
a material hexagon.
[Note 5\1: Aristotle, Dr Whately, Dugald Stewart, &c.]
4. As I have already said, 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 {62} 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.
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.
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 {63} make 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.
5. I have taken examples of necessary truths from the
properties of number and space; but such truths exist no
less in other subjects, although the discipline of thought
which is requisite to perceive them distinctly, may not be
so usual among men with regard to the sciences of mechanics
and hydrostatics, as it is with regard to the sciences of
geometry and arithmetic. Yet every one may perceive that
there are such truths in mechanics. If I press the table
with my hand, the table presses my hand with an equal force:
here is a self-evident and necessary truth. In any machine,
constructed in whatever manner to increase the force which I
can exert, it is certain that what I gain in force I must
lose in the velocity which I communicate. This is not a
contingent truth, borrowed from and limited by observation;
for a man of sound mechanical views applies it with like
confidence, however novel be the construction of the
machine. When I come to speak of the ideas which are
involved in our mechanical knowledge, I may, perhaps, be
able to bring more clearly into view the necessary truth of
general propositions on such subjects. That reaction is
equal and opposite to action, is as necessarily true as that
two straight lines cannot inclose a space; it is as
impossible theoretically to make a perpetual motion by mere
mechanism as to make the diagonal of a square commensurable
with the side. {64}
6. Necessary truths must be _universal_ truths. If any
property belong to a right-angled triangle _necessarily_, it
must belong to _all_ right-angled triangles. And it shall be
proved in the following Chapter, that truths possessing
these two characters, of Necessity and Universality, cannot
possibly be the mere results of experience.
[Necessary truths are not considered as a portion of the
_Inductive_ Sciences. They are Deductions from our Ideas.
Thus the necessary truths which constitute the Science of
Geometry are Deductions from our Idea of Space: the
necessary truths which constitute the Science of Arithmetic
are Deductions from our notions of Number; which perhaps
involves necessarily the Idea of Time. But though we do not
call those Sciences _Inductive_ which involve properties of
Space, Number and Time alone, the properties of Space, Time
and Number enter in many very important ways into the
Inductive Sciences; and therefore the Ideas of Space, Time
and Number require to be considered in the first place. And
moreover the examination of these Ideas is an essential step
towards the examination of other Ideas: and the conditions
of the possibility and certainty of truth, which are
exemplified in Geometry and Arithmetic, open to us important
views respecting the conditions of the possibility and
certainty of all Scientific Truth. We shall therefore in the
next Book examine the Ideas on which the Pure Sciences,
Geometry and Arithmetic, are founded. But we must first say
a little more of Ideas in general.]
{{65}}
CHAPTER IV.
OF EXPERIENCE.
1. I HERE employ the term Experience in a more definite and
limited sense than that which it possesses in common usage;
for I restrict it to matters belonging to the domain of
science. In such cases, the knowledge which we acquire, by
means of experience, is of a clear and precise nature; and
the passions and feelings and interests, which make the
lessons of experience in practical matters so difficult to
read aright, no longer disturb and confuse us. We may,
therefore, hope, by attending to such cases, to learn what
efficacy experience really has, in the discovery of truth.
That from _experience_ (including intentional experience, or
_observation_,) we obtain much knowledge which is highly
important, and which could not be procured from any other
source, is abundantly clear. We have already taken several
examples of such knowledge. We know by experience that
animals which ruminate are cloven-hoofed; and we know this
in no other manner. We know, in like manner, that all the
planets and their satellites revolve round the sun from west
to east. It has been found by experience that all meteoric
stones contain chrome. Many similar portions of our
knowledge might be mentioned.
Now what we have here to remark is this;--that in no case
can experience prove a proposition to be _necessarily_ or
_universally_ true. However many instances we may have
observed of the truth of a proposition, yet if it be known
merely by observation, there is nothing to assure us that
the next case shall not be an exception to the rule. If it
be strictly true that every ruminant animal yet known has
cloven hoofs, we {66} still cannot be sure that some
creature will not hereafter be discovered which has the
first of these attributes without having the other. When the
planets and their satellites, as far as Saturn, had been all
found to move round the sun in one direction, it was still
possible that there might be other such bodies not obeying
this rule; and, accordingly, when the satellites of Uranus
were detected, they appeared to offer an exception of this
kind. Even in the mathematical sciences, we have examples of
such rules suggested by experience, and also of their
precariousness. However far they may have been tested, we
cannot depend upon their correctness, except we see some
reason for the rule. For instance, various rules have been
given, for the purpose of pointing out _prime numbers_; that
is, those which cannot be divided by any other number. We
may try, as an example of such a rule, this one--any odd
power of the number two, diminished by one. Thus the third
power of two, diminished by one, is seven; the fifth power,
diminished by one, is thirty-one; the seventh power so
diminished is one hundred and twenty-seven. All these are
prime numbers: and we might be led to suppose that the rule
is universal. But the next example shows us the
fallaciousness of such a belief. The ninth power of two,
diminished by one, is five hundred and eleven, which is not
a prime, being divisible by seven.
