Science and Hypothesis : The Complete Text

Science and Hypothesis is a classic text in history and philosophy of science. Widely popular since its original publication in 1902, this first new translation of the work in over a century features unpublished material missing from earlier editions. Addressing errors introduced by Greenstreet and Halstead in their early 20th-century translations, it incorporates all the changes, corrections and additions Poincare made over the years. Taking care to update the writing for a modern audience, Poincare's ideas and arguments become clearer and closer to his original meaning, while David Stump's introduction gives fresh insights into Poincare's philosophy of science. By approaching Science and Hypothesis from a contemporary perspective, it presents a better understanding of Poincare's hierarchy of the sciences, with arithmetic as the foundation, geometry as the science of space, then mechanics and the rest of physics. For philosophers of science and scientists working on problems of space, time and relatively, this is a much needed translation of a ground-breaking work which demonstrates why Poincare is still relevant today. Cover page......Page 1 Halftitle page......Page 2 Series page......Page 3 Title page......Page 4 Copyright page......Page 5 Contents......Page 6 Foreword......Page 8 Acknowledgments......Page 23 Original Sources of the Material in Science and Hypothesis......Page 24 Author’s Preface to the Halsted Translation......Page 28 Introduction......Page 34 Part One Number and Magnitude......Page 38 I......Page 40 II......Page 41 III......Page 42 IV......Page 45 V......Page 46 VI......Page 47 VII......Page 48 2 Mathematical Magnitude and Experience......Page 52 Definition of incommensurables......Page 53 Creation of the mathematical continuum......Page 55 Measurable magnitude......Page 58 Various remarks......Page 59 The multidimensional physical continuum......Page 60 The multidimensional mathematical continuum......Page 61 Part Two Space......Page 64 3 Non-Euclidian Geometries......Page 66 Lobachevskiian geometry......Page 67 Riemann’s geometry......Page 68 Surfaces with a constant curvature......Page 69 Interpretation of non-Euclidean geometries......Page 70 Implicit axioms......Page 71 Lie’s theorem......Page 73 On the nature of axioms......Page 74 Geometrical space and representative space......Page 78 Visual space......Page 79 Tactile space and motor space......Page 80 Characteristics of representative space......Page 81 Changes of state and changes of position......Page 82 Conditions of compensation......Page 83 Solid bodies and geometry......Page 84 The law of homogeneity......Page 85 The non-Euclidean world6......Page 86 The four-dimensional world......Page 88 Conclusions......Page 89 3 Geometry and astronomy......Page 92 4......Page 93 5......Page 94 6......Page 96 7......Page 97 8......Page 99 Ancestral experience6......Page 101 Part Three Force......Page 102 6 Classical Mechanics......Page 104 The principle of inertia......Page 105 The law of acceleration......Page 108 Anthropomorphic mechanics......Page 113 The “School of the Thread”......Page 114 The principle of relative motion......Page 116 Newton’s argument......Page 117 Energetics......Page 124 Thermodynamics*......Page 127 General Conclusions for Part Th ree......Page 132 Part Four Nature......Page 134 The role of experiment and generalization......Page 136 The unity of nature......Page 138 The role of hypotheses......Page 141 Origin of mathematical physics......Page 143 The meaning of physical theories......Page 148 Physics and mechanism......Page 151 The current state of physics......Page 154 11 Probability Calculus......Page 160 I: Classification of problems of probability......Page 163 II: Probability in mathematics......Page 165 III: Probability in the physical sciences......Page 167 IV: Red and black......Page 170 V: Probabilistic causation......Page 171 VI: Theory of errors......Page 173 VII: Conclusions......Page 175 Fresnel’s theory......Page 176 Maxwell’s theory......Page 177 The mechanical explanation of physical phenomena......Page 179 I Ampère’s theory......Page 184 II Helmholtz’s theory......Page 190 IV Maxwell’s theory......Page 192 V Rowland’s experiments......Page 193 VI Lorentz’s theory......Page 194 14 The End of Matter*......Page 196 Index......Page 200 Cover page 1 Halftitle page 2 Series page 3 Title page 4 Copyright page 5 Contents 6 Foreword 8 Acknowledgments 23 Original Sources of the Material in Science and Hypothesis 24 Author’s Preface to the Halsted Translation 28 Introduction 34 Part One Number and Magnitude 38 1 On the Nature of Mathematical Reasoning 40 I 40 II 41 III 42 IV 45 V 46 VI 47 VII 48 2 Mathematical Magnitude and Experience 52 Definition of incommensurables 53 The physical continuum 55 Creation of the mathematical continuum 55 Measurable magnitude 58 Various remarks 59 The multidimensional physical continuum 60 The multidimensional mathematical continuum 61 Part Two Space 64 3 Non-Euclidian Geometries 66 Lobachevskiian geometry 67 Riemann’s geometry 68 Surfaces with a constant curvature 69 Interpretation of non-Euclidean geometries 70 Implicit axioms 71 The fourth geometry6 73 Lie’s theorem 73 Riemann’s geometries 74 Hilbert’s geometries8 74 On the nature of axioms 