NOVUM ORGANON
RENOVATUM.
BY WILLIAM WHEWELL, D.D.,
MASTER OF TRINITY COLLEGE, CAMBRIDGE, AND
CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE.
BEING THE SECOND PART OF THE PHILOSOPHY
OF THE INDUCTIVE SCIENCES.
_THE THIRD EDITION, WITH LARGE ADDITIONS._
ΛΑΜΠΑΔIΑ ΕΧΟΝΤΕΣ ΔIΑΔΩΣΟΥΣIΝ ΑΛΛΗΛΟIΣ
LONDON:
JOHN W. PARKER AND SON, WEST STRAND.
1858.
IT is to our immortal countryman; Bacon, that we owe the broad
announcement of this grand and fertile principle; and the
developement of the idea, that the whole of natural philosophy
consists entirely of a series of inductive generalizations,
commencing with the most circumstantially stated particulars, and
carried up to universal laws, or axioms, which comprehend in their
statements every subordinate degree of generality; and of a
corresponding series of inverted reasoning from generals to
particulars, by which these axioms are traced back into their
remotest consequences, and all particular propositions deduced from
them; as well those by whose immediate considerations we rose to
their discovery, as those of which we had no previous knowledge.
HERSCHEL, _Discourse on Natural Philosophy_, Art. 96.
CAMBRIDGE: PRINTED BY C. J. CLAY, M.A. AT THE UNIVERSITY PRESS.
{{iii}}
PREFACE.
EVEN if Bacon's _Novum Organon_ had possessed the character to which
it aspired as completely as was possible in its own day, it would at
present need renovation: and even if no such book had ever been
written, it would be a worthy undertaking to determine the
machinery, intellectual, social and material, by which human
knowledge can best be augmented. Bacon could only divine how
sciences might be constructed; we can trace, in their history, how
their construction has taken place. However sagacious were his
conjectures, the facts which have really occurred must give
additional instruction: however large were his anticipations, the
actual progress of science since his time has illustrated them in
all their extent. And as to the structure and operation of the
_Organ_ by which truth is to be collected from nature,--that is, the
Methods by which science is to be promoted--we know that, though
Bacon's general maxims are sagacious and animating, his particular
precepts failed in his hands, and are now practically useless. This,
perhaps, was not wonderful, seeing that they were, as I have said,
mainly derived from conjectures respecting knowledge and the
progress of knowledge; but at {iv} the present day, when, in several
provinces of knowledge, we have a large actual progress of solid
truth to look back upon, we may make the like attempt with the
prospect of better success, at least on that ground. It may be a
task, not hopeless, to extract from the past progress of science the
elements of an effectual and substantial method of Scientific
Discovery. The advances which have, during the last three centuries,
been made in the physical sciences;--in Astronomy, in Physics, in
Chemistry, in Natural History, in Physiology;--these are allowed by
all to be real, to be great, to be striking; may it not be that the
steps of progress in these different cases have in them something
alike? May it not be that in each advancing movement of such
knowledge there is some common principle, some common process? May
it not be that discoveries are made by an _Organ_ which has
something uniform in its working? If we can shew that this is so, we
shall have the _New Organ_, which Bacon aspired to construct,
_renovated_ according to our advanced intellectual position and
office.
It was with the view of opening the way to such an attempt that I
undertook that survey of the past progress of physical knowledge, of
which I have given the results in the _History of the Sciences_, and
the _History of Scientific Ideas_[1\P]; the former containing the
history of the sciences, so far as it depends on {v} observed
_Facts_; the latter containing the history of those _Ideas_ by which
such Facts are bound into Theories.
[Note 1\P: Published in two former editions as part of the
_Philosophy of the Inductive Sciences_ (b. i--x.).]
It can hardly happen that a work which treats of Methods of
Scientific Discovery, shall not seem to fail in the positive results
which it offers. For an Art of Discovery is not possible. At each
step of the investigation are needed Invention, Sagacity,
Genius,--elements which no art can give. We may hope in vain, as
Bacon hoped, for an Organ which shall enable all men to construct
Scientific Truths, as a pair of compasses enables all men to
construct exact circles[2\P]. This cannot be. The practical results
of the Philosophy of Science must be rather classification and
analysis of what has been done, than precept and method for future
doing. Yet I think that the methods of discovery which I have to
recommend, though gathered from a wider survey of scientific
history, both as to subjects and as to time, than (so far as I am
aware) has been elsewhere attempted, are quite as definite and
practical as any others which have been proposed; with the great
additional advantage of being the methods by which all great
discoveries in science have really been made. This may be said, for
instance, of _the Method of Gradation_ and _the Method of Natural
Classification_, spoken of b. iii. c. viii; and in a narrower sense,
of _the Method of Curves_, _the Method of_ {vi} _Means_, _the Method
of Least Squares_ and _the Method of Residues_, spoken of in chap.
vii. of the same Book. Also the Remarks on the _Use of Hypotheses_
and on the _Tests of Hypotheses_ (b. ii. c. v.) point out features
which mark the usual course of discovery.
[Note 2\P: _Nov. Org._ lib. i. aph. 61.]
But one of the principal lessons resulting from our views is
undoubtedly this:--that different sciences may be expected to
advance by different modes of procedure, according to their present
condition; and that in many of these sciences, an Induction
performed by any of the methods which have just been referred to is
not the next step which we may expect to see made. Several of the
sciences may not be in a condition which fits them for such a
_Colligation of Facts_; (to use the phraseology to which the
succeeding analysis has led me). The Facts may, at the present time,
require to be more fully observed, or the Idea by which they are to
be colligated may require to be more fully unfolded.
But in this point also, our speculations are far from being barren
of practical results. The examination to which we have subjected
each science, gives us the means of discerning whether what is
needed for the further progress of the science, has its place in the
Observations, or in the Ideas, or in the union of the two. If
observations be wanted, the Methods of Observation, given in b. iii.
c. ii. may be referred to. If those who are to make the next
discoveries need, for that purpose, a developement of their Ideas,
the modes in which such a developement has usually taken {vii} place
are treated of in Chapters iii. and iv. of that Book.
No one who has well studied the history of science can fail to see
how important a part of that history is the explication, or as I
might call it, the _clarification_ of men's Ideas. This, the
metaphysical aspect of each of the physical sciences, is very far
from being, as some have tried to teach, an aspect which it passes
through at an early period of progress, and previously to the stage
of positive knowledge. On the contrary, the metaphysical movement is
a necessary part of the inductive movement. This, which is evidently
so by the nature of the case, was proved by a copious collection of
historical evidences, in the _History of Scientific Ideas_. The ten
Books of that History contain an account of the principal
philosophical controversies which have taken place in all the
physical sciences, from Mathematics to Physiology. These
controversies, which must be called _metaphysical_ if anything be so
called, have been conducted by the greatest discoverers in each
science, and have been an essential part of the discoveries made.
Physical discoverers have differed from barren speculators, not by
having _no_ metaphysics in their heads, but by having _good_
metaphysics in their heads while their adversaries had bad; and by
binding their metaphysics to their physics, instead of keeping the
two asunder. I trust that the _History of Scientific Ideas_ is of
some value, even as a record of a number of remarkable
controversies; but I conceive that it also contains an indisputable
proof that there {viii} is, in progressive science, a metaphysical
as well as a physical element;--ideas as well as facts;--thoughts as
well as things. Metaphysics is the process of ascertaining that
thought is consistent with itself: and if it be not so, our
supposed knowledge is not knowledge.
In Chapter vi. of the Second Book, I have spoken of _the Logic of
Induction_. Several writers[3\P] have quoted very emphatically my
assertion that the Logic of Induction does not exist in previous
writers: using it as an introduction to Logical Schemes of their
own. They seem to have overlooked the fact that at the same time
that I noted the deficiency, I offered a scheme which I think fitted
to supply this want. And I am obliged to say that I do not regard
the schemes proposed by any of those gentlemen as at all
satisfactory for the purpose. But I must defer to a future occasion
any criticism of authors who have written on the subjects here
treated. A critical notice of such authors formed the Twelfth Book
of the former edition of the _Philosophy of the Sciences_. I have
there examined the opinions concerning the Nature of Real Knowledge
and the mode of acquiring it, which have been promulgated in all
ages, from Plato and Aristotle, to Roger Bacon, to Francis Bacon, to
Newton, to Herschel. Such a survey, with the additions which I
should now have to make to it, may hereafter be put forth as a
separate book: but I {ix} have endeavoured to confine the present
volume to such positive teaching regarding Knowledge and Science as
results from the investigations pursued in the other works of this
series. But with regard to this matter, of the _Logic of Induction_,
I may venture to say, that we shall not find anything deserving the
name explained in the common writers on Logic, or exhibited under
the ordinary Logical Forms. _That_ in previous writers which comes
the nearest to the notice of such a Logic as the history of science
has suggested and verified, is the striking declaration of Bacon in
two of his Aphorisms (b. i. aph. civ. cv.).
[Note 3\P: Apelt _Die Theorie der Induction_: Gratry _Logique_.]
"There will be good hopes for the Sciences then, and not till then,
when by a true SCALE or Ladder, and by successive steps, following
continuously without gaps or breaks, men shall ascend from
particulars to the narrower Propositions, from those to intermediate
ones, rising in order one above another, and at last to the most
general.
"But in establishing such propositions, we must devise some other
FORM OF INDUCTION than has hitherto been in use; and this must be
one which serves not only to prove and discover _Principles_, (as very
general Propositions are called,) but also the narrower and the
intermediate, and in short, all true Propositions."
And he elsewhere speaks of successive FLOORS of Induction.
All the truths of an extensive science form a Series of such Floors,
connected by such Scales or Ladders; and a part of the Logic of
Induction consists, as I {x} conceive, in the construction of a
_Scheme_ of such Floors. Converging from a wide basis of various
classes of particulars, at last to one or a few general truths,
these schemes necessarily take the shape of a Pyramid. I have
constructed such Pyramids for Astronomy and for Optics[4\P]; and the
illustrious Von Humboldt in speaking of the former subject, does me
the honour to say that my attempt in that department is perfectly
successful[5\P]. The Logic of Induction contains other portions,
which may be seen in the following work, b. ii. c. vi.
[Note 4\P: See the Tables at the end of book ii.]
[Note 5\P: _Cosmos_, vol. ii. n. 35.]
I have made large additions to the present edition, especially in
what regards the Application of Science, (b. iii. c. ix.) and the
Language of Science. The former subject I am aware that I have
treated very imperfectly. It would indeed, of itself, furnish
material for a large work; and would require an acquaintance with
practical arts and manufactures of the most exact and extensive
kind. But even a general observer may see how much more close the
union of Art with Science is now than it ever was before; and what
large and animating hopes this union inspires, both for the progress
of Art and of Science. On another subject also I might have dilated
to a great extent,--what I may call (as I have just now called it)
the _social_ machinery for the advancement of science. There can be
no doubt that at certain stages of sciences, {xi} Societies and
Associations may do much to promote their further progress; by
combining their observations, comparing their views, contributing to
provide material means of observation and calculation, and dividing
the offices of observer and generalizer. We have had in Europe in
general, and especially in this country, very encouraging examples
of what may be done by such Associations. For the present I have
only ventured to propound one Aphorism on the subject, namely this;
(Aph. LV.) That it is worth considering whether a continued and
connected system of observation and calculation, like that of
Astronomy, might not be employed in improving our knowledge of other
subjects; as Tides, Currents, Winds, Clouds, Rain, Terrestrial
Magnetism, Aurora Borealis, composition of crystals, and the like.
In saying this, I have mentioned those subjects which are, as
appears to me, most likely to profit by continued and connected
observations.
I have thrown the substance of my results into Aphorisms, as Bacon
had done in his _Novum Organum_. This I have done, not in the way of
delivering dogmatic assertions or oracular sentences; for the
Aphorisms are all supported by reasoning, and were, in fact, written
after the reasoning, and extracted from it. I have adopted this mode
of gathering results into compact sentences, because it seems to
convey lessons with additional clearness and emphasis.
I have only to repeat what I have already said; that this task of
adapting the _Novum Organum_ to the {xii} present state of Physical
Science, and of constructing a _Newer Organ_ which may answer the
purposes at which Bacon aimed, seems to belong to the present
generation; and being here founded upon a survey of the past history
and present condition of the Physical Sciences, will I hope, not be
deemed presumptuous.
TRINITY LODGE,
1 _November_, 1858.
{{xiii}}
TABLE OF CONTENTS.
PAGE
PREFACE **iii
BOOK I.
APHORISMS CONCERNING IDEAS.
APHORISMS I.--XVIII. Ideas in general 5--7
XIX.--XLIV. Ideas in the Pure Sciences 8--12
XLV.--LV. Ideas in the Mechanical Sciences 13--15
LVI.--LXXI. Ideas in the Secondary Mechanical
Sciences. 15--18
LXXII.--**LXXIII. Ideas in the Mechanico-chemical
Sciences 18
LXXIV.--LXXIX. Ideas in Chemistry 18
LXXX.--LXXXI. Ideas in Morphology 19
**LXXXII.--C. Ideas in Classificatory Science 20--23
CI.--CVI. Ideas in Biology 23--24
CVII.--CXVII. Ideas in Palæontology 24--26
BOOK II.
OF KNOWLEDGE.
CHAP. I. OF TWO PRINCIPAL PROCESSES BY WHICH SCIENCE IS
CONSTRUCTED 27
CHAP. II. OF THE EXPLICATION OF CONCEPTIONS 30
_Sect._ I. _The Historical Progress._
_Art._ 1. The Explication of Conceptions,
2. Has taken place historically by discussions.
{xiv}
_Art._ 3. False Doctrines when exposed appear impossible:
4. But were plausible before
5. Men's Minds gradually cleared.
_Sect._ II. _Use of definitions._
_Art._ 6. Controversies about Definitions.
7. Not arbitrary Definitions.
8. Attention to Facts requisite.
9. Definition is not essential.
10. The omission of Definition not always blameable.
_Sect._ III. _Use of Axioms._
_Art._ 11. Axioms serve to express Ideas.
_Sect._ IV. _Clear and appropriate Ideas._
_Art._ 12. We must see the Axioms clearly.
13. Inappropriate Ideas cannot lead to Truth.
14. The fault is in the Conceptions.
15. Rules cannot teach Discovery;
16. But are not useless.
17. Discussion as well as Facts needed.
_Sect._ V. _Accidental Discoveries._
_Art._ 18. No Scientific Discovery is accidental.
19. Such accidents do not happen to common Men.
20. Examples.
21. So far Explication of Conceptions.
CHAP. III. OF FACTS AS THE MATERIALS OF SCIENCE 50
_Art._ 1. Facts must be true.
2. Facts not separable from Ideas.
3. The Ideas must be distinct.
4. Conceptions of the Intellect only to be admitted.
5. Facts are to be observed with reference to
Space and Time:
6. And also to other Ideas.
7. The Decomposition of Facts.
{xv}
_Art._ 8. This step is not sufficient.
9. It introduces Technical Terms,
10. And Classification.
11. The materials of Science.
CHAP. IV. OF THE COLLIGATION OF FACTS 59
_Art._ 1. Facts are colligated by Conceptions.
2. Science begins with common Observation.
3. Facts must be decomposed.
4. What Ideas first give Sciences.
5. Facts must be referred to Ideas.
6. Sagacity needed.
7. Discovery made by Guesses.
8. False Hypotheses preluding to true ones.
9. New Hypotheses not mere modifications of old ones.
10. Hypotheses may have superfluous parts.
11. Hypotheses to be compared with Facts.
12. Secondary Steps.
CHAP. V. OF CERTAIN CHARACTERISTICS OF SCIENTIFIC INDUCTION 70
_Sect._ I. _Invention a part of Induction._
_Art._ 1. Induction the source of Knowledge.
2. Induction involves a New Element.
3. Meaning of Induction.
4. The New Element is soon forgotten.
5. Induction includes a Definition and a Proposition.
_Sect._ II. _Use of Hypotheses._
_Art._ 6. Discoveries made by Guesses,
7. Which must be compared with Facts.
8. Hypotheses are suspected.
9. Hypotheses may be useful though inaccurate.
_Sect._ III. _Tests of Hypotheses._
_Art._ 10. True Hypotheses foretel Phenomena,
11. Even of different kinds.--Consilience of Inductions.
{xvi}
_Art._ 12. True Theories tend to Simplicity.
13. Connexion of the last Tests.
CHAP. VI. OF THE LOGIC OF INDUCTION 97
_Art._ 1. Steps of Generalization,
2. May be expressed by _Tables_.
3. Which exhibit Inductive Steps;
4. And the Consilience of Inductions;
5. And the tendency to Simplicity;
6. And the names of Discoverers;
7. And the Verifications of Theory;
8. By means of several easy steps.
9. This resembles Book-keeping.
10. The Logic of Induction.
11. Attention at each step required.
12. General Truths are not mere additions of
particulars:
13. But a new view is introduced.
14. Formula of Inductive Logic:
15. May refer to Definition.
16. Formula inadequate.
17. Deductive Connexion of Steps.
18. Relation of Deductive and Inductive Reasoning.
19. The Criterion of Truth.
20. Theory and Fact.
21. Higher and Lower Generalizations.
CHAP. VII. OF LAWS OF PHENOMENA AND OF CAUSES 118
_Art._ 1. Knowledge of Laws of Phenomena.
2. _Formal_ and _Physical_ Sciences.
3. Causes in Astronomy.
4. Different Mechanical Causes in other Sciences.
5. Chemical and Vital Forces as Causes.
6. Difference of these kinds of Force.
7. Difficulty of conceiving new Causes.
8. Men willingly take old Causes.
9. Is the Magnetic Fluid real?
10. Are Causes to be sought? (Comte's Doctrine.)
11. Both Laws and Causes to be studied.
{xvii}
CHAP. VIII. OF ART AND SCIENCE 129
_Art._ 1. Art precedes Science.
2. Contrast of Art and Science.
3. Instinct and Insight.
4. Difference of Art and Instinct.
5. Does Art involve Science?
6. Science unfolds Principles.
7. Science may improve Art.
8. Arts not classified with Sciences.
CHAP. IX. OF THE CLASSIFICATION OF SCIENCES 136
_Art._ 1. Use and Limits of such Classification.
2. Classification depends on the Ideas.
3. This points out Transitions.
4. The Classification.
INDUCTIVE TABLE OF ASTRONOMY 140
INDUCTIVE TABLE OF OPTICS 140
BOOK III.
OF METHODS EMPLOYED IN THE FORMATION OF SCIENCE.
CHAP. I. INTRODUCTION 141
_Art._ 1. Object of this Book.
2. An Art of Discovery not possible.
3. Use of Methods.
4. Series of Six Processes.
5. Methods of Observation and Induction.
CHAP. II. OF METHODS OF OBSERVATION 145
_Art._ 1. Referring to Number, Space, and Time.
2. Observations are never perfect.
3. (I.) _Number is naturally exact_.
4. (II.) _Measurement of Space_.
5. Instruments Invented in Astronomy,
6. And improved.
{xviii}
_Art._ 7. Goniometer.
8. Standard of Length.
10. (III.) _Measurement of Time_.
11. Unit of Time.
12. Transit Instrument.
13. Chronometers.
14. (IV.) _Conversion of Space and Time_.
15. Space may Measure Time.
16. Time may Measure Space.
17. (V.) _The Method of Repetition_.
18. The Method of Coincidences.
19. Applied to Pendulums.
20. (VI.) _Measurement of Weight_.
21. Standard of Weight.
22. (VII.) _Measurement of Secondary Qualities_.
23. "The Howl" in Harmonics.
24. (VIII.) _Manipulation_.
25. Examples in Optics.
26. (IX.) _The Education of the Senses_,
27. By the Study of Natural History.
28. Preparation for Ideas.
CHAP. III. OF METHODS OF ACQUIRING CLEAR SCIENTIFIC IDEAS;
_and first_ OF INTELLECTUAL EDUCATION 164
_Art._ 1. (I.) _Idea of Space_.
2. Education by Geometry.
3. (II.) _Idea of Number_.
4. Effect of the usual Education.
5. (III.) _Idea of Force_.
6. Study of Mechanics needed,
7. To make Newton intelligible.
8. No _Popular_ Road.
9. (IV.) _Chemical Ideas_.
10. (V.) _Natural History Ideas_.
11. Natural Classes to be taught.
12. Mathematical Prejudices,
13. To be corrected by Natural History.
14. Method of Natural History,
15. Resembles common language.
{xix}
_Art._ 16. Its Lessons.
17. (VI.) _Well-established Ideas alone to be used_.
18. How are Ideas cleared?
CHAP. IV. OF METHODS OF ACQUIRING CLEAR SCIENTIFIC IDEAS,
_continued_.--OF THE DISCUSSION OF IDEAS 180
_Art._ 1. Successive Clearness,
2. Produced by Discussion.
3. Examples.
4. Disputes not useless,
5. Although "metaphysical."
6. Connected with Facts.
CHAP. V. ANALYSIS OF THE PROCESS OF INDUCTION 186
_Sect._ I. _The Three Steps of Induction._
_Art._ 1. Methods may be useful.
2. The three Steps.
3. Examples.
4. Mathematical names of the Steps.
_Sect._ II. _Of the Selection of the Fundamental Idea._
_Art._ 5. Examples.
6. The Idea to be found by trying,
7. Till the Discovery is made;
8. Preluded by Guesses.
9. Idea and Facts homogeneous.
10. Idea tested by the Facts.
CHAP. VI. GENERAL RULES FOR THE CONSTRUCTION OF THE CONCEPTION 195
_Art._ 1. First: for Quantity.
2. Formula and Coefficients found together.
3. Example. Law of Cooling.
4. Determined by Experiment.
5. Progressive Series of Numbers.
6. Recurrent Series.
7. Use of Hypotheses.
8. Even with this there are difficulties.
{xv}
CHAP. VII. SPECIAL METHODS OF INDUCTION APPLICABLE TO QUANTITY 202
_Sect._ I. _The Method of Curves._
_Art._ 1. Its Process.
2. Its Use.
3. With imperfect Observations.
4. It corrects Observations.
5. _Obstacles_. (I.) Ignorance of the argument.
6. (II.) Combination of Laws.
_Sect._ II. _The Method of Means._
_Art._ 7. Its Relation to the Method of Curves.
8. Its process.
9. _Argument_ required to be known.
10. Use of the Method.
11. Large masses of Observations used.
12. Proof of the Use of the Method.
_Sect._ III. _The Method of Least Squares._
_Art._ 13. Is a Method of Means.
14. Example.
_Sect._ IV. _The Method of Residues._
_Art._ 15. Occasion for its Use.
16. Its Process.
17. Examples.
18. Its Relation to the Method of Means.
19. Example.
20. "Residual Phenomena."
CHAP. VIII. METHODS OF INDUCTION DEPENDING ON RESEMBLANCE 220
_Sect._ I. _The Law of Continuity._
_Art._ 1. Its Nature and Application,
2. To Falling Bodies,
3. To Hard Bodies,
4. To Gravitation.
5. The Evidence.
{xxi}
_Sect._ II. _The Method of Gradation._
_Art._ 6. Occasions of its Use.
7. Examples.
8. Not enjoined by Bacon.
9. Other Examples.
10. Its Value in Geology.
11. Limited Results.
_Sect._ III. _The Method of Natural Classification._
_Art._ 12. Examples of its Use.
13. Its Process.
14. Negative Results.
15. Is opposed to Arbitrary Definitions.
16. Propositions and Definitions correlative.
17. Definitions only provisional.
CHAP. IX. OF THE APPLICATION OF INDUCTIVE TRUTHS 233
_Art._ 1. This forms the Sequel of Discovery.
2. Systematic Verification of Discoveries.
3. Correction of Coefficients.
4. Astronomy a Model.
5. Verification by new cases.
6. Often requires fresh calculation.
7. Cause of Dew.
8. Useful Applications.
CHAP. X. OF THE INDUCTION OF CAUSES 247
_Art._ 1. Is to be pursued.
2. Induction of Substance.
3. Induction of Force.
4. Induction of Polarity.
5. Is Gravity Polar?
6. Induction of Ulterior Causes.
7. Of the Supreme Cause.
{xxii}
BOOK IV,
OF THE LANGUAGE OF SCIENCE.
INTRODUCTION 257
APHORISMS CONCERNING THE LANGUAGE OF SCIENCE.
_Aphorism_ I. Relative to the Ancient Period 258
_Art._ 1. Common Words.
2. Descriptive Terms.
3. Theoretical Terms.
_Aphorism_ II. Relative to the Modern Period 269
_Art._ 1. Systematic Nomenclature.
2. Systematic Terminology.
3. Systematic Modification.
_Aphorisms_ (III. IV. V. VI. VII) relative to the
Application of Common Words 278
_Aphorisms_ (VIII. IX. X. XI. XII. XIII.) relative to the
Construction of New Terms 285
_Aphorism_ XIV. Binary Nomenclature 307
XV. Linnæan Maxims 308
XVI. Numerical Names 309
XVII. Names of more than two Steps 310
XVIII. No arbitrary _Terms_ 311
XIX. Forms fixed by Convention 314
XX. _Form_ of Terms 318
_Art._ 1. Terms derived from Latin and Greek.
2. German Terms.
3. Descriptive Terms.
4. Nomenclature. Zoology.
5. ------------- Mineralogy.
6. ------------- Botany.
7. ------------- Chemistry.
8. ------------- Crystallography.
{xxiii}
_Aphorism_ XXI. Philological Rules 328
_Art._ 1. Hybrids.
2. Terminations of Substantives.
3. Formations of Substantives (names of things).
4. Abstract Substantives.
5. Rules of derivation from Greek and Latin.
6. Modification of Terminations.
_Aphorism_ XXII. Introduction of Changes 341
FURTHER ILLUSTRATIONS OF THE APHORISMS ON SCIENTIFIC
LANGUAGE, FROM THE RECENT COURSE OF SCIENCES.
1. BOTANY.
_Aphorism_ XXIII. Multiplication of Genera 346
2. COMPARATIVE ANATOMY.
_Aphorism_ XXIV. Single Names to be used 353
XXV. The History of Science is the History
of its Language 355
XXVI. Algebraical Symbols 357
XXVII. Algebraical Analogies 364
XXVIII. Capricious Derivations 365
XXIX. Inductions are our Definitions 368
{{1}}
NOVUM ORGANON RENOVATUM.
DE Scientiis tum demum bene sperandum est, quando per SCALAM veram
et per gradus continuos, et non intermissos aut hiulcos, a
particularibus ascendetur ad Axiomata minora, et deinde ad media,
alia aliis superiora, et postremo demum ad generalissima.
In constituendo autem Axiomate, Forma INDUCTIONIS alia quam adhuc in
usu fuit, excogitanda est; et quæ non ad Principia tantum (quæ
vocant) probanda et invenienda, sed etiam ad Axiomata minora, et
media, denique omnia.
BACON, _Nov. Org._, Aph. civ. cv.
{{3}}
NOVUM ORGANON RENOVATUM.
THE name _Organon_ was applied to the works of Aristotle which
treated of Logic, that is, of the method of establishing and proving
knowledge, and of refuting errour, by means of Syllogisms. Francis
Bacon, holding that this method was insufficient and futile for the
augmentation of real and useful knowledge, published his _Novum
Organon_, in which he proposed for that purpose methods from which
he promised a better success. Since his time real and useful
knowledge has made great progress, and many Sciences have been
greatly extended or newly constructed; so that even if Bacon's
method had been the right one, and had been complete as far as the
progress of Science up to his time could direct it, there would be
room for the revision and improvement of the methods of arriving at
scientific knowledge.
Inasmuch as we have gone through the _Histories_ of the principal
_Sciences_, from the earliest up to the present time, in a previous
work, and have also traced the _History of Scientific Ideas_ in
another work, it may perhaps be regarded as not too presumptuous if
we attempt this revision and improvement of the methods by which
Sciences must rise and grow. This {4} is our task in the present
volume; and to mark the reference of this undertaking to the work of
Bacon, we name our book _Novum Organon Renovatum_.
Bacon has delivered his precepts in Aphorisms, some of them stated
nakedly, others expanded into dissertations. The general results at
which we have arrived by tracing the history of Scientific Ideas are
the groundwork of such Precepts as we have to give: and I shall
therefore begin by summing up these results in Aphorisms, referring
to the former work for the historical proof that these Aphorisms are
true.
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NOVUM ORGANON RENOVATUM.
BOOK I.
APHORISMS CONCERNING IDEAS DERIVED FROM THE HISTORY OF IDEAS.
I.
_MAN is the Interpreter of Nature, Science the right
interpretation._ (_History of Scientific Ideas_: Book I. Chapter 1.)
II.
_The_ Senses _place before us the_ Characters _of the Book of
Nature; but these convey no knowledge to us, till we have discovered
the Alphabet by which they are to be read._ (Ibid. I. 2.)
III.
_The_ Alphabet, _by means of which we interpret Phenomena, consists
of the_ Ideas _existing in our own minds; for these give to the
phenomena that coherence and significance which is not an object of
sense._ (I. 2.)
IV.
_The antithesis of_ Sense _and_ Ideas _is the foundation of the
Philosophy of Science. No knowledge can exist without the union, no
philosophy without the separation, of these two elements._ (I. 2.)
{6}
V.
Fact _and_ Theory _correspond to Sense on the one hand, and to Ideas
on the other, so far as we are_ conscious _of our Ideas: but all facts
involve ideas_ unconsciously; _and thus the distinction of Facts and
Theories is not tenable, as that of Sense and Ideas is._ (I. 2.)
VI.
_Sensations and Ideas in our knowledge are like Matter and Form in
bodies. Matter cannot exist without Form, nor Form without Matter:
yet the two are altogether distinct and opposite. There is no
possibility either of separating, or of confounding them. The same
is the case with Sensations and Ideas._ (I. 2.)
VII.
_Ideas are not_ trans_formed, but_ in_formed Sensations; for without
ideas, sensations have no form._ (I. 2.)
VIII.
_The Sensations are the_ Objective, _the Ideas the_ Subjective _part
of every act of perception or knowledge._ (I. 2.)
IX.
_General Terms denote_ Ideal Conceptions, _as a_ circle, _an_ orbit,
_a_ rose. _These are not_ Images _of real things, as was held by the
Realists, but Conceptions: yet they are conceptions, not bound
together by mere_ Name, _as the Nominalists held, but by an Idea._
(I. 2.)
X.
_It has been said by some, that all Conceptions are merely_ states
_or_ feelings of the mind, _but this assertion only tends to
confound what it is our business to distinguish._ (I. 2.)
XI.
_Observed Facts are connected so as to produce new truths, by
superinducing upon them an Idea: and such truths are obtained_ by
Induction. (I. 2.) {7}
XII.
_Truths once obtained by legitimate Induction are Facts: these Facts
may be again connected, so as to produce higher truths: and thus we
advance to_ Successive Generalizations. (I. 2.)
XIII.
_Truths obtained by Induction are made compact and permanent by
being expressed in_ Technical Terms. (I. 3.)
XIV.
_Experience cannot conduct us to universal and necessary
truths:--Not to universal, because she has not tried all cases:--Not
to necessary, because necessity is not a matter to which experience
can testify._ (I. 5.)
XV.
_Necessary truths derive their necessity from the_ Ideas _which they
involve; and the existence of necessary truths proves the existence
of Ideas not generated by experience._ (I. 5.)
XVI.
_In Deductive Reasoning, we cannot have any truth in the conclusion
which is not virtually contained in the premises._ (I. 6.)
XVII.
_In order to acquire any exact and solid knowledge, the student must
possess with perfect precision the ideas appropriate to that part of
knowledge: and this precision is tested by the student's_ perceiving
_the axiomatic evidence of the_ axioms _belonging to each_
Fundamental Idea. (I. 6.)
XVIII.
