Copyright, 1913
BY The Science Press

PRESS OF
THE NEW ERA PRINTING COMPANY
LANCASTER, PA.

CONTENTS

PAGE
Henri Poincaré[ix]
Author's Preface to the Translation[3]
[SCIENCE AND HYPOTHESIS]
Introduction by Royce[9]
Introduction[27]
Part I. Number and Magnitude
Chapter I.—On the Nature of Mathematical Reasoning[31]
Syllogistic Deduction[31]
Verification and Proof[32]
Elements of Arithmetic[33]
Reasoning by Recurrence[37]
Induction[40]
Mathematical Construction[41]
Chapter II.—Mathematical Magnitude and Experience[43]
Definition of Incommensurables[44]
The Physical Continuum[46]
Creation of the Mathematical Continuum[46]
Measurable Magnitude[49]
Various Remarks (Curves without Tangents)[50]
The Physical Continuum of Several Dimensions[52]
The Mathematical Continuum of Several Dimensions[53]
Part II. Space
Chapter III.—The Non-Euclidean Geometries[55]
The Bolyai-Lobachevski Geometry[56]
Riemann's Geometry[57]
The Surfaces of Constant Curvature[58]
Interpretation of Non-Euclidean Geometries[59]
The Implicit Axioms[60]
The Fourth Geometry[62]
Lie's Theorem[62]
Riemann's Geometries[63]
On the Nature of Axioms[63]
Chapter IV.—Space and Geometry[66]
Geometric Space and Perceptual Space[66]
Visual Space[67]
Tactile Space and Motor Space[68]
Characteristics of Perceptual Space[69]
Change of State and Change of Position[70]
Conditions of Compensation[72]
Solid Bodies and Geometry[72]
Law of Homogeneity[74]
The Non-Euclidean World[75]
The World of Four Dimensions[78]
Conclusions[79]
Chapter V.—Experience and Geometry[81]
Geometry and Astronomy[81]
The Law of Relativity[83]
Bearing of Experiments[86]
Supplement (What is a Point?)[89]
Ancestral Experience[91]
Part III. Force
Chapter VI.—The Classic Mechanics[92]
The Principle of Inertia[93]
The Law of Acceleration[97]
Anthropomorphic Mechanics[103]
The School of the Thread[104]
Chapter VII.—Relative Motion and Absolute Motion[107]
The Principle of Relative Motion[107]
Newton's Argument[108]
Chapter VIII.—Energy and Thermodynamics[115]
Energetics[115]
Thermodynamics[119]
General Conclusions on Part III[123]
Part IV. Nature
Chapter IX.—Hypotheses in Physics[127]
The Rôle of Experiment and Generalization[127]
The Unity of Nature[130]
The Rôle of Hypothesis[133]
Origin of Mathematical Physics[136]
Chapter X.—The Theories of Modern Physics[140]
Meaning of Physical Theories[140]
Physics and Mechanism[144]
Present State of the Science[148]
Chapter XI.—The Calculus of Probabilities[155]
Classification of the Problems of Probability[158]
Probability in Mathematics[161]
Probability in the Physical Sciences[164]
Rouge et noir[167]
The Probability of Causes[169]
The Theory of Errors[170]
Conclusions[172]
Chapter XII.—Optics and Electricity[174]
Fresnel's Theory[174]
Maxwell's Theory[175]
The Mechanical Explanation of Physical Phenomena[177]
Chapter XIII.—Electrodynamics[184]
Ampère's Theory[184]
Closed Currents[185]
Action of a Closed Current on a Portion of Current[186]
Continuous Rotations[187]
Mutual Action of Two Open Currents[189]
Induction[190]
Theory of Helmholtz[191]
Difficulties Raised by these Theories[193]
Maxwell's Theory[193]
Rowland's Experiment[194]
The Theory of Lorentz[196]
[THE VALUE OF SCIENCE]
Translator's Introduction[201]
Does the Scientist Create Science?[201]
The Mind Dispelling Optical Illusions[202]
Euclid not Necessary[202]
Without Hypotheses, no Science[203]
What Outcome?[203]
Introduction[205]
Part I. The Mathematical Sciences
Chapter I.—Intuition and Logic in Mathematics[210]
Chapter II.—The Measure of Time[223]
Chapter III.—The Notion of Space[235]
Qualitative Geometry[238]
The Physical Continuum of Several Dimensions[240]
The Notion of Point[244]
The Notion of Displacement[247]
Visual Space[252]
Chapter IV.—Space and its Three Dimensions[256]
The Group of Displacements[256]
Identity of Two Points[259]
Tactile Space[264]
Identity of the Different Spaces[268]
Space and Empiricism[271]
Rôle of the Semicircular Canals[276]
Part II. The Physical Sciences
Chapter V.—Analysis and Physics[279]
Chapter VI.—Astronomy[289]
Chapter VII.—The History of Mathematical Physics[297]
The Physics of Central Forces[297]
The Physics of the Principles[299]
Chapter VIII.—The Present Crisis in Physics[303]
The New Crisis[303]
Carnot's Principle[303]
The Principle of Relativity[305]
Newton's Principle[308]
Lavoisier's Principle[310]
Mayer's Principle[312]
Chapter IX.—The Future of Mathematical Physics[314]
The Principles and Experiment[314]
The Rôle of the Analyst[314]
Aberration and Astronomy[315]
Electrons and Spectra[316]
Conventions preceding Experiment[317]
Future Mathematical Physics[319]
Part III. The Objective Value of Science
Chapter X.—Is Science Artificial?[321]
The Philosophy of LeRoy[321]
Science, Rule of Action[323]
The Crude Fact and the Scientific Fact[325]
Nominalism and the Universal Invariant[333]
Chapter XI.—Science and Reality[340]
Contingence and Determinism[340]
Objectivity of Science[347]
The Rotation of the Earth[353]
Science for Its Own Sake[354]
[SCIENCE AND METHOD]
Introduction[359]
Book I. Science and the Scientist
Chapter I.—The Choice of Facts[362]
Chapter II.—The Future of Mathematics[369]
Chapter III.—Mathematical Creation[383]
Chapter IV.—Chance[395]
Book II. Mathematical Reasoning
Chapter I.—The Relativity of Space[413]
Chapter II.—Mathematical Definitions and Teaching[430]
Chapter III.—Mathematics and Logic[448]
Chapter IV.—The New Logics[460]
Chapter V.—The Latest Efforts of the Logisticians[472]
Book III. The New Mechanics
Chapter I.—Mechanics and Radium[486]
Chapter II.—Mechanics and Optics[496]
Chapter III.—The New Mechanics and Astronomy[512]
Book IV. Astronomic Science
Chapter I.—The Milky Way and the Theory of Gases[523]
Chapter II.—French Geodesy[535]
General Conclusions[544]
Index[547]

HENRI POINCARÉ

Sir George Darwin, worthy son of an immortal father, said, referring to what Poincaré was to him and to his work: "He must be regarded as the presiding genius—or, shall I say, my patron saint?"