74 4 Space and Geometry 78 Geometrical space and representative space 78 Visual space 79 Tactile space and motor space 80 Characteristics of representative space 81 Changes of state and changes of position 82 Conditions of compensation 83 Solid bodies and geometry 84 The law of homogeneity 85 The non-Euclidean world6 86 The four-dimensional world 88 Conclusions 89 5 Experience and Geometry 92 1 92 2 92 3 Geometry and astronomy 92 4 93 5 94 6 96 7 97 SUPPLEMENT 99 8 99 Ancestral experience6 101 Part Three Force 102 6 Classical Mechanics 104 The principle of inertia 105 The law of acceleration 108 Anthropomorphic mechanics 113 The “School of the Thread” 114 7 Relative and Absolute Motion 116 The principle of relative motion 116 Newton’s argument 117 8 Energy and Thermodynamics 124 Energetics 124 Thermodynamics* 127 General Conclusions for Part Th ree 132 Part Four Nature 134 9 Hypotheses in Physics 136 The role of experiment and generalization 136 The unity of nature 138 The role of hypotheses 141 Origin of mathematical physics 143 10 Theories of Modern Physics 148 The meaning of physical theories 148 Physics and mechanism 151 The current state of physics 154 11 Probability Calculus 160 I: Classification of problems of probability 163 II: Probability in mathematics 165 III: Probability in the physical sciences 167 IV: Red and black 170 V: Probabilistic causation 171 VI: Theory of errors 173 VII: Conclusions 175 12 Optics and Electricity 176 Fresnel’s theory 176 Maxwell’s theory 177 The mechanical explanation of physical phenomena 179 13 Electrodynamics 184 I Ampère’s theory 184 II Helmholtz’s theory 190 III Difficulties raised by these theories 192 IV Maxwell’s theory 192 V Rowland’s experiments 193 VI Lorentz’s theory 194 14 The End of Matter* 196 Index 200 "Science and Hypothesis is a classic text in history and philosophy of science. Widely popular since its original publication in 1902, this first new translation of the work in over a century features unpublished material missing from earlier editions. Addressing errors introduced by Greenstreet and Halsted in their early 20th-century translations, it incorporates all the changes, corrections and additions Poincaré made over the years. Taking care to update the writing for a modern audience, Poincarés ideas and arguments on the role of hypotheses in mathematics and in science become clearer and closer to his original meaning, while David J. Stump's introduction gives fresh insights into Poincaré's philosophy of science. By approaching Science and Hypothesis from a contemporary perspective, it presents a better understanding of Poincare's hierarchy of the sciences, with arithmetic as the foundation, geometry as the science of space, then mechanics and the rest of physics. For philosophers of science and scientists working on problems of space, time and relativity, this is a much needed translation of a ground-breaking work which demonstrates why Poincaré is still relevant today. Poincaré saw the recognition of the role of hypotheses in science as an important alternative to both rationalism and empiricism. In Science and Hypothesis, his aim is to show that both in mathematics and in the physical sciences, scientists rely on hypotheses that are neither necessary first principles, as the rationalists claim, nor learned from experience, as the empiricist claim. These hypotheses fall into distinct classes, but he is most famous for his thesis of the conventionality of metric geometry. Poincaré discusses the sciences in a sequence, starting with arithmetic. Mathematical induction is essential in arithmetic, because only by using it can we make assertions about all numbers. Poincaré considers mathematical induction to be a genuine synthetic a priori judgment. He next considers magnitude, which requires arithmetic, but goes further. Likewise, geometry extends our knowledge still further, but requires the theory of magnitude to make measurements, and arithmetic to combine numbers. Poincaré then considers classical mechanics, which again extends our knowledge while relying on the mathematics that came before it. Finally, he considers theories of physics, where we have genuine empirical results, but based on the mathematics, hypotheses and conventions that came before. Thus the sciences are laid out like expanding concentric circles, with new content being added to the base at each level."--Bloomsbury Publishing __Science and Hypothesis__Addressing errors introduced by Greenstreet and Halstead in their early 20th-century translations, it incorporates all the changes, corrections and additions Poincare made over the years. Taking care to update the writing for a modern audience, Poincare's ideas and arguments become clearer and closer to his original meaning, while David Stump's introduction gives fresh insights into Poincare's philosophy of science. By approachingfrom a contemporary perspective, it presents a better understanding of Poincare's hierarchy of the sciences, with arithmetic as the foundation, geometry as the science of space, then mechanics and the rest of physics.For philosophers of science and scientists working on problems of space, time and relatively, this is a much needed translation of a ground-breaking work which demonstrates why Poincare is still relevant today.