The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method
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THE FOUNDATIONS OF SCIENCE
CONTENTS
HENRI POINCARÉ
SCIENCE AND HYPOTHESIS
AUTHOR'S PREFACE TO THE TRANSLATION
INTRODUCTION
I
II
III
IV
V
I
II
III
IV
V
INTRODUCTION
I
II
III
IV
V
I
II
III
IV
V
SCIENCE AND HYPOTHESIS
INTRODUCTION
INTRODUCTION
PART I NUMBER AND MAGNITUDE
CHAPTER I
On the Nature of Mathematical Reasoning
I
II
III
IV
V
VI
VII
I
II
III
IV
V
VI
VII
CHAPTER II
Mathematical Magnitude and Experience
CHAPTER I
On the Nature of Mathematical Reasoning
I
II
III
IV
V
VI
VII
I
II
III
IV
V
VI
VII
CHAPTER II
Mathematical Magnitude and Experience
PART II SPACE
CHAPTER III
The Non-euclidean Geometries
CHAPTER IV
Space and Geometry
CHAPTER V
Experience and Geometry
Ancestral Experience
CHAPTER III
The Non-euclidean Geometries
CHAPTER IV
Space and Geometry
CHAPTER V
Experience and Geometry
Ancestral Experience
PART III FORCE
CHAPTER VI
The Classic Mechanics
CHAPTER VII
Relative Motion and Absolute Motion
CHAPTER VIII
Energy and Thermodynamics
General Conclusions on Part Third
CHAPTER VI
The Classic Mechanics
CHAPTER VII
Relative Motion and Absolute Motion
CHAPTER VIII
Energy and Thermodynamics
General Conclusions on Part Third
PART IV NATURE
CHAPTER IX
Hypotheses in Physics
CHAPTER X
The Theories of Modern Physics
CHAPTER XI
The Calculus of Probabilities
CHAPTER XII
Optics and Electricity
CHAPTER XIII
Electrodynamics
CHAPTER IX
Hypotheses in Physics
CHAPTER X
The Theories of Modern Physics
CHAPTER XI
The Calculus of Probabilities
CHAPTER XII
Optics and Electricity
CHAPTER XIII
Electrodynamics
THE VALUE OF SCIENCE
TRANSLATOR'S INTRODUCTION
INTRODUCTION
INTRODUCTION
PART I THE MATHEMATICAL SCIENCES
CHAPTER I
Intuition and Logic in Mathematics
I
II
III
IV
V
VI
I
II
III
IV
V
VI
CHAPTER II
The Measure of Time
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
XII
XIII
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
XII
XIII
CHAPTER III
The Notion of Space
1. Introduction
2. Qualitative Geometry
3. The Physical Continuum of Several Dimensions
4. The Notion of Point
5. The Notion of Displacement
6. Visual Space
1. Introduction
2. Qualitative Geometry
3. The Physical Continuum of Several Dimensions
4. The Notion of Point
5. The Notion of Displacement
6. Visual Space
CHAPTER IV
Space and its Three Dimensions
1. The Group of Displacements
2. Identity of Two Points
3. Tactile Space
4. Identity of the Different Spaces
5. Space and Empiricism
6. Mind and Space
7. Rôle of the Semicircular Canals
1. The Group of Displacements
2. Identity of Two Points
3. Tactile Space
4. Identity of the Different Spaces
5. Space and Empiricism
6. Mind and Space
7. Rôle of the Semicircular Canals
CHAPTER I
Intuition and Logic in Mathematics
I
II
III
IV
V
VI
I
II
III
IV
V
VI
CHAPTER II
The Measure of Time
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
XII
XIII
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
XII
XIII
CHAPTER III
The Notion of Space
1. Introduction
2. Qualitative Geometry
3. The Physical Continuum of Several Dimensions
4. The Notion of Point
5. The Notion of Displacement
6. Visual Space
1. Introduction
2. Qualitative Geometry
3. The Physical Continuum of Several Dimensions
4. The Notion of Point
5. The Notion of Displacement
6. Visual Space
CHAPTER IV
Space and its Three Dimensions
1. The Group of Displacements
2. Identity of Two Points
3. Tactile Space
4. Identity of the Different Spaces
5. Space and Empiricism
6. Mind and Space
7. Rôle of the Semicircular Canals
1. The Group of Displacements
2. Identity of Two Points
3. Tactile Space
4. Identity of the Different Spaces
5. Space and Empiricism
6. Mind and Space
7. Rôle of the Semicircular Canals
PART II THE PHYSICAL SCIENCES
CHAPTER V
Analysis and Physics
I
II
III
IV
I
II
III
IV
CHAPTER VI
Astronomy
CHAPTER VII
The History of Mathematical Physics
CHAPTER VIII
The Present Crisis of Mathematical Physics
CHAPTER IX
The Future of Mathematical Physics
CHAPTER V
Analysis and Physics
I
II
III
IV
I
II
III
IV
CHAPTER VI
Astronomy
CHAPTER VII
The History of Mathematical Physics
CHAPTER VIII
The Present Crisis of Mathematical Physics
CHAPTER IX
The Future of Mathematical Physics
PART III THE OBJECTIVE VALUE OF SCIENCE
CHAPTER X
Is Science Artificial?
