HISTORY
OF
SCIENTIFIC IDEAS.

By WILLIAM WHEWELL, D.D.,

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

BEING THE FIRST PART OF THE PHILOSOPHY
OF THE INDUCTIVE SCIENCES.

THE THIRD EDITION.

IN TWO VOLUMES.

Hand passing torch to hand

ΛΑΜΠΑΔIΑ ΕΧΟΝΤΕΣ ΔIΑΔΩΣΟΥΣIΝ ΑΛΛΗΛΟIΣ

VOLUME I.

LONDON:
JOHN W. PARKER AND SON, WEST STRAND.
1858.

PREFACE TO THIS EDITION.

THE Chapters now offered to the Reader were formerly published as a portion of The Philosophy of the Inductive Sciences, founded upon their History: but the nature and subject of these Chapters are more exactly described by the present title, The History of Scientific Ideas. For this part of the work is mainly historical, and was, in fact, collected from the body of scientific literature, at the same time that the History of the Inductive Sciences was so collected. The present work contains the history of Science so far as it depends on Ideas; the former work contains the same history so far as it is derived from Observation. The leading features in that were Theories inferred from Facts; the leading features of this are Discussions of Theories tending to make them consistent with the conditions of human thought.

The Ideas of which the History is here given are mainly the following:
Space, Time, Number, Motion, Cause, Force, Matter, Medium, Intensity, Scale, Polarity, Element, Affinity, Substance, Atom, Symmetry, Likeness, Natural Classes, Species, Life, Function, Vital Forces, Final vi Causes, Historical Causation, Catastrophe and Uniformity, First Cause.

The controversies to which the exact fixation of these Ideas and their properties have given occasion form a large and essential part of the History of Science: but they also form an important part of the Philosophy of Science, for no Philosophy of Science can be complete which does not solve the difficulties, antitheses, and paradoxes on which such controversies have turned. I have given a survey of such controversies, generally carried from their earliest origin to their latest aspect; and have stated what appeared to me the best solution of each problem. This has necessarily involved me in much thorny metaphysics; but such metaphysics is a necessary part of the progress of Science. The human mind deriving its knowledge of Truth from the observation of nature, cannot evade the task of determining at every step how Truth is consistent with itself. This is the Metaphysics of Progressive Knowledge, and this is the matter of this present History.

Of the remaining part of what was formerly published as the Philosophy of the Inductive Sciences, an additional part, described in the Introduction to the present work, will shortly be published.

Trinity Lodge,

May 24, 1858.

Erratum, p. 157, l. 11 from top, for sciences read science.

CONTENTS
OF
THE FIRST VOLUME.