_The Fundamental Ideas which it is most important to consider, as
being the Bases of the Material Sciences, are the Ideas of_ Space,
Time (_including Number_), Cause (_including Force and Matter_),
Outness _of Objects, and_ Media _of Perception of Secondary
Qualities,_ Polarity (_Contrariety_), {8} _Chemical_ Composition
_and_ Affinity, Substance, Likeness _and Natural_ Affinity, Means
and Ends (_whence the Notion of Organization_), Symmetry, _and the
Ideas of_ Vital Powers. (I. 8.)
XIX.
_The Sciences which depend upon the Ideas of Space and Number are_
Pure _Sciences, not_ Inductive _Sciences: they do not infer special
Theories from Facts, but deduce the conditions of all theory from
Ideas. The Elementary Pure Sciences, or Elementary Mathematics, are
Geometry, Theoretical Arithmetic and Algebra._ (II. 1.)
XX.
_The Ideas on which the Pure Sciences depend, are those of_ Space
_and_ Number; _but Number is a modification of the conception of
Repetition, which belongs to the Idea of_ Time. (II. 1.)
XXI.
_The_ Idea of Space _is not derived from experience, for experience
of external objects_ pre_supposes bodies to exist in Space, Space is a
condition under which the mind receives the impressions of sense,
and therefore the relations of space are necessarily and universally
true of all perceived objects. Space is a_ form _of our perceptions,
and regulates them, whatever the_ matter _of them may be._ (II. 2.)
XXII.
_Space is not a General Notion collected by abstraction from
particular cases; for we do not speak of_ Spaces _in general, but of
universal or absolute_ Space. _Absolute Space is infinite. All
special spaces are_ in _absolute space, and are parts of it._ (II. 3.)
XXIII.
_Space is not a real object or thing, distinct from the objects
which exist in it; but it is a real condition of the existence of
external objects._ (II. 3.) {9}
XXIV.
_We have an_ Intuition _of objects in space; that is, we contemplate
objects as_ made up _of spatial parts, and apprehend their spatial
relations by the same act by which we apprehend the objects
themselves._ (II. 3.)
XXV.
Form _or Figure is space limited by boundaries. Space has
necessarily_ three _dimensions, length, breadth, depth; and no
others which cannot be resolved into these._ (II. 3.)
XXVI.
_The Idea of Space is exhibited for scientific purposes, by the_
Definitions _and_ Axioms _of Geometry; such, for instance, as
these:--the_ Definition of a Right Angle, _and_ of a Circle;--_the_
Definition of Parallel Lines, _and the_ Axiom _concerning
them;--the_ Axiom _that_ two straight lines cannot inclose a space.
_These Definitions are necessary, not arbitrary; and the Axioms are
needed as well as the Definitions, in order to express the necessary
conditions which the Idea of Space imposes._ (II. 4.)
XXVII.
_The Definitions and Axioms of Elementary Geometry do not_
completely _exhibit the Idea of Space. In proceeding to the Higher
Geometry, we may introduce other additional and independent Axioms;
such as that of Archimedes, that_ a curve line which joins two
points is less than any broken line joining the same points and
including the curve line. (II. 4.)
XXVIII.
_The perception of a_ solid object _by sight requires that act of
mind by which, from figure and shade, we infer distance and position
in space. The perception of_ figure _by sight requires that act of
mind by which we give an outline to each object._ (II. 6.) {10}
XXIX.
_The perception of Form by touch is not an impression on the passive
sense, but requires an act of our muscular frame by which we become
aware of the position of our own limbs. The perceptive faculty
involved in this act has been called_ the muscular sense. (II. 6.)
XXX.
_The_ Idea of Time _is not derived from experience, for experience
of changes_ pre_supposes occurrences to take place in Time. Time is
a condition under which the mind receives the impressions of sense,
and therefore the relations of time are necessarily and universally
true of all perceived occurrences. Time is a_ form _of our
perceptions, and regulates them, whatever the_ matter _of them may
be._ (II. 7.)
XXXI.
_Time is not a General Notion collected by abstraction from
particular cases. For we do not speak of particular_ Times _as
examples of time in general, but as parts of a single and infinite_
Time. (II. 8.)
XXXII.
_Time, like Space, is a form, not only of perception, but of_
Intuition. _We consider the whole of any time as_ equal _to the_ sum
_of the parts; and an occurrence as_ coinciding _with the portion of
time which it occupies._ (II. 8.)
XXXIII.
_Time is analogous to Space of_ one dimension: _portions of both
have a beginning and an end, are long or short. There is nothing in
Time which is analogous to Space of two, or of three, dimensions,
and thus nothing which corresponds to Figure._ (II. 8.)
XXXIV.
_The Repetition of a set of occurrences, as, for example, strong and
weak, or long and short sounds, according to a_ {11} _steadfast order,
produces_ Rhythm, _which is a conception peculiar to Time, as Figure
is to Space._ (II. 8.)
XXXV.
_The simplest form of Repetition is that in which there is no
variety, and thus gives rise to the conception of_ Number. (II. 8.)
XXXVI.
_The simplest numerical truths are seen by Intuition; when we
endeavour to deduce the more complex from these simplest, we employ
such maxims as these_:--If equals be added to equals the wholes are
equal:--If equals be subtracted from equals the remainders are
equal:--The whole is equal to the sum of all its parts. (II. 9.)
XXXVII.
_The Perception of Time involves a constant and latent kind of
memory, which may be termed a_ Sense of Succession. _The Perception
of Number also involves this Sense of Succession, although in small
numbers we appear to apprehend the units simultaneously and not
successively._ (II. 10.)
XXXVIII.
_The Perception of Rhythm is not an impression on the passive sense,
but requires an act of thought by which we connect and group the
strokes which form the Rhythm._ (II. 10.)
XXXIX.
Intuitive _is opposed to_ Discursive _reason. In intuition, we obtain
our conclusions by dwelling upon_ one _aspect of the fundamental
Idea; in discursive reasoning, we combine_ several _aspects of the
Idea,_ (_that is, several axioms,_) _and reason from the
combination._ (II. 11.)
XL.
_Geometrical deduction_ (_and deduction in general_) _is called_
Synthesis, _because we introduce, at successive steps, the_ {12}
_results of new principles. But in reasoning on the relations of
space, we sometimes go on_ separating _truths into their component
truths, and these into other component truths; and so on: and this
is geometrical_ Analysis. (II. 11.)
XLI.
_Among the foundations of the Higher Mathematics, is the_ Idea of
Symbols _considered as general_ Signs _of Quantity. This idea of a
Sign is distinct from, and independent of other ideas. The Axiom to
which we refer in reasoning by means of Symbols of quantity is
this_:--The interpretation of such symbols must be perfectly
general. _This Idea **and Axiom are the bases of Algebra in its most
general form._ (II. 12.)
XLII.
_Among the foundations of the Higher Mathematics is also the_ Idea
of a Limit. _The Idea of a Limit cannot be superseded by any other
definitions or Hypotheses, The Axiom which we employ in introducing
this Idea into our reasoning is this_:--What is true up to the Limit
is true at the Limit. _This Idea and Axiom are the bases of all
Methods of Limits, Fluxions, Differentials, Variations, and the
like._ (II. 12.)
XLIII.
_There is a_ pure _Science of Motion, which does not depend upon
observed facts, but upon the Idea of motion. It may also be termed_
Pure Mechanism, _in opposition to Mechanics Proper, or_ Machinery,
_which involves the mechanical conceptions of force and matter. It
has been proposed to name this Pure Science of Motion,_ Kinematics.
(II. 13.)
XLIV.
_The pure Mathematical Sciences must be successfully cultivated, in
order that the progress of the principal Inductive Sciences may take
place. This appears in the case of Astronomy, in which Science, both
in ancient and in modern times, each advance of the theory has
depended upon the_ {13} _previous solution of problems in pure
mathematics. It appears also inversely in the Science of the Tides,
in which, at present, we cannot advance in the theory, because we
cannot solve the requisite problems in the Integral Calculus._
(II. 14.)
XLV.
_The_ Idea of Cause, _modified into the conceptions of mechanical
cause, or Force, and resistance to force, or Matter, is the
foundation of the Mechanical Sciences; that is, Mechanics,_
(_including Statics and Dynamics,_) _Hydrostatics, and Physical
Astronomy._ (III. 1.)
XLVI.
_The Idea of Cause is not derived from experience; for in judging of
occurrences which we contemplate, we consider them as being,
universally and necessarily, Causes and Effects, which a finite
experience could not authorize us to do. The Axiom, that every event
must have a cause, is true independently of experience, and beyond
the limits of experience._ (III. 2.)
XLVII.
_The Idea of Cause is expressed for purposes of science by these
three Axioms_:--Every Event must have a Cause:--Causes are measured
by their Effects:--Reaction is equal and opposite to Action.
(III. 4.)
XLVIII.
_The Conception of Force involves the Idea of Cause, as applied to
the motion and rest of bodies. The conception of_ force _is suggested
by muscular action exerted: the conception of_ matter _arises from
muscular action resisted. We necessarily ascribe to all bodies
solidity and inertia, since we conceive Matter as that which cannot
be compressed or moved without resistance._ (III. 5.)
XLIX.
_Mechanical Science depends on the Conception of Force; and is
divided into_ Statics, _the doctrine of Force preventing_ {14}
_motion, and_ Dynamics, _the doctrine of Force producing motion._
(III. 6.)
L.
_The Science of Statics depends upon the Axiom, that Action and
Reaction are equal, which in Statics assumes this form_:--When two
equal weights are supported on the middle point between them, the
pressure on the fulcrum is equal to the sum of the weights.
(III. 6.)
LI.
_The Science of Hydrostatics depends upon the Fundamental Principle
that_ fluids press equally in all directions. _This principle
necessarily results from the conception of a Fluid, as a body of
which the parts are perfectly moveable in all directions. For since
the Fluid is a body, it can transmit pressure; and the transmitted
pressure is equal to the original pressure, in virtue of the Axiom
that Reaction is equal to Action. That the Fundamental Principle is
not derived from experience, is plain both from its evidence and
from its history._ (III. 6.)
LII.
_The Science of Dynamics depends upon the three Axioms above stated
respecting Cause. The First Axiom,--that every change must have a
Cause,--gives rise to the First Law of Motion,--that_ a body not
acted upon by a force will move with a uniform velocity in a
straight line. _The Second Axiom,--that Causes are measured by their
Effects,--gives rise to the Second Law of Motion,--that_ when a
force acts upon a body in motion, the effect of the force is
compounded with the previously existing motion. _The Third
Axiom,--that_ Reaction is equal and opposite to Action,--_gives rise
to the Third Law of Motion, which is expressed in the same terms as
the Axiom; Action and Reaction being understood to signify momentum
gained and lost._ (III. 7.) {15}
LIII.
_The above Laws of Motion, historically speaking, were established
by means of experiment: but since they have been discovered and
reduced to their simplest form, they have been considered by many
philosophers as self-evident. This result is principally due to the
introduction and establishment of terms and definitions, which
enable us to express the Laws in a very simple manner._ (III. 7.)
LIV.
_In the establishment of the Laws of Motion, it happened, in several
instances, that Principles were assumed as self-evident which do not
now appear evident, but which have since been demonstrated from the
simplest and most evident principles. Thus it was assumed that_ a
perpetual motion is impossible;--_that_ the velocities of bodies
acquired by falling down planes or curves of the same vertical
height are equal;--_that_ the actual descent of the center of
gravity is equal to its potential ascent. _But we are not hence to
suppose that these assumptions were made without ground: for since
they really follow from the laws of motion, they were probably, in
the minds of the discoverers, the results of undeveloped
demonstrations which their sagacity led them to divine._ (III. 7.)
LV.
_It is a_ Paradox _that Experience should lead us to truths
confessedly universal, and apparently necessary, such as the Laws of
Motion are. The_ Solution _of this paradox is, that these laws are
interpretations of the Axioms of Causation. The axioms are
universally and necessarily true, but the right interpretation of
the terms which they involve, is learnt by experience. Our Idea of
Cause supplies the_ Form, _Experience, the_ Matter, _of these Laws._
(III. 8.)
LVI.
Primary _Qualities of Bodies are those which we can conceive as
directly perceived;_ Secondary _Qualities are those_ {16} _which we
conceive as perceived by means of a Medium._ (IV. 1.)
LVII.
_We necessarily perceive bodies as_ without _us; the Idea of_
Externality _is one of the conditions of perception._ (IV. 1.)
LVIII.
_We necessarily assume a_ Medium _for the perceptions of Light,
Colour, Sound, Heat, Odours, Tastes; and this Medium_ must _convey
impressions by means of its mechanical attributes._ (IV. 1.)
LIX.
_Secondary Qualities are not_ extended _but_ intensive: _their effects
are not augmented by addition of parts, but by increased operation
of the medium. Hence they are not measured directly, but by_ scales;
_not by_ units, _but by_ degrees. (IV. 4.)
LX.
_In the Scales of Secondary Qualities, it is a condition_ (_in order
that the scale may be complete,_) _that every example of the quality
must either_ agree _with one of the degrees of the Scale, or lie
between two_ contiguous _degrees._ (IV. 4.)
LXI.
_We perceive_ by means of _a medium and_ by means of _impressions on
the nerves: but we do not_ (_by our senses_) _perceive either the
medium or the impressions on the nerves._ (IV. 1.)
LXII.
_The_ Prerogatives of the Sight _are, that by this sense we
necessarily and immediately apprehend the_ position _of its objects:
and that from visible circumstances, we_ infer _the_ distance _of
objects from us, so readily that we seem to perceive and not to
infer._ (IV. 2.) {17}
LXIII.
_The_ Prerogatives of the Hearing _are, that by this sense we
perceive relations perfectly precise and definite between two notes,
namely,_ Musical Intervals (_as an_ Octave, _a_ Fifth); _and that
when two notes are perceived together, they are comprehended as
distinct,_ (_a_ Chord,) _and as having a certain relation,_ (Concord
_or_ Discord.) (IV. 2.)
LXIV.
_The Sight cannot decompose a compound colour into simple colours,
or distinguish a compound from a simple colour. The Hearing cannot
directly perceive the place, still less the distance, of its
objects: we infer these obscurely and vaguely from audible
circumstances._ (IV. 2.)
LXV.
_The_ First Paradox of Vision _is, that we see objects_ upright,
_though the images on the retina are_ inverted. _The solution is,
that we do not see the image on the retina at all, we only see by
means of it._ (IV. 2.)
LXVI.
_The_ Second Paradox of Vision _is, that we see objects_ single,
_though there are two images on the retinas, one in each eye. The
explanation is, that it is a Law of Vision that we see_ (_small or
distant_) _objects single, when their images fall on_ corresponding
points _of the two retinas._ (IV. 2.)
LXVII.
_The law of single vision for_ near _objects is this:--When the two
images in the two eyes are situated, part for part, nearly but not
exactly, upon corresponding points, the object is apprehended as
single and solid if the two objects are such as would be produced by
a single solid object seen by the eyes separately._ (IV. 2.)
LXVIII.
_The ultimate object of each of the Secondary Mechanical Sciences
is, to determine the nature and laws of the processes_ {18} _by
which the impression of the Secondary Quality treated of is
conveyed: but before we discover the cause, it may be necessary to
determine the_ laws _of the phenomena; and for this purpose a_
Measure _or_ Scale _of each quality is necessary._ (IV. 4.)
LXIX.
_Secondary qualities are measured by means of such effects as can be
estimated in number or space._ (IV. 4.)
LXX.
_The Measure of Sounds, as high or low, is the_ Musical Scale, _or_
Harmonic Canon. (IV. 4.)
LXXI.
_The Measures of Pure Colours are the_ Prismatic Scale; _the same,
including_ Fraunhofer's Lines; _and_ Newton's Scale _of Colours. The
principal Scales of Impure Colours are_ Werner's Nomenclature _of
Colours, and_ Merimée's Nomenclature _of Colours_. (IV. 4.)
LXXII.
_The Idea of_ Polarity _involves the conception of contrary
properties in contrary directions:--the properties being, for
example, attraction and repulsion, darkness and light, synthesis and
analysis; and the contrary directions being those which are directly
opposite, or, in some cases, those which are at right angles._
(V. 1.)
LXXIII. (Doubtful.)
_Coexistent polarities are fundamentally identical._ (V. 2.)
LXXIV.
_The Idea of Chemical_ Affinity, _as implied in Elementary
Composition, involves peculiar conceptions. It is not properly
expressed by assuming the qualities of bodies to_ resemble _those of
the elements, or to depend on the_ figure _of the elements, or on
their_ attractions. (VI. 1.) {19}
LXXV.
_Attractions take place between bodies, Affinities between the
particles of a body. The former may be compared to the alliances of
states, the latter to the ties of family._ (VI. 2.)
LXXVI.
_The governing principles of Chemical Affinity are, that it is_
elective; _that it is_ definite; _that it_ determines the properties
_of the compound; and that_ analysis is possible. (VI. 2.)
LXXVII.
_We have an idea of_ Substance: _and an axiom involved in this Idea
is, that_ the weight of a body is the sum of the weights of all its
elements. (VI. 3.)
LXXVIII.
_Hence Imponderable Fluids are not to be admitted as chemical
elements._ (VI. 4.)
LXXIX.
_The Doctrine of Atoms is admissible as a mode of expressing and
calculating laws of nature; but is not proved by any fact, chemical
or physical, as a philosophical truth._ (VI. 5.)
LXXX.
_We have an Idea of_ Symmetry; _and an axiom involved in this Idea
is, that in a symmetrical natural body, if there be a tendency to
modify any member in any manner, there is a tendency to modify all
the corresponding members in the same manner._ (VII. 1.)
LXXXI.
_All hypotheses respecting the manner in which the elements of
inorganic bodies are arranged in space, must be constructed with
regard to the general facts of crystallization._ (VII. 3.) {20}
LXXXII.
_When we consider any object as_ One, _we give unity to it by an act
of thought. The condition which determines what this unity shall
include, and what it shall exclude, is this;--that assertions
concerning the one thing shall be possible._ (VIII. 1.)
LXXXIII.
_We collect individuals into_ Kinds _by applying to them the Idea of
Likeness. Kinds of things are not determined by definitions, but by
this condition:--that general assertions concerning such kinds of
things shall be possible._ (VIII. 1.)
LXXXIV.
_The_ Names _of kinds of things are governed by their use; and that
may be a right name in one use which is not so in another. A whale
is not a_ fish _in natural history, but it is a_ fish _in commerce
and law._ (VIII. 1.)
LXXXV.
_We take for granted that each kind of things has a special_
character _which may be expressed by a Definition. The ground of our
assumption is this;--that reasoning must be possible._ (VIII. 1.)
LXXXVI.
_The "Five Words,"_ Genus, Species, Difference, Property, Accident,
_were used by the Aristotelians, in order to express the
subordination of Kinds, and to describe the nature of Definitions
and Propositions. In modern times, these technical expressions have
been more referred to by Natural Historians than by Metaphysicians._
(VIII. 1.)
LXXXVII.
_The construction of a Classificatory Science includes_ Terminology,
_the formation of a descriptive language;_--Diataxis, _the Plan of
the System of Classification, called_ {21} _also the_
Systematick;--Diagnosis, _the Scheme of the Characters by which the
different Classes are known, called also the_ Characteristick.
Physiography _is the knowledge which the System is employed to
convey. Diataxis includes_ Nomenclature. (VIII. 2.)
LXXXVIII.
Terminology _must be conventional, precise, constant; copious in
words, and minute in distinctions, according to the needs of the
science. The student must understand the terms,_ directly _according
to the convention, not through the medium of explanation or
comparison._ (VIII. 2.)
LXXXIX.
_The_ Diataxis,_ or Plan of the System, may aim at a Natural or at
an Artificial System. But no classes can be absolutely artificial,
for if they were, no assertions could be made concerning them._
(VIII. 2.)
XC.
_An_ Artificial System _is one in which the_ smaller _groups_ (_the
Genera_) _are_ natural; _and in which the_ wider _divisions_
(_Classes, Orders_) _are constructed by the_ peremptory _application
of selected Characters;_ (_selected, however, so as not to break up
the smaller groups._) (VIII. 2.)
XCI.
_A_ Natural System _is one which attempts to make_ all _the
divisions_ natural, _the widest as well as the narrowest; and
therefore applies_ no _characters_ peremptorily. (VIII. 2.)
XCII.
_Natural Groups are best described, not by any Definition which
marks their boundaries, but by a_ Type _which marks their center.
The Type of any natural group is an example which possesses in a
marked degree all the leading characters of the class._ (VIII. 2.)
{22}
XCIII.
_A Natural Group is steadily fixed, though not precisely limited; it
is given in position, though not circumscribed; it is determined,
not by a boundary without, but by a central point within;--not by
what it strictly excludes, but by what it eminently includes;--by a
Type, not by a Definition._ (VIII. 2.)
XCIV.
_The prevalence of Mathematics as an element of education has made
us think Definition the philosophical mode of fixing the meaning of
a word: if_ (_Scientific_) _Natural History were introduced into
education, men might become familiar with the fixation of the
signification of words by_ Types; _and this process agrees more
nearly with the common processes by which words acquire their
significations._ (VIII. 2.)
XCV.
_The attempts at Natural Classification are of three sorts;
according as they are made by the process of_ blind trial, _of_
general comparison, _or of_ subordination of characters. _The
process of Blind Trial professes to make its classes by attention to
all the characters, but without proceeding methodically. The process
of General Comparison professes to enumerate all the characters, and
forms its classes by the_ majority. _Neither of these methods can
really be carried into effect. The method of Subordination of
Characters considers some characters as_ more important _than
others; and this method gives more consistent results than the
others. This method, however, does not depend upon the Idea of
Likeness only, but introduces the Idea of Organization or Function._
(VIII. 2.)
XCVI.
_A_ Species _is a collection of individuals, which are descended
from a common stock, or which resemble such a collection as much as
these resemble each other: the resemblance being opposed to a_
definite _difference._ (VIII. 2.) {23}
XCVII.
_A_ Genus _is a collection of species which resemble each other more
than they resemble other species: the resemblance being opposed to
a_ definite _difference._ (VIII. 2.)
XCVIII.
_The_ Nomenclature _of a Classificatory Science is the collection of
the names of the Species, Genera, and other divisions. The_ binary
_nomenclature, which denotes a species by the_ generic _and_ specific
_name, is now commonly adopted in Natural History._ (VIII. 2.)
XCIX.
_The_ Diagnosis, _or Scheme of the Characters, comes, in the order
of philosophy, after the Classification. The characters do not_ make
_the classes, they only enable us to_ recognize _them. The Diagnosis
is an Artificial Key to a Natural System._ (VIII. 2.)
C.
_The basis of all Natural Systems of Classification is the Idea of
Natural Affinity. The Principle which this Idea involves is
this:--Natural arrangements, obtained from_ different _sets of
characters, must_ coincide _with each other._ (VIII. 4.)
CI.
_In order to obtain a Science of Biology, we must analyse the Idea
of Life. It has been proved by the biological speculations of past
time, that Organic Life cannot rightly be solved into Mechanical or
Chemical Forces, or the operation of a Vital Fluid, or of a Soul._
(IX. 2.)
CII.
_Life is a System of Vital Forces; and the conception of such Forces
involves a peculiar Fundamental Idea._ (IX. 3.) {24}
CIII.
_Mechanical, chemical, and vital Forces form an ascending
progression, each including the preceding. Chemical Affinity
includes in its nature Mechanical Force, and may often be
practically resolved into Mechanical Force._ (_Thus the ingredients
of gunpowder, liberated from their chemical union, exert great
mechanical Force: a galvanic battery acting by chemical process does
the like._) _Vital Forces include in their nature both chemical
Affinities and mechanical Forces: for Vital Powers produce both
chemical changes,_ (_as digestion,_) _and motions which imply
considerable mechanical force,_ (_as the motion of the sap and of
the blood._) (IX. 4.)
CIV.
_In_ voluntary _motions, Sensations produce Actions, and the
connexion is made by means of Ideas: in_ reflected _motions, the
connexion neither seems to be nor is made by means of Ideas: in_
instinctive _motions, the connexion is such as requires Ideas, but
we cannot believe the Ideas to exist._ (IX. 5.)
CV.
_The Assumption of a Final Cause in the structure of each part of
animals and plants is as inevitable as the assumption of an
Efficient Cause for every event. The maxim that in organized bodies
nothing is_ in vain, _is as necessarily true as the maxim that
nothing happens_ by chance. (IX. 6.)
CVI.
_The Idea of living beings as subject to_ disease _includes a
recognition of a Final Cause in organization; for disease is a state
in which the vital forces do not attain their_ proper ends. (IX. 7.)
CVII.
_The Palætiological Sciences depend upon the Idea of Cause: but the
leading conception which they involve is that of_ historical cause,
_not mechanical cause._ (X. 1.) {25}
CVIII.
_Each Palætiological Science, when complete, must possess three
members: the_ Phenomenology, _the_ Ætiology, _and the_ Theory. (X.
2.)
CIX.
_There are, in the Palætiological Sciences, two antagonist
doctrines:_ Catastrophes _and_ Uniformity. _The doctrine of a_
uniform course of nature _is tenable only when we extend the nation
of Uniformity so far that it shall include Catastrophes._ (X. 3.)
CX.
_The Catastrophist constructs Theories, the Uniformitarian
demolishes them. The former adduces evidence of an Origin, the
latter explains the evidence away. The Catastrophist's dogmatism is
undermined by the Uniformitarian's skeptical hypotheses. But when
these hypotheses are asserted dogmatically they cease to be
consistent with the doctrine of Uniformity._ (X. 3.)
CXI.
_In each of the Palætiological Sciences, we can ascend to remote
periods by a chain of causes, but in none can we ascend to a_
beginning _of the chain._ (X. 3.)
CXII.
_Since the Palætiological sciences deal with the conceptions of
historical cause,_ History, _including_ Tradition, _is an important
source of materials for such sciences._ (X. 4.)
CXIII.
_The history and tradition which present to us the providential
course of the world form a_ Sacred Narrative; _and in reconciling
the Sacred Narrative with the results of science, arise inevitable
difficulties which disturb the minds of those who reverence the
Sacred Narrative._ (X. 4.) {26}
CXIV.
_The disturbance of reverent minds, arising from scientific views,
ceases when such views become familiar, the Sacred Narrative being
then interpreted anew in accordance with such views._ (X. 4.)
CXV.
_A new interpretation of the Sacred Narrative, made for the purpose
of reconciling it with doctrines of science, should not be insisted
on till such doctrines are clearly proved; and when they are so
proved, should be frankly accepted, in the confidence that a
reverence for the Sacred Narrative is consistent with a reverence
for the Truth._ (X. 4.)
CXVI.
_In contemplating the series of causes and effects which constitutes
the world, we necessarily assume a_ First Cause _of the whole
series._ (X. 5.)
CXVII.
_The Palætiological Sciences point backwards with lines which are
broken, but which all converge to the_ same _invisible point: and
this point is the Origin of the Moral and Spiritual, as well as of
the Natural World._ (X. 5.)
NOVUM ORGANON RENOVATUM.
{{27}}
BOOK II.
OF THE CONSTRUCTION OF SCIENCE.
CHAPTER I.
OF TWO PRINCIPAL PROCESSES BY WHICH SCIENCE IS CONSTRUCTED.
APHORISM I.
_THE two processes by which Science is constructed are the_
Explication of Conceptions, _and the_ Colligation of Facts.
TO the subject of the present and next Book all that has preceded is
subordinate and preparatory. In former works we have treated of the
History of Scientific Discoveries and of the History of Scientific
Ideas. We have now to attempt to describe the manner in which
discoveries are made, and in which Ideas give rise to knowledge. It
has already been stated that Knowledge requires us to possess both
Facts and Ideas;--that every step in our knowledge consists in
applying the Ideas and Conceptions furnished by our minds to the
Facts which observation and experiment offer to us. When our
Conceptions are clear and distinct, when our Facts are certain and
sufficiently numerous, and when the Conceptions, being suited to the
nature of the {28} Facts, are applied to them so as to produce an
exact and universal accordance, we attain knowledge of a precise and
comprehensive kind, which we may term _Science_. And we apply this
term to our knowledge still more decidedly when, Facts being thus
included in exact and general Propositions, such Propositions are,
in the same manner, included with equal rigour in Propositions of a
higher degree of Generality; and these again in others of a still
wider nature, so as to form a large and systematic whole.
But after thus stating, in a general way, the nature of science, and
the elements of which it consists, we have been examining with a
more close and extensive scrutiny, some of those elements; and we
must now return to our main subject, and apply to it the results of
our long investigation. We have been exploring the realm of Ideas;
we have been passing in review the difficulties in which the
workings of our own minds involve us when we would make our
conceptions consistent with themselves: and we have endeavoured to
get a sight of the true solutions of these difficulties. We have now
to inquire how the results of these long and laborious efforts of
thought find their due place in the formation of our Knowledge. What
do we gain by these attempts to make our notions distinct and
consistent; and in what manner is the gain of which we thus become
possessed, carried to the general treasure-house of our permanent
and indestructible knowledge? After all this battling in the world
of ideas, all this struggling with the shadowy and changing forms of
intellectual perplexity, how do we secure to ourselves the fruits of
our warfare, and assure ourselves that we have really pushed
forwards the frontier of the empire of Science? It is by such an
appropriation, that the task which we have had in our hands during
the two previous works, (the _History of the Inductive Sciences_ and
the _History of Scientific Ideas_,) must acquire its real value and
true place in our design.
In order to do this, we must reconsider, in a more definite and
precise shape, the doctrine which has already been laid down;--that
our Knowledge consists {29} in applying Ideas to Facts; and that the
conditions of real knowledge are that the ideas be distinct and
appropriate, and exactly applied to clear and certain facts. The
steps by which our knowledge is advanced are those by which one or
the other of these two processes is rendered more complete;--by
which _Conceptions_ are _made more clear_ in themselves, or by which
the Conceptions more strictly _bind together the Facts_. These two
processes may be considered as together constituting the whole
formation of our knowledge; and the principles which have been
established in the History of Scientific Ideas bear principally upon
the former of these two operations;--upon the business of elevating
our conceptions to the highest possible point of precision and
generality. But these two portions of the progress of knowledge are
so clearly connected with each other, that we shall deal with them
in immediate succession. And having now to consider these operations
in a more exact and formal manner than it was before possible to do,
we shall designate them by certain constant and technical phrases.
We shall speak of the two processes by which we arrive at science,
as _the Explication of Conceptions_ and _the Colligation of Facts_:
we shall show how the discussions in which we have been engaged have
been necessary in order to promote the former of these offices; and
we shall endeavour to point out modes, maxims, and principles by
which the second of the two tasks may also be furthered.
{{30}}
CHAPTER II.
OF THE EXPLICATION OF CONCEPTIONS.
APHORISM II.
_The Explication of Conceptions, as requisite for the progress of
science, has been effected by means of discussions and controversies
among scientists; often by debates concerning definitions; these
controversies have frequently led to the establishment of a
Definition; but along with the Definition, a corresponding
Proposition has always been expressed or implied. The essential
requisite for the advance of science is the clearness of the
Conception, not the establishment of a Definition. The construction
of an exact Definition is often very difficult. The requisite
conditions of clear Conceptions may often be expressed by Axioms as
well as by Definitions._
APHORISM III.
_Conceptions, for purposes of science, must be_ appropriate _as well
as clear: that is, they must be modifications of_ that _Fundamental
Idea, by which the phenomena can really be interpreted. This maxim
may warn us from errour, though it may not lead to discovery.
Discovery depends upon the previous cultivation or natural clearness
of the appropriate Idea, and therefore_ no discovery is the work of
accident.