1. The Philosophy of M. LeRoy
2. Science, Rule of Action
3. The Crude Fact and the Scientific Fact
4. 'Nominalism' and 'the Universal Invariant'
1. The Philosophy of M. LeRoy
2. Science, Rule of Action
3. The Crude Fact and the Scientific Fact
4. 'Nominalism' and 'the Universal Invariant'
CHAPTER XI
Science and Reality
5. Contingence and Determinism
6. Objectivity of Science
7. The Rotation of the Earth
8. Science for Its Own Sake
5. Contingence and Determinism
6. Objectivity of Science
7. The Rotation of the Earth
8. Science for Its Own Sake
CHAPTER X
Is Science Artificial?
1. The Philosophy of M. LeRoy
2. Science, Rule of Action
3. The Crude Fact and the Scientific Fact
4. 'Nominalism' and 'the Universal Invariant'
1. The Philosophy of M. LeRoy
2. Science, Rule of Action
3. The Crude Fact and the Scientific Fact
4. 'Nominalism' and 'the Universal Invariant'
CHAPTER XI
Science and Reality
5. Contingence and Determinism
6. Objectivity of Science
7. The Rotation of the Earth
8. Science for Its Own Sake
5. Contingence and Determinism
6. Objectivity of Science
7. The Rotation of the Earth
8. Science for Its Own Sake
SCIENCE AND METHOD
INTRODUCTION
BOOK I SCIENCE AND THE SCIENTIST
CHAPTER I
The Choice of Facts
CHAPTER II
The Future of Mathematics
Arithmetic
Algebra
Geometry
Cantorism
The Investigation of the Postulates
CHAPTER III
Mathematical Creation
CHAPTER IV
Chance
I
II
III
IV
V
VI
VII
VIII
IX
X
I
II
III
IV
V
VI
VII
VIII
IX
X
CHAPTER I
The Choice of Facts
CHAPTER II
The Future of Mathematics
Arithmetic
Algebra
Geometry
Cantorism
The Investigation of the Postulates
CHAPTER III
Mathematical Creation
CHAPTER IV
Chance
I
II
III
IV
V
VI
VII
VIII
IX
X
I
II
III
IV
V
VI
VII
VIII
IX
X
BOOK II MATHEMATICAL REASONING
CHAPTER I
The Relativity of Space
I
II
III
IV
V
VI
I
II
III
IV
V
VI
CHAPTER II
Mathematical Definitions and Teaching
Arithmetic
Geometry
Mechanics
CHAPTER III
Mathematics and Logic
Introduction
I
II
III
IV
V
VI
VII
Pasigraphy
VIII
Introduction
I
II
III
IV
V
VI
VII
Pasigraphy
VIII
CHAPTER IV
The New Logics
I
The Russell Logic
II
III
IV
V
Arithmetic
VI
The Logic of Hilbert
VII
VIII
IX
X
Geometry
XI
Conclusion
XII
XIII
I
The Russell Logic
II
III
IV
V
Arithmetic
VI
The Logic of Hilbert
VII
VIII
IX
X
Geometry
XI
Conclusion
XII
XIII
CHAPTER V
The Latest Efforts of the Logisticians
I
II
The Infallibility of Logistic
III
The Liberty of Contradiction
IV
The Second Objection
V
The Cantor Antinomies
VI
Zigzag Theory and No-class Theory
VII
The True Solution
VIII
The Demonstrations of the Principle of Induction
IX
X
Zermelo's Assumption
XI
Conclusions
I
II
The Infallibility of Logistic
III
The Liberty of Contradiction
IV
The Second Objection
V
The Cantor Antinomies
VI
Zigzag Theory and No-class Theory
VII
The True Solution
VIII
The Demonstrations of the Principle of Induction
IX
X
Zermelo's Assumption
XI
Conclusions
CHAPTER I
The Relativity of Space
I
II
III
IV
V
VI
I
II
III
IV
V
VI
CHAPTER II
Mathematical Definitions and Teaching
Arithmetic
Geometry
Mechanics
CHAPTER III
Mathematics and Logic
Introduction
I
II
III
IV
V
VI
VII
Pasigraphy
VIII
Introduction
I