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. Experience being
thus unable to prove a fact to be universal, is, as will
readily be seen, still more incapable of proving a truth to
be necessary. Experience cannot, indeed, offer the smallest
ground for the necessity of a proposition. She can observe
and record what has happened; but she cannot find, in any
case, or in any accumulation of cases, any reason for what
must happen. She may see objects side by side; but she
cannot see a reason why they must ever be side by side. She
finds certain events to occur in succession; but the
succession supplies, in its occurrence, no {67} reason for
its recurrence. She contemplates external objects; but she
cannot detect any internal bond, which indissolubly connects
the future with the past, the possible with the real. To
learn a proposition by experience, and to see it to be
necessarily true, are two altogether different processes of
thought.
2. But it may be said, that we do learn by means of
observation and experience many universal truths; indeed,
all the general truths of which science consists. Is not the
doctrine of universal gravitation learnt by experience? Are
not the laws of motion, the properties of light, the general
principles of chemistry, so learnt? How, with these examples
before us, can we say that experience teaches no universal
truths?
To this we reply, that these 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, and that necessity of which she has no
comprehension. If these doctrines _are_ universally true,
this universality flows from the _ideas_ which we apply to
our experience, and which are, as we have seen, the real
sources of necessary truth. How far these ideas can
communicate their universality and necessity to the results
of experience, it will hereafter be our business to
consider. It will then appear, that when the mind collects
from observation truths of a wide and comprehensive kind,
which approach to the simplicity and universality of the
truths of pure science; she gives them this character by
throwing upon them the light of her own Fundamental Ideas.
But the truths which we discover by observation of the
external world, even when most strikingly simple and
universal, are not necessary truths. Is the doctrine of
universal gravitation necessarily true? It was doubted by
Clairaut (so far as it refers to the moon), when the
progression of the apogee in fact appeared to be twice as
great as the theory admitted. It has been doubted, even more
recently, with respect to the planets, their mutual
perturbations appearing to indicate a deviation from the
law. It is doubted still, by some {68} persons, with respect
to the double stars. But suppose all these doubts to be
banished, and the law to be universal; is it then proved to
be necessary? Manifestly not: the very existence of these
doubts proves that it is not so. For the doubts were
dissipated by reference to observation and calculation, not
by reasoning on the nature of the law. Clairaut's difficulty
was removed by a more exact calculation of the effect of the
sun's force on the motion of the apogee. The suggestion of
Bessel, that the intensity of gravitation might be different
for different planets, was found to be unnecessary, when
Professor Airy gave a more accurate determination of the
mass of Jupiter. And the question whether the extension of
the law of the inverse square to the double stars be true,
(one of the most remarkable questions now before the
scientific world,) must be answered, not by any speculations
concerning what the laws of attraction must necessarily be,
but by carefully determining the actual laws of the motion
of these curious objects, by means of the observations such
as those which Sir John Herschel has collected for that
purpose, by his unexampled survey of both hemispheres of the
sky. And since the extent of this truth is thus to be
determined by reference to observed facts, it is clear that
no mere accumulation of them can make its universality
certain, or its necessity apparent.
Thus no knowledge of the necessity of any truths can result
from the observation of what really happens. This being
clearly understood, we are led to an important inquiry.
The characters of universality and necessity in the truths
which form part of our knowledge, can never be derived from
experience, by which so large a part of our knowledge is
obtained. But since, as we have seen, we really do possess a
large body of truths which are necessary, and because
necessary, therefore universal, the question still recurs,
from what source these characters of universality and
necessity are derived.
The answer to this question we will attempt to give in the
next chapter.
{{69}}
CHAPTER V.
OF THE GROUNDS OF NECESSARY TRUTHS.
1. TO the question just stated, I reply, that the necessity
and universality of the truths which form a part of our
knowledge, are derived from the _Fundamental Ideas_ which
those truths involve. These ideas entirely shape and
circumscribe our knowledge; they regulate the active
operations of our minds, without which our passive
sensations do not become knowledge. They govern these
operations, according to rules which are not only fixed and
permanent, but which may be expressed in plain and definite
terms; and these rules, when thus expressed, may be made the
basis of demonstrations by which the necessary relations
imparted to our knowledge by our Ideas may be traced to
their consequences in the most remote ramifications of
scientific truth.