SECT. I.--_Historical Progress of the Explication of Conceptions._
1. WE have given the appellation of _Ideas_ to certain comprehensive
forms of thought,--as _space_, _number_, _cause_, _composition_,
_resemblance_,--which we apply to the phenomena which we
contemplate. But the special modifications of these ideas which are
{31} exemplified in particular facts, we have termed _Conceptions_;
as _a circle_, _a square number_, _an accelerating force_, _a
neutral combination_ of elements, a _genus_. Such Conceptions
involve in themselves certain necessary and universal relations
derived from the Ideas just enumerated; and these relations are an
indispensable portion of the texture of our knowledge. But to
determine the contents and limits of this portion of our knowledge,
requires an examination of the Ideas and Conceptions from which it
proceeds. The Conceptions must be, as it were, carefully _unfolded_,
so as to bring into clear view the elements of truth with which they
are marked from their ideal origin. This is one of the processes by
which our knowledge is extended and made more exact; and this I
shall describe as the _Explication of Conceptions_.
In the several Books of the History of Ideas we have discussed a
great many of the Fundamental Ideas of the most important existing
sciences. We have, in those Books, abundant exemplifications of the
process now under our consideration. We shall here add a few general
remarks, suggested by the survey which we have thus made.
2. Such discussions as those in which we have been engaged
concerning our fundamental Ideas, have been the course by which,
historically speaking, those Conceptions which the existing sciences
involve have been rendered so clear as to be fit elements of exact
knowledge. Thus, the disputes concerning the various kinds and
measures of _Force_ were an important part of the progress of the
science of Mechanics. The struggles by which philosophers attained a
right general conception of _plane_, of _circular_, of _elliptical
Polarization_, were some of the most difficult steps in the modern
discoveries of Optics. A Conception of the _Atomic Constitution_ of
bodies, such as shall include what we know, and assume nothing more,
is even now a matter of conflict among Chemists. The debates by
which, in recent times, the Conceptions of _Species_ and _Genera_
have been rendered more exact, have improved the science of Botany:
the imperfection of the science of {32} Mineralogy arises in a great
measure from the circumstance, that in that subject, the Conception
of a _Species_ is not yet fixed. In Physiology, what a vast advance
would that philosopher make, who should establish a precise,
tenable, and consistent Conception of _Life_!
Thus discussions and speculations concerning the import of very
abstract and general terms and notions, may be, and in reality have
been, far from useless and barren. Such discussions arose from the
desire of men to impress their opinions on others, but they had the
effect of making the opinions much more clear and distinct. In
trying to make others understand them, they learnt to understand
themselves. Their speculations were begun in twilight, and ended in
the full brilliance of day. It was not easily and at once, without
expenditure of labour or time, that men arrived at those notions
which now form the elements of our knowledge; on the contrary, we
have, in the history of science, seen how hard, discoverers, and the
forerunners of discoverers, have had to struggle with the
indistinctness and obscurity of the intellect, before they could
advance to the critical point at which truth became clearly visible.
And so long as, in this advance, some speculators were more forward
than others, there was a natural and inevitable ground of difference
of opinion, of argumentation, of wrangling. But the tendency of all
such controversy is to diffuse truth and to dispel errour. Truth is
consistent, and can bear the tug of war; Errour is incoherent, and
falls to pieces in the struggle. True Conceptions can endure the
sun, and become clearer as a fuller light is obtained; confused and
inconsistent notions vanish like visionary spectres at the break of
a brighter day. And thus all the controversies concerning such
Conceptions as science involves, have ever ended in the
establishment of the side on which the truth was found.
3. Indeed, so complete has been the victory of truth in most of
these instances, that at present we can hardly imagine the struggle
to have been necessary. The very essence of these triumphs is that
they lead us to regard the views we reject as not only false, {33}
but inconceivable. And hence we are led rather to look back upon the
vanquished with contempt than upon the victors with gratitude. We
now despise those who, in the Copernican controversy, could not
conceive the apparent motion of the sun on the heliocentric
hypothesis;--or those who, in opposition to Galileo, thought that a
uniform force might be that which generated a velocity proportional
to the space;--or those who held there was something absurd in
Newton's doctrine of the different refrangibility of differently
coloured rays;--or those who imagined that when elements combine,
their sensible qualities must be manifest in the compound;--or those
who were reluctant to give up the distinction of vegetables into
herbs, shrubs, and trees. We cannot help thinking that men must have
been singularly dull of comprehension, to find a difficulty in
admitting what is to us so plain and simple. We have a latent
persuasion that we in their place should have been wiser and more
clear-sighted;--that we should have taken the right side, and given
our assent at once to the truth.
4. Yet in reality, such a persuasion is a mere delusion. The persons
who, in such instances as the above, were on the losing side, were
very far, in most cases, from being persons more prejudiced, or
stupid, or narrow-minded, than the greater part of mankind now are;
and the cause for which they fought was far from being a manifestly
bad one, till it had been so decided by the result of the war. It is
the peculiar character of scientific contests, that what is only an
epigram with regard to other warfare is a truth in this;--They who
are defeated are really in the wrong. But they may, nevertheless, be
men of great subtilty, sagacity, and genius; and we nourish a very
foolish self-complacency when we suppose that we are their
superiors. That this is so, is proved by recollecting that many of
those who have made very great discoveries have laboured under the
imperfection of thought which was the obstacle to the next step in
knowledge. Though Kepler detected with great acuteness the Numerical
Laws of the solar system, he laboured in {34} vain to conceive the
very simplest of the Laws of Motion by which the paths of the
planets are governed. Though Priestley made some important steps in
chemistry, he could not bring his mind to admit the doctrine of a
general Principle of Oxidation. How many ingenious men in the last
century rejected the Newtonian Attraction as an impossible chimera!
How many more, equally intelligent, have, in the same manner, in our
own time, rejected, I do not now mean as false, but as
inconceivable, the doctrine of Luminiferous Undulations! To err in
this way is the lot, not only of men in general, but of men of great
endowments, and very sincere love of truth.
5. And those who liberate themselves from such perplexities, and who
thus go on in advance of their age in such matters, owe their
superiority in no small degree to such discussions and controversies
as those to which we now refer. In such controversies, the
Conceptions in question are turned in all directions, examined on
all sides; the strength and the weakness of the maxims which men
apply to them are fully tested; the light of the brightest minds is
diffused to other minds. Inconsistency is unfolded into
self-contradiction; axioms are built up into a system of necessary
truths; and ready exemplifications are accumulated of that which is
to be proved or disproved, concerning the ideas which are the basis
of the controversy.
The History of Mechanics from the time of Kepler to that of
Lagrange, is perhaps the best exemplification of the mode in which
the progress of a science depends upon such disputes and
speculations as give clearness and generality to its elementary
conceptions. This, it is to be recollected, is the kind of progress
of which we are now speaking; and this is the principal feature in
the portion of scientific history which we have mentioned. For
almost all that was to be done by reference to observation, was
executed by Galileo and his disciples. What remained was the task of
generalization and simplification. And this was promoted in no small
degree by the various controversies which took place within that
period concerning {35} mechanical conceptions:--as, for example, the
question concerning the measure of the Force of Percussion;--the war
of the _Vis Viva_;--the controversy of the Center of
Oscillation;--of the independence of Statics and Dynamics;--of the
principle of Least Action;--of the evidence of the Laws of
Motion;--and of the number of Laws really distinct. None of these
discussions was without its influence in giving generality and
clearness to the mechanical ideas of mathematicians: and therefore,
though remote from general apprehension, and dealing with very
abstract notions, they were of eminent use in the perfecting the
science of Mechanics. Similar controversies concerning fundamental
notions, those, for example, which Galileo himself had to maintain,
were no less useful in the formation of the science of Hydrostatics.
And the like struggles and conflicts, whether they take the form of
controversies between several persons, or only operate in the
efforts and fluctuations of the discoverer's mind, are always
requisite, before the conceptions acquire that clearness which makes
them flt to appear in the enunciation of scientific truth. This,
then, was one object of the History of Ideas;--to bring under the
reader's notice the main elements of the controversies which have
thus had so important a share in the formation of the existing body
of science, and the decisions on the controverted points to which
the mature examination of the subject has led; and thus to give an
abundant exhibition of that step which we term the Explication of
Conceptions.
SECT. II.--_Use of Definitions._
6. The result of such controversies as we have been speaking of,
often appears to be summed up in a _Definition_; and the controversy
itself has often assumed the form of a battle of definitions. For
example, the inquiry concerning the Laws of Falling Bodies led to
the question whether the proper Definition of a _uniform force_ is,
that it generates a velocity proportional to the _space_ from rest,
or to the _time_. The controversy of the _Vis Viva_ was, what was
the {36} proper Definition of the _measure of force_. A principal
question in the classification of minerals is, what is the
Definition of a _mineral species_. Physiologists have endeavoured to
throw light on their subject, by Defining _organization_, or some
similar term.
7. It is very important for us to observe, that these controversies
have never been questions of insulated and _arbitrary_ Definitions,
as men seem often tempted to suppose them to have been. In all cases
there is a tacit assumption of some Proposition which is to be
expressed by means of the Definition, and which gives it its
importance. The dispute concerning the Definition thus acquires a
real value, and becomes a question concerning true and false. Thus
in the discussion of the question, What is a Uniform Force? it was
taken for granted that 'gravity is a uniform force:'--in the debate
of the _Vis Viva_, it was assumed that 'in the mutual action of
bodies the whole effect of the force is unchanged:'--in the
zoological definition of Species, (that it consists of individuals
which have, or may have, sprung from the same parents,) it is
presumed that 'individuals so related resemble each other more than
those which are excluded by such a definition;' or perhaps, that
'species so defined have permanent and definite differences.' A
definition of Organization, or of any other term, which was not
employed to express some principle, would be of no value.
The establishment, therefore, of a right Definition of a Term may be
a useful step in the Explication of our Conceptions; but this will
be the case _then_ only when we have under our consideration some
Proposition in which the Term is employed. For then the question
really is, how the Conception shall be understood and defined in
order that the Proposition may be true.
8. The establishment of a Proposition requires an attention to
observed Facts, and can never be rightly derived from our
Conceptions alone. We must hereafter consider the necessity which
exists that the Facts should be rightly bound together, as well as
that our Conceptions should be clearly employed, in order to {37}
lead us to real knowledge. But we may observe here that, in such
cases at least as we are now considering, the two processes are
co-ordinate. To unfold our Conceptions by the means of Definitions,
has never been serviceable to science, except when it has been
associated with an immediate _use_ of the Definitions. The endeavour
to define a uniform Force was combined with the assertion that
'gravity is a uniform force:' the attempt to define Accelerating
Force was immediately followed by the doctrine that 'accelerating
forces may be compounded:' the process of defining Momentum was
connected with the principle that 'momenta gained and lost are
equal:' naturalists would have given in vain the Definition of
Species which we have quoted, if they had not also given the
'characters' of species so separated. Definition and Proposition are
the two handles of the instrument by which we apprehend truth; the
former is of no use without the latter. Definition may be the best
mode of explaining our Conception, but that which alone makes it
worth while to explain it in any mode, is the opportunity of using
it in the expression of Truth. When a Definition is propounded to us
as a useful step in knowledge, we are always entitled to ask what
Principle it serves to enunciate. If there be no answer to this
inquiry, we define and give clearness to our conceptions in vain.
While we labour at such a task, we do but light up a vacant
room;--we sharpen a knife with which we have nothing to cut;--we
take exact aim, while we load our artillery with blank
cartridge;--we apply strict rules of grammar to sentences which have
no meaning.
If, on the other hand, we have under our consideration a proposition
probably established, every step which we can make in giving
distinctness and exactness to the Terms which this proposition
involves, is an important step towards scientific truth. In such
cases, any improvement in our Definition is a real advance in the
explication of our Conception. The clearness of our impressions
casts a light upon the Ideas which we contemplate and convey to
others. {38}
9. But though _Definition_ may be subservient to a right explication
of our conceptions, it is _not essential_ to that process. It is
absolutely necessary to every advance in our knowledge, that those
by whom such advances are made should possess clearly the
conceptions which they employ: but it is by no means necessary that
they should unfold these conceptions in the words of a formal
Definition. It is easily seen, by examining the course of Galileo's
discoveries, that he had a distinct conception of the _Moving Force_
which urges bodies downwards upon an inclined plane, while he still
hesitated whether to call it _Momentum_, _Energy_, _Impetus_, or
_Force_, and did not venture to offer a Definition of the thing
which was the subject of his thoughts. The Conception of
_Polarization_ was clear in the minds of many optical speculators,
from the time of Huyghens and Newton to that of Young and Fresnel.
This Conception we have defined to be 'Opposite properties depending
upon opposite positions;' but this notion was, by the discoverers,
though constantly assumed and expressed by means of superfluous
hypotheses, never clothed in definite language. And in the mean
time, it was the custom, among subordinate writers on the same
subjects, to say, that the term _Polarization_ had no definite
meaning, and was merely an expression of our ignorance. The
Definition which was offered by Haüy and others of a _Mineralogical
Species_;--'The same elements combined in the same proportions, with
the same fundamental form;'--was false, inasmuch as it was incapable
of being rigorously applied to any one case; but this defect did not
prevent the philosophers who propounded such a Definition from
making many valuable additions to mineralogical knowledge, in the
way of identifying some species and distinguishing others. The right
Conception which they possessed in their minds prevented their being
misled by their own very erroneous Definition. The want of any
precise Definitions of _Strata_, and _Formations_, and _Epochs_,
among geologists, has not prevented the discussions which they have
carried on upon such subjects from being highly serviceable {39} in
the promotion of geological knowledge. For however much the apparent
vagueness of these terms might leave their arguments open to cavil,
there was a general understanding prevalent among the most
intelligent cultivators of the science, as to what was meant in such
expressions; and this common understanding sufficed to determine
what evidence should be considered conclusive and what inconclusive,
in these inquiries. And thus the distinctness of Conception, which
is a real requisite of scientific progress, existed in the minds of
the inquirers, although Definitions, which are a partial and
accidental evidence of this distinctness, had not yet been hit upon.
The Idea had been developed in men's minds, although a clothing of
words had not been contrived for it, nor, perhaps, the necessity of
such a vehicle felt: and thus that essential condition of the
progress of knowledge, of which we are here speaking, existed; while
it was left to the succeeding speculators to put this unwritten Rule
in the form of a verbal Statute.
10. Men are often prone to consider it as a thoughtless _omission_
of an essential circumstance, and as a _neglect_ which involves some
blame, when knowledge thus assumes a form in which Definitions, or
rather Conceptions, are implied but are not expressed. But in such a
judgment, they assume _that_ to be a matter of choice requiring
attention only, which is in fact as difficult and precarious as any
other portion of the task of discovery. To _define_, so that our
Definition shall have any scientific value, requires no small
portion of that sagacity by which truth is detected. As we have
already said, Definitions and Propositions are co-ordinate in their
use and in their origin. In many cases, perhaps in most, the
Proposition which contains a scientific truth, is apprehended with
confidence, but with some vagueness and vacillation, before it is
put in a positive, distinct, and definite form.--It is thus known to
be true, before it can be enunciated in terms each of which is
rigorously defined. The business of Definition is part of the
business of discovery. When it has been clearly seen what ought to
be our Definition, it {40} must be pretty well known what truth we
have to state. The Definition, as well as the discovery, supposes a
decided step in our knowledge to have been made. The writers on
Logic in the middle ages, made Definition the last stage in the
progress of knowledge; and in this arrangement at least, the history
of science, and the philosophy derived from the history, confirm
their speculative views. If the Explication of our Conceptions ever
assume the form of a Definition, this will come to pass, not as an
arbitrary process, or as a matter of course, but as the mark of one
of those happy efforts of sagacity to which all the successive
advances of our knowledge are owing.
SECT. III.--_Use of Axioms._
11. Our Conceptions, then, even when they become so clear as the
progress of knowledge requires, are not adequately expressed, or
necessarily expressed at all, by means of Definitions. We may ask,
then, whether there is any _other mode_ of expression in which we
may look for the evidence and exposition of that peculiar exactness
of thought which the formation of Science demands. And in answer to
this inquiry, we may refer to the discussions respecting many of the
Fundamental Ideas of the sciences contained in our _History_ of such
Ideas. It has there been seen that these Ideas involve many
elementary truths which enter into the texture of our knowledge,
introducing into it connexions and relations of the most important
kind, although these elementary truths cannot be deduced from any
verbal definition of the idea. It has been seen that these
elementary truths may often be enunciated by means of _Axioms_,
stated in addition to, or in preference to, Definitions. For
example, the Idea of Cause, which forms the basis of the science of
Mechanics, makes its appearance in our elementary mechanical
reasonings, not as a Definition, but by means of the Axioms that
'Causes are measured by their effects,' and that 'Reaction is equal
and opposite to action.' Such axioms, tacitly assumed or {41}
occasionally stated, as maxims of acknowledged validity, belong to
all the Ideas which form the foundations of the sciences, and are
constantly employed in the reasoning and speculations of those who
think clearly on such subjects. It may often be a task of some
difficulty to detect and enunciate in words the Principles which are
thus, perhaps silently and unconsciously, taken for granted by those
who have a share in the establishment of scientific truth: but
inasmuch as these Principles are an essential element in our
knowledge, it is very important to our present purpose to separate
them from the associated materials, and to trace them to their
origin. This accordingly I attempted to do, with regard to a
considerable number of the most prominent of such Ideas, in the
_History_. The reader will there find many of these Ideas resolved
into Axioms and Principles by means of which their effect upon the
elementary reasonings of the various sciences may be expressed. That
Work is intended to form, in some measure, a representation of the
Ideal Side of our physical knowledge;--a Table of those contents of
our Conceptions which are not received directly from facts;--an
exhibition of Rules to which we know that truth must conform.
SECT. IV.--_Clear and appropriate Ideas._
12. In order, however, that we may see the necessary cogency of
these rules, we must possess, clearly and steadily, the Ideas from
which the rules flow. In order to perceive the necessary relations
of the Circles of the Sphere, we must possess clearly the Idea of
Solid Space:--in order that we may see the demonstration of the
composition of forces, we must have the Idea of Cause moulded into a
distinct Conception of Statical Force. This is that _Clearness of
Ideas_ which we stipulate for in any one's mind, as the first
essential condition of his making any new step in the discovery of
truth. And we now see what answer we are able to give, if we are
asked for a Criterion of this Clearness of {42} Idea. The Criterion
is, that the person shall _see_ the necessity of the Axioms belonging
to each Idea;--shall accept them in such a manner as to perceive the
cogency of the reasonings founded upon them. Thus, a person has a
clear Idea of Space who follows the reasonings of geometry and fully
apprehends their conclusiveness. The Explication of Conceptions,
which we are speaking of as an essential part of real knowledge, is
the process by which we bring the Clearness of our Ideas to bear
upon the Formation of our knowledge. And this is done, as we have
now seen, not always, nor generally, nor principally, by laying down
a Definition of the Conception; but by acquiring such a possession
of it in our minds as enables, indeed compels us, to admit, along
with the Conception, all the Axioms and Principles which it
necessarily implies, and by which it produces its effect upon our
reasonings.
13. But in order that we may make any real advance in the discovery
of truth, our Ideas must not only be clear, they must also be
_appropriate_. Each science has for its basis a different class of
Ideas; and the steps which constitute the progress of one science
can never be made by employing the Ideas of another kind of science.
No genuine advance could ever be obtained in Mechanics by applying
to the subject the Ideas of Space and Time merely:--no advance in
Chemistry, by the use of mere Mechanical Conceptions:--no discovery
in Physiology, by referring facts to mere Chemical and Mechanical
Principles. Mechanics must involve the Conception of
_Force_;--Chemistry, the Conception of _Elementary
Composition_;--Physiology, the Conception of _Vital Powers_. Each
science must advance by means of its appropriate Conceptions. Each
has its own field, which extends as far as its principles can be
applied. I have already noted the separation of several of these
fields by the divisions of the Books of the _History_ of Ideas. The
Mechanical, the Secondary Mechanical, the Chemical, the
Classificatory, the Biological Sciences form so many great Provinces
in the Kingdom of knowledge, each in a great measure possessing its
own peculiar fundamental principles. Every attempt to build up a
{43} new science by the application of principles which belong to an
old one, will lead to frivolous and barren speculations.
This truth has been exemplified in all the instances in which subtle
speculative men have failed in their attempts to frame new sciences,
and especially in the essays of the ancient schools of philosophy in
Greece, as has already been stated in the History of Science.
Aristotle and his followers endeavoured in vain to account for the
mechanical relation of forces in the lever by applying the
_inappropriate_ geometrical conceptions of the properties of the
circle:--they speculated to no purpose about the elementary
composition of bodies, because they assumed the _inappropriate_
conception of _likeness_ between the elements and the compound,
instead of the genuine notion of elements merely _determining_ the
qualities of the compound. And in like manner, in modern times, we
have seen, in the history of the fundamental ideas of the
physiological sciences, how all the _inappropriate_ mechanical and
chemical and other ideas which were applied in succession to the
subject failed in bringing into view any genuine physiological
truth.
14. That the real cause of the failure in the instances above
mentioned lay in the _Conceptions_, is plain. It was not ignorance
of the facts which in these cases prevented the discovery of the
truth. Aristotle was as well acquainted with the fact of the
proportion of the weights which balance on a Lever as Archimedes
was, although Archimedes alone gave the true mechanical reason for
the proportion.
With regard to the doctrine of the Four Elements indeed, the
inapplicability of the conception of composition of qualities,
required, perhaps, to be proved by some reference to facts. But this
conception was devised at first, and accepted by succeeding times,
in a blind and gratuitous manner, which could hardly have happened
if men had been awake to the necessary condition of our
knowledge;--that the conceptions which we introduce into our
doctrines are not arbitrary or accidental notions, but certain
peculiar modes of {44} apprehension strictly determined by the
subject of our speculations.
15. It may, however, be said that this injunction that we are to
employ _appropriate_ Conceptions only in the formation of our
knowledge, cannot be of practical use, because we can only determine
what Ideas _are_ appropriate, by finding that they truly combine the
facts. And this is to a certain extent true. Scientific discovery
must ever depend upon some happy thought, of which we cannot trace
the origin;--some fortunate cast of intellect, rising above all
rules. No maxims can be given which inevitably lead to discovery. No
precepts will elevate a man of ordinary endowments to the level of a
man of genius: nor will an inquirer of truly inventive mind need to
come to the teacher of inductive philosophy to learn how to exercise
the faculties which nature has given him. Such persons as Kepler or
Fresnel, or Brewster, will have their powers of discovering truth
little augmented by any injunctions respecting Distinct and
Appropriate Ideas; and such men may very naturally question the
utility of rules altogether.
16. But yet the opinions which such persons may entertain, will not
lead us to doubt concerning the value of the attempts to analyse and
methodize the process of discovery. Who would attend to Kepler if he
had maintained that the speculations of Francis Bacon were
worthless? Notwithstanding what has been said, we may venture to
assert that the Maxim which points out the necessity of Ideas
appropriate as well as clear, for the purpose of discovering truth,
is not without its use. It may, at least, have a value as a caution
or prohibition, and may thus turn us away from labours certain to be
fruitless. We have already seen, in the _History_ of Ideas, that
this maxim, if duly attended to, would have at once condemned, as
wrongly directed, the speculations of physiologists of the
mathematical, mechanical, chemical, and vital-fluid schools; since
the Ideas which the teachers of these schools introduce, cannot
suffice for the purposes of physiology, which seeks truths
respecting the vital powers. Again, {45} it is clear from similar
considerations that no definition of a mineralogical species by
chemical characters alone can answer the end of science, since we
seek to make mineralogy, not an analytical but a classificatory
science[1\2]. Even before the appropriate conception is matured in
men's minds so that they see clearly what it is, they may still have
light enough to see what it is not.
[Note 1\2: This agrees with what M. Necker has well observed in his
_Règne Mineral_, that those who have treated mineralogy as a merely
chemical science, have substituted the analysis of substances for
the classification of individuals. See _History of Ideas_, b. viii.
chap. iii.]
17. Another result of this view of the necessity of appropriate
Ideas, combined with a survey of the history of science is, that
though for the most part, as we shall see, the progress of science
consists in accumulating and combining Facts rather than in debating
concerning Definitions; there are still certain periods when the
_discussion_ of Definitions may be the most useful mode of
cultivating some special branch of science. This discussion is of
course always to be conducted by the light of facts; and, as has
already been said, along with the settlement of every good
Definition will occur the corresponding establishment of some
Proposition. But still at particular periods, the want of a
Definition, or of the clear conceptions which Definition supposes,
may be peculiarly felt. A good and tenable Definition of _Species_
in Mineralogy would at present be perhaps the most important step
which the science could make. A just conception of the nature of
_Life_, (and if expressed by means of a Definition, so much the
better,) can hardly fail to give its possessor an immense advantage
in the speculations which now come under the considerations of
physiologists. And controversies respecting Definitions, in these
cases, and such as these, may be very far from idle and
unprofitable.
Thus the knowledge that Clear and Appropriate Ideas are requisite
for discovery, although it does not lead to any very precise
precepts, or supersede the value of natural sagacity and
inventiveness, may still {46} be of use to us in our pursuit after
truth. It may show us what course of research is, in each stage of
science, recommended by the general analogy of the history of
knowledge; and it may both save us from hopeless and barren paths of
speculation, and make us advance with more courage and confidence,
to know that we are looking for discoveries in the manner in which
they have always hitherto been made.
SECT. V.--_Accidental Discoveries._
18. Another consequence follows from the views presented in this
Chapter, and it is the last I shall at present mention. _No
scientific discovery_ can, with any justice, be considered _due to
accident_. In whatever manner facts may be presented to the notice
of a discoverer, they can never become the materials of exact
knowledge, except they find his mind already provided with precise
and suitable conceptions by which they may be analysed and
connected. Indeed, as we have already seen, facts cannot be observed
as Facts, except in virtue of the Conceptions which the
observer[2\2] himself unconsciously supplies; and they are not Facts
of Observation for any purpose of Discovery, except these familiar
and unconscious acts of thought be themselves of a just and precise
kind. But supposing the Facts to be adequately observed, they can
never be combined into any new Truth, except by means of some new
Conceptions, clear and appropriate, such as I have endeavoured to
characterize. When the observer's mind is prepared with such
instruments, a very few facts, or it may be a single one, may bring
the process of discovery into action. But in such cases, this
previous condition of the intellect, and not the single fact, is
really the main and peculiar cause of the success. The fact is
merely the occasion by which the engine of discovery is brought into
play sooner or later. It is, as I have elsewhere said, only the
spark which discharges a gun already loaded and pointed; and there
{47} is little propriety in speaking of such an accident as the
cause why the bullet hits the mark. If it were true that the fall of
an apple was the occasion of Newton's pursuing the train of thought
which led to the doctrine of universal gravitation, the habits and
constitution of Newton's intellect, and not the apple, were the real
source of this great event in the progress of knowledge. The common
love of the marvellous, and the vulgar desire to bring down the
greatest achievements of genius to our own level, may lead men to
ascribe such results to any casual circumstances which accompany
them; but no one who fairly considers the real nature of great
discoveries, and the intellectual processes which they involve, can
seriously hold the opinion of their being the effect of accident.
[Note 2\2: B. i. of this vol. Aphorism III.]
19. Such accidents never happen to common men. Thousands of men,
even of the most inquiring and speculative men, had seen bodies
fall; but who, except Newton, ever followed the accident to such
consequences? And in fact, how little of his train of thought was
contained in, or even directly suggested by, the fall of the apple!
If the apple fall, said the discoverer, 'why should not the moon,
the planets, the satellites, fall?' But how much previous
thought,--what a steady conception of the universality of the laws
of motion gathered from other sources,--were requisite, that the
inquirer should see any connexion in these cases! Was it by accident
that he saw in the apple an image of the moon, and of every body in
the solar system?
20. The same observations may be made with regard to the other cases
which are sometimes adduced as examples of accidental discovery. It
has been said, 'By the accidental placing of a rhomb of calcareous
spar upon a book or line Bartholinus discovered the property of the
_Double Refraction_ of light.' But Bartholinus could have seen no
such consequence in the accident if he had not previously had a
clear conception of _single refraction_. A lady, in describing an
optical experiment which had been shown her, said of her teacher,
'He told me to _increase and diminish_ {48} _the angle of
refraction_, and at last I found that he only meant me to move my
head up and down.' At any rate, till the lady had acquired the
notions which the technical terms convey, she could not have made
Bartholinus's discovery by means of his accident. 'By accidentally
combining two rhombs in different positions,' it is added, 'Huyghens
discovered the _Polarization_ of Light.' Supposing that this
experiment had been made without design, what Huyghens really
observed was, that the images appeared and disappeared alternately
as he turned one of the rhombs round. But was it an easy or an
obvious business to analyze this curious alternation into the
circumstances of the rays of light having _sides_, as Newton
expressed it, and into the additional hypotheses which are implied
in the term 'polarization'? Those will be able to answer this
question, who have found how far from easy it is to understand
clearly what is meant by 'polarization' in this case, now that the
property is fully established. Huyghens's success depended on his
clearness of thought, for this enabled him to perform the
intellectual analysis, which never would have occurred to most men,
however often they had 'accidentally combined two rhombs in
different positions.' 'By accidentally looking through a prism of
the same substance, and turning it round, Malus discovered the
polarization of light by reflection.' Malus saw that, in some
positions of the prism, the light reflected from the windows of the
Louvre thus seen through the prism, became dim. A common man would
have supposed this dimness the result of accident; but Malus's mind
was differently constituted and disciplined. He considered the
position of the window, and of the prism; repeated the experiment
over and over; and in virtue of the eminently distinct conceptions
of space which he possessed, resolved the phenomena into its
geometrical conditions. A believer in accident would not have sought
them; a person of less clear ideas would not have found them. A
person must have a strange confidence in the virtue of chance, and
the worthlessness of intellect, who can say that {49} 'in all these
fundamental discoveries appropriate ideas had no share,' and that
the discoveries 'might have been made by the most ordinary
observers.'
21. I have now, I trust, shown in various ways, how the _Explication
of Conceptions_, including in this term their clear development from
Fundamental Ideas in the discoverer's mind, as well as their precise
expression in the form of Definitions or Axioms, when that can be
done, is an essential part in the establishment of all exact and
general physical truths. In doing this, I have endeavoured to
explain in what sense the possession of clear and appropriate ideas
is a main requisite for every step in scientific discovery. That it
is far from being the only step, I shall soon have to show; and if
any obscurity remain on the subject treated of in the present
chapter, it will, I hope, be removed when we have examined the other
elements which enter into the constitution of our knowledge.
{{50}}
CHAPTER III.
OF FACTS AS THE MATERIALS OF SCIENCE.
APHORISM IV.
_Facts are the materials of science, but all Facts involve Ideas.
Since in observing Facts, we cannot exclude Ideas, we must, for the
purposes of science, take care that the Ideas are clear and
rigorously applied._
APHORISM V.
_The last Aphorism leads to such Rules as the following:--That
Facts, for the purposes of material science, must involve
Conceptions of the Intellect only, and not Emotions:--That Facts
must be observed with reference to our most exact conceptions,
Number, Place, Figure, Motion:--That they must also be observed with
reference to any other exact conceptions which the phenomena
suggest, as Force, in mechanical phenomena, Concord, in musical._
APHORISM VI.
_The resolution of complex Facts into precise and measured partial
Facts, we call the_ Decomposition of Facts. _This process is
requisite for the progress of science, but does not necessarily lead
to progress._
1. WE have now to examine how Science is built up by the combination
of Facts. In doing this, we suppose that we have already attained a
supply of definite and certain Facts, free from obscurity and doubt.
We must, therefore, first consider under what conditions Facts can
assume this character.
When we inquire what Facts are to be made the materials of Science,
perhaps the answer which we {51} should most commonly receive would
be, that they must be _True Facts_, as distinguished from any mere
inferences or opinions of our own. We should probably be told that
we must be careful in such a case to consider as Facts, only what we
really observe;--that we must assert only what we see; and believe
nothing except upon the testimony of our senses.
