TABLE OF CONTENTS.PAGEPrefaceiiiBOOK I.APHORISMS CONCERNING IDEAS.AphorismsI.—XVIII.Ideas in general5—7XIX.—XLIV.Ideas in the Pure Sciences8—12XLV.—LV.Ideas in the Mechanical Sciences13—15LVI.—LXXI.Ideas in the Secondary Mechanical Sciences15—18LXXII.—LXXIII.Ideas in the Mechanico-chemical Sciences18LXXIV.—LXXIX.Ideas in Chemistry18LXXX.—LXXXI.Ideas in Morphology19LXXXII.—C.Ideas in Classificatory Science20—23CI.—CVI.Ideas in Biology23—24CVII.—CXVII.Ideas in Palæontology24—26BOOK II.OF KNOWLEDGE.Chap. I.Of Two Principal Processes by which Science is constructed27Chap. II.Of the Explication of Conceptions30Sect.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 before5.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 Science50Art.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 Facts59Art.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 Induction70Sect.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 Induction97Art.1.Steps of Generalization,2.May be expressed byTables.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 Causes118Art.1.Knowledge of Laws of Phenomena.2.FormalandPhysicalSciences.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 Science129Art.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 Sciences136Art.1.Use and Limits of such Classification.2.Classification depends on the Ideas.3.This points out Transitions.4.The Classification.Inductive Table of Astronomy140Inductive Table of Optics140BOOK III.OF METHODS EMPLOYED IN THE FORMATION OF SCIENCE.Chap. I.Introduction141Art.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 Observation145Art.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 firstof Intellectual Education164Art.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.NoPopularRoad.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 Ideas180Art.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 Induction186Sect.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 Conception195Art.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 Quantity202Sect.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.Argumentrequired 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 Resemblance220Sect.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 Truths233Art.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 Causes247Art.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.Introduction257Aphorisms concerning the Language of Science.AphorismI.Relative to the Ancient Period258Art.1.Common Words.2.Descriptive Terms.3.Theoretical Terms.AphorismII.Relative to the Modern Period269Art.1.Systematic Nomenclature.2.Systematic Terminology.3.Systematic Modification.Aphorisms(III. IV. V. VI. VII.) relative to the Application of Common Words278Aphorisms(VIII. IX. X. XI. XII. XIII.) relative to the Construction of New Terms285AphorismXIV.Binary Nomenclature307XV.Linnæan Maxims308XVI.Numerical Names309XVII.Names of more than two Steps310XVIII.No arbitraryTerms311XIX.Forms fixed by Convention314XX.Formof Terms318Art.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}AphorismXXI.Philological Rules328Art.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.AphorismXXII.Introduction of Changes341FURTHER ILLUSTRATIONS OF THE APHORISMS ON SCIENTIFIC LANGUAGE, FROM THE RECENT COURSE OF SCIENCES.1.Botany.AphorismXXIII.Multiplication of Genera3462.Comparative Anatomy.AphorismXXIV.Single Names to be used353XXV.The History of Science is the History of its Language355XXVI.Algebraical Symbols357XXVII.Algebraical Analogies364XXVIII.Capricious Derivations365XXIX.Inductions are our Definitions368
TABLE OF CONTENTS.