These enunciations of the necessary and evident conditions
imposed upon our knowledge by the Fundamental Ideas which it
involves, are termed _Axioms_. Thus the Axioms of Geometry
express the necessary conditions which result from the Idea
of Space; the Axioms of Mechanics express the necessary
conditions which flow from the Ideas of Force and Motion;
and so on.
2. It will be the office of several of the succeeding Books
of this work to establish and illustrate in detail what I
have thus stated in general terms. I shall there pass in
review many of the most important fundamental ideas on which
the existing body of our science depends; and I shall
endeavour to show, for each such idea in succession, that
knowledge involves an active as well as a passive element;
that it is not possible without an act of the mind,
regulated by certain {70} laws. I shall further attempt to
enumerate some of the principal fundamental relations which
each idea thus introduces into our thoughts, and to express
them by means of definitions and axioms, and other suitable
forms.
I will only add a remark or two to illustrate further this
view of the ideal grounds of our knowledge.
3. To persons familiar with any of the demonstrative
sciences, it will be apparent that if we state all the
Definitions and Axioms which are employed in the
demonstrations, we state the whole basis on which those
reasonings rest. For the whole process of demonstrative or
deductive reasoning in any science, (as in geometry, for
instance,) consists entirely in combining some of these
first principles so as to obtain the simplest propositions
of the science; then combining these so as to obtain other
propositions of greater complexity; and so on, till we
advance to the most recondite demonstrable truths; these
last, however intricate and unexpected, still involving no
principles except the original definitions and axioms. Thus,
by combining the Definition of a triangle, and the
Definitions of equal lines and equal angles, namely, that
they are such as when applied to each other, coincide, with
the Axiom respecting straight lines (that two such lines
cannot inclose a space,) we demonstrate the equality of
triangles, under certain assumed conditions. Again, by
combining this result with the Definition of parallelograms,
and with the Axiom that if equals be taken from equals the
wholes are equal, we prove the equality of parallelograms
between the same parallels and upon the same base. From this
proposition, again, we prove the equality of the square on
the hypotenuse of a triangle to the squares on the two sides
containing the right angle. But in all this there is nothing
contained which is not rigorously the result of our
geometrical Definitions and Axioms. All the rest of our
treatises of geometry consists only of terms and phrases of
reasoning, the object of which is to connect those first
principles, and to exhibit the effects of their combination
in the shape of demonstration. {71}
4. This combination of first principles takes place
according to the forms and rules of _Logic_. All the steps
of the demonstration may be stated in the shape in which
logicians are accustomed to exhibit processes of reasoning
in order to show their conclusiveness, that is, in
_Syllogisms_. Thus our geometrical reasonings might be
resolved into such steps as the following:--
All straight lines drawn from the centre of a circle to its
circumference are equal:
But the straight lines AB, AC, are drawn from the centre of
a circle to its circumference:
Therefore the straight lines AB, AC, are equal.
Each step of geometrical, and all other demonstrative
reasoning, may be resolved into three such clauses as these;
and these three clauses are termed respectively, the _major
premiss_, the _minor premiss_, and the _conclusion_; or,
more briefly, the _major_, the _minor_, and the
_**conclusion_.
The principle which justifies the reasoning when exhibited
in this syllogistic form, is this:--that a truth which can
be asserted as generally, or rather as universally true, can
be asserted as true also in each particular case. The
_minor_ only asserts a certain particular case to be an
example of such conditions as are spoken of in the _major_;
and hence the conclusion, which is true of the major by
supposition, is true of the minor by consequence; and thus
we proceed from syllogism to syllogism, in each one
employing some general truth in some particular instance.
Any proof which occurs in geometry, or any other science of
demonstration, may thus be reduced to a series of processes,
in each of which we pass from some general proposition to
the narrower and more special propositions which it
includes. And this process of deriving truths by the mere
combination of general principles, applied in particular
hypothetical cases, is called _deduction_; being opposed to
_induction_, in which, as we have seen (chap. i. sect. 3), a
new general principle is introduced at every step.
5. Now we have to remark that, this being so, however far we
follow such deductive reasoning, we can {72} never have, in
our conclusion any truth which is not virtually included in
the original principles from which the reasoning started.