But such maxims are far from being easy to apply, as a little
examination will convince us.
2. It has been explained, in preceding works, that all perception of
external objects and occurrences involves an active as well as a
passive process of the mind;--includes not only Sensations, but also
Ideas by which Sensations are bound together, and have a unity given
to them. From this it follows, that there is a difficulty in
separating in our perceptions what we receive from without, and what
we ourselves contribute from within;--what we perceive, and what we
infer. In many cases, this difficulty is obvious to all: as, for
example, when we witness the performances of a juggler or a
ventriloquist. In these instances, we imagine ourselves to see and
to hear what certainly we do not see and hear. The performer takes
advantage of the habits by which our minds supply interruptions and
infer connexions; and by giving us fallacious indications, he leads
us to perceive as an actual fact, what does not happen at all. In
these cases, it is evident that we ourselves assist in making the
fact; for we make one which does not really exist. In other cases,
though the fact which we perceive be true, we can easily see that a
large portion of the perception is our own act; as when, from the
sight of a bird of prey we infer a carcase, or when we read a
half-obliterated inscription. In the latter case, the mind supplies
the meaning, and perhaps half the letters; yet we do not hesitate to
say that we actually _read_ the inscription. Thus, in many cases,
our own inferences and interpretations enter into our facts. But
this happens in many instances in which it is at first sight less
obvious. When any one has seen an oak-tree blown down by a strong
gust of wind, he does not think of the occurrence {52} any otherwise
than as a _Fact_ of which he is assured by his senses. Yet by what
sense does he perceive the Force which he thus supposes the wind to
exert? By what sense does he distinguish an Oak-tree from all other
trees? It is clear upon reflexion, that in such a case, his own mind
supplies the conception of extraneous impulse and pressure, by which
he thus interprets the motions observed, and the distinction of
different kinds of trees, according to which he thus names the one
under his notice. The Idea of Force, and the idea of definite
Resemblances and Differences, are thus combined with the impressions
on our senses, and form an undistinguished portion of that which we
consider as the Fact. And it is evident that we can in no other way
perceive Force, than by seeing motion; and cannot give a Name to any
object, without not only seeing a difference of single objects, but
supposing a difference of classes of objects. When we speak as if we
saw impulse and attraction, things and classes, we really see only
objects of various forms and colours, more or less numerous,
variously combined. But do we really perceive so much as this? When
we see the form, the size, the number, the motion of objects, are
these really mere impressions on our senses, unmodified by any
contribution or operation of the mind itself? A very little
attention will suffice to convince us that this is not the case.
When we see a windmill turning, it may happen, as we have elsewhere
noticed[3\2], that we mistake the direction in which the sails turn:
when we look at certain diagrams, they may appear either convex or
concave: when we see the moon first in the horizon and afterwards
high up in the sky, we judge her to be much larger in the former
than in the latter position, although to the eye she subtends the
same angle. And in these cases and the like, it has been seen that
the errour and confusion which we thus incur arise from the mixture
of acts of the mind itself with impressions on the senses. But such
acts are, as we have also seen, _inseparable_ portions of the
process {53} of perception. A certain activity of the mind is
involved, not only in seeing objects erroneously, but in seeing them
at all. With regard to solid objects, this is generally
acknowledged. When we seem to see an edifice occupying space in all
dimensions, we really see only a representation of it as it appears
referred by perspective to a surface. The inference of the solid
form is an operation of our own, alike when we look at a reality and
when we look at a picture. But we may go further. Is plane Figure
really a mere Sensation? If we look at a decagon, do we see at once
that it has ten sides, or is it not necessary for us to count them:
and is not counting an act of the mind? All objects are seen in
space; all objects are seen as one or many: but are not the Idea of
Space and the Idea of Number requisite in order that we may thus
apprehend what we see? That these Ideas of Space and Number involve
a connexion derived from the mind, and not from the senses, appears,
as we have already seen, from this, that those Ideas afford us the
materials of universal and necessary truths:--such truths as the
senses cannot possibly supply. And thus, even the perception of such
facts as the size, shape, and number of objects, cannot be said to
be impressions of sense, distinct from all acts of mind, and cannot
be expected to be free from errour on the ground of their being mere
observed Facts.
[Note 3\2: _History of Ideas_, B. ii. c. vi. s. 6.]
Thus the difficulty which we have been illustrating, of
distinguishing Facts from inferences and from interpretations of
facts, is not only great, but amounts to an impossibility. The
separation at which we aimed in the outset of this discussion, and
which was supposed to be necessary in order to obtain a firm
groundwork for science, is found to be unattainable. We cannot
obtain a sure basis of Facts, by rejecting all inferences and
judgments of our own, for such inferences and judgments form an
unavoidable element in all Facts. We cannot exclude our Ideas from
our Perceptions, for our Perceptions involve our Ideas.
3. But still, it cannot be doubted that in selecting the Facts which
are to form the foundation of Science, {54} we must reduce them to
their most simple and certain form; and must reject everything from
which doubt or errour may arise. Now since this, it appears, cannot
be done, by rejecting the Ideas which all Facts involve, in what
manner are we to conform to the obvious maxim, that the Facts which
form the basis of Science must be perfectly definite and certain?
The analysis of facts into Ideas and Sensations, which we have so
often referred to, suggests the answer to this inquiry. We are not
able, nor need we endeavour, to exclude Ideas from our Facts; but we
may be able to discern, with perfect distinctness, the Ideas which
we include. We cannot observe any phenomena without applying to them
such Ideas as Space and Number, Cause and Resemblance, and usually,
several others; but we may avoid applying these Ideas in a wavering
or obscure manner, and confounding Ideas with one another. We cannot
read any of the inscriptions which nature presents to us, without
interpreting them by means of some language which we ourselves are
accustomed to speak; but we may make it our business to acquaint
ourselves perfectly with the language which we thus employ, and to
interpret it according to the rigorous rules of grammar and analogy.
This maxim, that when Facts are employed as the basis of Science, we
must distinguish clearly the Ideas which they involve, and must
apply these in a distinct and rigorous manner, will be found to be a
more precise guide than we might perhaps at first expect. We may
notice one or two Rules which flow from it.
4. In the first place. Facts, when used as the materials of physical
Science, must be _referred to Conceptions of the Intellect only_,
all emotions of fear, admiration, and the like, being rejected or
subdued. Thus, the observations of phenomena which are related as
portents and prodigies, striking terrour and boding evil, are of no
value for purposes of science. The tales of armies seen warring in
the sky, the sound of arms heard from the clouds, fiery dragons,
chariots, swords seen in the air, may refer to meteorological
phenomena; but the records of phenomena observed in the {55} state
of mind which these descriptions imply can be of no scientific
value. We cannot make the poets our observers.
Armorum sonitum toto Germania cœlo
Audiit; insolitis tremuerunt motibus Alpes.
Vox quoque per lucos vulgo exaudita silentes
Ingens; et simulacra modis pallentia miris
Visa sub obscurum noctis: pecudesque locutæ.
The mixture of fancy and emotion with the observation of facts has
often disfigured them to an extent which is too familiar to all to
need illustration. We have an example of this result, in the manner
in which Comets are described in the treatises of the middle ages.
In such works, these bodies are regularly distributed into several
classes, accordingly as they assume the form of a sword, of a spear,
of a cross, and so on. When such resemblances had become matters of
interest, the impressions of the senses were governed, not by the
rigorous conceptions of form and colour, but by these assumed
images; and under these circumstances, we can attach little value to
the statement of what was seen.
In all such phenomena, the reference of the objects to the exact
Ideas of Space, Number, Position, Motion, and the like, is the first
step of Science: and accordingly, this reference was established at
an early period in those sciences which made an early progress, as,
for instance, Astronomy. Yet even in astronomy there appears to have
been a period when the predominant conceptions of men in regarding
the heavens and the stars pointed to mythical story and supernatural
influence, rather than to mere relations of space, time, and motion:
and of this primeval condition of those who gazed at the stars, we
seem to have remnants in the Constellations, in the mythological
Names of the Planets, and in the early prevalence of Astrology. It
was only at a later period, when men had begun to measure the
places, or at least to count the revolutions of the stars, that
Astronomy had its birth.
5. And thus we are led to another Rule:--that in collecting Facts
which are to be made the basis of {56} Science, the Facts are to be
observed, as far as possible, _with reference to place, figure,
number, motion_, and the like Conceptions; which, depending upon the
Ideas of Space and Time, are the most universal, exact, and simple
of our conceptions. It was by early attention to these relations in
the case of the heavenly bodies, that the ancients formed the
science of Astronomy: it was by not making precise observations of
this kind in the case of terrestrial bodies, that they failed in
framing a science of the Mechanics of Motion. They succeeded in
Optics as far as they made observations of this nature; but when
they ceased to trace the geometrical paths of rays in the actual
experiment, they ceased to go forwards in the knowledge of this
subject.
6. But we may state a further Rule:--that though these relations of
Time and Space are highly important in almost all Facts, we are not
to confine ourselves to these: but are to consider the phenomena
_with reference to other Conceptions also_: it being always
understood that these conceptions are to be made as exact and
rigorous as those of geometry and number. Thus the science of
Harmonics arose from considering sounds with reference to _Concords_
and _Discords_; the science of Mechanics arose from not only
observing motions as they take place in Time and Space, but further,
referring them to _Force_ as their _Cause_. And in like manner,
other sciences depend upon other Ideas, which, as I have endeavoured
to show, are not less fundamental than those of Time and Space; and
like them, capable of leading to rigorous consequences.
7. Thus the Facts which we assume as the basis of Science are to be
freed from all the mists which imagination and passion throw round
them; and to be separated into those elementary Facts which exhibit
simple and evident relations of Time, or Space, or Cause, or some
other Ideas equally clear. We resolve the complex appearances which
nature offers to us, and the mixed and manifold modes of looking at
these appearances which rise in our thoughts, into limited,
definite, and clearly-understood portions. This process we may term
the _Decomposition of Facts_. It is the {57} beginning of exact
knowledge,--the first step in the formation of all Science. This
Decomposition of Facts into Elementary Facts, clearly understood and
surely ascertained, must precede all discovery of the laws of
nature.
8. But though this step is necessary, it is not infallibly
sufficient. It by no means follows that when we have thus decomposed
Facts into Elementary Truths of observation, we shall soon be able
to combine these, so as to obtain Truths of a higher and more
speculative kind. We have examples which show us how far this is
from being a necessary consequence of the former step. Observations
of the weather, made and recorded for many years, have not led to
any general truths, forming a science of Meteorology: and although
great numerical precision has been given to such observations by
means of barometers, thermometers, and other instruments, still, no
general laws regulating the cycles of change of such phenomena have
yet been discovered. In like manner the faces of crystals, and the
sides of the polygons which these crystals form, were counted, and
thus numerical facts were obtained, perfectly true and definite, but
still of no value for purposes of science. And when it was
discovered what Element of the form of crystals it was important to
observe and measure, namely, the Angle made by two faces with each
other, this discovery was a step of a higher order, and did not
belong to that department, of mere exact observation of manifest
Facts, with which we are here concerned.
9. When the Complex Facts which nature offers to us are thus
decomposed into Simple Facts, the decomposition, in general, leads
to the introduction of _Terms_ and Phrases, more or less technical,
by which these Simple Facts are described. When Astronomy was thus
made a science of measurement, the things measured were soon
described as _Hours_, and _Days_, and _Cycles_, _Altitude_ and
_Declination_, _Phases_ and _Aspects_. In the same manner, in Music,
the concords had names assigned them, as _Diapente_, _Diatessaron_,
_Diapason_; in studying Optics, the _Rays_ of light were spoken of
as {58} having their course altered by _Reflexion_ and _Refraction_;
and when useful observations began to be made in Mechanics, the
observers spoke of _Force_, _Pressure_, _Momentum_, _Inertia_, and
the like.
10. When we take phenomena in which the leading Idea is Resemblance,
and resolve them into precise component Facts, we obtain some kind
of Classification; as, for instance, when we lay down certain Rules
by which particular trees, or particular animals are to be known.
This is the earliest form of Natural History; and the Classification
which it involves is that which corresponds, nearly or exactly, with
the usual Names of the objects thus classified.
11. Thus the first attempts to render observation certain and exact,
lead to a decomposition of the obvious facts into Elementary Facts,
connected by the Ideas of Space, Time, Number, Cause, Likeness, and
others: and into a Classification of the Simple Facts; a
classification more or less just, and marked by Names either common
or technical. Elementary Facts, and Individual Objects, thus
observed and classified, form the materials of Science; and any
improvement in Classification or Nomenclature, or any discovery of a
Connexion among the materials thus accumulated, leads us fairly
within the precincts of Science. We must now, therefore, consider
the manner in which Science is built up of such materials;--the
process by which they are brought into their places, and the texture
of the bond which unites and cements them.
{{59}}
CHAPTER IV.
OF THE COLLIGATION OF FACTS.
APHORISM VII.
_Science begins with_ common _observation of facts; but even at this
stage, requires that the observations be precise. Hence the sciences
which depend upon space and number were the earliest formed. After
common observation, come Scientific_ Observation _and_ Experiment.
APHORISM VIII.
_The Conceptions by which Facts are bound together, are suggested by
the sagacity of discoverers. This sagacity cannot be taught. It
commonly succeeds by guessing; and this success seems to consist in
framing several_ tentative hypotheses _and selecting the right one.
But a supply of appropriate hypotheses cannot be constructed by
rule, nor without inventive talent._
APHORISM IX.
_The truth of tentative hypotheses must be tested by their
application to facts. The discoverer must be ready, carefully to try
his hypotheses in this manner, and to reject them if they will not
bear the test, in spite of indolence and vanity._
1. FACTS such as the last Chapter speaks of are, by means of such
Conceptions as are described in the preceding Chapter, bound
together so as to give rise to those general Propositions of which
Science consists. Thus the Facts that the planets revolve {60} about
the sun in certain periodic times and at certain distances, are
included and connected in Kepler's Law, by means of such Conceptions
as the _squares of numbers_, the _cubes of distances_, and the
_proportionality_ of these quantities. Again the existence of this
proportion in the motions of any two planets, forms a set of Facts
which may all be combined by means of the Conception of a certain
_central accelerating force_, as was proved by Newton. The whole of
our physical knowledge consists in the establishment of such
propositions; and in all such cases, Facts are bound together by the
aid of suitable Conceptions. This part of the formation of our
knowledge I have called the _Colligation of Facts_: and we may apply
this term to every case in which, by an act of the intellect, we
establish a precise connexion among the phenomena which are
presented to our senses. The knowledge of such connexions,
accumulated and systematized, is Science. On the steps by which
science is thus collected from phenomena we shall proceed now to
make a few remarks.
2. Science begins with _Common_ Observation of facts, in which we
are not conscious of any peculiar discipline or habit of thought
exercised in observing. Thus the common perceptions of the
appearances and recurrences of the celestial luminaries, were the
first steps of Astronomy: the obvious cases in which bodies fall or
are supported, were the beginning of Mechanics; the familiar aspects
of visible things, were the origin of Optics; the usual distinctions
of well-known plants, first gave rise to Botany. Facts belonging to
such parts of our knowledge are noticed by us, and accumulated in
our memories, in the common course of our habits, almost without our
being aware that we are observing and collecting facts. Yet such
facts may lead to many scientific truths; for instance, in the first
stages of Astronomy (as we have shown in the _History_) such facts
led to Methods of Intercalation and Rules of the Recurrence of
Eclipses. In succeeding stages of science, more especial attention
and preparation on the part of the observer, and a selection of
certain {61} _kinds_ of facts, becomes necessary; but there is an
early period in the progress of knowledge at which man is a physical
philosopher, without seeking to be so, or being aware that he is so.
3. But in all stages of the progress, even in that early one of
which we have just spoken, it is necessary, in order that the facts
may be fit materials of any knowledge, that they should be
decomposed into Elementary Facts, and that these should be observed
with precision. Thus, in the first infancy of astronomy, the
recurrence of phases of the moon, of places of the sun's rising and
setting, of planets, of eclipses, was observed to take place at
intervals of certain definite numbers of days, and in a certain
exact order; and thus it was, that the observations became portions
of astronomical science. In other cases, although the facts were
equally numerous, and their general aspect equally familiar, they
led to no science, because their exact circumstances were not
apprehended. A vague and loose mode of looking at facts very easily
observable, left men for a long time under the belief that a body,
ten times as heavy as another, falls ten times as fast;--that
objects immersed in water are always magnified, without regard to
the form of the surface;--that the magnet exerts an irresistible
force;--that crystal is always found associated with ice;--and the
like. These and many others are examples how blind and careless men
can be, even in observation of the plainest and commonest
appearances; and they show us that the mere faculties of perception,
although constantly exercised upon innumerable objects, may long
fail in leading to any exact knowledge.
4. If we further inquire what was the favourable condition through
which some special classes of facts were, from the first, fitted to
become portions of science, we shall find it to have been
principally this;--that these facts were considered with reference
to the Ideas of Time, Number, and Space, which are Ideas possessing
peculiar definiteness and precision; so that with regard to them,
confusion and indistinctness are hardly possible. The interval from
new moon to new {62} moon was always a particular number of days:
the sun in his yearly course rose and set near to a known succession
of distant objects: the moon's path passed among the stars in a
certain order:--these are observations in which mistake and
obscurity are not likely to occur, if the smallest degree of
attention is bestowed upon the task. To count a number is, from the
first opening of man's mental faculties, an operation which no
science can render more precise. The relations of space are nearest
to those of number in obvious and universal evidence. Sciences
depending upon these Ideas arise with the first dawn of intellectual
civilization. But few of the other Ideas which man employs in the
acquisition of knowledge possess this clearness in their common use.
The Idea of _Resemblance_ may be noticed, as coming next to those of
Space and Number in original precision; and the Idea of _Cause_, in
a certain vague and general mode of application, sufficient for the
purposes of common life, but not for the ends of science, exercises
a very extensive influence over men's thoughts. But the other Ideas
on which science depends, with the Conceptions which arise out of
them, are not unfolded till a much later period of intellectual
progress; and therefore, except in such limited cases as I have
noticed, the observations of common spectators and uncultivated
nations, however numerous or varied, are of little or no effect in
giving rise to Science.
5. Let us now suppose that, besides common everyday perception of
facts, we turn our attention to some other occurrences and
appearances, with a design of obtaining from them speculative
knowledge. This process is more peculiarly called _Observation_, or,
when we ourselves occasion the facts, _Experiment_. But the same
remark which we have already made, still holds good here. These
facts can be of no value, except they are resolved into those exact
Conceptions which contain the essential circumstances of the case.
They must be determined, not indeed necessarily, as has sometimes
been said, 'according to Number, Weight, and Measure;' for, as we
have endeavoured to show {63} in the preceding Books[4\2], there are
many other Conceptions to which phenomena may be subordinated, quite
different from these, and yet not at all less definite and precise.
But in order that the facts obtained by observation and experiment
may be capable of being used in furtherance of our exact and solid
knowledge, they must be apprehended and analysed according to some
Conceptions which, applied for this purpose, give distinct and
definite results, such as can be steadily taken hold of and reasoned
from; that is, the facts must be referred to Clear and Appropriate
Ideas, according to the manner in which we have already explained
this condition of the derivation of our knowledge. The phenomena of
light, when they are such as to indicate sides in the ray, must be
referred to the Conception of _polarization_; the phenomena of
mixture, when there is an alteration of qualities as well as
quantities, must be combined by a Conception of _elementary
composition_. And thus, when mere position, and number, and
resemblance, will no longer answer the purpose of enabling us to
connect the facts, we call in other Ideas, in such cases more
efficacious, though less obvious.
[Note 4\2: _Hist. of Sci. Id._ Bs. v. vi. vii. viii. ix. x.]
6. But how are we, in these cases, to discover such Ideas, and to
judge which will be efficacious, in leading to a scientific
combination of our experimental data? To this question, we must in
the first place answer, that the first and great instrument by which
facts, so observed with a view to the formation of exact knowledge,
are combined into important and permanent truths, is that peculiar
Sagacity which belongs to the genius of a Discoverer; and which,
while it supplies those distinct and appropriate Conceptions which
lead to its success, cannot be limited by rules, or expressed in
definitions. It would be difficult or impossible to describe in
words the habits of thought which led Archimedes to refer the
conditions of equilibrium on the Lever to the Conception of
_pressure_, while Aristotle could not see in them anything more than
the results {64} of the strangeness of the properties of the
circle;--or which impelled Pascal to explain by means of the
Conception of the _weight of air_, the facts which his predecessors
had connected by the notion of nature's horrour of a vacuum;--or
which caused Vitello and Roger Bacon to refer the magnifying power
of a convex lens to the bending of the rays of light towards the
perpendicular by _refraction_, while others conceived the effect to
result from the matter of medium, with no consideration of its form.
These are what are commonly spoken of as felicitous and inexplicable
strokes of inventive talent; and such, no doubt, they are. No rules
can ensure to us similar success in new cases; or can enable men who
do not possess similar endowments, to make like advances in
knowledge.
7. Yet still, we may do something in tracing the process by which
such discoveries are made; and this it is here our business to do.
We may observe that these, and the like discoveries, are not
improperly described as happy _Guesses_; and that Guesses, in these
as in other instances, imply various suppositions made, of which
some one turns out to be the right one. We may, in such cases,
conceive the discoverer as inventing and trying many conjectures,
till he finds one which answers the purpose of combining the
scattered facts into a single rule. The discovery of general truths
from special facts is performed, commonly at least, and more
commonly than at first appears, by the use of a series of
Suppositions, or _Hypotheses_, which are looked at in quick
succession, and of which the one which really leads to truth is
rapidly detected, and when caught sight of, firmly held, verified,
and followed to its consequences. In the minds of most discoverers,
this process of invention, trial, and acceptance or rejection of the
hypothesis, goes on so rapidly that we cannot trace it in its
successive steps. But in some instances, we can do so; and we can
also see that the other examples of discovery do not differ
essentially from these. The same intellectual operations take place
in other cases, although this often happens so instantaneously that
we lose the trace of the {65} progression. In the discoveries made
by Kepler, we have a curious and memorable exhibition of this
process in its details. Thanks to his communicative disposition, we
know that he made nineteen hypotheses with regard to the motion of
Mars, and calculated the results of each, before he established the
true doctrine, that the planet's path is an ellipse. We know, in
like manner, that Galileo made wrong suppositions respecting the
laws of falling bodies, and Mariotte, concerning the motion of water
in a siphon, before they hit upon the correct view of these cases.
8. But it has very often happened in the history of science, that
the erroneous hypotheses which preceded the discovery of the truth
have been made, not by the discoverer himself, but by his
precursors; to whom he thus owed the service, often an important one
in such cases, of exhausting the most tempting forms of errour. Thus
the various fruitless suppositions by which Kepler endeavoured to
discover the law of reflection, led the way to its real detection by
Snell; Kepler's numerous imaginations concerning the forces by which
the celestial motions are produced,--his 'physical reasonings' as he
termed them,--were a natural prelude to the truer physical
reasonings of Newton. The various hypotheses by which the suspension
of vapour in air had been explained, and their failure, left the
field open for Dalton with his doctrine of the mechanical mixture of
gases. In most cases, if we could truly analyze the operation of the
thoughts of those who make, or who endeavour to make discoveries in
science, we should find that many more suppositions pass through
their minds than those which are expressed in words; many a possible
combination of conceptions is formed and soon rejected. There is a
constant invention and activity, a perpetual creating and selecting
power at work, of which the last results only are exhibited to us.
Trains of hypotheses are called up and pass rapidly in review; and
the judgment makes its choice from the varied group.
9. It would, however, be a great mistake to suppose that the
hypotheses, among which our choice thus {66} lies, are constructed
by an enumeration of obvious cases, or by a wanton alteration of
relations which occur in some first hypothesis. It may, indeed,
sometimes happen that the proposition which is finally established
is such as may be formed, by some slight alteration, from those
which are justly rejected. Thus Kepler's elliptical theory of Mars's
motions, involved relations of lines and angles much of the same
nature as his previous false suppositions: and the true law of
refraction so much resembles those erroneous ones which Kepler
tried, that we cannot help wondering how he chanced to miss it. But
it more frequently happens that new truths are brought into view by
the application of new Ideas, not by new modifications of old ones.
The cause of the properties of the Lever was learnt, not by
introducing any new _geometrical_ combination of lines and circles,
but by referring the properties to genuine _mechanical_ Conceptions.
When the Motions of the Planets were to be explained, this was done,
not by merely improving the previous notions, of cycles of time, but
by introducing the new conception of _epicycles_ in space. The
doctrine of the Four Simple Elements was expelled, not by forming
any new scheme of elements which should impart, according to new
rules, their sensible qualities to their compounds, but by
considering the elements of bodies as _neutralizing_ each other. The
Fringes of Shadows could not be explained by ascribing new
properties to the single rays of light, but were reduced to law by
referring them to the _interference_ of several rays.
Since the true supposition is thus very frequently something
altogether diverse from all the obvious conjectures and
combinations, we see here how far we are from being able to reduce
discovery to rule, or to give any precepts by which the want of real
invention and sagacity shall be supplied. We may warn and encourage
these faculties when they exist, but we cannot create them, or make
great discoveries when they are absent.
10. The Conceptions which a true theory requires are very often
clothed in a _Hypothesis_ which connects {67} with them several
superfluous and irrelevant circumstances. Thus the Conception of the
Polarization of Light was originally represented under the image of
particles of light having their poles all turned in the same
direction. The Laws of Heat may be made out perhaps most
conveniently by conceiving Heat to be a _Fluid_. The Attraction of
Gravitation might have been successfully applied to the explanation
of facts, if Newton had throughout treated Attraction as the result
of an _Ether_ diffused through space; a supposition which he has
noticed as a possibility. The doctrine of Definite and Multiple
Proportions may be conveniently expressed by the hypothesis of
_Atoms_. In such cases, the Hypothesis may serve at first to
facilitate the introduction of a new Conception. Thus a pervading
Ether might for a time remove a difficulty, which some persons find
considerable, of imagining a body to exert force at a distance. A
Particle with Poles is more easily conceived than Polarization in
the abstract. And if hypotheses thus employed will really explain
the facts by means of a few simple assumptions, the laws so obtained
may afterwards be reduced to a simpler form than that in which they
were first suggested. The general laws of Heat, of Attraction, of
Polarization, of Multiple Proportions, are now certain, whatever
image we may form to ourselves of their ultimate causes.
11. In order, then, to discover scientific truths, suppositions
consisting either of new Conceptions, or of new Combinations of old
ones, are to be made, till we find one supposition which succeeds in
binding together the Facts. But how are we to find this? How is the
trial to be made? What is meant by 'success' in these cases? To this
we reply, that our inquiry must be, whether the Facts have the same
relation in the Hypothesis which they have in reality;--whether the
results of our suppositions agree with the phenomena which nature
presents to us. For this purpose, we must both carefully observe the
phenomena, and steadily trace the consequences of our assumptions,
till we can {68} bring the two into comparison. The Conceptions
which our hypotheses involve, being derived from certain Fundamental
Ideas, afford a basis of rigorous reasoning, as we have shown in the
Books of the _History_ of those Ideas. And the results to which this
reasoning leads, will be susceptible of being verified or
contradicted by observation of the facts. Thus the Epicyclical
Theory of the Moon, once assumed, determined what the moon's place
among the stars ought to be at any given time, and could therefore
be tested by actually observing the moon's places. The doctrine that
musical strings of the same length, stretched with weights of 1, 4,
9, 16, would give the musical intervals of an octave, a fifth, a
fourth, in succession, could be put to the trial by any one whose
ear was capable of appreciating those intervals: and the inference
which follows from this doctrine by numerical reasoning,--that there
must be certain imperfections in the concords of every musical
scale,--could in like manner be confirmed by trying various modes of
_Temperament_. In like manner all received theories in science, up
to the present time, have been established by taking up some
supposition, and comparing it, directly or by means of its remoter
consequences, with the facts it was intended to embrace. Its
agreement, under certain cautions and conditions, of which we may
hereafter speak, is held to be the evidence of its truth. It answers
its genuine purpose, the Colligation of Facts.
12. When we have, in any subject, succeeded in one attempt of this
kind, and obtained some true Bond of Unity by which the phenomena
are held together, the subject is open to further prosecution; which
ulterior process may, for the most part, be conducted in a more
formal and technical manner. The first great outline of the subject
is drawn; and the finishing of the resemblance of nature demands a
more minute pencilling, but perhaps requires less of genius in the
master. In the pursuance of this task, rules and precepts may be
given, and features and leading circumstances pointed out, of which
it may often be useful to the inquirer to be aware. {69}
Before proceeding further, I shall speak of some characteristic
marks which belong to such scientific processes as are now the
subject of our consideration, and which may sometimes aid us in
determining when the task has been rightly executed.
{{70}}
CHAPTER V.
OF CERTAIN CHARACTERISTICS OF SCIENTIFIC INDUCTION.
APHORISM X.
_The process of scientific discovery is cautious and rigorous, not
by abstaining from hypotheses, but by rigorously comparing
hypotheses with facts, and by resolutely rejecting all which the
comparison does not confirm._
APHORISM XI.
_Hypotheses may be useful, though involving much that is
superfluous, and even erroneous: for they may supply the true bond
of connexion of the facts; and the superfluity and errour may
afterwards be pared away._
APHORISM XII.
_It is a test of true theories not only to account for, but to
predict phenomena._
APHORISM XIII.
Induction _is a term applied to describe the process of a true
Colligation of Facts by means of an exact and appropriate
Conception._ An Induction _is also employed to denote the_
proposition _which results from this process._
APHORISM XIV.
The Consilience of Inductions _takes place when an Induction,
obtained from one class of facts, coincides with an Induction,
obtained from another different class. This_ {71} _Consilience is a
test of the truth of the Theory in which it occurs._
APHORISM XV.
_An Induction is not the mere_ sum _of the Facts which are colligated.
The Facts are not only brought together, but seen in a new point of
view. A new mental Element is_ superinduced; _and a peculiar
constitution and discipline of mind are requisite in order to make
this Induction._
APHORISM XVI.
_Although in Every Induction a new conception is superinduced upon
the Facts; yet this once effectually done, the novelty of the
conception is overlooked, and the conception is considered as a part
of the fact._
SECT. I.--_Invention a part of Induction._
1. THE two operations spoken of in the preceding chapters,--the
Explication of the Conceptions of our own minds, and the Colligation
of observed Facts by the aid of such Conceptions,--are, as we have
just said, inseparably connected with each other. When united, and
employed in collecting knowledge from the phenomena which the world
presents to us, they constitute the mental process of _Induction_;
which is usually and justly spoken of as the genuine source of all
our _real general knowledge_ respecting the external world. And we
see, from the preceding analysis of this process into its two
constituents, from what origin it derives each of its characters. It
is _real_, because it arises from the combination of Real Facts, but
it is _general_, because it implies the possession of General Ideas.
Without the former, it would not be knowledge of the External World;
without the latter, it would not be Knowledge at all. When Ideas and
Facts are separated from each other, the neglect of Facts gives rise
to empty speculations, idle subtleties, visionary inventions, false
opinions concerning the laws of phenomena, disregard of the true
aspect of nature: {72} while the want of Ideas leaves the mind
overwhelmed, bewildered, and stupified by particular sensations,
with no means of connecting the past with the future, the absent
with the present, the example with the rule; open to the impression
of all appearances, but capable of appropriating none. Ideas are the
_Form_, facts the _Material_, of our structure. Knowledge does not
consist in the empty mould, or in the brute mass of matter, but in
the rightly-moulded substance. Induction gathers general truths from
particular facts;--and in her harvest, the corn and the reaper, the
solid ears and the binding band, are alike requisite. All our
knowledge of nature is obtained by Induction; the term being
understood according to the explanation we have now given. And our
knowledge is then most complete, then most truly deserves the name
of Science, when both its elements are most perfect;--when the Ideas
which have been concerned in its formation have, at every step, been
clear and consistent; and when they have, at every step also, been
employed in binding together real and certain Facts. Of such
Induction, I have already given so many examples and illustrations
in the two preceding chapters, that I need not now dwell further
upon the subject.
