| 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] |