For since at any step we merely take out of a general
proposition something included in it, while at the preceding
step we have taken this general proposition out of one more
general, and so on perpetually, it is manifest that our last
result was really included in the principle or principles
with which we began. I say _principles_, because, although
our logical conclusion can only exhibit the legitimate issue
of our first principles, it may, nevertheless, contain the
result of the combination of several such principles, and
may thus assume a great degree of complexity, and may appear
so far removed from the parent truths, as to betray at first
sight hardly any relationship with them. Thus the
proposition which has already been quoted respecting the
squares on the sides of a right-angled triangle, contains
the results of many elementary principles; as, the
definitions of parallels, triangle, and square; the axioms
respecting straight lines, and respecting parallels; and,
perhaps, others. The conclusion is complicated by containing
the effects of the combination of all these elements; but it
contains nothing, and can contain nothing, but such elements
and their combinations.
This doctrine, that logical reasoning produces no new
truths, but only unfolds and brings into view those truths
which were, in effect, contained in the first principles of
the reasoning, is assented to by almost all who, in modern
times, have attended to the science of logic. Such a view is
admitted both by those who defend, and by those who
depreciate the value of logic. 'Whatever is established by
reasoning, must have been contained and virtually asserted
in the premises[6\1].' 'The only truth which such
propositions can possess consists in conformity to the
original principles.'
[Note 6\1: Whately's _Logic_, pp. 237, 238.]
In this manner the whole substance of our geometry is
reduced to the Definitions and Axioms which we employ in our
elementary reasonings; and in like {73} manner we reduce the
demonstrative truths of any other science to the definitions
and axioms which we there employ.
6. But in reference to this subject, it has sometimes been
said that demonstrative sciences do in reality depend upon
Definitions only; and that no additional kind of principle,
such as we have supposed Axioms to be, is absolutely
required. It has been asserted that in geometry, for
example, the source of the necessary truth of our
propositions is this, that they depend upon definitions
alone, and consequently merely state the identity of the
same thing under different aspects.
That in the sciences which admit of demonstration, as
geometry, mechanics, and the like, Axioms as well as
Definitions are needed, in order to express the grounds of
our necessary convictions, must be shown hereafter by an
examination of each of these sciences in particular. But
that the propositions of these sciences, those of geometry
for example, do not merely assert the identity of the same
thing, will, I think, be generally allowed, if we consider
the assertions which we are enabled to make. When we declare
that 'a straight line is the shortest distance between two
points,' is this merely an identical proposition? the
definition of a straight line in another form? Not so: the
definition of a straight line involves the notion of form
only, and does not contain anything about magnitude;
consequently, it cannot contain anything equivalent to
'shortest.' Thus the propositions of geometry are not merely
identical propositions; nor have we in their general
character anything to countenance the assertion, that they
are the results of definitions alone. And when we come to
examine this and other sciences more closely, we shall find
that axioms, such as are usually in our treatises made the
fundamental principles of our demonstrations, neither have
ever been, nor can be, dispensed with. Axioms, as well as
Definitions, are in all cases requisite, in order properly
to exhibit the grounds of necessary truth.
7. Thus the real logical basis of every body of demonstrated
truths are the Definitions and Axioms {74} which are the
first principles of the reasonings. But when we are arrived
at this point, the question further occurs, what is the
ground of the truth of these Axioms? It is not the logical,
but the philosophical, not the formal, but the real
foundation of necessary truth, which we are seeking. Hence
this inquiry necessarily comes before us, What is the ground
of the Axioms of Geometry, of Mechanics, and of any other
demonstrable science?
The answer which we are led to give, by the view which we
have taken of the nature of knowledge, has already been
stated. The ground of the axioms belonging to each science
is the _Idea_ which the axiom involves. The ground of the
Axioms of Geometry is the _Idea of Space_: the ground of the
Axioms of Mechanics is the _Idea of Force_, of _Action_ and
_Reaction_, and the like. And hence these Ideas are
Fundamental Ideas; and since they are thus the foundations,
not only of demonstration but of truth, an examination into
their real import and nature is of the greatest consequence
to our purpose.
8. Not only the Axioms, but the definitions which form the
basis of our reasonings, depend upon our Fundamental Ideas.
And the Definitions are not arbitrary definitions, but are
determined by a necessity no less rigorous than the Axioms
themselves. We could not think of geometrical truths without
conceiving a circle; and we could not reason concerning such
truths without defining a circle in some mode equivalent to
that which is commonly adopted. The Definitions of
parallels, of right angles, and the like, are quite as
necessarily prescribed by the nature of the case, as the
Axioms which these Definitions bring with them. Indeed we
may substitute one of these kinds of principles for another.