2. Induction is familiarly spoken of as the process by which we
collect a _General Proposition_ from a number of _Particular Cases_:
and it appears to be frequently imagined that the general
proposition results from a mere juxta-position of the cases, or at
most, from merely conjoining and extending them. But if we consider
the process more closely, as exhibited in the cases lately spoken
of, we shall perceive that this is an inadequate account of the
matter. The particular facts are not merely brought together, but
there is a New Element added to the combination by the very act of
thought by which they are combined. There is a Conception of the
mind introduced in the general proposition, which did not exist in
any of the observed facts. When the Greeks, after long observing the
motions of the planets, saw that these motions might be rightly
considered as produced by the motion of one {73} wheel revolving in
the inside of another wheel, these Wheels were Creations of their
minds, added to the Facts which they perceived by sense. And even if
the wheels were no longer supposed to be material, but were reduced
to mere geometrical spheres or circles, they were not the less
products of the mind alone,--something additional to the facts
observed. The same is the case in all other discoveries. The facts
are known, but they are insulated and unconnected, till the
discoverer supplies from his own stores a Principle of Connexion.
The pearls are there, but they will not hang together till some one
provides the String. The distances and periods of the planets were
all so many separate facts; by Kepler's Third Law they are connected
into a single truth: but the Conceptions which this law involves
were supplied by Kepler's mind, and without these, the facts were of
no avail. The planets described ellipses round the sun, in the
contemplation of others as well as of Newton; but Newton conceived
the deflection from the tangent in these elliptical motions in a new
light,--as the effect of a Central Force following a certain law;
and then it was, that such a force was discovered truly to exist.
Thus[5\2] in each inference made by Induction, there is introduced
some General Conception, which is given, not by the phenomena, but
by the mind. The conclusion is not contained in the premises, but
includes them by the introduction of a New Generality. In order to
obtain our inference, we travel beyond the cases which we have
before us; we consider them as mere exemplifications of some Ideal
Case in which the relations are complete and intelligible. We take a
Standard, and measure the facts by it; and this Standard is
constructed by us, not offered by Nature. We assert, for example,
that a body left to itself will move on with unaltered velocity; not
because our senses ever disclosed to us a body doing this, but
because (taking this as our Ideal Case) we find that all {74} actual
cases are intelligible and explicable by means of the Conception of
_Forces_, causing change and motion, and exerted by surrounding
bodies. In like manner, we see bodies striking each other, and thus
moving and stopping, accelerating and retarding each other: but in
all this, we do not perceive by our senses that abstract quantity,
_Momentum_, which is always lost by one body as it is gained by
another. This Momentum is a creation of the mind, brought in among
the facts, in order to convert their apparent confusion into order,
their seeming chance into certainty, their perplexing variety into
simplicity. This the Conception of _Momentum gained and lost_ does:
and in like manner, in any other case in which a truth is
established by Induction, some Conception is introduced, some Idea
is applied, as the means of binding together the facts, and thus
producing the truth.
[Note 5\2: I repeat here remarks made at the end of the _Mechanical
Euclid_, p. 178.]
3. Hence in every inference by Induction, there is some Conception
_superinduced_ upon the Facts: and we may henceforth conceive this
to be the peculiar import of the term _Induction_. I am not to be
understood as asserting that the term was originally or anciently
employed with this notion of its meaning; for the peculiar feature
just pointed out in Induction has generally been overlooked. This
appears by the accounts generally given of Induction. 'Induction,'
says Aristotle[6\2], 'is when by means of one extreme term[7\2] we
infer the other extreme term to be true of the middle term.' Thus,
(to take such exemplifications as belong to our subject,) from
knowing that Mercury, Venus, Mars, describe ellipses about the Sun,
we infer that all Planets describe ellipses about the Sun. In making
this inference syllogistically, we assume that the evident
proposition, 'Mercury, Venus, Mars, do what all Planets do,' may be
taken _conversely_, 'All {75} Planets do what Mercury, Venus, Mars,
do.' But we may remark that, in this passage, Aristotle (as was
natural in his line of discussion) turns his attention entirely to
the _evidence_ of the inference; and overlooks a step which is of
far more importance to our knowledge, namely, the _invention_ of the
second extreme term. In the above instance, the particular
luminaries, Mercury, Venus, Mars, are one logical _Extreme_; the
general designation Planets is the _Middle Term_; but having these
before us, how do we come to think of _description of ellipses_,
which is the other Extreme of the syllogism? When we have once
invented this 'second Extreme Term,' we may, or may not, be
satisfied with the evidence of the syllogism; we may, or may not, be
convinced that, so far as this property goes, the extremes are
co-extensive with the middle term[8\2]; but the _statement_ of the
syllogism is the important step in science. We know how long Kepler
laboured, how hard he fought, how many devices he tried, before he
hit upon this _Term_, the Elliptical Motion. He rejected, as we
know, many other 'second extreme Terms,' for example, various
combinations of epicyclical constructions, because they did not
represent with sufficient accuracy the special facts of observation.
When he had established his premiss, that 'Mars does describe an
Ellipse about the Sun,' he does not hesitate to _guess_ at least
that, in this respect, he might _convert_ the other premiss, and
assert that 'All the Planets do what Mars does.' But the main
business was, the inventing and verifying the proposition respecting
the Ellipse. The Invention of the Conception was the great step in
the _discovery_; the Verification of the Proposition was the great
step in the _proof_ of the discovery. If Logic consists in pointing
out the conditions of proof, the Logic of Induction must consist in
showing what are the conditions of proof, in such inferences as
this: but this subject must be pursued in the next chapter; I now
speak principally of the act of {76} _Invention_, which is requisite
in every inductive inference.
[Note 6\2: _Analyt. Prior._ lib. ii. c. xxiii. Περὶ τῆς ἐπαγωγῆς.]
[Note 7\2: The syllogism here alluded to would be this:--
Mercury, Venus, Mars, describe ellipses about the Sun;
All Planets do what Mercury, Venus, Mars, do;
Therefore all Planets describe ellipses about the Sun.]
[Note 8\2: Εἰ οὖν ἀντιστρέφει τὸ Γ τῷ Β καὶ μὴ ὑπερτείνει τὸ
μέσον.--Aristot. _Ibid._]
4. Although in every inductive inference, an act of invention is
requisite, the act soon slips out of notice. Although we bind
together facts by superinducing upon them a new Conception, this
Conception, once introduced and applied, is looked upon as
inseparably connected with the facts, and necessarily implied in
them. Having once had the phenomena bound together in their minds in
virtue of the Conception, men can no longer easily restore them back
to the detached and incoherent condition in which they were before
they were thus combined. The pearls once strung, they seem to form a
chain by their nature. Induction has given them a unity which it is
so far from costing us an effort to preserve, that it requires an
effort to imagine it dissolved. For instance, we usually represent
to ourselves the Earth as _round_, the Earth and the Planets as
_revolving_ about the Sun, and as _drawn_ to the Sun by a Central
Force; we can hardly understand how it could cost the Greeks, and
Copernicus, and Newton, so much pains and trouble to arrive at a
view which to us is so familiar. These are no longer to us
Conceptions caught hold of and kept hold of by a severe struggle;
they are the simplest modes of conceiving the facts: they are really
Facts. We are willing to _own_ our obligation to those discoverers,
but we hardly _feel_ it: for in what other manner (we ask in our
thoughts) could we represent the facts to ourselves?
Thus we see why it is that this step of which we now speak, the
Invention of a new Conception in every inductive inference, is so
generally overlooked that it has hardly been noticed by preceding
philosophers. When once performed by the discoverer, it takes a
fixed and permanent place in the understanding of every one. It is a
thought which, once breathed forth, permeates all men's minds. All
fancy they nearly or quite knew it before. It oft was thought, or
almost thought, though never till now expressed. Men accept it and
retain it, and know it cannot be taken {77} from them, and look upon
it as their own. They will not and cannot part with it, even though
they may deem it trivial and obvious. It is a secret, which once
uttered, cannot be recalled, even though it be despised by those to
whom it is imparted. As soon as the leading term of a new theory has
been pronounced and understood, all the phenomena change their
aspect. There is a standard to which we cannot help referring them.
We cannot fall back into the helpless and bewildered state in which
we gazed at them when we possessed no principle which gave them
unity. Eclipses arrive in mysterious confusion: the notion of a
_Cycle_ dispels the mystery. The Planets perform a tangled and mazy
dance; but _Epicycles_ reduce the maze to order. The Epicycles
themselves run into confusion; the conception of an _Ellipse_ makes
all clear and simple. And thus from stage to stage, new elements of
intelligible order are introduced. But this intelligible order is so
completely adopted by the human understanding, as to seem part of
its texture. Men ask Whether Eclipses follow a Cycle; Whether the
Planets describe Ellipses; and they imagine that so long as they do
not _answer_ such questions rashly, they take nothing for granted.
They do not recollect how much they assume in _asking_ the
question:--how far the conceptions of Cycles and of Ellipses are
beyond the visible surface of the celestial phenomena:--how many
ages elapsed, how much thought, how much observation, were needed,
before men's thoughts were fashioned into the words which they now
so familiarly use. And thus they treat the subject, as we have seen
Aristotle treating it; as if it were a question, not of invention,
but of proof; not of substance, but of form: as if the main thing
were not _what_ we assert, but _how_ we assert it. But for our
purpose, it is requisite to bear in mind the feature which we have
thus attempted to mark; and to recollect that, in every inference by
induction, there is a Conception supplied by the mind and
superinduced upon the Facts.
5. In collecting scientific truths by Induction, we often find (as
has already been observed) a Definition {78} and a Proposition
established at the same time,--introduced together, and mutually
dependent on each other. The combination of the two constitutes the
Inductive act; and we may consider the Definition as representing
the superinduced Conception, and the Proposition as exhibiting the
Colligation of Facts.
SECT. II.--_Use of Hypotheses._
6. To discover a Conception of the mind which will justly represent
a train of observed facts is, in some measure, a process of
conjecture, as I have stated already; and as I then observed, the
business of conjecture is commonly conducted by calling up before
our minds several suppositions, and selecting that one which most
agrees with what we know of the observed facts. Hence he who has to
discover the laws of nature may have to invent many suppositions
before he hits upon the right one; and among the endowments which
lead to his success, we must reckon that fertility of invention
which ministers to him such imaginary schemes, till at last he finds
the one which conforms to the true order of nature. A facility in
devising hypotheses, therefore, is so far from being a fault in the
intellectual character of a discoverer, that it is, in truth, a
faculty indispensable to his task. It is, for his purposes, much
better that he should be too ready in contriving, too eager in
pursuing systems which promise to introduce law and order among a
mass of unarranged facts, than that he should be barren of such
inventions and hopeless of such success. Accordingly, as we have
already noticed, great discoverers have often invented hypotheses
which would not answer to all the facts, as well as those which
would; and have fancied themselves to have discovered laws, which a
more careful examination of the facts overturned.
The tendencies of our speculative nature[9\2], carrying {79} us
onwards in pursuit of symmetry and rule, and thus producing all true
theories, perpetually show their vigour by overshooting the mark.
They obtain something, by aiming at much more. They detect the order
and connexion which exist, by conceiving imaginary relations of
order and connexion which have no existence. Real discoveries are
thus mixed with baseless assumptions; profound sagacity is combined
with fanciful conjecture; not rarely, or in peculiar instances, but
commonly, and in most cases; probably in all, if we could read the
thoughts of discoverers as we read the books of Kepler. To try wrong
guesses is, with most persons, the only way to hit upon right ones.
The character of the true philosopher is, not that he never
conjectures hazardously, but that his conjectures are clearly
conceived, and brought into rigid contact with facts. He sees and
compares distinctly the Ideas and the Things;--the relations of his
notions to each other and to phenomena. Under these conditions, it
is not only excusable, but necessary for him, to snatch at every
semblance of general rule,--to try all promising forms of simplicity
and symmetry.
[Note 9\2: I here take the liberty of characterizing inventive minds
in general in the same phraseology which, in the History of Science,
I have employed in reference to particular examples. These
expressions are what I have used in speaking of the discoveries of
Copernicus.--_Hist. Ind. Sc._ b. v. c. ii.]
Hence advances in knowledge[10\2] are not commonly made without the
previous exercise of some boldness and license in guessing. The
discovery of new truths requires, undoubtedly, minds careful and
scrupulous in examining what is suggested; but it requires, no less,
such as are quick and fertile in suggesting. What is Invention,
except the talent of rapidly calling before us the many
possibilities, and selecting the appropriate one? It is true, that
when we have rejected all the inadmissible suppositions, they are
often quickly forgotten; and few think it necessary to dwell on
these discarded hypotheses, and on the process by which they were
condemned. But all who discover truths, must have reasoned upon many
errours to obtain each truth; {80} every accepted doctrine must have
been one chosen out of many candidates. If many of the guesses of
philosophers of bygone times now appear fanciful and absurd, because
time and observation have refuted them, others, which were at the
time equally gratuitous, have been conformed in a manner which makes
them appear marvellously sagacious. To form hypotheses, and then to
employ much labour and skill in refuting them, if they do not
succeed in establishing them, is a part of the usual process of
inventive minds. Such a proceeding belongs to the _rule_ of the
genius of discovery, rather than (as has often been taught in modern
times) to the _exception_.
[Note 10\2: These observations are made on occasion of Kepler's
speculations, and are illustrated by reference to his
discoveries.--_Hist. Ind. Sc._ b. v. c. iv. sect. 1.]
7. But if it be an advantage for the discoverer of truth that he be
ingenious and fertile in inventing hypotheses which may connect the
phenomena of nature, it is indispensably requisite that he be
diligent and careful in comparing his hypotheses with the facts, and
ready to abandon his invention as soon as it appears that it does
not agree with the course of actual occurrences. This constant
comparison of his own conceptions and supposition with observed
facts under all aspects, forms the leading employment of the
discoverer: this candid and simple love of truth, which makes him
willing to suppress the most favourite production of his own
ingenuity as soon as it appears to be at variance with realities,
constitutes the first characteristic of his temper. He must have
neither the blindness which cannot, nor the obstinacy which will
not, perceive the discrepancy of his fancies and his facts. He must
allow no indolence, or partial views, or self-complacency, or
delight in seeming demonstration, to make him tenacious of the
schemes which he devises, any further than they are confirmed by
their accordance with nature. The framing of hypotheses is, for the
inquirer after truth, not the end, but the beginning of his work.
Each of his systems is invented, not that he may admire it and
follow it into all its consistent consequences, but that he may make
it the occasion of a course of active experiment and observation.
And if the results of this process {81} contradict his fundamental
assumptions, however ingenious, however symmetrical, however elegant
his system may be, he rejects it without hesitation. He allows no
natural yearning for the offspring of his own mind to draw him aside
from the higher duty of loyalty to his sovereign, Truth: to her he
not only gives his affections and his wishes, but strenuous labour
and scrupulous minuteness of attention.
We may refer to what we have said of Kepler, Newton, and other
eminent philosophers, for illustrations of this character. In Kepler
we have remarked[11\2] the courage and perseverance with which he
undertook and executed the task of computing his own hypotheses:
and, as a still more admirable characteristic, that he never allowed
the labour he had spent upon any conjecture to produce any
reluctance in abandoning the hypothesis, as soon as he had evidence
of its inaccuracy. And in the history of Newton's discovery that the
moon is retained in her orbit by the force of gravity, we have
noticed the same moderation in maintaining the hypothesis, after it
had once occurred to the author's mind. The hypothesis required that
the moon should fall from the tangent of her orbit every second
through a space of sixteen feet; but according to his first
calculations it appeared that in fact she only fell through a space
of thirteen feet in that time. The difference seems small, the
approximation encouraging, the theory plausible; a man in love with
his own fancies would readily have discovered or invented some
probable cause of the difference. But Newton acquiesced in it as a
disproof of his conjecture, and 'laid aside at that time any further
thoughts of this matter[12\2].'
[Note 11\2: _Hist. Ind. Sc._ b. v. c. iv. sect. 1.]
[Note 12\2: _Hist. Ind. Sc._ b. vii. c. ii. sect. 3.]
8. It has often happened that those who have undertaken to instruct
mankind have not possessed this pure love of truth and comparative
indifference to the maintenance of their own inventions. Men have
frequently adhered with great tenacity and vehemence to the
hypotheses which they have once framed; and in their {82} affection
for these, have been prone to overlook, to distort, and to
misinterpret facts. In this manner, _Hypotheses_ have so often been
prejudicial to the genuine pursuit of truth, that they have fallen
into a kind of obloquy; and have been considered as dangerous
temptations and fallacious guides. Many warnings have been uttered
against the fabrication of hypotheses, by those who profess to teach
philosophy; many disclaimers of such a course by those who cultivate
science.
Thus we shall find Bacon frequently discommending this habit, under
the name of 'anticipation of the mind,' and Newton thinks it
necessary to say emphatically 'hypotheses non fingo.' It has been
constantly urged that the inductions by which sciences are formed
must be _cautious_ and _rigorous_; and the various imaginations
which passed through Kepler's brain, and to which he has given
utterance, have been blamed or pitied, as lamentable instances of an
unphilosophical frame of mind. Yet it has appeared in the preceding
remarks that hypotheses rightly used are among the helps, far more
than the dangers, of science;--that scientific induction is not a
'cautious' or a 'rigorous' process in the sense of _abstaining from_
such suppositions, but in _not adhering_ to them till they are
confirmed by fact, and in carefully seeking from facts confirmation
or refutation. Kepler's distinctive character was, not that he was
peculiarly given to the construction of hypotheses, but that he
narrated with extraordinary copiousness and candour the course of
his thoughts, his labours, and his feelings. In the minds of most
persons, as we have said, the inadmissible suppositions, when
rejected, are soon forgotten: and thus the trace of them vanishes
from the thoughts, and the successful hypothesis alone holds its
place in our memory. But in reality, many other transient
suppositions must have been made by all discoverers;--hypotheses
which are not afterwards asserted as true systems, but entertained
for an instant;--'tentative hypotheses,' as they have been called.
Each of these hypotheses is followed by its corresponding train of
observations, from which it derives its power of leading to truth.
The hypothesis is {83} like the captain, and the observations like
the soldiers of an army: while he appears to command them, and in
this way to work his own will, he does in fact derive all his power
of conquest from their obedience, and becomes helpless and useless
if they mutiny.
Since the discoverer has thus constantly to work his way onwards by
means of hypotheses, false and true, it is highly important for him
to possess talents and means for rapidly _testing_ each supposition as
it offers itself. In this as in other parts of the work of
discovery, success has in general been mainly owing to the native
ingenuity and sagacity of the discoverer's mind. Yet some Rules
tending to further this object have been delivered by eminent
philosophers, and some others may perhaps be suggested. Of these we
shall here notice only some of the most general, leaving for a
future chapter the consideration of some more limited and detailed
processes by which, in certain cases, the discovery of the laws of
nature may be materially assisted.
SECT. III.--_Tests of Hypotheses._
9. A maxim which it may be useful to recollect is this;--that
_hypotheses may often be of service to science, when they involve a
certain portion of incompleteness, and even of errour_. The object
of such inventions is to bind together facts which without them are
loose and detached; and if they do this, they may lead the way to a
perception of the true rule by which the phenomena are associated
together, even if they themselves somewhat misstate the matter. The
imagined arrangement enables us to contemplate, as a whole, a
collection of special cases which perplex and overload our minds
when they are considered in succession; and if our scheme has so
much of truth in it as to conjoin what is really connected, we may
afterwards duly correct or limit the mechanism of this connexion. If
our hypothesis renders a reason for the agreement of cases really
similar, we may afterwards find this reason to be {84} false, but we
shall be able to translate it into the language of truth.
A conspicuous example of such an hypothesis,--one which was of the
highest value to science, though very incomplete, and as a
representation of nature altogether false,--is seen in the _Doctrine
of epicycles_ by which the ancient astronomers explained the motions
of the sun, moon, and planets. This doctrine connected the places
and velocities of these bodies at particular times in a manner which
was, in its general features, agreeable to nature. Yet this doctrine
was erroneous in its assertion of the _circular_ nature of all the
celestial motions, and in making the heavenly bodies revolve _round
the earth_. It was, however, of immense value to the progress of
astronomical science; for it enabled men to express and reason upon
many important truths which they discovered respecting the motion of
the stars, up to the time of Kepler. Indeed we can hardly imagine
that astronomy could, in its outset, have made so great a progress
under any other form, as it did in consequence of being cultivated
in this shape of the incomplete and false _epicyclical hypothesis_.
We may notice another instance of an exploded hypothesis, which is
generally mentioned only to be ridiculed, and which undoubtedly is
both false in the extent of its assertion, and unphilosophical in
its expression; but which still, in its day, was not without merit.
I mean the doctrine of _Nature's horrour of a vacuum_ (_fuga
vacui_), by which the action of siphons and pumps and many other
phenomena were explained, till Mersenne and Pascal taught a truer
doctrine. This hypothesis was of real service; for it brought
together many facts which really belong to the same class, although
they are very different in their first aspect. A scientific writer
of modern times[13\2] appears to wonder that men did not at once
divine the weight of the air, from which the phenomena formerly
ascribed to the _fuga vacui_ really result. 'Loaded, {85} compressed
by the atmosphere,' he says, 'they did not recognize its action. In
vain all nature testified that air was elastic and heavy; they shut
their eyes to her testimony. The water rose in pumps and flowed in
siphons at that time, as it does at this day. They could not
separate the boards of a pair of bellows of which the holes were
stopped; and they could not bring together the same boards without
difficulty, if they were at first separated. Infants sucked the milk
of their mothers; air entered rapidly into the lungs of animals at
every inspiration; cupping-glasses produced tumours on the skin; and
in spite of all these striking proofs of the weight and elasticity
of the air, the ancient philosophers maintained resolutely that air
was light, and explained all these phenomena by the horrour which
they said nature had for a vacuum.' It is curious that it should not
have occurred to the author while writing this, that if these facts,
so numerous and various, can all be accounted for by _one_
principle, there is a strong presumption that the principle is not
altogether baseless. And in reality is it not true that nature _does_
abhor a vacuum, and does all she can to avoid it? No doubt this
power is not unlimited; and moreover we can trace it to a mechanical
cause, the pressure of the circumambient air. But the tendency,
arising from this pressure, which the bodies surrounding a space
void of air have to rush into it, may be expressed, in no
extravagant or unintelligible manner, by saying that nature has a
repugnance to a vacuum.
[Note 13\2: Deluc, _Modifications de l'Atmosphère_, Partie 1.]
That imperfect and false hypotheses, though they may thus explain
_some_ phenomena, and may be useful in the progress of science,
cannot explain _all_ phenomena;--and that we are never to rest in
our labours or acquiesce in our results, till we have found some
view of the subject which _is_ consistent with _all_ the observed
facts;--will of course be understood. We shall afterwards have to
speak of the other steps of such a progress.
10. Thus the hypotheses which we accept ought to explain phenomena
which we have observed. But they {86} ought to do more than this:
our hypotheses ought to _foretel_ phenomena which have not yet been
observed; at least all phenomena of the same kind as those which the
hypothesis was invented to explain. For our assent to the hypothesis
implies that it is held to be true of all particular instances. That
these cases belong to past or to future times, that they have or
have not already occurred, makes no difference in the applicability
of the rule to them. Because the rule prevails, it includes all
cases; and will determine them all, if we can only calculate its
real consequences. Hence it will predict the results of new
combinations, as well as explain the appearances which have occurred
in old ones. And that it does this with certainty and correctness,
is one mode in which the hypothesis is to be verified as right and
useful.
The scientific doctrines which have at various periods been
established have been verified in this manner. For example, the
_Epicyclical Theory_ of the heavens was confirmed by its
_predicting_ truly eclipses of the sun and moon, configurations of
the planets, and other celestial phenomena; and by its leading to
the construction of Tables by which the places of the heavenly
bodies were given at every moment of time. The truth and accuracy of
these predictions were a proof that the hypothesis was valuable,
and, at least to a great extent, true; although, as was afterwards
found, it involved a false representation of the structure of the
heavens. In like manner, the discovery of the _Laws of Refraction_
enabled mathematicians to _predict_, by calculation, what would be
the effect of any new form or combination of transparent lenses.
Newton's hypothesis of _Fits of Easy Transmission and Easy
Reflection_ in the particles of light, although not confirmed by
other kinds of facts, involved a true statement of the law of the
phenomena which it was framed to include, and served to _predict_
the forms and colours of thin plates for a wide range of given
cases. The hypothesis that Light operates by _Undulations_ and
_Interferences_, afforded the means of _predicting_ results under a
still larger extent of conditions. In like manner in the {87}
progress of chemical knowledge, the doctrine of _Phlogiston_
supplied the means of _foreseeing_ the consequence of many
combinations of elements, even before they were tried; but the
_Oxygen Theory_, besides affording predictions, at least equally
exact, with regard to the general results of chemical operations,
included all the facts concerning the relations of weight of the
elements and their compounds, and enabled chemists to _foresee_ such
facts in untried cases. And the Theory of _Electromagnetic Forces_,
as soon as it was rightly understood, enabled those who had mastered
it to _predict_ motions such as had not been before observed, which
were accordingly found to take place.
Men cannot help believing that the laws laid down by discoverers
must be in a great measure identical with the real laws of nature,
when the discoverers thus determine effects beforehand in the same
manner in which nature herself determines them when the occasion
occurs. Those who can do this, must, to a considerable extent, have
detected nature's secret;--must have fixed upon the conditions to
which she attends, and must have seized the rules by which she
applies them. Such a coincidence of untried facts with speculative
assertions cannot be the work of chance, but implies some large
portion of truth in the principles on which the reasoning is
founded. To trace order and law in that which has been observed, may
be considered as interpreting what nature has written down for us,
and will commonly prove that we understand her alphabet. But to
predict what has not been observed, is to attempt ourselves to use
the legislative phrases of nature; and when she responds plainly and
precisely to that which we thus utter, we cannot but suppose that we
have in a great measure made ourselves masters of the meaning and
structure of her language. The prediction of results, even of the
same kind as those which have been observed, in new cases, is a
proof of real success in our inductive processes.
11. We have here spoken of the prediction of facts _of the same
kind_ as those from which our rule was collected. But the evidence
in favour of our {88} induction is of a much higher and more
forcible character when it enables us to explain and determine cases
of a _kind different_ from those which were contemplated in the
formation of our hypothesis. The instances in which this has
occurred, indeed, impress us with a conviction that the truth of our
hypothesis is certain. No accident could give rise to such an
extraordinary coincidence. No false supposition could, after being
adjusted to one class of phenomena, exactly represent a different
class, where the agreement was unforeseen and uncontemplated. That
rules springing from remote and unconnected quarters should thus
leap to the same point, can only arise from _that_ being the point
where truth resides.
Accordingly the cases in which inductions from classes of facts
altogether different have thus _jumped together_, belong only to the
best established theories which the history of science contains. And
as I shall have occasion to refer to this peculiar feature in their
evidence, I will take the liberty of describing it by a particular
phrase; and will term it the _Consilience of Inductions_.
It is exemplified principally in some of the greatest discoveries.
Thus it was found by Newton that the doctrine of the Attraction of
the Sun varying according to the Inverse Square of this distance,
which explained Kepler's _Third Law_, of the proportionality of the
cubes of the distances to the squares of the periodic times of the
planets, explained also his _First_ and _Second Laws_, of the
elliptical motion of each planet; although no connexion of these
laws had been visible before. Again, it appeared that the force of
universal Gravitation, which had been inferred from the
_Perturbations_ of the moon and planets by the sun and by each
other, also accounted for the fact, apparently altogether dissimilar
and remote, of the _Precession of the equinoxes_. Here was a most
striking and surprising coincidence, which gave to the theory a
stamp of truth beyond the power of ingenuity to counterfeit. In like
manner in Optics; the hypothesis of alternate Fits of easy
Transmission and Reflection would explain {89} the colours of thin
plates, and indeed was devised and adjusted for that very purpose;
but it could give no account of the phenomena of the fringes of
shadows. But the doctrine of Interferences, constructed at first
with reference to phenomena of the nature of the _Fringes_,
explained also the _Colours of thin plates_ better than the
supposition of the Fits invented for that very purpose. And we have
in Physical Optics another example of the same kind, which is quite
as striking as the explanation of Precession by inferences from the
facts of Perturbation. The doctrine of Undulations propagated in a
Spheroidal Form was contrived at first by Huyghens, with a view to
explain the laws of _Double Refraction_ in calc-spar; and was
pursued with the same view by Fresnel. But in the course of the
investigation it appeared, in a most unexpected and wonderful
manner, that this same doctrine of spheroidal undulations, when it
was so modified as to account for the _directions_ of the two
refracted rays, accounted also for the positions of their _Planes of
Polarization_[14\2], a phenomenon which, taken by itself, it had
perplexed previous mathematicians, even to represent.
[Note 14\2: _Hist. Ind. Sc._ b. ix. c. xi. sect. 4.]
The Theory of Universal Gravitation, and of the Undulatory Theory of
Light, are, indeed, full of examples of this Consilience of
Inductions. With regard to the latter, it has been justly asserted
by Herschel, that the history of the undulatory theory was a
succession of _felicities_[15\2]. And it is precisely the unexpected
coincidences of results drawn from distant parts of the subject
which are properly thus described. Thus the Laws of the
_Modification of polarization_ to which Fresnel was led by his
general views, accounted for the Rule respecting the _Angle at which
light is polarized_, discovered by Sir D. Brewster[16\2]. The
conceptions of the theory pointed out peculiar _Modifications_ of
the phenomena when _Newton's rings_ were produced by polarised
light, which modifications were {90} ascertained to take place in
fact, by Arago and Airy[17\2]. When the beautiful phenomena of
_Dipolarized light_ were discovered by Arago and Biot, Young was
able to declare that they were reducible to the general laws of
_Interference_ which he had already established[18\2]. And what was no
less striking a confirmation of the truth of the theory, _Measures_
of the same element deduced from various classes of facts were found
to coincide. Thus the _Length_ of a luminiferous undulation,
calculated by Young from the measurement of _Fringes_ of shadows,
was found to agree very nearly with the previous calculation from
the colours of _Thin plates_[19\2].
[Note 15\2: See _Hist. Ind. Sc._ b. ix. c. xii.]
[Note 16\2: _Ib._ c. xi. sect. 4.]
[Note 17\2: See _Hist. Ind. Sc._ b. ix. c. xiii. sect. 6.]
[Note 18\2: _Ib._ c. xi. sect. 5.]
[Note 19\2: _Ib._ c. xi. sect. 2.]
No example can be pointed out, in the whole history of science, so
far as I am aware, in which this Consilience of Inductions has given
testimony in favour of an hypothesis afterwards discovered to be
false. If we take one class of facts only, knowing the law which
they follow, we may construct an hypothesis, or perhaps several,
which may represent them: and as new circumstances are discovered,
we may often adjust the hypothesis so as to correspond to these
also. But when the hypothesis, of itself and without adjustment for
the purpose, gives us the rule and reason of a class of facts not
contemplated in its construction, we have a criterion of its
reality, which has never yet been produced in favour of falsehood.
12. In the preceding Article I have spoken of the hypothesis with
which we compare our facts as being framed _all at once_, each of
its parts being included in the original scheme. In reality,
however, it often happens that the various suppositions which our
system contains are _added_ upon occasion of different researches.
Thus in the Ptolemaic doctrine of the heavens, new epicycles and
eccentrics were added as new inequalities of the motions of the
heavenly bodies were discovered; and in the Newtonian doctrine of
material rays of light, the supposition that these rays had {91}
'fits,' was added to explain the colours of thin plates; and the
supposition that they had 'sides' was introduced on occasion of the
phenomena of polarization. In like manner other theories have been
built up of parts devised at different times.
