Chapter I: Front Matter

SCIENCE AND EDUCATION

A SERIES OF VOLUMES FOR THE PROMOTION OF
SCIENTIFIC RESEARCH AND EDUCATIONAL PROGRESS

EDITED BY J. MCKEEN CATTELL

VOLUME I--THE FOUNDATIONS OF SCIENCE

UNDER THE SAME EDITORSHIP

SCIENCE AND EDUCATION. A series of volumes for the promotion of
scientific research and educational progress.

Volume I. The Foundations of Science. By H. POINCARÉ. Containing
the authorised English translation by George Bruce Halsted of
"Science and Hypothesis," "The Value of Science," and "Science
and Method."

Volume II. Medical Research and Education. By Richard Mills
Pearce, William H. Welch, W. H. Howell, Franklin P. Mall,
Lewellys F. Barker, Charles S. Minot, W. B. Cannon, W. T.
Councilman Theobald Smith, G. N. Stewart, C. M. Jackson,
E. P. Lyon, James B. Herrick, John M. Dodson, C. R. Bardeen,
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Donaldson, Christian A. Herter, and Henry P. Bowditch.

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authors.

AMERICAN MEN OF SCIENCE. A Biographical Directory.

SCIENCE. A weekly journal devoted to the advancement of science.
The official organ of the American Association for the
Advancement of Science.

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THE SCIENCE PRESS

NEW YORK GARRISON, N. Y.

THE FOUNDATIONS
OF SCIENCE

SCIENCE AND HYPOTHESIS
THE VALUE OF SCIENCE
SCIENCE AND METHOD

BY
H. POINCARÉ

AUTHORIZED TRANSLATION BY
GEORGE BRUCE HALSTED

WITH A SPECIAL PREFACE BY POINCARÉ, AND AN INTRODUCTION
BY JOSIAH ROYCE, HARVARD UNIVERSITY

THE SCIENCE PRESS
NEW YORK AND GARRISON, N. Y.
1913

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