We cannot always put a Definition in the place of an Axiom;
but we may always find an Axiom which shall take the place
of a Definition. If we assume a proper Axiom respecting
straight lines, we need no Definition of a straight line.
But in whatever shape the principle appear, as Definition or
as Axiom, it has about it nothing casual or {75} arbitrary,
but is determined to be what it is, as to its import, by the
most rigorous necessity, growing out of the Idea of Space.
9. These principles,--Definitions, and Axioms,--thus
exhibiting the primary developments of a fundamental idea,
do in fact express the idea, so far as its expression in
words forms part of our science. They are different views of
the same body of truth; and though each principle, by
itself, exhibits only one aspect of this body, taken
together they convey a sufficient conception of it for our
purposes. The Idea itself cannot be fixed in words; but
these various lines of truth proceeding from it, suggest
sufficiently to a fitly-prepared mind, the place where the
idea resides, its nature, and its efficacy.
It is true that these principles,--our elementary
Definitions and Axioms,--even taken all together, express
the Idea incompletely. Thus the Definitions and Axioms of
Geometry, as they are stated in our elementary works, do not
fully express the Idea of Space as it exists in our minds.
For, in addition to these, other Axioms, independent of
these, and no less evident, can be stated; and are in fact
stated when we come to the Higher Geometry. Such, for
instance, is the Axiom of Archimedes--that a curve line
which joins two points is less than a broken line which
joins the same points and includes the curve. And thus the
Idea is disclosed but not fully revealed, imparted but not
transfused, by the use we make of it in science. When we
have taken from the fountain so much as serves our purpose,
there still remains behind a deep well of truth, which we
have not exhausted, and which we may easily believe to be
inexhaustible.
{{76}}
CHAPTER VI.
THE FUNDAMENTAL IDEAS ARE NOT DERIVED FROM EXPERIENCE.
1. BY the course of speculation contained in the last three
Chapters, we are again led to the conclusion which we have
already stated, that our knowledge contains an ideal
element, and that this element is not derived from
experience. For we have seen that there are propositions
which are known to be necessarily true; and that such
knowledge is not, and cannot be, obtained by mere
observation of actual facts. It has been shown, also, that
these necessary truths are the results of certain
fundamental ideas, such as those of space, number, and the
like. Hence it follows inevitably that these ideas and
others of the same kind are not derived from experience. For
these ideas possess a power of infusing into their
developments that very necessity which experience can in no
way bestow. This power they do not borrow from the external
world, but possess by their own nature. Thus we unfold out
of the Idea of Space the propositions of geometry, which are
plainly truths of the most rigorous necessity and
universality. But if the idea of space were merely collected
from observation of the external world, it could never
enable or entitle us to assert such propositions: it could
never authorize us to say that not merely some lines, but
_all_ lines, not only have, but _must_ have, those
properties which geometry teaches. Geometry in every
proposition speaks a language which experience never dares
to utter; and indeed of which she but half comprehends the
meaning. Experience sees that the assertions are true, but
she sees not how profound and absolute is their truth. {77}
She unhesitatingly assents to the laws which geometry
delivers, but she does not pretend to see the origin of
their obligation. She is always ready to acknowledge the
sway of pure scientific principles as a matter of fact, but
she does not dream of offering her opinion on their
authority as a matter of right; still less can she justly
claim to be herself the source of that authority.
David Hume asserted[7\1], that we are incapable of seeing in
any of the appearances which the world presents anything of
necessary connexion; and hence he inferred that our
knowledge cannot extend to any such connexion. It will be
seen from what we have said that we assent to his remark as
to the fact, but we differ from him altogether in the
consequence to be drawn from it. Our inference from Hume's
observation is, not the truth of his conclusion, but the
falsehood of his premises;--not that, therefore, we can know
nothing of natural connexion, but that, therefore, we have
some other source of knowledge than experience:--not, that
we can have no idea of connexion or causation, because, in
his language, it cannot be the copy of an impression; but
that since we have such an idea, our ideas are not the
copies of our impressions.
[Note 7\1: _Essays_, vol. ii. p. 70.]
Since it thus appears that our fundamental ideas are not
acquired from the external world by our senses, but have
some separate and independent origin, it is important for us
to examine their nature and properties, as they exist in
themselves; and this it will be our business to do through a
portion of the following pages. But it may be proper first
to notice one or two objections which may possibly occur to
some readers.
