Poincare's Philosophy From Conventionalism to Phenomenology

by Zahar, Elie

• ISBN13: 9780812694352
• ISBN10: 081269435X
• Format: Paperback
• Copyright: 2001-06-05
• Publisher: Open Court

Summary

Henri Poincare (1854–1912) was one of the greatest mathematicians and philosophers of all time. He founded topology and made important contributions to theoretical physics. Yet despite his numerous achievements Poincare never constructed a systematic philosophy. In this book, Elie Zahar presents Poincare’s work for the first time as a unified system of thought.

Author Biography

Elie Zahar is Reader Emeritus in Logic and Scientific Method at the London School of Economics and Associate Member of the History and Philosophy of Science Department, University of Cambridge

Table of Contents

Introduction	p. 1
Poincare's General Philosophy of Science	p. 7
The Character of Physical Theory	p. 7
Unity versus Induction	p. 8
The Falsifiability of Scientific Laws	p. 10
Conventionalism and the Empiricist Meaning-Criterion	p. 11
Convenience, Non-Adhoc Explanations, and the Principle of Unity	p. 16
Adhocness and Parameter Adjustment	p. 17
The Problem of the Empirical Basis: Popper versus Poincare	p. 20
Refutation of the Psychologist Thesis	p. 24
Unmanageable Largism?	p. 33
Poincare's Structural Realism and his Logic of Discovery	p. 37
Realism and the Reality of Universals	p. 37
Interpretation versus Reduction: Duhem's and Poincare's Views about the Structure of Physical Theory	p. 41
Continuity of Sense or Continuity of Reference?	p. 50
The Structure of Poincare's Argument in Favour of Structural Realism	p. 54
Does Realism Have a Cognitive or Merely a Motivational Content?	p. 61
Poincare's Philosophy of Geometry	p. 65
Conventionalism and Geometry	p. 65
Poincare's Concept of Physical Geometry	p. 68
Poincare's Half-Plane and Trivial Semantic Conventionalism (TSC)	p. 74
Poincare's Disk Model	p. 82
The Unity of Poincare's Heuristic, or His Simultaneous Discovery of Fuchsian Functions and of Different Models for Hyperbolic Geometry	p. 88
Discovery or Invention of Universal Fields?	p. 93
Poincare's Relativity Programme	p. 107
First Steps towards Relativity	p. 108
Convention and Physical Fact	p. 112
An Outline of Poincare's Relativity Programme	p. 116
The Correspondence Principle	p. 118
The Regulative Role of Symmetry Principles	p. 123
The Reform of Electromagnetism	p. 128
Poincare's 4-Dimensional World	p. 132
A Synopsis of Poincare's Gravitational Theory	p. 135
The Foundations of Mathematics according to Poincare and Russell	p. 137
An Overview of Poincare's Philosophy of Mathematics	p. 137
Mathematical Induction	p. 141
The Logical Paradoxes	p. 146
Epistemological Fundamentalism (or Integralism)	p. 148
The Integrity of Mathematics	p. 148
Banning Adhoc Stratagems	p. 149
Russell's Principle of Syntactical Prevention	p. 160
A Critique of Russellian Logic	p. 163
Russell's Latent Constuctivism	p. 163
Wittgenstein's Paradox and the Primacy of Arithmetic	p. 168
The Partial Failure of Logicism	p. 174
Poincare's Partial Solution to the Paradoxes	p. 179
Poincare, Russell, and Modern Empiricism	p. 185
The Vienna Circile	p. 185
The Problem of Mathematical Realism within the Physical Sciences	p. 189
Hartry Field's Dismissal of Mathematical Ontology	p. 192
Field's Results and His Method of Proof	p. 193
The Ultimate Failure of Field's Programme	p. 195
Formalism, Intentionality, or Platonism?	p. 201
The Problem of Mathematical Ontology	p. 201
Husserl's Programme	p. 202
The Phenomenological Constitution of Logic and Mathematics	p. 206
The Ultimate Failure of Husserl's Programme	p. 210
Positivism and Idealism versus Poincare's Structural Realism	p. 213
Conclusion	p. 221
Appendixes	p. 223
Logical Independence	p. 225
Natural Axiomatisation	p. 227
The Empirical Unity of Scientific Systems and Watkins's Organic Fertility Requirement (OFR)	p. 233
Ramseyfication and Structural Realism	p. 236
Bibliography	p. 253
Index	p. 257
Table of Contents provided by Syndetics. All Rights Reserved.