This being the mode in which theories are often framed, we have to
notice a distinction which is found to prevail in the progress of
true and false theories. In the former class all the additional
suppositions _tend to simplicity_ and harmony; the new suppositions
resolve themselves into the old ones, or at least require only some
easy modification of the hypothesis first assumed: the system
becomes more coherent as it is further extended. The elements which
we require for explaining a new class of facts are already contained
in our system. Different members of the theory run together, and we
have thus a constant convergence to unity. In false theories, the
contrary is the case. The new suppositions are something altogether
additional;--not suggested by the original scheme; perhaps difficult
to reconcile with it. Every such addition adds to the complexity of
the hypothetical system, which at last becomes unmanageable, and is
compelled to surrender its place to some simpler explanation.
Such a false theory, for example, was the ancient doctrine of
eccentrics and epicycles. It explained the general succession of the
Places of the Sun, Moon, and Planets; it would not have explained
the proportion of their Magnitudes at different times, if these
could have been accurately observed; but this the ancient
astronomers were unable to do. When, however, Tycho and other
astronomers came to be able to observe the planets accurately in all
positions, it was found that _no_ combination of _equable_ circular
motions would exactly represent all the observations. We may see, in
Kepler's works, the many new modifications of the epicyclical
hypothesis which offered themselves to him; some of which would have
agreed with the phenomena with a certain degree of accuracy, but not
with so great a degree as Kepler, fortunately for the progress of
science, insisted upon obtaining. After these {92} epicycles had
been thus accumulated, they all disappeared and gave way to the
simpler conception of an _elliptical_ motion. In like manner, the
discovery of new inequalities in the Moon's motions encumbered her
system more and more with new machinery, which was at last rejected
all at once in favour of the _elliptical_ theory. Astronomers could
not but suppose themselves in a wrong path, when the prospect grew
darker and more entangled at every step.
Again; the Cartesian system of Vortices might be said to explain the
primary phenomena of the revolutions of planets about the sun, and
satellites about planets. But the elliptical form of the orbits
required new suppositions. Bernoulli ascribed this curve to the
shape of the planet, operating on the stream of the vortex in a
manner similar to the rudder of a boat. But then the motions of the
aphelia, and of the nodes,--the perturbations,--even the action of
gravity towards the earth,--could not be accounted for without new
and independent suppositions. Here was none of the simplicity of
truth. The theory of Gravitation, on the other hand, became more
simple as the facts to be explained became more numerous. The
attraction of the sun accounted for the motions of the planets; the
attraction of the planets was the cause of the motion of the
satellites. But this being assumed, the perturbations, and the
motions of the nodes and aphelia, only made it requisite to extend
the attraction of the sun to the satellites, and that of the planets
to each other:--the tides, the spheroidal form of the earth, the
precession, still required nothing more than that the moon and sun
should attract the parts of the earth, and that these should attract
each other;--so that all the suppositions resolved themselves into
the single one, of the universal gravitation of all matter. It is
difficult to imagine a more convincing manifestation of simplicity
and unity.
Again, to take an example from another science;--the doctrine of
Phlogiston brought together many facts in a very plausible
manner,--combustion, acidification, and others,--and very naturally
prevailed for a while. {93} But the balance came to be used in
chemical operations, and the facts of weight as well as of
combination were to be accounted for. On the phlogistic theory, it
appeared that this could not be done without a new supposition, and
_that_, a very strange one;--that phlogiston was an element not only
not heavy, but absolutely light, so that it diminished the weight of
the compounds into which it entered. Some chemists for a time
adopted this extravagant view, but the wiser of them saw, in the
necessity of such a supposition to the defence of the theory, an
evidence that the hypothesis of an element _phlogiston_ was
erroneous. And the opposite hypothesis, which taught that oxygen was
subtracted, and not phlogiston added, was accepted because it
required no such novel and inadmissible assumption.
Again, we find the same evidence of truth in the progress of the
Undulatory Theory of light, in the course of its application from
one class of facts to another. Thus we explain Reflection and
Refraction by undulations; when we come to Thin Plates, the
requisite 'fits' are already involved in our fundamental hypothesis,
for they are the length of an undulation: the phenomena of
Diffraction also require such intervals; and the intervals thus
required agree exactly with the others in magnitude, so that no new
property is needed. Polarization for a moment appears to require
some new hypothesis; yet this is hardly the case; for the direction
of our vibrations is hitherto arbitrary:--we allow polarization to
decide it, and we suppose the undulations to be transverse. Having
done this for the sake of Polarization, we turn to the phenomena of
Double Refraction, and inquire what new hypothesis they require. But
the answer is, that they require none: the supposition of transverse
vibrations, which we have made in order to explain Polarization,
gives us also the law of Double Refraction. Truth may give rise to
such a coincidence; falsehood cannot. Again, the facts of
Dipolarization come into view. But they hardly require any new
assumption; for the difference of optical elasticity of crystals in
different directions, {94} which is already assumed in uniaxal
crystals[20\2], is extended to biaxal exactly according to the law
of symmetry; and this being done, the laws of the phenomena, curious
and complex as they are, are fully explained. The phenomena of
Circular Polarization by internal reflection, instead of requiring a
new hypothesis, are found to be given by an interpretation of an
apparently inexplicable result of an old hypothesis. The Circular
Polarization of Quartz and the Double Refraction does indeed appear
to require a new assumption, but still not one which at all disturbs
the form of the theory; and in short, the whole history of this
theory is a progress, constant and steady, often striking and
startling, from one degree of evidence and consistence to another of
a higher order.
[Note 20\2: _Hist. Ind. Sc._ b. ix. c. xi. sect. 5.]
In the Emission Theory, on the other hand, as in the theory of solid
epicycles, we see what we may consider as the natural course of
things in the career of a false theory. Such a theory may, to a
certain extent, explain the phenomena which it was at first
contrived to meet; but every new class of facts requires a new
supposition--an addition to the machinery: and as observation goes
on, these incoherent appendages accumulate, till they overwhelm and
upset the original frame-work. Such has been the hypothesis of the
Material Emission of light. In its original form, it explained
Reflection and Refraction: but the colours of Thin Plates added to
it the Fits of easy Transmission and Reflection; the phenomena of
Diffraction further invested the emitted particles with complex laws
of Attraction and Repulsion; Polarization gave them Sides: Double
Refraction subjected them to peculiar Forces emanating from the axes
of the crystal: Finally, Dipolarization loaded them with the complex
and unconnected contrivance of Moveable Polarization: and even when
all this had been done, additional mechanism was wanting. There is
here no unexpected success, no happy coincidence, no convergence of
principles from remote quarters. The philosopher builds {95} the
machine, but its parts do not fit. They hold together only while he
presses them. This is not the character of truth.
As another example of the application of the Maxim now under
consideration, I may perhaps be allowed to refer to the judgment
which, in the History of Thermotics, I have ventured to give
respecting Laplace's Theory of Gases. I have stated[21\2], that we
cannot help forming an unfavourable judgment of this theory, by
looking for that great characteristic of true theory; namely, that
the hypotheses which were assumed to account for _one class_ of
facts are found to explain _another class_ of a different nature.
Thus Laplace's first suppositions explain the connexion of
Compression with Density, (the law of Boyle and Mariotte,) and the
connexion of Elasticity with Heat, (the law of Dalton and Gay
Lussac). But the theory requires other assumptions when we come to
Latent Heat; and yet these new assumptions produce no effect upon
the calculations in any application of the theory. When the
hypothesis, constructed with reference to the Elasticity and
Temperature, is applied to another class of facts, those of Latent
Heat, we have no Simplification of the Hypothesis, and therefore no
evidence of the truth of the theory.
[Note 21\2: _Hist. Ind. Sc._ b. x. c. iv.]
13. The last two sections of this chapter direct our attention to
two circumstances, which tend to prove, in a manner which we may
term irresistible, the truth of the theories which they
characterize:--the _Consilience of Inductions_ from different and
separate classes of facts;--and the progressive _Simplification of
the Theory_ as it is extended to new cases. These two Characters
are, in fact, hardly different; they are exemplified by the same
cases. For if these Inductions, collected from one class of facts,
supply an unexpected explanation of a new class, which is the case
first spoken of, there will be no need for new machinery in the
hypothesis to apply it to the newly-contemplated facts; and thus, we
have a case in which the system does not become {96} more complex
when its application is extended to a wider field, which was the
character of true theory in its second aspect. The Consiliences of
our Inductions give rise to a constant Convergence of our Theory
towards Simplicity and Unity.
But, moreover, both these cases of the extension of the theory,
without difficulty or new suppositions, to a wider range and to new
classes of phenomena, may be conveniently considered in yet another
point of view; namely, as successive steps by which we gradually
ascend in our speculative views to a higher and higher point of
generality. For when the theory, either by the concurrence of two
indications, or by an extension without complication, has included a
new range of phenomena, we have, in fact, a new induction of a more
general kind, to which the inductions formerly obtained are
subordinate, as particular cases to a general proposition. We have
in such examples, in short, an instance of _successive
generalization_. This is a subject of great importance, and
deserving of being well illustrated; it will come under our notice
in the next chapter.
{{97}}
CHAPTER VI.
OF THE LOGIC OF INDUCTION.
APHORISM XVII.
_The_ Logic of Induction _consists in stating the Facts and the
Inference in such a manner, that the Evidence of the Inference is
manifest: just as the Logic of Deduction consists in stating the
Premises and the Conclusion in such a manner that the Evidence of
the Conclusion is manifest._
APHORISM XVIII.
_The Logic of Deduction is exhibited by means of a certain Formula;
namely, a Syllogism; and every train of deductive reasoning, to be
demonstrative, must be capable of resolution into a series of such
Formulæ legitimately constructed. In like manner, the Logic of
Induction may be exhibited by means of certain_ Formulæ; _and every
train of inductive inference to be sound, must be capable of
resolution into a scheme of such Formulæ, legitimately constructed._
APHORISM XIX.
_The_ inductive act of thought _by which several Facts are
colligated into one Proposition, may be expressed by saying:_ The
several Facts are exactly expressed as one Fact, if, and only if, we
adopt the Conceptions and the Assertion _of the Proposition._
APHORISM XX.
_The One Fact, thus inductively obtained from several Facts, may be
combined with other Facts, and colligated with them by a new act of
Induction. This process may be_ {98} _indefinitely repeated: and
these successive processes are the_ Steps _of Induction, or of_
Generalization, _from the lowest to the highest._
APHORISM XXI.
_The relation of the successive Steps of Induction may be exhibited
by means of an_ Inductive Table, _in which the several Facts are
indicated, and tied together by a Bracket, and the Inductive
Inference placed on the other side of the Bracket; and this
arrangement repeated, so as to form a genealogical Table of each
Induction, from the lowest to the highest._
APHORISM XXII.
_The Logic of Induction is the_ Criterion of Truth _inferred from
Facts, as the Logic of Deduction is the Criterion of Truth deduced
from necessary Principles. The Inductive Table enables us to apply
such a Criterion; for we can determine whether each Induction is
verified and justified by the Facts which its Bracket includes; and
if each induction in particular be sound, the highest, which merely
combines them all, must necessarily be sound also._
APHORISM XXIII.
_The distinction of_ Fact _and_ Theory _is only relative. Events and
phenomena, considered as Particulars which may be colligated by
Induction, are_ Facts; _considered as Generalities already obtained
by colligation of other Facts, they are_ Theories. _The same event
or phenomenon is a Fact or a Theory, according as it is considered
as standing on one side or the other of the Inductive Bracket._
1. THE subject to which the present chapter refers is described by
phrases which are at the present day familiarly used in speaking of
the progress of knowledge. We hear very frequent mention of
_ascending from particular to general_ propositions, and from these
to propositions still more general;--of {99} truths _included_ in
other truths of a higher degree of generality;--of different _stages
of generalization_;--and of the _highest step_ of the process of
discovery, to which all others are subordinate and preparatory. As
these expressions, so familiar to our ears, especially since the
time of Francis Bacon, denote, very significantly, processes and
relations which are of great importance in the formation of science,
it is necessary for us to give a clear account of them, illustrated
with general exemplifications; and this we shall endeavour to do.
We have, indeed, already explained that science consists of
Propositions which include the Facts from which they were collected;
and other wider Propositions, collected in like manner from the
former, and including them. Thus, that the stars, the moon, the sun,
rise, culminate, and set, are facts _included_ in the proposition
that the heavens, carrying with them all the celestial bodies, have
a diurnal revolution about the axis of the earth. Again, the
observed monthly motions of the moon, and the annual motions of the
sun, are _included_ in certain propositions concerning the movements
of those luminaries with respect to the stars. But all these
propositions are really _included_ in the doctrine that the earth,
revolving on its axis, moves round the sun, and the moon round the
earth. These movements, again, considered as facts, are explained
and _included_ in the statement of the forces which the earth exerts
upon the moon, and the sun upon the earth. Again, this doctrine of
the forces of these three bodies is _included_ in the assertion,
that all the bodies of the solar system, and all parts of matter,
exert forces, each upon each. And we might easily show that all the
leading facts in astronomy are comprehended in the same
generalization. In like manner with regard to any other science, so
far as its truths have been well established and fully developed, we
might show that it consists of a gradation of propositions,
proceeding from the most special facts to the most general
theoretical assertions. We shall exhibit this gradation in some of
the principal branches of science. {100}
2. This gradation of truths, successively included in other truths,
may be conveniently represented by Tables resembling the
genealogical tables by which the derivation of descendants from a
common ancestor is exhibited; except that it is proper in this case
to invert the form of the Table, and to make it converge to unity
downwards instead of upwards, since it has for its purpose to
express, not the derivation of many from one, but the collection of
one truth from many things. Two or more co-ordinate facts or
propositions may be ranged side by side, and joined by some mark of
connexion, (a bracket, as ⏟ or ⎵,) beneath which may be placed the
more general proposition which is collected by induction from the
former. Again, propositions co-ordinate with this more general one
may be placed on a level with it; and the combination of these, and
the result of the combination, may be indicated by brackets in the
same manner; and so on, through any number of gradations. By this
means the streams of knowledge from various classes of facts will
constantly run together into a smaller and smaller number of
channels; like the confluent rivulets of a great river, coming
together from many sources, uniting their ramifications so as to
form larger branches, these again uniting in a single trunk. The
_genealogical tree_ of each great portion of science, thus formed,
will contain all the leading truths of the science arranged in their
due co-ordination and subordination. Such Tables, constructed for
the sciences of Astronomy and of Optics, will be given at the end of
this chapter.
3. The union of co-ordinate propositions into a proposition of a
higher order, which occurs in this Tree of Science wherever two
twigs unite in one branch, is, in each case, an example of
_Induction_. The single proposition is collected by the process of
induction from its several members. But here we may observe, that
the image of a mere _union_ of the parts at each of these points,
which the figure of a tree or a river presents, is very inadequate
to convey the true state of the case; for in Induction, as we have
seen, besides mere collection of particulars, there is always a _new
conception_, a {101} principle of connexion and unity, supplied by
the mind, and superinduced upon the particulars. There is not merely
a juxta-position of materials, by which the new proposition contains
all that its component parts contained; but also a formative act
exerted by the understanding, so that these materials are contained
in a new shape. We must remember, therefore, that our Inductive
Tables, although they represent the elements and the order of these
inductive steps, do not fully represent the whole signification of
the process in each case.
4. The principal features of the progress of science spoken of in
the last chapter are clearly exhibited in these Tables; namely, the
_Consilience of Inductions_ and the constant Tendency to Simplicity
observable in true theories. Indeed in all cases in which, from
propositions of considerable generality, propositions of a still
higher degree are obtained, there is a convergence of inductions;
and if in one of the lines which thus converge, the steps be rapidly
and suddenly made in order to meet the other line, we may consider
that we have an example of Consilience. Thus when Newton had
collected, from Kepler's Laws, the Central Force of the sun, and
from these, combined with other facts, the Universal Force of all
the heavenly bodies, he suddenly turned round to include in his
generalization the Precession of the Equinoxes, which he declared to
arise from the attraction of the sun and moon upon the protuberant
part of the terrestrial spheroid. The apparent remoteness of this
fact, in its nature, from the other facts with which he thus
associated it, causes this part of his reasoning to strike us as a
remarkable example of _Consilience_. Accordingly, in the Table of
Astronomy we find that the columns which contain the facts and
theories relative to the _sun_ and _planets_, after exhibiting
several stages of induction within themselves, are at length
suddenly connected with a column till then quite distinct,
containing the _precession of the equinoxes_. In like manner, in the
Table of Optics, the columns which contain the facts and theories
relative to _double refraction_, and those which {102} include
_polarization by crystals_, each go separately through several
stages of induction; and then these two sets of columns are suddenly
connected by Fresnel's mathematical induction, that double
refraction and polarization arise from the same cause: thus
exhibiting a remarkable _Consilience_.
5. The constant _Tendency to Simplicity_ in the sciences of which the
progress is thus represented, appears from the form of the Table
itself; for the single trunk into which all the branches converge,
contains in itself the substance of all the propositions by means of
which this last generalization was arrived at. It is true, that this
ultimate result is sometimes not so simple as in the Table it
appears: for instance, the ultimate generalization of the Table
exhibiting the progress of Physical Optics,--namely, that Light
consists in Undulations,--must be understood as including some other
hypotheses; as, that the undulations are transverse, that the ether
through which they are propagated has its elasticity in crystals and
other transparent bodies regulated by certain laws; and the like.
Yet still, even acknowledging all the complication thus implied, the
Table in question evidences clearly enough the constant advance
towards unity, consistency, and simplicity, which have marked the
progress of this Theory. The same is the case in the Inductive Table
of Astronomy in a still greater degree.
6. These Tables naturally afford the opportunity of assigning to
each of the distinct steps of which the progress of science
consists, the name of the _Discoverer_ to whom it is due. Every one
of the inductive processes which the brackets of our Tables mark,
directs our attention to some person by whom the induction was first
distinctly made. These names I have endeavoured to put in their due
places in the Tables; and the Inductive Tree of our knowledge in
each science becomes, in this way, an exhibition of the claims of
each discoverer to distinction, and, as it were, a Genealogical Tree
of scientific nobility. It is by no means pretended that such a tree
includes the {103} names of all the meritorious labourers in each
department of science. Many persons are most usefully employed in
collecting and verifying truths, who do not advance to any new
truths. The labours of a number of such are included in each stage
of our ascent. But such Tables as we have now before us will present
to us the names of all the most eminent discoverers: for the main
steps of which the progress of science consists, are transitions
from more particular to more general truths, and must therefore be
rightly given by these Tables; and those must be the greatest names
in science to whom the principal events of its advance are thus due.
7. The Tables, as we have presented them, exhibit the course by
which we pass from Particular to General through various gradations,
and so to the most general. They display the order of _discovery_.
But by reading them in an inverted manner, beginning at the single
comprehensive truths with which the Tables end, and tracing these
back into the more partial truths, and these again into special
facts, they answer another purpose;--they exhibit the process of
_verification_ of discoveries once made. For each of our general
propositions is true in virtue of the truth of the narrower
propositions which it involves; and we cannot satisfy ourselves of
its truth in any other way than by ascertaining that these its
constituent elements are true. To assure ourselves that the sun
attracts the planets with forces varying inversely as the square of
the distance, we must analyse by geometry the motion of a body in an
ellipse about the focus, so as to see that such a motion does imply
such a force. We must also verify those calculations by which the
observed places of each planet are stated to be included in an
ellipse. These calculations involve assumptions respecting the path
which the earth describes about the sun, which assumptions must
again be verified by reference to observation. And thus, proceeding
from step to step, we resolve the most general truths into their
constituent parts; and these again into their parts; and by testing,
at each step, both the reality of the asserted ingredients and the
propriety {104} of the conjunction, we establish the whole system of
truths, however wide and various it may be.
8. It is a very great advantage, in such a mode of exhibiting
scientific truths, that it resolves the verification of the most
complex and comprehensive theories, into a number of small steps, of
which almost any one falls within the reach of common talents and
industry. That _if_ the particulars of any one step be true, the
generalization also is true, any person with a mind properly
disciplined may satisfy himself by a little study. That each of
these particular propositions _is_ true, may be ascertained, by the
same kind of attention, when this proposition is resolved into _its_
constituent and more special propositions. And thus we may proceed,
till the most general truth is broken up into small and manageable
portions. Of these portions, each may appear by itself narrow and
easy; and yet they are so woven together, by hypothesis and
conjunction, that the truth of the parts necessarily assures us of
the truth of the whole. The verification is of the same nature as
the verification of a large and complex statement of great sums
received by a mercantile office on various accounts from many
quarters. The statement is separated into certain comprehensive
heads, and these into others less extensive; and these again into
smaller collections of separate articles, each of which can be
inquired into and reported on by separate persons. And thus at last,
the mere addition of numbers performed by these various persons, and
the summation of the results which they obtain, executed by other
accountants, is a complete and entire security that there is no
errour in the whole of the process.
9. This comparison of the process by which we verify scientific
truth to the process of Book-keeping in a large commercial
establishment, may appear to some persons not sufficiently dignified
for the subject. But, in fact, the possibility of giving this formal
and business-like aspect to the evidence of science, as involved in
the process of successive generalization, is an inestimable
advantage. For if no one could pronounce concerning a wide and
profound theory except he who {105} could at once embrace in his
mind the whole range of inference, extending from the special facts
up to the most general principles, none but the greatest geniuses
would be entitled to judge concerning the truth or errour of
scientific discoveries. But, in reality, we seldom need to verify
more than one or two steps of such discoveries at one time; and this
may commonly be done (when the discoveries have been fully
established and developed,) by any one who brings to the task clear
conceptions and steady attention. The progress of science is
gradual: the discoveries which are successively made, are also
verified successively. We have never any very large collections of
them on our hands at once. The doubts and uncertainties of any one
who has studied science with care and perseverance are generally
confined to a few points. If he can satisfy himself upon these, he
has no misgivings respecting the rest of the structure; which has
indeed been repeatedly verified by other persons in like manner. The
fact that science is capable of being resolved into separate
processes of verification, is that which renders it possible to form
a great body of scientific truth, by adding together a vast number
of truths, of which many men, at various times and by multiplied
efforts, have satisfied themselves. The treasury of Science is
constantly rich and abundant, because it accumulates the wealth
which is thus gathered by so many, and reckoned over by so many
more: and the dignity of Knowledge is no more lowered by the
multiplicity of the tasks on which her servants are employed, and
the narrow field of labour to which some confine themselves, than
the rich merchant is degraded by the number of offices which it is
necessary for him to maintain, and the minute articles of which he
requires an exact statement from his accountants.
10. The analysis of doctrines inductively obtained, into their
constituent facts, and the arrangement of them in such a form that
the conclusiveness of the induction may be distinctly seen, may be
termed the _Logic of Induction_. By _Logic_ has generally been meant
a system which teaches us so to arrange our {106} reasonings that
their truth or falsehood shall be evident in their form. In
_deductive_ reasonings, in which the general principles are assumed,
and the question is concerning their application and combination in
particular cases, the device which thus enables us to judge whether
our reasonings are conclusive is the _Syllogism_; and this _form_,
along with the rules which belong to it, does in fact supply us with
a criterion of deductive or demonstrative reasoning. The _Inductive
Table_, such as it is presented in the present chapter, in like
manner supplies the means of ascertaining the truth of our inductive
inferences, so far as the form in which our reasoning may be stated
can afford such a criterion. Of course some care is requisite in
order to reduce a train of demonstration into the form of a series
of syllogisms; and certainly not less thought and attention are
required for resolving all the main doctrines of any great
department of science into a graduated table of co-ordinate and
subordinate inductions. But in each case, when this task is once
executed, the evidence or want of evidence of our conclusions
appears immediately in a most luminous manner. In each step of
induction, our Table enumerates the particular facts, and states the
general theoretical truth which includes these and which these
constitute. The special act of attention by which we satisfy
ourselves that the facts _are_ so included,--that the general truth
_is_ so constituted,--then affords little room for errour, with
moderate attention and clearness of thought.
11. We may find an example of this _act of attention_ thus required,
at any one of the steps of induction in our Tables; for instance, at
the step in the early progress of astronomy at which it was
inferred, that the earth is a globe, and that the sphere of the
heavens (relatively) performs a diurnal revolution round this globe
of the earth. How was this established in the belief of the Greeks,
and how is it fixed in our conviction? As to the globular form, we
find that as we travel to the north, the apparent pole of the
heavenly motions, and the constellations which are near it, seem to
mount higher, and as we proceed southwards they descend. {107}
Again, if we proceed from two different points considerably to the
east and west of each other, and travel directly northwards from
each, as from the south of Spain to the north of Scotland, and from
Greece to Scandinavia, these two north and south lines will be much
nearer to each other in their northern than in their southern parts.
These and similar facts, as soon as they are clearly estimated and
connected in the mind, are _seen to be consistent_ with a convex
surface of the earth, and with no other: and this notion is further
confirmed by observing that the boundary of the earth's shadow upon
the moon is always circular; it being supposed to be already
established that the moon receives her light from the sun, and that
lunar eclipses are caused by the interposition of the earth. As for
the assertion of the (relative) diurnal revolution of the starry
sphere, it is merely putting the visible phenomena in an exact
geometrical form: and thus we establish and verify the doctrine of
the revolution of the sphere of the heavens about the globe of the
earth, by contemplating it so as to see that it does really and
exactly include the particular facts from which it is collected.
We may, in like manner, illustrate this mode of verification by any
of the other steps of the same Table. Thus if we take the great
Induction of Copernicus, the heliocentric scheme of the solar
system, we find it in the Table exhibited as including and
explaining, _first_, the diurnal revolution just spoken of;
_second_, the motions of the moon among the fixed stars; _third_,
the motions of the planets with reference to the fixed stars and the
sun; _fourth_, the motion of the sun in the ecliptic. And the scheme
being clearly conceived, we _see_ that all the particular facts
_are_ faithfully represented by it; and this agreement, along with
the simplicity of the scheme, in which respect it is so far superior
to any other conception of the solar system, persuade us that it is
really the plan of nature.
In exactly the same way, if we attend to any of the several
remarkable discoveries of Newton, which form the principal steps in
the latter part of the Table, as for instance, the proposition that
the sun attracts all {108} the planets with a force which varies
inversely as the square of the distance, we find it proved by its
including three other propositions previously established;--_first_,
that the sun's mean force on different planets follows the specified
variation (which is proved from Kepler's third law); _second_, that
the force by which each planet is acted upon in different parts of
its orbit tends to the sun (which is proved by the equable
description of areas); _third_, that this force in different parts
of the same orbit is also inversely as the square of the distance
(which is proved from the elliptical form of the orbit). And the
Newtonian generalization, when its consequences are mathematically
traced, is _seen_ to agree with each of these particular
propositions, and thus is fully established.
12. But when we say that the more general proposition _includes_ the
several more particular ones, we must recollect what has before been
said, that these particulars form the general truth, not by being
merely enumerated and added together, but by being seen _in a new
light_. No mere verbal recitation of the particulars can decide
whether the general proposition is true; a special act of thought is
requisite in order to determine how truly each is included in the
supposed induction. In this respect the Inductive Table is not like
a mere schedule of accounts, where the rightness of each part of the
reckoning is tested by mere addition of the particulars. On the
contrary, the Inductive truth is never the mere _sum_ of the facts.
It is made into something more by the introduction of a new mental
element; and the mind, in order to be able to supply this element,
must have peculiar endowments and discipline. Thus looking back at
the instances noticed in the last article, how are we to see that a
convex surface of the earth is necessarily implied by the
convergence of meridians towards the north, or by the visible
descent of the north pole of the heavens as we travel south?
Manifestly the student, in order to see this, must have clear
conceptions of the relations of space, either naturally inherent in
his mind, or established there by geometrical cultivation,--by {109}
studying the properties of circles and spheres. When he is so
prepared, he will feel the force of the expressions we have used,
that the facts just mentioned are _seen to be consistent_ with a
globular form of the earth; but without such aptitude he will not
see this consistency: and if this be so, the mere assertion of it in
words will not avail him in satisfying himself of the truth of the
proposition.
In like manner, in order to perceive the force of the Copernican
induction, the student must have his mind so disciplined by
geometrical studies, or otherwise, that he sees clearly how absolute
motion and relative motion would alike produce apparent motion. He
must have learnt to cast away all prejudices arising from the
seeming fixity of the earth; and then he will see that there is
nothing which stands in the way of the induction, while there is
much which is on its side. And in the same manner the Newtonian
induction of the law of the sun's force from the elliptical form of
the orbit, will be evidently satisfactory to him only who has such
an insight into Mechanics as to see that a curvilinear path must
arise from a constantly deflecting force; and who is able to follow
the steps of geometrical reasoning by which, from the properties of
the ellipse, Newton proves this deflection to be in the proportion
in which he asserts the force to be. And thus in all cases the
inductive truth must indeed be verified by comparing it with the
particular facts; but then this comparison is possible for him only
whose mind is properly disciplined and prepared in the use of those
conceptions, which, in addition to the facts, the act of induction
requires.
13. In the Tables some indication is given, at several of the steps,
of the act which the mind must thus perform, besides the mere
conjunction of facts, in order to attain to the inductive truth.
Thus in the cases of the Newtonian inductions just spoken of, the
inferences are stated to be made 'By Mechanics;' and in the case of
the Copernican induction, it is said that, 'By the nature of motion,
the apparent motion is the same, whether the heavens or the earth
have a {110} diurnal motion; and the latter is more simple.' But
these verbal statements are to be understood as mere hints[22\2]:
they cannot supersede the necessity of the student's contemplating
for himself the mechanical principles and the nature of motion thus
referred to.
[Note 22\2: In the Inductive Tables they are marked by an
asterisk.]
14. In the common or Syllogistic Logic, a certain _Formula_ of
language is used in stating the reasoning, and is useful in enabling
us more readily to apply the Criterion of Form to alleged
demonstrations. This formula is the usual Syllogism; with its
members, Major Premiss, Minor Premiss, and Conclusion. It may
naturally be asked whether in Inductive Logic there is any such
Formula? whether there is any standard form of words in which we may
most properly express the inference of a general truth from
particular facts?
At first it might be supposed that the formula of Inductive Logic
need only be of this kind: 'These particulars, and all known
particulars of the same kind, are exactly included in the following
general proposition.' But a moment's reflection on what has just
been said will show us that this is not sufficient: for the
particulars are not merely _included_ in the general proposition. It
is not enough that they appertain to it by enumeration. It is, for
instance, no adequate example of Induction to say, 'Mercury
describes an elliptical path, so does Venus, so do the Earth, Mars,
Jupiter, Saturn, Uranus; therefore all the Planets describe
elliptical paths.' This is, as we have seen, the mode of stating the
_evidence_ when the proposition is once suggested; but the Inductive
step consists in the _suggestion_ of a conception not before
apparent. When Kepler, after trying to connect the observed places
of the planet Mars in many other ways, found at last that the
conception of an _ellipse_ would include them all, he obtained a
truth by induction: for this conclusion was not obviously included
in the phenomena, and had not been applied to these {111} facts
previously. Thus in our Formula, besides stating that the
particulars are included in the general proposition, we must also
imply that the generality is constituted by a new Conception,--new
at least in its application.
Hence our Inductive Formula might be something like the following:
'These particulars, and all known particulars of the same kind, are
exactly expressed by adopting the Conceptions and Statement of the
following Proposition.' It is of course requisite that the
Conceptions should be perfectly clear, and should precisely embrace
the facts, according to the explanation we have already given of
those conditions.
15. It may happen, as we have already stated, that the Explication
of a Conception, by which it acquires its due distinctness, leads to
a Definition, which Definition may be taken as the summary and total
result of the intellectual efforts to which this distinctness is
due. In such cases, the Formula of Induction may be modified
according to this condition; and we may state the inference by
saying, after an enumeration and analysis of the appropriate facts,
'These facts are completely and distinctly expressed by adopting the
following Definition and Proposition.'