2. It may be said that without the use of our senses, of
sight and touch, for instance, we should never have any idea
of space; that this idea, therefore, may properly be said to
be derived from those senses. And to this I reply, by
referring to a parallel instance. Without light we should
have no perception of visible {78} figure; yet the power of
perceiving visible figure cannot be said to be derived from
the light, but resides in the structure of the eye. If we
had never seen objects in the light, we should be quite
unaware that we possessed a power of vision; yet we should
not possess it the less on that account. If we had never
exercised the senses of sight and touch (if we can conceive
such a state of human existence) we know not that we should
be conscious of an idea of space. But the light reveals to
us at the same time the existence of external objects and
our own power of seeing. And in a very similar manner, the
exercise of our senses discloses to us, at the same time,
the external world, and our own ideas of space, time, and
other conditions, without which the external world can
neither be observed nor conceived. That light is necessary
to vision, does not, in any degree, supersede the importance
of a separate examination of the laws of our visual powers,
if we would understand the nature of our own bodily
faculties and the extent of the information they can give
us. In like manner, the fact that intercourse with the
external world is necessary for the conscious employment of
our ideas, does not make it the less essential for us to
examine those ideas in their most intimate structure, in
order that we may understand the grounds and limits of our
knowledge. Even before we see a single object, we have a
faculty of vision; and in like manner, if we can suppose a
man who has never contemplated an object in space or time,
we must still assume him to have the faculties of
entertaining the ideas of space and time, which faculties
are called into play on the very first occasion of the use
of the senses.
3. In answer to such remarks as the above, it has sometimes
been said that to assume separate faculties in the mind for
so many different processes of thought, is to give a mere
verbal explanation, since we learn nothing concerning our
idea of space by being told that we have a faculty of
forming such an idea. It has been said that this course of
explanation leads to an endless multiplication of elements
in man's nature, without any advantage to our knowledge of
his true {79} constitution. We may, it is said, assert man
to have a faculty of walking, of standing, of breathing, of
speaking; but what, it is asked, is gained by such
assertions? To this I reply, that we undoubtedly have such
faculties as those just named; that it is by no means
unimportant to consider them; and that the main question in
such cases is, whether they are separate and independent
faculties, or complex and derivative ones; and, if the
latter be the case, what are the simple and original
faculties by the combination of which the others are
produced. In walking, standing, breathing, for instance, a
great part of the operation can be reduced to one single
faculty; the voluntary exercise of our muscles. But in
breathing this does not appear to be the whole of the
process. The operation is, in part at least, involuntary;
and it has been held that there is a certain sympathetic
action of the nerves, in addition to the voluntary agency
which they transmit, which is essential to the function. To
determine whether or no this sympathetic faculty is real and
distinct, and if so, what are its laws and limits, is
certainly a highly philosophical inquiry, and well deserving
the attention which has been bestowed upon it by eminent
physiologists. And just of the same nature are the inquiries
with respect to man's intellectual constitution, on which we
propose to enter. For instance, man has a faculty of
apprehending time, and a faculty of reckoning numbers: are
these distinct, or is one faculty derived from the other? To
analyze the various combinations of our ideas and
observations into the original faculties which they involve;
to show that these faculties are original, and not capable
of further analysis: to point out the characters which mark
these faculties and lead to the most important features of
our knowledge;--these are the kind of researches on which we
have now to enter, and these, we trust, will be found to be
far from idle or useless parts of our plan. If we succeed in
such attempts, it will appear that it is by no means a
frivolous or superfluous step to distinguish separate
faculties in the mind. If we do not learn much by being told
that we have a faculty {80} of forming the idea of space, we
at least, by such a commencement, circumscribe a certain
portion of the field of our investigations, which, we shall
afterwards endeavour to show, requires and rewards a special
examination. And though we shall thus have to separate the
domain of our philosophy into many provinces, these are, as
we trust it will appear, neither arbitrarily assigned, nor
vague in their limits, nor infinite in number.
{{81}}
CHAPTER VII.
OF THE PHILOSOPHY OF THE SCIENCES.
WE proceed, in the ensuing Books, to the closer examination
of a considerable number of those Fundamental Ideas on which
the sciences, hitherto most successfully cultivated, are
founded. In this task, our objects will be to explain and
analyze such Ideas so as to bring into view the Definitions
and Axioms, or other forms, in which we may clothe the
conditions to which our speculative knowledge is subjected.
I shall also try to prove, for some of these Ideas in
particular, what has been already urged respecting them in
general, that they are not derived from observation, but
necessarily impose their conditions upon that knowledge of
which observation supplies the materials. I shall further,
in some cases, endeavour to trace the history of these Ideas
as they have successively come into notice in the progress
of science; the gradual development by which they have
arrived at their due purity and clearness; and, as a
necessary part of such a history, I shall give a view of
some of the principal controversies which have taken place
with regard to each portion of knowledge.
