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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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