		PAGE
Preface		v
PART I.
OF IDEAS.
Introduction		3
BOOK I.
OF IDEAS IN GENERAL.
Chap. I. Of the Fundamental Antithesis of Philosophy		23
Sect. 1.	Thoughts and Things	—
2.	Necessary and Experiential Truths	25
3.	Deduction and Induction	27
4.	Theories and Facts	29
5.	Ideas and Sensations	30
6.	Reflexion and Sensation	33
7.	Subjective and Objective	35
8.	Matter and Form	38
9.	Man the Interpreter of Nature	41
10.	The Fundamental Antithesis is inseparable	43
11.	Successive Generalization	49
viii
Chap. II. Of Technical Terms		54
Art. 1.	Examples.
2.	Use of Terms.
Chap. III. Of Necessary Truths		57
Art. 1.	The two Elements of Knowledge,
2.	Shown by necessary Truths.
3.	Examples of necessary Truths in numbers.
4.	The opposite cannot be distinctly conceived.
5.	Other Examples.
6.	Universal Truths.
Chap. IV. Of Experience		65
Art. 1.	Experience cannot prove necessary Truths,
2.	Except when aided by Ideas.
Chap. V. Of the Grounds of Necessary Truths		69
Art. 1.	These Grounds are Fundamental Ideas.
2.	These are to be reviewed.
3.	Definitions and Axioms.
4.	Syllogism,
5.	Produces no new Truths.
6.	Axioms needed.
7.	Axioms depend on Ideas:
8.	So do Definitions.
9.	Idea not completely expressed.
Chap. VI. The Fundamental Ideas are not derived from Experience		76
Art. 1.	No connexion observed.
2.	Faculties implied in observation.
3.	We are to examine our Faculties.
Chap. VII. Of the Philosophy of the Sciences		81
Sciences arranged according to Ideas.
ix
BOOK II.
THE PHILOSOPHY OF THE PURE SCIENCES.
Chap. I. Of the Pure Sciences		88
Art. 1.	Geometry, Arithmetic, Algebra,
2.	Are not Inductive Sciences:
3.	Are Mathematical Sciences.
4.	Mixed Mathematics.
5.	Space, Time, Number.
Chap. II. Of the Idea of Space		91
Art. 1.	Space is an Idea,
2.	Not derived from Experience,
3.	As Geometrical Truth shows.
4.	Space is a Form of Experience.
5.	The phrase not essential.
Chap. III. Of some Peculiarities of the Idea of Space		95
Art. 1.	Space is not an Abstract Notion.
2.	Space is infinite.
3.	Space is real.
4.	Space is a Form of Intuition.
5.	Figure.
6.	Three Dimensions.
Chap. IV. Of the Definitions and Axioms which relate to Space		98
Art. 1.	Geometry.
2.	Definitions.
3.	Axioms.
4.	Not Hypotheses.
5.	Axioms necessary.
6.	Straight Lines.
7.	Planes.
8.	Elementary Geometry.
Chap. V. Of some Objections which have been made to the Doctrines stated in the previous Chapter		107
Art. 1.	How is Geometry hypothetical?
2.	What was Stewart's view?
x
3.	'Legitimate filiations' of Definitions.
4.	Is a Definition a complete explanation?
5.	Are some Axioms Definitions?
6.	Axiom concerning Circles.
7.	Can Axioms become truisms?
8.	Use of such.
Chap. VI. Of the Perception of Space		117
Art. 1.	Which Senses apprehend Space?
2.	Perception of solid figure.
3.	Is an interpretation.
4.	May be analysed.
5.	Outline.
6.	Reversed convexity.
7.	Do we perceive Space by Touch?
8.	Brown’s Opinion.
9.	The Muscular Sense.
10.	Bell’s Opinion.
11.	Perception includes Activity.
12.	Perception of the Skyey Dome.
13.	Reid’s Idomenians.
14.	Motion of the Eye.
15.	Searching Motion.
16.	Sensible Spot.
17.	Expressions implying Motion.
Chap. VII. Of the Idea of Time		131
Art. 1.	Time an Idea not derived from Experience.
2.	Time is a Form of Experience.
3.	Number.
4.	Is Time derived from Motion?
Chap. VIII. Of some Peculiarities in the Idea of Time		134
Art. 1.	Time is not an Abstract Notion.
2.	Time is infinite.
3.	Time is a Form of Intuition.