An exposition and discussion of the Fundamental Ideas of
each Science may, with great propriety, be termed the
PHILOSOPHY OF such SCIENCE. These ideas contain in
themselves the elements of those truths which the science
discovers and enunciates; and in the progress of the
sciences, both in the world at large and in the mind of each
individual student, the most important steps consist in
apprehending these ideas clearly, and in bringing them into
accordance with the observed facts. I shall, therefore, in a
series of Books, {82} treat of the _Philosophy of the Pure
Sciences_, the _Philosophy of the Mechanical Sciences_, the
_Philosophy of Chemistry_, and the like, and shall analyze
and examine the ideas which these sciences respectively
involve.
In this undertaking, inevitably somewhat long, and involving
many deep and subtle discussions, I shall take, as a chart
of the country before me, by which my course is to be
guided, the scheme of the sciences which I was led to form
by travelling over the history of each in order[8\1]. Each
of the sciences of which I then narrated the progress,
depends upon several of the Fundamental Ideas of which I
have to speak: some of these Ideas are peculiar to one field
of speculation, others are common to more. A previous
enumeration of Ideas thus collected may serve both to show
the course and limits of this part of our plan, and the
variety of interest which it offers.
[Note 8\1: _History of the Inductive Sciences._]
I shall, then, successively, have to speak Of the Ideas
which are the foundation of Geometry and Arithmetic, (and
which also regulate all sciences depending upon these, as
Astronomy and Mechanics;) namely, the Ideas of _Space_,
_Time_, and _Number_ (Book II.):
Of the Ideas on which the Mechanical Sciences (as Mechanics,
Hydrostatics, Physical Astronomy) more peculiarly rest; the
ideas of _Force_ and _Matter_, or rather the idea of
_Cause_, which is the basis of these (Book III.):
Of the Ideas which the Secondary Mechanical Sciences
(Acoustics, Optics, and Thermotics) involve; namely, the
Ideas of the _Externality_ of objects, and of the _Media_ by
which we perceive their qualities (Book IV.):
Of the Ideas which are the basis of Mechanico-chemical and
Chemical Science; _Polarity_, _Chemical Affinity_, and
_Substance_; and the Idea of _Symmetry_, a necessary part of
the Philosophy of Crystallography (Books V. VI.):
Of the Ideas on which the Classificatory Sciences proceed
(Mineralogy, Botany, and Zoology); namely, {83} the Ideas of
_Resemblance_, and of its gradations, and of _Natural
Affinity_ (Books VII. VIII.):
Finally, of those Ideas on which the Physiological Sciences
are founded; the Ideas of separate Vital Powers, such as
_Assimilation_ and _Irritability_; and the Idea of _Final
Cause_ (Book IX.):
We have, besides these, the Palætiological Sciences, which
proceed mainly on the conception of _Historical Causation_
(Book X.):
It is plain that when we have proceeded so far as this, we
have advanced to the verge of those speculations which have
to do with mind as well as body. The extension of our
philosophy to such a field, if it can be justly so extended,
will be one of the most important results of our researches;
but on that very account we must fully study the lessons
which we learn in those fields of speculation where our
doctrines are most secure, before we venture into a region
where our principles will appear to be more precarious, and
where they are inevitably less precise.
We now proceed to the examination of the above Ideas, and to
such essays towards the philosophy of each Science as this
course of investigation may suggest.
{{85}}
BOOK II.
THE
PHILOSOPHY
OF THE
PURE SCIENCES.
The way in which we are led to regard human knowledge is
like the way in which Copernicus was led to regard the
heavens. When the explanation of the celestial motions could
not be made to go right so long as he assumed that all the
host of stars turns round the spectator, he tried whether it
would not answer better if he made the spectator turn, and
left the stars at rest. We may make a similar trial in
Metaphysics, as to our way of looking at objects. If our
view of them must be governed altogether by the properties
of the objects themselves, I see not how man can know
anything about them _à priori_. But if the thing, as an
object of the senses, is regulated by the constitution of
our power of knowing, I can very readily represent to myself
this possibility.
KANT, _Kritik d. R. V. Pref._
{{87}}
BOOK II.
THE PHILOSOPHY OF THE PURE SCIENCES.
