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The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

By Henri Poincaré
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Table of Contents
  • 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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