4.	Time is of one Dimension,
5.	And no more.
6.	Rhythm.
7.	Alternation.
8.	Arithmetic.
xi
Chap. IX. Of the Axioms which relate to Number		138
Art. 1.	Grounds of Arithmetic.
2.	Intuition.
3.	Arithmetical Axioms,
4.	Are Conditions of Numerical Reasoning
5.	In all Arithmetical Operations.
6.	Higher Numbers.
Chap. X. Of the Perception of Time and Number		141
Art. 1.	Memory.
2.	Sense of Successiveness
3.	Implies Activity.
4.	Number also does so.
5.	And apprehension of Rhythm.
Note to Chapter X.		145
Chap. XI. Of Mathematical Reasoning		147
Art. 1.	Discursive Reasoning.
2.	Technical Terms of Reasoning.
3.	Geometrical Analysis and Synthesis.
Chap. XII. Of the Foundations of the Higher Mathematics		151
Art. 1.	The Idea of a Limit.
2.	The use of General Symbols.
3.	Connexion of Symbols and Analysis.
Chap. XIII. The Doctrine of Motion		156
Art. 1.	Pure Mechanism.
2.	Formal Astronomy.
Chap. XIV. Of the Application of Mathematics to the Inductive Sciences		159
Art. 1.	The Ideas of Space and Number are clear from the first.
2.	Their application in Astronomy.
3.	Conic Sections, &c.
4.	Arabian Numerals.
5.	Newton’s Lemmas.
6.	Tides.
7.	Mechanics.
8.	Optics.
9.	Conclusion.
xii
BOOK III.
THE PHILOSOPHY OF THE MECHANICAL SCIENCES.
Chap. I. Of the Mechanical Sciences		171
Chap. II. Of the Idea of Cause		173
Art. 1.	Not derived from Observation,
2.	As appears by its use.
3.	Cause cannot be observed.
4.	Is Cause only constant succession?
5.	Other reasons.
Chap. III. Modern Opinions respecting the Idea of Cause		178
Art. 1.	Hume’s Doctrine.
2.	Stewart and Brown.
3.	Kant.
4.	Relation of Kant and Brown.
5.	Axioms flow from the Idea.
6.	The Idea implies activity in the Mind.
Chap. IV. Of the Axioms which relate to the Idea of Cause		184
Art. 1.	Causes are Abstract Conceptions.
2.	First Axiom.
3.	Second Axiom.
4.	Limitation of the Second Axiom.
5.	Third Axiom.
6.	Extent of the Third Axiom.
Chap. V. Of the Origin of our Conceptions of Force and Matter		205
Art. 1.	Force.
2.	Matter.
3.	Solidity.
4.	Inertia.
5.	Application.
xiii
Chap. VI. Of the Establishment of the Principles of Statics		212
Art. 1.	Object of the Chapter.
2.	Statics and Dynamics.
3.	Equilibrium.
4.	Measure of Statical Forces.
5.	The Center of Gravity.
6.	Oblique Forces.
7.	Force acts at any point of its Direction.
8.	The Parallelogram of Forces
9.	Is a necessary Truth.
10.	Center of Gravity descends.
11.	Stevinus's Proof.
12.	Principle of Virtual Velocities.
13.	Fluids press equally.
14.	Foundation of this Axiom.
Chap. VII. Of the Establishment of the Principles of Dynamics		235
Art. 1.	History.
2.	The First Law of Motion.
3.	Gravity is a Uniform Force.
4.	The Second Law of Motion.
5.	The Third Law of Motion.
6.	Action and Reaction in Moving Bodies.
7.	D’Alembert’s Principle.
8.	Connexion of Statics and Dynamics.
9.	Mechanical Principles grow more evident.
10.	Controversy of the Measure of Force.
Chap. VIII. Of the Paradox of Universal Propositions obtained from Experience		263
Art. 1.	Experience cannot establish necessary Truths;
2.	But can interpret Axioms.
3.	Gives us the Matter of Truths.
4.	Exemplifies Truths.
5.	Cannot shake Axioms.
6.	Is this applicable in other cases?
Chap. IX. Of the Establishment of the Law of Universal Gravitation		272
Art. 1.	General course of the History.
xiv
2.	Particulars as to the Law.
3.	As to the Gravity of Matter.
4.	Universality of the Law.
5.	Is Gravity an essential quality?