II
III
IV
V
VI
VII
Pasigraphy
VIII
CHAPTER IV
The New Logics
I
The Russell Logic
II
III
IV
V
Arithmetic
VI
The Logic of Hilbert
VII
VIII
IX
X
Geometry
XI
Conclusion
XII
XIII
I
The Russell Logic
II
III
IV
V
Arithmetic
VI
The Logic of Hilbert
VII
VIII
IX
X
Geometry
XI
Conclusion
XII
XIII
CHAPTER V
The Latest Efforts of the Logisticians
I
II
The Infallibility of Logistic
III
The Liberty of Contradiction
IV
The Second Objection
V
The Cantor Antinomies
VI
Zigzag Theory and No-class Theory
VII
The True Solution
VIII
The Demonstrations of the Principle of Induction
IX
X
Zermelo's Assumption
XI
Conclusions
I
II
The Infallibility of Logistic
III
The Liberty of Contradiction
IV
The Second Objection
V
The Cantor Antinomies
VI
Zigzag Theory and No-class Theory
VII
The True Solution
VIII
The Demonstrations of the Principle of Induction
IX
X
Zermelo's Assumption
XI
Conclusions
BOOK III THE NEW MECHANICS
CHAPTER I
Mechanics and Radium
I
Introduction
II
Mass Longitudinal and Mass Transversal
III
The Canal Rays
IV
The Theory of Lorentz
V
Mechanical Consequences
I
Introduction
II
Mass Longitudinal and Mass Transversal
III
The Canal Rays
IV
The Theory of Lorentz
V
Mechanical Consequences
CHAPTER II
Mechanics and Optics
I
Aberration
II
The Principle of Relativity
III
The Principle of Reaction
IV
Consequences of the Principle of Relativity
V
Kaufmann's Experiment
VI
The Principle of Inertia
VII
The Wave of Acceleration
I
Aberration
II
The Principle of Relativity
III
The Principle of Reaction
IV
Consequences of the Principle of Relativity
V
Kaufmann's Experiment
VI
The Principle of Inertia
VII
The Wave of Acceleration
CHAPTER III
The New Mechanics and Astronomy
I
Gravitation
II
Comparison with Astronomic Observations
III
The Theory of Lesage
IV
Conclusions
I
Gravitation
II
Comparison with Astronomic Observations
III
The Theory of Lesage
IV
Conclusions
CHAPTER I
Mechanics and Radium
I
Introduction
II
Mass Longitudinal and Mass Transversal
III
The Canal Rays
IV
The Theory of Lorentz
V
Mechanical Consequences
I
Introduction
II
Mass Longitudinal and Mass Transversal
III
The Canal Rays
IV
The Theory of Lorentz
V
Mechanical Consequences
CHAPTER II
Mechanics and Optics
I
Aberration
II
The Principle of Relativity
III
The Principle of Reaction
IV
Consequences of the Principle of Relativity
V
Kaufmann's Experiment
VI
The Principle of Inertia
VII
The Wave of Acceleration
I
Aberration
II
The Principle of Relativity
III
The Principle of Reaction
IV
Consequences of the Principle of Relativity
V
Kaufmann's Experiment
VI
The Principle of Inertia
VII
The Wave of Acceleration
CHAPTER III
The New Mechanics and Astronomy
I
Gravitation
II
Comparison with Astronomic Observations
III
The Theory of Lesage
IV
Conclusions
I
Gravitation
II
Comparison with Astronomic Observations
III
The Theory of Lesage
IV
Conclusions
BOOK IV ASTRONOMIC SCIENCE
CHAPTER I
The Milky Way and the Theory of Gases
CHAPTER II
French Geodesy
GENERAL CONCLUSIONS
CHAPTER I
The Milky Way and the Theory of Gases
CHAPTER II
French Geodesy
GENERAL CONCLUSIONS
INDEX
FOOTNOTES
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