This Formula has been adopted in stating the Inductive Propositions
which constitute the basis of the science of Mechanics, in a work
intitled _The Mechanical Euclid_. The fundamental truths of the
subject are expressed in _Inductive Pairs_ of Assertions, consisting
each of a Definition and a Proposition, such as the following:
DEF.--A _Uniform Force_ is that which acting in the direction of the
body's motion, adds or subtracts equal velocities in equal times.
PROP.--Gravity is a Uniform Force.
Again,
DEF.--Two _Motions_ are _compounded_ when each produces its separate
effect in a direction parallel to itself.
PROP.--When any Force acts upon a body in motion, the motion which
the Force would produce in the {112} body at rest is compounded with
the previous motion of the body.
And in like manner in other cases.
In these cases the proposition is, of course, established, and the
definition realized, by an enumeration of the facts. And in the case
of inferences made in such a form, the Definition of the Conception
and the Assertion of the Truth are both requisite and are
correlative to one another. Each of the two steps contains the
verification and justification of the other. The Proposition derives
its meaning from the Definition; the Definition derives its reality
from the Proposition. If they are separated, the Definition is
arbitrary or empty, the Proposition vague or ambiguous.
16. But it must be observed that neither of the preceding Formulæ
expresses the full cogency of the inductive proof. They declare only
that the results can be clearly explained and rigorously deduced by
the employment of a certain Definition and a certain Proposition.
But in order to make the conclusion demonstrative, which in perfect
examples of Induction it is, we ought to be able to declare that the
results can be clearly explained and rigorously declared _only_ by
the Definition and Proposition which we adopt. And in reality, the
conviction of the sound inductive reasoner does reach to this point.
The Mathematician asserts the Laws of Motion, seeing clearly that
they (or laws equivalent to them) afford the only means of clearly
expressing and deducing the actual facts. But this conviction, that
the inductive inference is not only consistent with the facts, but
necessary, finds its place in the mind gradually, as the
contemplation of the consequences of the proposition, and the
various relations of the facts, becomes steady and familiar. It is
scarcely possible for the student at once to satisfy himself that
the inference is thus inevitable. And when he arrives at this
conviction, he sees also, in many cases at least, that there may be
other ways of expressing the substance of the truth established,
besides that special Proposition which he has under his notice.
{113}
We may, therefore, without impropriety, renounce the undertaking of
conveying in our formula this final conviction of the necessary
truth of our inference. We may leave it to be thought, without
insisting upon saying it, that in such cases what _can_ be true,
_is_ true. But if we wish to express the ultimate significance of
the Inductive Act of thought, we may take as our Formula for the
Colligation of Facts by Induction, this:--'The several Facts are
exactly expressed as one Fact if, _and only if_, we adopt the
Conception and the Assertion' of the inductive inference.
17. I have said that the mind must be properly disciplined in order
that it may see the necessary connexion between the facts and the
general proposition in which they are included. And the perception
of this connexion, though treated as _one step_ in our inductive
inference, may imply _many steps_ of demonstrative proof. The
connexion is this, that the particular case is included in the
general one, that is, may be _deduced_ from it: but this deduction
may often require many links of reasoning. Thus in the case of the
inference of the law of the force from the elliptical form of the
orbit by Newton, the proof that in the ellipse the deflection from
the tangent is inversely as the square of the distance from the
focus of the ellipse, is a ratiocination consisting of several
steps, and involving several properties of Conic Sections; these
properties being supposed to be previously established by a
geometrical system of demonstration on the special subject of the
Conic Sections. In this and similar cases the Induction involves
many steps of Deduction. And in such cases, although the Inductive
Step, the Invention of the Conception, is really the most important,
yet since, when once made, it occupies a familiar place in men's
minds; and since the Deductive Demonstration is of considerable
length and requires intellectual effort to follow it at every step;
men often admire the deductive part of the proposition, the
geometrical or algebraical demonstration, far more than that part in
which the philosophical merit really resides. {114}
18. Deductive reasoning is virtually a collection of syllogisms, as
has already been stated: and in such reasoning, the general
principles, the Definitions and Axioms, necessarily stand at the
_beginning_ of the demonstration. In an inductive inference, the
Definitions and Principles are the _final result_ of the reasoning,
the ultimate effect of the proof. Hence when an Inductive
Proposition is to be established by a proof involving several steps
of demonstrative reasoning, the enunciation of the Proposition will
contain, explicitly or implicitly, principles which the
demonstration proceeds upon as axioms, but which are really
inductive inferences. Thus in order to prove that the force which
retains a planet in an ellipse varies inversely as the square of the
distance, it is taken for granted that the Laws of Motion are true,
and that they apply to the planets. Yet the doctrine that this is
so, as well as the law of the force, were established only by this
and the like demonstrations. The doctrine which is the _hypothesis_
of the deductive reasoning, is the _inference_ of the inductive
process. The special facts which are the basis of the inductive
inference, are the conclusion of the train of deduction. And in this
manner the deduction establishes the induction. The principle which
we gather from the facts is true, because the facts can be derived
from it by rigorous demonstration. Induction moves upwards, and
deduction downwards, on the same stair.
But still there is a great difference in the character of their
movements. Deduction descends steadily and methodically, step by
step: Induction mounts by a leap which is out of the reach of
method. She bounds to the top of the stair at once; and then it is
the business of Deduction, by trying each step in order, to
establish the solidity of her companion's footing. Yet these must be
processes of the same mind. The Inductive Intellect makes an
assertion which is subsequently justified by demonstration; and it
shows its sagacity, its peculiar character, by enunciating the
proposition when as yet the demonstration does not {115} exist: but
then it shows that it _is_ sagacity, by also producing the
demonstration.
It has been said that inductive and deductive reasoning are contrary
in their scheme; that in Deduction we infer particular from general
truths; while in Induction we infer general from particular: that
Deduction consists of many steps, in each of which we apply known
general propositions in particular cases; while in Induction we have
a single step, in which we pass from many particular truths to one
general proposition. And this is truly said; but though contrary in
their motions, the two are the operation of the same mind travelling
over the same ground. Deduction is a necessary part of Induction.
Deduction justifies by calculation what Induction had happily
guessed. Induction recognizes the ore of truth by its weight;
Deduction confirms the recognition by chemical analysis. Every step
of Induction must be confirmed by rigorous deductive reasoning,
followed into such detail as the nature and complexity of the
relations (whether of quantity or any other) render requisite. If
not so justified by the supposed discoverer, it is _not_ Induction.
19. Such Tabular arrangements of propositions as we have constructed
may be considered as the _Criterion of Truth_ for the doctrines
which they include. They are the Criterion of Inductive Truth, in
the same sense in which Syllogistic Demonstration is the Criterion
of Necessary Truth,--of the certainty of conclusions, depending upon
evident First Principles. And that such Tables are really a
Criterion of the truth of the propositions which they contain, will
be plain by examining their structure. For if the connexion which
the inductive process assumes be ascertained to be in each case real
and true, the assertion of the general proposition merely collects
together ascertained truths; and in like manner each of those more
particular propositions is true, because it merely expresses
collectively more special facts: so that the most general theory is
only the assertion of a great body of facts, duly classified and
subordinated. When we {116} assert the truth of the Copernican
theory of the motions of the solar system, or of the Newtonian
theory of the forces by which they are caused, we merely assert the
groups of propositions which, in the Table of Astronomical
Induction, are included in these doctrines; and ultimately, we may
consider ourselves as merely asserting at once so many Facts, and
therefore, of course, expressing an indisputable truth.
20. At any one of these steps of Induction in the Table, the
inductive proposition is a _Theory_ with regard to the Facts which
it includes, while it is to be looked upon as a _Fact_ with respect
to the higher generalizations in which it is included. In any other
sense, as was formerly shown, the opposition of _Fact_ and _Theory_
is untenable, and leads to endless perplexity and debate. Is it a
Fact or a Theory that the planet Mars revolves in an Ellipse about
the Sun? To Kepler, employed in endeavouring to combine the separate
observations by the Conception of an Ellipse, it is a Theory; to
Newton, engaged in inferring the law of force from a knowledge of
the elliptical motion, it is a Fact. There are, as we have already
seen, no special attributes of Theory and Fact which distinguish
them from one another. Facts are phenomena apprehended by the aid of
conceptions and mental acts, as Theories also are. We commonly call
our observations _Facts_, when we apply, without effort or
consciousness, conceptions perfectly familiar to us: while we speak
of Theories, when we have previously contemplated the Facts and the
connecting Conception separately, and have made the connexion by a
conscious mental act. The real difference is a difference of
relation; as the same proposition in a demonstration is the
_premiss_ of one syllogism and the _conclusion_ in another;--as the
same person is a father and a son. Propositions are Facts and
Theories, according as they stand above or below the Inductive
Brackets of our Tables.
21. To obviate mistakes I may remark that the terms _higher_ and
_lower_, when used of generalizations, are unavoidably represented
by their opposites in our Inductive Tables. The highest
generalization is that {117} which includes all others; and this
stands the lowest on our page, because, reading downwards, that is
the place which we last reach.
There is a distinction of the knowledge acquired by Scientific
Induction into two kinds, which is so important that we shall
consider it in the succeeding chapter.
{{118}}
CHAPTER VII.
OF LAWS OF PHENOMENA AND OF CAUSES.
APHORISM XXIV.
_Inductive truths are of two kinds_, Laws of Phenomena, _and_
Theories of Causes. _It is necessary to begin in every science with
the Laws of Phenomena; but it is impossible that we should be
satisfied to stop short of a Theory of Causes. In Physical
Astronomy, Physical Optics, Geology, and other sciences, we have
instances showing that we can make a great advance in inquiries
after true Theories of Causes._
1. IN the first attempts at acquiring an exact and connected
knowledge of the appearances and operations which nature presents,
men went no further than to learn _what_ takes place, not _why_ it
occurs. They discovered an Order which the phenomena follow, Rules
which they obey; but they did not come in sight of the Powers by
which these rules are determined, the Causes of which this order is
the effect. Thus, for example, they found that many of the celestial
motions took place as if the sun and stars were carried round by the
revolutions of certain celestial spheres; but what causes kept these
spheres in constant motion, they were never able to explain. In like
manner in modern times, Kepler discovered that the planets describe
ellipses, before Newton explained why they select this particular
curve, and describe it in a particular manner. The laws of
reflection, refraction, dispersion, and other properties of light
have long been known; the causes of these laws are at present under
discussion. And the same might be {119} said of many other sciences.
The discovery of _the Laws of Phenomena_ is, in all cases, the first
step in exact knowledge; these Laws may often for a long period
constitute the whole of our science; and it is always a matter
requiring great talents and great efforts, to advance to a knowledge
of the _Causes_ of the phenomena.
Hence the larger part of our knowledge of nature, at least of the
certain portion of it, consists of the knowledge of the Laws of
Phenomena. In Astronomy indeed, besides knowing the rules which
guide the appearances, and resolving them into the real motions from
which they arise, we can refer these motions to the forces which
produce them. In Optics, we have become acquainted with a vast
number of laws by which varied and beautiful phenomena are governed;
and perhaps we may assume, since the evidence of the Undulatory
Theory has been so fully developed, that we know also the Causes of
the Phenomena. But in a large class of sciences, while we have
learnt many Laws of Phenomena, the causes by which these are
produced are still unknown or disputed. Are we to ascribe to the
operation of a fluid or fluids, and if so, in what manner, the facts
of heat, magnetism, electricity, galvanism? What are the forces by
which the elements of chemical compounds are held together? What are
the forces, of a higher order, as we cannot help believing, by which
the course of vital action in organized bodies is kept up? In these
and other cases, we have extensive departments of science; but we
are as yet unable to trace the effects to their causes; and our
science, so far as it is positive and certain, consists entirely of
the laws of phenomena.
2. In those cases in which we have a division of the science which
teaches us the doctrine of the causes, as well as one which states
the rules which the effects follow, I have, in the _History_,
distinguished the two portions of the science by certain terms. I
have thus spoken of _Formal_ Astronomy and _Physical_ Astronomy. The
latter phrase has long been commonly employed to describe that
department of Astronomy which deals with {120} those forces by which
the heavenly bodies are guided in their motions; the former
adjective appears well suited to describe a collection of rules
depending on those ideas of space, time, position, number, which
are, as we have already said, the _forms_ of our apprehension of
phenomena. The laws of phenomena may be considered as _formulæ_,
expressing results in terms of those ideas. In like manner, I have
spoken of Formal Optics and Physical Optics; the latter division
including all speculations concerning the machinery by which the
effects are produced. Formal Acoustics and Physical Acoustics may be
distinguished in like manner, although these two portions of science
have been a good deal mixed together by most of those who have
treated of them. Formal Thermotics, the knowledge of the laws of the
phenomena of heat, ought in like manner to lead to Physical
Thermotics, or the Theory of Heat with reference to the cause by
which its effects are produced;--a branch of science which as yet
can hardly be said to exist.
3. What _kinds of cause_ are we to admit in science? This is an
important, and by no means an easy question. In order to answer it,
we must consider in what manner our progress in the knowledge of
causes has hitherto been made. By far the most conspicuous instance
of success in such researches, is the discovery of the causes of the
motions of the heavenly bodies. In this case, after the formal laws
of the motions,--their conditions as to space and time,--had become
known, men were enabled to go a step further; to reduce them to the
familiar and general cause of motion--mechanical force; and to
determine the laws which this force follows. That this was a step in
addition to the knowledge previously possessed, and that it was a
real and peculiar truth, will not be contested. And a step in any
other subject which should be analogous to this in astronomy;--a
discovery of causes and forces as certain and clear as the discovery
of universal gravitation;--would undoubtedly be a vast advance upon
a body of science consisting only of the laws of phenomena. {121}
4. But although physical astronomy may well be taken as a standard
in estimating the value and magnitude of the advance from the
knowledge of phenomena to the knowledge of causes; the peculiar
features of the transition from formal to physical science in that
subject must not be allowed to limit too narrowly our views of the
nature of this transition in other cases. We are not, for example,
to consider that the step which leads us to the knowledge of causes
in any province of nature must necessarily consist in the discovery
of centers of forces, and collections of such centers, by which the
effects are produced. The discovery of the causes of phenomena may
imply the detection of a fluid by whose undulations, or other
operations, the results are occasioned. The phenomena of acoustics
are, we know, produced in this manner by the air; and in the cases
of light, heat, magnetism, and others, even if we reject all the
theories of such fluids which have hitherto been proposed, we still
cannot deny that such theories are intelligible and possible, as the
discussions concerning them have shown. Nor can it be doubted that
if the assumption of such a fluid, in any case, were as well
evidenced as the doctrine of universal gravitation is, it must be
considered as a highly valuable theory.
5. But again; not only must we, in aiming at the formation of a
Causal Section in each Science of Phenomena, consider Fluids and
their various modes of operation admissible, as well as centers of
mechanical force; but we must be prepared, if it be necessary, to
consider the forces, or powers to which we refer the phenomena,
under still more general aspects, and invested with characters
different from mere mechanical force. For example; the forces by
which the chemical elements of bodies are bound together, and from
which arise, both their sensible texture, their crystalline form,
and their chemical composition, are certainly forces of a very
different nature from the mere attraction of matter according to its
mass. The powers of assimilation and reproduction in plants and
animals are obviously still more removed from mere mechanism; yet
{122} these powers are not on that account less real, nor a less fit
and worthy subject of scientific inquiry.
6. In fact, these forces--mechanical, chemical and vital,--as we
advance from one to the other, each bring into our consideration new
characters; and what these characters are, has appeared in the
historical survey which we made of the Fundamental Ideas of the
various sciences. It was then shown that the forces by which
chemical effects are produced necessarily involve the Idea of
Polarity,--they are polar forces; the particles tend together in
virtue of opposite properties which in the combination neutralize
each other. Hence, in attempting to advance to a theory of Causes in
chemistry, our task is by no means to invent laws of _mechanical_
force, and collections of forces, by which the effects may be
produced. We know beforehand that no such attempt can succeed. Our
aim must be to conceive such new kinds of force, including Polarity
among their characters, as may best render the results intelligible.
7. Thus in advancing to a Science of Cause in any subject, the
labour and the struggle is, not to analyse the phenomena according
to any preconceived and already familiar ideas, but to form
distinctly new conceptions, such as do really carry us to a more
intimate view of the processes of nature. Thus in the case of
astronomy, the obstacle which deferred the discovery of the true
causes from the time of Kepler to that of Newton, was the difficulty
of taking hold of mechanical conceptions and axioms with sufficient
clearness and steadiness; which, during the whole of that interval,
mathematicians were learning to do. In the question of causation
which now lies most immediately in the path of science, that of the
causes of electrical and chemical phenomena, the business of rightly
fixing and limiting the conception of polarity, is the proper object
of the efforts of discoverers. Accordingly a large portion of Mr
Faraday's recent labours[23\2] is directed, not to {123} the attempt
at discovering new laws of phenomena, but to the task of throwing
light upon the conception of polarity, and of showing how it must be
understood, so that it shall include electrical induction and other
phenomena, which have commonly been ascribed to forces acting
mechanically at a distance. He is by no means content, nor would it
answer the ends of science that he should be, with stating the
results of his experiments; he is constantly, in every page,
pointing out the interpretation of his experiments, and showing how
the conception of Polar Forces enters into this interpretation. 'I
shall,' he says[24\2], 'use every opportunity which presents itself
of returning to that strong test of truth, experiment; but,' he
adds, 'I shall necessarily have occasion to speak theoretically, and
even hypothetically.' His hypothesis that electrical inductive
action always takes place by means of a continuous line of polarized
particles, and not by attraction and repulsion at a distance, if
established, cannot fail to be a great step on our way towards a
knowledge of causes, as well as phenomena, in the subjects under his
consideration.
[Note 23\2: Eleventh, Twelfth, and Thirteenth Series of Researches,
_Phil. Trans._ 1837 and 8.]
[Note 24\2: Art. 1318.]
8. The process of obtaining new conceptions is, to most minds, far
more unwelcome than any labour in employing old ideas. The effort is
indeed painful and oppressive; it is feeling in the dark for an
object which we cannot find. Hence it is not surprising that we
should far more willingly proceed to seek for new causes by applying
conceptions borrowed from old ones. Men were familiar with solid
frames, and with whirlpools of fluid, when they had not learnt to
form any clear conception of attraction at a distance. Hence they at
first imagined the heavenly motions to be caused by Crystalline
Spheres, and by Vortices. At length they were taught to conceive
Central Forces, and then they reduced the solar system to these. But
having done this, they fancied that all the rest of the machinery of
nature must be central forces. We find Newton {124} expressing this
conviction[25\2], and the mathematicians of the last century acted
upon it very extensively. We may especially remark Laplace's labours
in this field. Having explained, by such forces, the phenomena of
capillary attraction, he attempted to apply the same kind of
explanation to the reflection, refraction, and double refraction of
light;--to the constitution of gases;--to the operation of heat. It
was soon seen that the explanation of refraction was arbitrary, and
that of double refraction illusory; while polarization entirely
eluded the grasp of this machinery. Centers of force would no longer
represent the modes of causation which belonged to the phenomena.
Polarization required some other contrivance, such as the undulatory
theory supplied. No theory of light can be of any avail in which the
fundamental idea of Polarity is not clearly exhibited.
[Note 25\2: Multa me movent, &c.,--Pref. to the _Principia_, already
quoted in the _History_.]
9. The sciences of magnetism and electricity have given rise to
theories in which this relation of polarity is exhibited by means of
two opposite fluids[26\2];--a positive and a negative fluid, or a
vitreous and a resinous, for electricity, and a boreal and an
austral fluid for magnetism. The hypothesis of such fluids gives
results agreeing in a remarkable manner with the facts and their
measures, as Coulomb and others have shown. It may be asked how far
we may, in such a case, suppose that we have discovered the true
cause of the phenomena, and whether it is sufficiently proved that
these fluids really exist. The right answer seems to be, that the
hypothesis certainly represents the truth so far as regards the
polar relation of the two energies, and the laws of the attractive
and repulsive forces of the particles in which these energies
reside; but that we are not entitled to assume that the vehicles of
these energies possess other attributes of material fluids, or that
the forces thus ascribed to the particles are the primary elementary
forces from which {125} the action originates. We are the more bound
to place this cautious limit to our acceptance of the Coulombian
theory, since in electricity Faraday has in vain endeavoured to
bring into view one of the polar fluids without the other: whereas
such a result ought to be possible if there were two separable
fluids. The impossibility of this separate exhibition of one fluid
appears to show that the fluids are _real_ only so far as they are
_polar_. And Faraday's view above mentioned, according to which the
attractions at a distance are resolved into the action of lines of
polarized particles of air, appears still further to show that the
conceptions hitherto entertained of electrical forces, according to
the Coulombian theory, do not penetrate to the real and intimate
nature of the causation belonging to this case.
[Note 26\2: _Hist. Ind. Sc._ b. xi. c. ii.]
10. Since it is thus difficult to know when we have seized the true
cause of the phenomena in any department of science, it may appear
to some persons that physical inquirers are imprudent and
unphilosophical in undertaking this Research of Causes; and that it
would be safer and wiser to confine ourselves to the investigation
of the laws of phenomena, in which field the knowledge which we
obtain is definite and certain. Hence there have not been wanting
those who have laid it down as a maxim that 'science must study only
the laws of phenomena, and never the mode of production[27\2].' But
it is easy to see that such a maxim would confine the breadth and
depth of scientific inquiries to a most scanty and miserable limit.
Indeed, such a rule would defeat its own object; for the laws of
phenomena, in many cases, cannot be even expressed or understood
without some hypothesis respecting their mode of production. How
could the phenomena of polarization have been conceived or reasoned
upon, except by imagining a polar arrangement of particles, or
transverse vibrations, or some equivalent hypothesis? The doctrines
of fits of easy transmission, the doctrine of moveable polarization,
and the like, even when {126} erroneous as representing the whole of
the phenomena, were still useful in combining some of them into
laws; and without some such hypotheses the facts could not have been
followed out. The doctrine of a fluid caloric may be false; but
without imagining such a fluid, how could the movement of heat from
one part of a body to another be conceived? It may be replied that
Fourier, Laplace, Poisson, who have principally cultivated the
Theory of Heat, have not conceived it as a fluid, but have referred
conduction to the radiation of the molecules of bodies, which they
suppose to be separate points. But this molecular constitution of
bodies is itself an assumption of the mode in which the phenomena
are produced; and the radiation of heat suggests inquiries
concerning a fluid emanation, no less than its conduction does. In
like manner, the attempts to connect the laws of phenomena of heat
and of gases, have led to hypotheses respecting the constitution of
gases, and the combination of their particles with those of caloric,
which hypotheses may be false, but are probably the best means of
discovering the truth.
[Note 27\2: Comte, _Philosophie Positive_.]
To debar science from inquiries like these, on the ground that it is
her business to inquire into facts, and not to speculate about
causes, is a curious example of that barren caution which hopes for
truth without daring to venture upon the quest of it. This temper
would have stopped with Kepler's discoveries, and would have refused
to go on with Newton to inquire into the mode in which the phenomena
are produced. It would have stopped with Newton's optical facts, and
would have refused to go on with him and his successors to inquire
into the mode in which these phenomena are produced. And, as we have
abundantly shown, it would, on that very account, have failed in
seeing what the phenomena really are.
In many subjects the attempt to study the laws of phenomena,
independently of any speculations respecting the causes which have
produced them, is neither possible for human intelligence nor for
human temper. Men cannot contemplate the phenomena without clothing
them in terms of some hypothesis, and will {127} not be schooled to
suppress the questionings which at every moment rise up within them
concerning the causes of the phenomena. Who can attend to the
appearances which come under the notice of the geologist;--strata
regularly bedded, full of the remains of animals such as now live in
the depths of the ocean, raised to the tops of mountains, broken,
contorted, mixed with rocks such as still flow from the mouths of
volcanos,--who can see phenomena like these, and imagine that he
best promotes the progress of our knowledge of the earth's history,
by noting down the facts, and abstaining from all inquiry whether
these are really proof of past states of the earth and of
subterraneous forces, or merely an accidental imitation of the
effects of such causes? In this and similar cases, to proscribe the
inquiry into causes would be to annihilate the science.
Finally, this caution does not even gain its own single end, the
escape from hypotheses. For, as we have said, those who will not
seek for new and appropriate causes of newly-studied phenomena, are
almost inevitably led to ascribe the facts to modifications of
causes already familiar. They may declare that they will not hear of
such causes as vital powers, elective affinities, electric, or
calorific, or luminiferous ethers or fluids; but they will not the
less on that account assume hypotheses equally unauthorized;--for
instance--universal mechanical forces; a molecular constitution of
bodies; solid, hard, inert matter;--and will apply these hypotheses
in a manner which is arbitrary in itself as well as quite
insufficient for its purpose.
11. It appears, then, to be required, both by the analogy of the
most successful efforts of science in past times and by the
irrepressible speculative powers of the human mind, that we should
attempt to discover both the _laws of phenomena_, and their
_causes_. In every department of science, when prosecuted far
enough, these two great steps of investigation must succeed each
other. The laws of phenomena must be known before we can speculate
concerning causes; the causes must be inquired into when the
phenomena have been {128} reduced to rule. In both these
speculations the suppositions and conceptions which occur must be
constantly tested by reference to observation and experiment. In
both we must, as far as possible, devise hypotheses which, when we
thus test them, display those characters of truth of which we have
already spoken;--an agreement with facts such as will stand the most
patient and rigid inquiry; a provision for predicting truly the
results of untried cases; a consilience of inductions from various
classes of facts; and a progressive tendency of the scheme to
simplicity and unity.
We shall attempt hereafter to give several rules of a more precise
and detailed kind for the discovery of the causes, and still more,
of the laws of phenomena. But it will be useful in the first place
to point out the Classification of the Sciences which results from
the principles already established in this **work. And for this
purpose we must previously decide the question, whether the
practical Arts, as Medicine and Engineering, must be included in our
list of Sciences.
{{129}}
CHAPTER VIII.
OF ART AND SCIENCE.
APHORISM XXV.
_Art and Science differ. The object of Science is Knowledge; the
objects of Art, are Works. In Art, truth is a means to an end; in
Science, it is the only end. Hence the Practical Arts are not to be
classed among the Sciences._
APHORISM XXVI.
_Practical Knowledge, such as Art implies, is not Knowledge such as
Science includes. Brute animals have a practical knowledge of
relations of space and force; but they have no knowledge of Geometry
or Mechanics._
1. THE distinction of Arts and Sciences very materially affects all
classifications of the departments of Human Knowledge. It is often
maintained, expressly or tacitly, that the Arts are a part of our
knowledge, in the same sense in which the Sciences are so; and that
Art is the application of Science to the purposes of practical life.
It will be found that these views require some correction, when we
understand _Science_ in the exact sense in which we have throughout
endeavoured to contemplate it, and in which alone our examination of
its nature can instruct us in the true foundations of our knowledge.
When we cast our eyes upon the early stages of the histories of
nations, we cannot fail to be struck with the consideration, that in
many countries the Arts of life already appear, at least in some
rude form or other, when, as yet, nothing of science exists. A {130}
practical knowledge of Astronomy, such as enables them to reckon
months and years, is found among all nations except the mere
savages. A practical knowledge of Mechanics must have existed in
those nations which have left us the gigantic monuments of early
architecture. The pyramids and temples of Egypt and Nubia, the
Cyclopean walls of Italy and Greece, the temples of Magna Græcia and
Sicily, the obelisks and edifices of India, the cromlechs and
Druidical circles of countries formerly Celtic,--must have demanded
no small practical mechanical skill and power. Yet those modes of
reckoning time must have preceded the rise of speculative Astronomy;
these structures must have been erected before the theory of
Mechanics was known. To suppose, as some have done, a great body of
science, now lost, to have existed in the remote ages to which these
remains belong, is not only quite gratuitous, and contrary to all
analogy, but is a supposition which cannot be extended so far as to
explain all such cases. For it is impossible to imagine that _every_
art has been preceded by the science which renders a reason for its
processes. Certainly men formed wine from the grape, before they
possessed a Science of Fermentation; the first instructor of every
artificer in brass and iron can hardly be supposed to have taught
the Chemistry of metals as a Science; the inventor of the square and
the compasses had probably no more knowledge of demonstrated
Geometry than have the artisans who now use those implements; and
finally, the use of speech, the employment of the inflections and
combinations of words, must needs be assumed as having been prior to
any general view of the nature and analogy of Language. Even at this
moment, the greater part of the arts which exist in the world are
not accompanied by the sciences on which they theoretically depend.
Who shall state to us the general chemical truths to which the
manufactures of glass, and porcelain, and iron, and brass, owe their
existence? Do not almost all artisans practise many successful
artifices long before science explains the ground of the process? Do
not arts at this day exist, in a high state {131} of perfection, in
countries in which there is no science, as China and India? These
countries and many others have no theories of mechanics, of optics,
of chemistry, of physiology; yet they construct and use mechanical
and optical instruments, make chemical combinations, take advantage
of physiological laws. It is too evident to need further
illustration that Art may exist without Science;--that the former
has usually been anterior to the latter, and even now commonly
advances independently, leaving science to follow as it can.
2. We here mean by _Science_, that exact, general, speculative
knowledge, of which we have, throughout this work, been endeavouring
to exhibit the nature and rules. Between such Science and the
_practical Arts_ of life, the points of difference are sufficiently
manifest. The object of Science is _Knowledge_; the object of Art
are _Works_. The latter is satisfied with producing its material
results; to the former, the operations of matter, whether natural or
artificial, are interesting only so far as they can be embraced by
intelligible principles. The End of Art is the Beginning of Science;
for when it is seen _what_ is done, then comes the question _why_ it
is done. Art may have fixed general rules, stated in words; but she
has these merely as means to an end: to Science, the propositions
which she obtains are each, in itself, a sufficient end of the
effort by which it is acquired. When Art has brought forth her
product, her task is finished; Science is constantly led by one step
of her path to another: each proposition which she obtains impels
her to go onwards to other propositions more general, more profound,
more simple. Art puts elements together, without caring to know what
they are, or why they coalesce. Science analyses the compound, and
at every such step strives not only to perform, but to understand
the analysis. Art advances in proportion as she becomes able to
bring forth products more multiplied, more complex, more various;
but Science, straining her eyes to penetrate more and more deeply
into the nature of things, reckons her success in proportion as she
sees, in all the phenomena, however {132} multiplied; complex, and
varied, the results of one or two simple and general laws.
3. There are many acts which man, as well as animals, performs by
the guidance of nature, without seeing or seeking the reason why he
does so; as, the acts by which he balances himself in standing or
moving, and those by which he judges of the form and position of the
objects around him. These actions have their reason in the
principles of geometry and mechanics; but of such reasons he who
thus acts is unaware: he works blindly, under the impulse of an
unknown principle which we call _Instinct_. When man's speculative
nature seeks and finds the reasons why he should act thus or
thus;--why he should stretch out his arm to prevent his falling, or
assign a certain position to an object in consequence of the angles
under which it is seen;--he may perform the same actions as before,
but they are then done by the aid of a different faculty, which, for
the sake of distinction, we may call _Insight_. Instinct is a purely
active principle; it is seen in deeds alone; it has no power of
looking inwards; it asks no questions; it has no tendency to
discover reasons or rules; it is the opposite of Insight.
4. Art is not identical with Instinct: on the contrary, there are
broad differences. Instinct is stationary; Art is progressive.
Instinct is mute; it acts, but gives no rules for acting: Art can
speak; she can lay down rules. But though Art is thus separate from
Instinct, she is not essentially combined with Insight. She can see
what to do, but she needs not to see why it is done. She may lay
down Rules, but it is not her business to give Reasons. When man
makes _that_ his employment, he enters upon the domain of Science.