[The principal question discussed in the last Book was this
(see chaps. V. and VI.): How are _necessary_ and _universal_
truths possible? And the answer then given was: that the
necessity and universality of truths are derived from the
_Fundamental Ideas_ which they involve. And we proceed in
this Book to exemplify this doctrine in the case of the
truths of Geometry and Arithmetic, which derive their
necessity and universality from the Fundamental Ideas of
Space, and Time, or Number.
The question thus examined is that which Kant undertook to
deal with in his celebrated work, _Kritik der reinen
Vernunft_ (_Examination of the Pure Reason_): and our
solution of the Problem, so far as the Ideas of Space and
Time are concerned, agrees in the main with his. The
arguments contained in chapters II. and **VII. of this Book,
are the leading arguments respecting Space and Time, in
Kant's _Kritik_. Kant, however, instead of calling Space and
Time _Ideas_, calls them the necessary _Forms_ of our
experience, as I have stated in the text.
But though I have adopted Kant's arguments as to Space and
Time, all that follows in the succeeding Books, with regard
to other Ideas, has no resemblance to any doctrines of Kant
or his school (with the exception, perhaps, of some of the
views on the Idea of _Cause_). The nature and character of
the other Scientific Ideas which I have examined, in the
succeeding Books, have been established by an analysis of
the history of the several Sciences to which those Ideas are
essential, and an examination of the writings of the
principal discoverers in those Sciences.]
{{88}}
CHAPTER I.
OF THE PURE SCIENCES.
1. ALL external objects and events which we can contemplate
are viewed as having relations of Space, Time, and Number;
and are subject to the general conditions which these Ideas
impose, as well as to the particular laws which belong to
each class of objects and occurrences. The special laws of
nature, considered under the various aspects which
constitute the different sciences, are obtained by a mixed
reference to Experience and to the Fundamental Ideas of each
science. But besides the sciences thus formed by the aid of
special experience, the conditions which flow from those
more comprehensive ideas first mentioned, Space, Time, and
Number, constitute a body of science, applicable to objects
and changes of all kinds, and deduced without recurrence
being had to any observation in particular. These sciences,
thus unfolded out of ideas alone, unmixed with any reference
to the phenomena of matter, are hence termed _Pure_
Sciences. The principal sciences of this class are Geometry,
Theoretical Arithmetic, and Algebra considered in its most
general sense, as the investigation of the relations of
space and number by means of general symbols.
2. These Pure Sciences were not included in our survey of
the history of the sciences, because they are not
_inductive_ sciences. Their progress has not consisted in
collecting laws from phenomena, true theories from observed
facts, and more general from more limited laws; but in
tracing the consequences of the ideas themselves, and in
detecting the most general and intimate analogies and
connexions which prevail {89} among such conceptions as are
derivable from the ideas. These sciences have no principles
besides definitions and axioms, and no process of proof but
_deduction_; this process, however, assuming here a most
remarkable character; and exhibiting a combination of
simplicity and complexity, of rigour and generality, quite
unparalleled in other subjects.
3. The universality of the truths, and the rigour of the
demonstrations of these pure sciences, attracted attention
in the earliest times; and it was perceived that they
offered an exercise and a discipline of the intellectual
faculties, in a form peculiarly free from admixture of
extraneous elements. They were strenuously cultivated by the
Greeks, both with a view to such a discipline, and from the
love of speculative truth which prevailed among that people:
and the name _mathematics_, by which they are designated,
indicates this their character of _disciplinal_ studies.
4. As has already been said, the ideas which these sciences
involve extend to all the objects and changes which we
observe in the external world; and hence the consideration
of mathematical relations forms a large portion of many of
the sciences which treat of the phenomena and laws of
external nature, as Astronomy, Optics, and Mechanics. Such
sciences are hence often termed _Mixed Mathematics_, the
relations of space and number being, in these branches of
knowledge, combined with principles collected from special
observation; while Geometry, Algebra, and the like subjects,
which involve no result of experience, are called _Pure
Mathematics_.
5. Space, time, and number, may be conceived as _forms_ by
which the knowledge derived from our sensations is moulded,
and which are independent of the differences in the _matter_
of our knowledge, arising from the sensations themselves.
Hence the sciences which have these ideas for their subject
may be termed _Formal Sciences_. In this point of view, they
are distinguished from sciences in which, besides these mere
formal laws by which appearances are corrected, we endeavour
to apply to the phenomena the idea of cause, {90} or some of
the other ideas which penetrate further into the principles
of nature. We have thus, in the History, distinguished
Formal Astronomy and Formal Optics from Physical Astronomy
and Physical Optics.
We now proceed to our examination of the Ideas which
constitute the foundation of these formal or pure
mathematical sciences, beginning with the Idea of Space.
{{91}}