6.	Newton’s Rule of Philosophizing.
7.	Hypotheses respecting Gravity.
8.	Do Bodies act at a distance?
Chap. X. Of the general Diffusion of clear Mechanical Ideas		279
Art. 1.	Nature of the Process
2.	Among the Ancients.
3.	Kepler, &c.
4.	Lord Monboddo, &c.
5.	Schelling, &c.
6.	Common usage.
7.	Effect of Phrases.
8.	Contempt of Predecessors.
9.	Less detail hereafter.
10.	Mechanico-Chemical Sciences.
11.	Secondary Mechanical Sciences.
BOOK IV.
THE PHILOSOPHY OF THE SECONDARY MECHANICAL SCIENCES.
Chap. I. Of the Idea of a Medium as commonly employed		293
Art. 1.	Of Primary and Secondary Qualities.
2.	The Idea of Externality.
3.	Sensation by a Medium.
4.	Process of Perception of Secondary Qualities.
Chap. II. On Peculiarities in the Perceptions of the Different Senses		302
Art. 1.	Difference of Senses.
Sect. I.	Prerogatives of Sight.
Art. 2.	Position.
3.	Distance.
xv
Sect. II.	Prerogatives of Hearing.
Art. 4.	Musical Intervals.
5.	Chords.
6.	Rhythm.
Sect. III.	The Paradoxes of Vision.
Art. 7.	First Paradox.
8.	Second Paradox.
9.	The same for near Objects.
10.	Objections answered.
Sect. IV.	The Perception of Visible Figures.
Art. 11.	Brown’s Opinion.
Chap. III. Successive Attempts at the Scientific Application of the Idea of a Medium		322
Art. 1.	Introduction.
2.	Sound.
3.	Light.
4.	Heat.
Chap. IV. Of the Measure of Secondary Qualities		333
Sect. I.	Scales of Qualities in General.
Art. 1.	Intensity.
2.	Quantity and Quality.
Sect. II.	The Musical Scale.
Art. 3.	Musical Relations.
4.	Musical Standard.
Sect. III.	Scales of Colour.
Art. 5.	The Prismatic Scale.
6.	Newton’s Scale.
7.	Scales of Impure Colours.
8.	Chromatometer.
Sect. IV.	Scales of Light.
Art. 9.	Photometer.
10.	Cyanometer.
Sect. V.	Scales of Heat.
Art. 11.	Thermometers.
12.	Their progress.
13.	Fixed Points.
14.	Concordance of Thermometers.
15.	Natural Measure.
16.	Law of Cooling.
xvi
17.	Theory of Exchanges.
18.	Air Thermometer.
19.	Theory of Heat.
20.	Other Instruments.
Sect. VI.	Scales of other Quantities.
Art. 21.	Tastes and Smells.
22.	Quality of Sounds.
23.	Articulate Sounds.
24.	Transition.
BOOK V.
OF THE PHILOSOPHY OF THE MECHANICO-CHEMICAL SCIENCES.
Chap. I. Attempts at the Scientific Application of the Idea of Polarity		359
Art. 1.	Introduction of the Idea.
2.	Magnetism.
3.	Electricity.
4.	Voltaic Electricity.
5.	Light.
6.	Crystallization.
7.	Chemical Affinity.
8.	General Remarks.
9.	Like repels like.
Chap. II. Of the Connexion of Polarities		371
Art. 1.	Different Polar Phenomena from one Cause.
2.	Connexion of Magnetic and Electric Polarity.
3.	Ampère’s Theory.
4.	Faraday’s views.
5.	Connexion of Electrical and Chemical Polarity.
6.	Davy’s and Faraday’s views
7.	Depend upon Ideas as well as Experiments.
8.	Faraday’s Anticipations.
9.	Connexion of Chemical and Crystalline Polarities.
10.	Connexion of Crystalline and Optical Polarities.
11.	Connexion of Polarities in general.
12.	Schelling’s Speculations.
13.	Hegel’s vague notions.
14.	Ideas must guide Experiment.

The Project Gutenberg eBook of History of scientific ideas

HISTORY
OF
SCIENTIFIC IDEAS.

PREFACE TO THIS EDITION.

CONTENTS
OF
THE FIRST VOLUME.

CONTENTS
OF
THE SECOND VOLUME.

The Project Gutenberg eBook of History of scientific ideas

HISTORY OF SCIENTIFIC IDEAS.

PREFACE TO THIS EDITION.

CONTENTS OF THE FIRST VOLUME.

CONTENTS OF THE SECOND VOLUME.

HISTORY
OF
SCIENTIFIC IDEAS.

CONTENTS
OF
THE FIRST VOLUME.

CONTENTS
OF
THE SECOND VOLUME.