Art takes the phenomena and laws of nature as she finds them: that
they are multiplied, complex, capricious, incoherent, disturbs her
not. She is content that the rules of nature's operations should be
perfectly arbitrary and unintelligible, provided they are constant,
so that she can depend upon their effects. But Science is impatient
of all appearance of caprice, {133} inconsistency, irregularity, in
nature. She will not believe in the existence of such characters.
She resolves one apparent anomaly after another; her task is not
ended till every thing is so plain and simple, that she is tempted
to believe that she sees that it could by no possibility have been
otherwise than it is.
5. It may be said that, after all, Art does really involve the
knowledge which Science delivers;--that the artisan who raises large
weights, practically _knows_ the properties of the mechanical
powers;--that he who manufactures chemical compounds is virtually
acquainted with the laws of chemical combination. To this we reply,
that it might on the same grounds be asserted, that he who acts upon
the principle that two sides of a triangle are greater than the
third is really acquainted with geometry; and that he who balances
himself on one foot knows the properties of the center of gravity.
But this is an acquaintance with geometry and mechanics which even
brute animals possess. It is evident that it is not of such
knowledge as this that we have here to treat. It is plain that this
mode of possessing principles is altogether different from that
contemplation of them on which science is founded. We neglect the
most essential and manifest differences, if we confound our
unconscious assumptions with our demonstrative reasonings.
6. The real state of the case is, that the principles which Art
_involves_, Science alone _evolves_. The truths on which the success
of Art depends, lurk in the artist's mind in an undeveloped state;
guiding his hand, stimulating his invention, balancing his judgment;
but not appearing in the form of enunciated Propositions. Principles
are not to him direct objects of meditation: they are secret Powers
of Nature, to which the forms which tenant the world owe their
constancy, their movements, their changes, their luxuriant and
varied growth, but which he can nowhere directly contemplate. That
the creative and directive Principles which have their lodgment in
the artist's mind, when _unfolded_ by our speculative powers into
{134} systematic shape, become Science, is true; but it is precisely
this process of _development_ which gives to them their character of
Science. In practical Art, principles are unseen guides, leading us
by invisible strings through paths where the end alone is looked at:
it is for Science to direct and purge our vision so that these airy
ties, these principles and laws, generalizations and theories,
become distinct objects of vision. Many may feel the intellectual
monitor, but it is only to her favourite heroes that the Goddess of
Wisdom visibly reveals herself.
7. Thus Art, in its earlier stages at least, is widely different
from Science, is independent of it, and is anterior to it. At a
later period, no doubt, Art may borrow aid from Science; and the
discoveries of the philosopher may be of great value to the
manufacturer and the artist. But even then, this application forms
no essential part of the science: the interest which belongs to it
is not an intellectual interest. The augmentation of human power and
convenience may impel or reward the physical philosopher; but the
processes by which man's repasts are rendered more delicious, his
journeys more rapid, his weapons more terrible, are not, therefore,
Science. They may involve principles which are of the highest
interest to science; but as the advantage is not practically more
precious because it results from a beautiful theory, so the
theoretical principle has no more conspicuous place in science
because it leads to convenient practical consequences. The nature of
Science is purely intellectual; Knowledge alone,--exact general
Truth,--is her object; and we cannot mix with such material, as
matters of the same kind, the merely Empirical maxims of Art,
without introducing endless confusion into the subject, and making
it impossible to attain any solid footing in our philosophy.
8. I shall therefore not place, in our Classification of the
Sciences, the Arts, as has generally been done; nor shall I notice
the applications of sciences to art, as forming any separate portion
of each science. The sciences, considered as bodies of general
speculative {135} truths, are what we are here concerned with; and
applications of such truths, whether useful or useless, are
important to us only as illustrations and examples. Whatever place
in human knowledge the Practical Arts may hold, they are not
Sciences. And it is only by this rigorous separation of the
Practical from the Theoretical, that we can arrive at any solid
conclusions respecting the nature of Truth, and the mode of arriving
at it, such as it is our object to attain.
{{136}}
CHAPTER IX.
OF THE CLASSIFICATION OF SCIENCES.
1. THE Classification of Sciences has its chief use in pointing out
to us the extent of our powers of arriving at truth, and the
analogies which may obtain between those certain and lucid portions
of knowledge with which we are here concerned, and those other
portions, of a very different interest and evidence, which we here
purposely abstain to touch upon. The classification of human
knowledge will, therefore, have a more peculiar importance when we
can include in it the moral, political, and metaphysical, as well as
the physical portions of our knowledge. But such a survey does not
belong to our present undertaking: and a general view of the
connexion and order of the branches of sciences which our review has
hitherto included, will even now possess some interest; and may
serve hereafter as an introduction to a more complete scheme of the
general body of human knowledge.
2. In this, as in any other case, a sound classification must be the
result, not of any assumed principles imperatively applied to the
subject, but of an examination of the objects to be classified;--of
an analysis of them into the principles in which they agree and
differ. The Classification of Sciences must result from the
consideration of their nature and contents. Accordingly, that review
of the Sciences in which the _History_ of the Sciences engaged us,
led to a Classification, of which the main features are indicated in
that work. The Classification thus obtained, depends neither upon
the faculties of the mind to which the separate parts of our
knowledge owe their origin, nor upon the objects which each science
contemplates; but upon a more {137} natural and fundamental
element;--namely, the _Ideas_ which each science involves. The Ideas
regulate and connect the facts, and are the foundations of the
reasoning, in each science: and having in another work more fully
examined these _Ideas_, we are now prepared to state here the
classification to which they lead. If we have rightly traced each
science to the Conceptions which are really fundamental _with regard
to it_, and which give rise to the first principles on which it
depends, it is not necessary for our purpose that we should decide
whether these Conceptions are absolutely ultimate principles of
thought, or whether, on the contrary, they can be further resolved
into other Fundamental Ideas. We need not now suppose it determined
whether or not _Number_ is a mere modification of the Idea of Time,
and _Force_ a mere modification of the Idea of Cause: for however
this may be, our Conception of Number is the foundation of
Arithmetic, and our Conception of Force is the foundation of
Mechanics. It is to be observed also that in our classification,
each Science may involve, not only the Ideas or Conceptions which
are placed opposite to it in the list, but also all which _precede_
it. Thus Formal Astronomy involves not only the Conception of
Motion, but also those which are the foundation of Arithmetic and
Geometry. In like manner. Physical Astronomy employs the Sciences of
Statics and Dynamics, and thus, rests on their foundations; and
they, in turn, depend upon the Ideas of Space and of Time, as well
as of Cause.
3. We may further observe, that this arrangement of Sciences
according to the Fundamental Ideas which they involve, points out
the transition from those parts of human knowledge which have been
included in our History and Philosophy, to other regions of
speculation into which we have not entered. We have repeatedly found
ourselves upon the borders of inquiries of a psychological, or
moral, or theological nature. Thus the History of Physiology[28\2]
led us to the consideration {138} of Life, Sensation, and Volition;
and at these Ideas we stopped, that we might not transgress the
boundaries of our subject as then predetermined. It is plain that
the pursuit of such conceptions and their consequences, would lead
us to the sciences (if we are allowed to call them sciences) which
contemplate not only animal, but human principles of action, to
Anthropology, and Psychology. In other ways, too, the Ideas which we
hare examined, although manifestly the foundations of sciences such
as we have here treated of also plainly pointed to speculations of a
different order; thus the Idea of a Final Cause is an indispensable
guide in Biology, as we have seen; but the conception of Design as
directing the order of nature, once admitted, soon carries us to
higher contemplations. Again, the Class of Palætiological Sciences
which we were in the _History_ led to construct, although we there
admitted only one example of the Class, namely Geology, does in
reality include many vast lines of research; as the history and
causes of the division of plants and animals, the history of
languages, arts, and consequently of civilization. Along with these
researches, comes the question how far these histories point
backwards to a natural or a supernatural origin; and the Idea of a
First Cause is thus brought under our consideration. Finally, it is
not difficult to see that as the Physical Sciences have their
peculiar governing Ideas, which support and shape them, so the Moral
and Political Sciences also must similarly have their fundamental
and formative Ideas, the source of universal and certain truths,
each of their proper kind. But to follow out the traces of this
analogy, and to verify the existence of those Fundamental Ideas in
Morals and Politics, is a task quite out of the sphere of the work
in which we are here engaged.
[Note 28\2: _Hist. Ind. Sc._ b. xvii. c. v. sect. 2.]
4. We may now place before the reader our Classification of the
Sciences. I have added to the list of Sciences, a few not belonging
to our present subject, that the nature of the transition by which
we are to extend our philosophy into a wider and higher region may
be in some measure perceived. {139}
The Classification of the Sciences is given over leaf.
A few remarks upon it offer themselves.
The _Pure_ Mathematical Sciences can hardly be called _Inductive_
Sciences. Their principles are not obtained by Induction from Facts,
but are necessarily assumed in reasoning upon the subject matter
which those sciences involve.
The Astronomy of the Ancients aimed only at explaining the motions
of the heavenly bodies, as a _mechanism_. Modern Astronomy, explains
these motions on the principles of Mechanics.
The term _Physics_, when confined to a peculiar class of Sciences,
is usually understood to exclude the Mechanical Sciences on the one
side, and Chemistry on the other; and thus embraces the Secondary
Mechanical and Analytico-Mechanical Sciences. But the adjective
_Physical_ applied to any science and opposed to _Formal_, as in
Astronomy and Optics, implies those speculations in which we
consider not only the Laws of Phenomena but their Causes; and
generally, as in those cases, their Mechanical Causes.
The term _Metaphysics_ is applied to subjects in which the Facts
examined are emotions, thoughts and mental conditions; subjects not
included in our present survey. {140}
Fundamental Ideas or Sciences. Classification.
Conceptions.
Space Geometry )
Time ) Pure Mathematical
_Number_ Arithmetic }
Sign Algebra ) Sciences.
Limit Differentials )
_Motion_ Pure Mechanism } Pure Motional
Formal Astronomy } Sciences.
Cause
_Force_ Statics )
_Matter_ Dynamics ) Mechanical
_Inertia _ Hydrostatics }
_Fluid Pressure_ Hydrodynamics ) Sciences.
Physical Astronomy )
Outness
Medium _of Sensation_ Acoustics )
Intensity _of Qualities_ Formal Optics ) Secondary
_Scales of Qualities_ Physical Optics } Mechanical
Thermotics ) Sciences.
Atmology ) (_Physics_.)
Polarity Electricity ) Analytico-Mecha-
Magnetism } nical Sciences.
Galvanism ) (_Physics_.)
Element (_Composition_)
_Chemical_ Affinity
Substance (_Atoms_) Chemistry Analytical Science.
Symmetry Crystallography } Analytico-Classifi-
Likeness Systematic Mineralogy } catory Sciences.
_Degrees of Likeness_ Systematic Botany )
Systematic Zoology } Classificatory
_Natural_ Affinity Comparative Anatomy ) Sciences.
(_Vital Powers_)
Assimilation
Irritability
(_Organization_) Biology Organical Sciences.
Final Cause
Instinct
Emotion Psychology (_Metaphysics_.)
Thought
Historical Causation Geology )
Distribution of ) Palætiological
Plants and Animals } Sciences.
Glossology )
Ethnography )
First Cause Natural Theology.
[*Transcriber's Note: The two following tables were inserted on
separate sheets at this point. They were structured as trees, but
have here been converted into a diagram to be read from left to
right, and an associated key. Arrows have replaced the brackets
Whewell used. In the original, the names of discoverers and comments
about inadequate explanations were printed in red.]
INDUCTIVE TABLE OF ASTRONOMY
a r ) { )
) { )
b → j s ) { J )
) → z { )
c → k ) { )
) )
d → l t ) )
)
e → m ) ) { b1 → c1 → m1 )
u ) → A E → H ) → M { N → Q → W )
f → n ) ) { b1 → d1 → n1 ) )
) ) )
) { R → X b1 → e1 ) ) )
g → o v → B F → I K ) { ) ) )
) { O S → Y b1 → f1 )→ o1 ) )
) { ) ) )
) { S → Z b1 → g1 ) ) )→ u1
h → p w → C G L ) )→ t1 )
P T b1 → h1 → p1 ) )
) )
q x → D b1 i1 → q1 ) )
) )
i y b1 j1 → r1 ) )
) )
U → a1 b1 k1 → s1 ) )
) )
V b1 → l1 ) )
a = THE EARTH appears to be immovable.
b = THE STARS keep their relative places in the vault of the sky,
and with the Sun and Moon, rise, move, and set.
c = THE MOON'S bright part is of the shape of a ball enlightened by
the Sun.
d = THE MOON'S ECLIPSES occur when she is full.
e = ECLIPSES OF THE SUN AND MOON often occur.
f = THE MOON rises and sets at different times and places. Her
course among the Stars varies.
g = THE PLANETS are morning and evening Stars: are direct,
stationary, and retrograde.
h = THE SUN rises, culminates, and sets in different times and
places at different seasons: different CONSTELLATIONS are visible at
night.
i = THE TIDES ebb and flow.
j = Chald^ns. _The Sphere of the Heavens appears to make a Diurnal
Revolution._
k = Greeks. The Moon receives her light _from the Sun_.
l = Greeks. The Moon's Eclipses are caused by the _Earth's shadow._
m = Chald^ns. The Moon's Eclipses follow certain cycles.
n = Greeks. The Moon appears to revolve monthly in an _oblique
orbit_, which has _Nodes_ and an _Apogee_.
o = Chaldeans. The Planets have proper motions and certain _Cycles_.
p = Pythagoras. The Sun appears to move annually in an _Ecliptic_
oblique to the diurnal motion.
q = The places of Stars are determined by their Longitude measured
from the Equinox.
r = The forms and dist^s of known parts of the earth are such as fit
a convex surface.
s = The visible Pole of the Heavens rises or drops as we travel N.
or S.
t = The boundary of the Earth's shadow is always circular.
u = By observations of Eclipses, the Moon's Nodes and Apogee
revolve, and her motion is unequal according to certain laws.
v = By observations of the Planets, their progressions, stations,
and retrogradations.
w = By observations of the Sun, his motion is unequal according to
certain laws.
x = By observations, Longitudes of Stars increase.
y = By observations, the Tides depend on the Moon and Sun.
z = Aristotle? The Earth is a _Globe_, about which the Sphere of the
Heavens performs a _Diurnal Revolution_.
A = Hipparchus. The Moon appears to move in an _Epicycle_ carried by
a Deferent: the _Velocity of Apogee_ and _Nodes_ determined.
B = Eudoxus. The Planets appear to move in Epicycles carried by
_Deferents_.
C = Hipparchus. The Sun appears to move in an _Eccentric_, his
_Apogee_ being fixed.
D = Hippar. There is a _Precession of the Equinoxes_.
E = By additional observations, the Moon's motion has another
inequality. Evection.
F = By additional observations, the Planets' motions in their
Epicycles are unequal according to certain laws.
G = By additional observations, the Sun's Apogee moves. Albategnius.
H = Ptolemy. The Moon appears to move in an _Epicycle_ carried by an
_Eccentric_.
I = Ptolemy. The Planets appear to move in _Epicycles_ carried by
_Eccentrics_.
J = * _By the nature of motion_, the apparent motion is the same
whether the Heavens or the Earth have a diurnal revolution: the
latter is _simpler_.
K = * _By the nature of motion_, the apparent motion is the same if
the Planets revolve about the Sun: this is _simpler_.
L = * _By the nature of motion_, the apparent motion of the Sun is
the same if the Earth revolve round the Sun: this is _simpler_.
M = * Copernicus. The Earth and Planets revolve about the Sun as a
center in Orbits nearly circular. The Earth revolves about its axis
inclined to the Ecliptic in a constant position, and the Moon
revolves about the Earth. The _Heliocentric Theory_ governs
subsequent speculations.
N = Retaining Moon's Eccentric and Epicycle; By additional
observations, the Moon's motion has other inequalities.
O = Retaining but referring to the Sun as center the Planets'
Epicycles and Eccentrics and the annual Orbit;
P = Retaining obs^ns. Earth's Aphelion revolves.
Q = Tycho. Moon's _Variation_; _Unequal Motion of Node_; _Change of
Inclination_.
R = By calc^ns. of the periodic times and distances.
S = By additional observations and calculations.
T = Planets' Aphelia revolve. Jupiter and Saturn's motions have an
inequality dep^g. on their mutual positions.
U = THE WEIGHT of bodies dimin^s in going towards the Equator.
V = THE SATELLITES of Jupiter and Saturn revolve according to
Kepler's Laws.
W = Horrox. Halley. The Moon moves in an _Ellipse_ with variable
_axis_ and _eccentricity_.
X = Kepler. Distances cubed are as times squared.
Y = Kepler. Areas as described by Planets are as times.
Z = Kepler. Curves described by Planets are as ellipses.
a1 = Newton. Earth is oblate.
b1 = * By Mechanics.
c1 = * Newton. Moon is attracted by the Earth. Fall of heavy bodies.
d1 = * Newton. Moon's inequalities produced by attraction of Sun.
e1 = * Newton. Wren. Hooke. Sun's force on different Planets is
invers. as square of distance.
f1 = * Newton. Planets are attracted by the Sun.
g1 = * Newton. Sun attracts Planets invers. as square of distance.
h1 = * Newton. These inequalities are produced by mutual attraction
of the Planets.
i1 = Precession of Equinoxes is produced by attraction of Moon and
Sun on oblate Earth.
j1 = Tides are produced by attraction of Moon and Sun on
Sea. Explanation imperfect.
k1 = Diminution of gravity and oblateness of Earth arise from
attractions of parts.
l1 = * Newton. Jupiter and Saturn attract their Satellites inversely
as the square of the distance, and the Sun attracts Planets and
Satellites alike.
m1 = Newton. Earth attracts Moon invers. as square of distance.
n1 = Newton. Sun attracts Moon.
o1 = Newton. Sun attracts Planets inversely as the square of the
distance.
p1 = Newton. Planets attract each other.
q1 = * Newton. Moon and Sun attract parts of the Earth.
r1 = * Newton. Moon and Sun attract the Ocean.
s1 = * Newton. Parts of the Earth attract each other.
t1 = Newton. All parts of the Earth, Sun, Moon. and Planets
attract _each other_ with Forces inversely as the square of the
distance.
u1 = Newton. THE THEORY OF UNIVERSAL GRAVITATION. (All bodies
attract each other with a Force of _Gravity_ which is inversely as
the squares of the distances.)
INDUCTIVE TABLE OF OPTICS
First Facts. The common and obvious Phænomena of Light and Vision.
By the _Idea of a Medium_ Light and Vision take place by means of
something intermediate.
First Law of Phænomena. The effects take place in straight lines
denoted by the Term _Rays_.
Facts of
a → m h1 ) ( ) )
) ( ) )
b → n ) ) i1 ) ( ) )
)→ r ) ) ( C1 ) )
c o ) )→ K ) ) ( ) → F1 )
) ) j1 )→ x1 ( ) )
d p ) L S ) ) ( ) )
) ) )
e s → M ) T h1 ) D1 ) ) ) → H1 )
)→ ) ) ) )
f t ) U k1 ) ( ) → G1 ) )
( E1 ) ) )
g ) ( u → W l1 ) ( ) ) )
) ( ) ) )
) ( v → X l1 )→ y1 ) )
)→ q ( ) ) )
) ( w → Y j1 ) ) )
) ( )
) ( x → Z ) ) ) )
( ) m1 ) ) )
( y → a1 ) ) ) )
( ) ) → I1 )
( z n1 )→ z1 ) )
( ) ) ) → K1
( A N b1 o1 ) ) )
q ←( ) ) )
( B O p1 ) ) )
( )
( C ) c1 q1 ) ) )
( ) V ) ) )
( D ) d1 q1 ) ) )
( ) ) )
( E j1 )→ A1 ) )
( ) ) )
( F P e1 ) ) ) )
( ) r1 ) ) )
( G f1 ) ) ) )
( ) → J1 )
( H Q s1 )
)
h ( R g1 t1 ) )
( ) )
i ( I u1 ) )
( ) )
j ( v1 )→ B1 )
) )
k ( w1 ) )
( J ) )
l ( w1 ) )
a = Rays falling on water, specula, &c.
b = Rays passing through water, glass, &c. Measures. Ptolemy.
c = Colours seen by prisms, in rainbow, &c.
d = Colours in diff. transp. Substances. Optical instrum^ts.
e = Two Images in Rhomb. of Calcspar.
f = Two Images in other crystals.
g = Two Rhombs of Calcspar make 4 images alternately appear and
disappear.
h = Fringes of shadows. Grimaldi. Hook. Newton.
i = Spectra of gratings. Fraunhofer.
j = Colours of striated surfaces. Coventry's Micromet^r. Barton's
Buttons. Young.
k = Colours of _thick Plates_. Newton.
l = Colours of _thin Plates_. Hook. Newton.
m = Euclid. Ang. Inc. equals Ang. Reflection.
n = Snell. Sin. Refr. to Sin. Inc. in giv. _Ratio_ in same med.
o = By measures of Refraction.
p = Dispersion of colours is same when Refr. is diff. Measures.
Dollond.
q = Huyghens. Rays of light have four Sides with regard to which
their properties alternate.
Newton. Idea of _Polarization_ introduced, which governs subsequent
observations. _Dipolarization_ with Colours.
r = Newt. Refr. R^o. is diff. for diff. colours, but in same med. is
const. for each colour.
s = Measures. Huyghens.
t = Double Refr. in biaxal crystals. Brewster.
u = Rays are polarized by Calcspar, Quartz, &c.
v = Rays are polarized by biaxal crystals.
w = Rays are polarized by Tourmaline, Agate, &c.
x = Rays are polarised by Refl. at glass.
y = Rays are polarized by transmission through glass.
z = Variable q^y. of pol. refl. light paral. plane of Refl. Arago.
A = Variable q^y. of pol. refl. light perp. plane of Refl.
B = Whole light reflected by internal Refl.
C = Pol. Rays through uniaxal crystals give colours. Rings.
Wollaston.
D = Pol. Rays through biaxal crystals give colours. Arago.
E = Pol. Rays. through imperf. crystallized bodies give colours.
(Glass strained, jellies prest.) Brewster.
F = Pol. Rays in axis of Quartz give a peculiar set of colours.
Plane of Pol^n twisted diff^ly. for diff. colours. Biot. Arago.
G = Pol. Rays oblique in Quartz give peculiar rings, &c.
H = Pol. Rays through certain liquids give a peculiar set of colours.
I = The Laws of these Phænomena were never discovered till Theory
had indicated them.
J = _Newton's Scale of Colours._
_Fits_ of Rays. Newton.
K = Dollond.
L = Prop^n of Ref. R^s is diff. in diff. med. _Achromatism_.
M = Huygh^s. Law of Double Ref. exp. by a spheroid.
N = Change of plane of pol. by Refl. Arago
O = Light is _circularly pol._ by 2 Refl. in _Fresnel's Rhomb._
Fresnel.
P = + in dir^n of plagihedral faces. J. Herschel.
Q = Plane of Pol^n. twisted. Biot
R = Fringes obliterated by stopping light from one edge or
interposing a glass. Young. Arago.
S = Ratios not reconcilable. _Irrationality_. Blair.
T = Fresnel.
U = Law exp. by surface of 4 dim^s.
V = Optical classification of crystals. Brewster.
W = Newt. Malus. Ray pol. in _principal plane_ of Rhomb.; and perp.
to it.
X = Brews. Biot. Ray pol. in plane bisecting ang. at axis; and perp.
to it.
Y = Brews. Ray pol. paral. to axis.
Z = Malus. Ray pol. in plane of Refl. for _given angle_.
a1 = Malus. Ray partially pol. in plane perp. to plane of
Reflection.
b1 = None Refl^d. if tan. ang. equal Refr. R^o. Brewster.
c1 = Tint is as sq. of sin. Biot.
d1 = Tint is as sin. α sin. β. Brewster. Biot.
Lemniscates. J. Herschel.
e1 = * By interf. of resolved undul^ns. of 2 rays circularly pol^d.
in opp. directions. * Fresnel.
f1 = * By interf. of resolved undul^ns. of 2 rays elliptically
pol^d. in opp. directions. * Airy.
g1 = * By interf. of rays from edges. Young.
h1 = * Refl. produced by spherical undul^ns.
i1 = * Refr. produced by spherical undul^ns. of diff. vel. for diff.
colour.
j1 = † Explanation imperfect.
k1 = * Refr. produced by curved surf. undul^ns.
l1 = * Pol^n. being prod. by resolution of transv^e undul^ns.
m1 = * Polarization being produced by resolution of transverse
undulations.
n1 = * Undul^ns. being com^d. acc. to laws of elastic bodies.
o1 = * Undul^ns. being com^d. acc. to a certain hypothesis.
p1 = * Impossible formulæ being interpreted by analogy.
q1 = * By interf. of resolved parts of transverse undul^ns.
r1 = * Same hypothesis explains separation of rays in axis and
oblique. † Explanation imperfect. * Maccullagh.
s1 = † Explan. wanting.
t1 = * By interf. of rays from all parts. * Young. * Fresnel.
u1 = * By interf. of undul^ns. from all parts. * Fraunhofer.
v1 = * By interf. of rays from striæ. * Young.
w1 = * By interf. of undul^ns. from two surfaces. * Young.
x1 = * Huyghens. Reflection and Refraction are propagation of
undulations.
y1 = * Young. * Fresnel. Polarization in crystals is transverse
undulations.
z1 = * Fresnel. Polarization in Reflection and Refraction is
transverse undulations.
A1 = * Fresnel. * Arago. Dipolarized Colours are produced by
interference of Rays polarized in same plane; length of undulation
being different for different colours.
B1 = * Young. * Fresnel. Colours of Fringes, Gratings, Striæ, thick
Plates, thin Plates &c. are produced by interference of undulations;
length of undulation being different for different colours.
C1 = * Undulations being propagated by the uniform elasticity of
each medium.
D1 = * Undul^ns. prop. by el^y. of medium diff. in 2 diff. dir^ns,
(_axis of crystal._)
E1 = * Undul^ns. being prop. by elasticity of med. diff. in 3 diff.
directions (_axes_).
F1 = Young. Reflection and double Refraction are propagation of
undulations by crystalline elasticity.
G1 = * Fresnel. Double Refr. and Pol. arise from same cause.
H1 = Young. Fresnel. Light is transverse undulations propagated in
media by elasticity dependent on axis, when crystalline.
I1 = Fresnel. Light is transverse undul^ns. transmitted from one
med. to another according to probable hypotheses.
J1 = Young. Fresnel. Colours result from interferences, the lengths
of undulation being different for different colours.
K1 = THE UNDULATORY THEORY OF LIGHT.
{{141}}
NOVUM ORGANON RENOVATUM.
BOOK III.
OF METHODS EMPLOYED IN THE FORMATION OF SCIENCE.
CHAPTER I.
INTRODUCTION.
APHORISM XXVII.
_The Methods by which the construction of Science is promoted are,_
Methods of Observation, Methods of obtaining clear Ideas, _and_
Methods of Induction.
1. IN the preceding Book, we pointed out certain general Characters
of scientific knowledge which may often serve to distinguish it from
opinions of a looser or vaguer kind. In the course of the progress
of knowledge from the earliest to the present time, men have been
led to a perception, more or less clear, of these characteristics.
Various philosophers, from Plato and Aristotle in the ancient world,
to Richard de Saint Victor and Roger Bacon in the middle ages,
Galileo and Gilbert, Francis Bacon and Isaac Newton, in modern
times, were led to offer precepts and maxims, as fitted to guide us
to a real and fundamental knowledge of nature. It may on another
occasion be our business to estimate the value of these precepts and
maxims. And other contributions of the same kind to the philosophy
of science might be noticed, and some which {142} contain still more
valuable suggestions, and indicate a more practical acquaintance
with the subject. Among these, I must especially distinguish Sir
John Herschel's _Discourse on the Study of Natural Philosophy_. But
my object at present is not to relate the history, but to present
the really valuable results of preceding labours: and I shall
endeavour to collect, both from them and from my own researches and
reflections, such views and such rules as seem best adapted to
assist us in the discovery and recognition of scientific truth; or,
at least, such as may enable us to understand the process by which
this truth is obtained. I would present to the reader the Philosophy
and, if possible, the Art of Discovery.
2. But, in truth, we must acknowledge, before we proceed with this
subject, that, speaking with strictness, an _Art of Discovery_ is
not possible;--that we can give no Rules for the pursuit of truth
which shall be universally and peremptorily applicable;--and that
the helps which we can offer to the inquirer in such cases are
limited and precarious. Still, we trust it will be found that aids
may be pointed out which are neither worthless nor uninstructive.
The mere classification of examples of successful inquiry, to which
our rules give occasion, is full of interest for the philosophical
speculator. And if our maxims direct the discoverer to no operations
which might not have occurred to his mind of themselves, they may
still concentrate our attention on that which is most important and
characteristic in these operations, and may direct us to the best
mode of insuring their success. I shall, therefore, attempt to
resolve the Process of Discovery into its parts, and to give an
account as distinct as may be of Rules and Methods which belong to
each portion of the process.
3. In Book II. we considered the three main parts of the process by
which science is constructed: namely, the Decomposition and
Observation of Complex Facts; the Explication of our Ideal
Conceptions; and the Colligation of Elementary Facts by means of
those Conceptions. The first and last of {143} these three steps are
capable of receiving additional accuracy by peculiar processes. They
may further the advance of science in a more effectual manner, when
directed by special technical _Methods_, of which in the present
Book we must give a brief view. In this more technical form, the
observation of facts involves the _Measurement of Phenomena_; and
the Colligation of Facts includes all arts and rules by which the
process of Induction can be assisted. Hence we shall have here to
consider _Methods of Observation_, and _Methods of Induction_, using
these phrases in the widest sense. The second of the three steps
above mentioned, the Explication of our Conceptions, does not admit
of being much assisted by methods, although something may be done by
Education and Discussion.
4. The Methods of Induction, of which we have to speak, apply only
to the first step in our ascent from phenomena to laws of
nature;--the discovery of _Laws of Phenomena_. A higher and ulterior
step remains behind, and follows in natural order the discovery of
Laws of Phenomena; namely, the _Discovery of Causes_; and this must
be stated as a distinct and essential process in a complete view of
the course of science. Again, when we have thus ascended to the
causes of phenomena and of their laws, we can often reason downwards
from the cause so discovered; and we are thus led to suggestions of
new phenomena, or to new explanations of phenomena already known.
Such proceedings may be termed _Applications_ of our Discoveries;
including in the phrase, _Verifications_ of our Doctrines by such an
application of them to observed facts. Hence we have the following
series of processes concerned in the formation of science.
(1.) Decomposition of Facts;
(2.) Measurement of Phenomena;
(3.) Explication of Conceptions;
(4.) Induction of Laws of Phenomena;
(5.) Induction of Causes;
(6.) Application of Inductive Discoveries.
5. Of these six processes, the methods by which the second and
fourth may be assisted are here our {144} peculiar object of
attention. The treatment of these subjects in the present work must
necessarily be scanty and imperfect, although we may perhaps be able
to add something to what has hitherto been systematically taught on
these heads. Methods of Observation and of Induction might of
themselves form an abundant subject for a treatise, and hereafter
probably will do so, in the hands of future writers. A few remarks,
offered as contributions to this subject, may serve to show how
extensive it is, and how much more ready it now is than it ever
before was, for a systematic discussion.
Of the above steps of the formation of science, the first, the
Decomposition of Facts, has already been sufficiently explained in
the last Book: for if we pursue it into further detail and
exactitude, we find that we gradually trench upon some of the
succeeding parts. I, therefore, proceed to treat of the second step,
the Measurement of Phenomena;--of _Methods_ by which this work, in
its widest sense, is executed, and these I shall term Methods of
Observation.
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