Philosophy of Science, Logic, and Mathematics in the Twentieth Century

By Stuart G. Shanker | Go to book overview

Introduction

S.G. Shanker

In this volume we survey the striking developments that have taken place in the philosophies of logic, mathematics and science in the twentieth century. The very use of a genitive case here bears eloquent testimony to the dramatic changes that have occurred. Prior to this century, few philosophers troubled to break 'philosophy' down into its constituent parts. Nor did they display any pronounced interest in the nature of philosophy per se, or the relation in which philosophy stands to science. Indeed, subjects that we now regard as totally distinct from philosophy-such as mathematics or psychology, and even physics or biology-were once all located within the auspices of philosophy.

It is interesting to note, for example, how Hilbert obtained his doctorate from the philosophy department. Now we are much more careful to distinguish between axiomatics, proof theory, categorization theory, the foundations of mathematics, mathematical logic, formal logic, and the philosophy of mathematics. That hardly means that philosophers are only active in the latter areas, however, while mathematicians get to rule over the former. Rather, philosophers and mathematicians move about freely in all these fields. To be sure, it is always possible to distinguish between the work of a mathematician and that of a philosopher: the approach, the techniques, and most especially the intentions and the conclusions drawn, invariably betray the author's occupation. But the fact that philosophers and mathematicians are working side-by-side, that they are reading each other's work and attending each other's conferences, is an intellectual development whose significance has yet to be fully absorbed.

Significantly, the major figures in the philosophies of logic and mathematics this century-Frege, Russell, Wittgenstein, Brouwer, Poincaré, Hilbert, Gödel, Tarski, Carnap, Quine-all moved from logic or mathematics to philosophy. Perhaps more than any single factor, it was this dynamic that determined the nature of analytical philosophy. For

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Philosophy of Science, Logic, and Mathematics in the Twentieth Century
Table of contents

Table of contents

  • Title Page iii
  • Contents v
  • General Editors' Preface vii
  • Acknowledgements xiii
  • Chronology xv
  • Introduction 1
  • Notes 8
  • Chapter 1 - Philosophy of Logic 9
  • Bibliography 39
  • Chapter 2 - Philosophy of Mathematics in the Twentieth Century 50
  • Chapter 3 - Frege 124
  • Bibliography 153
  • Chapter 4 - Wittgenstein's Tractatus 157
  • Notes 187
  • Chapter 5 - Logical Positivism 193
  • Bibliography 210
  • Chapter 6 - The Philosophy of Physics 214
  • Bibliography 233
  • Chapter 7 - The Philosophy of Science Today 235
  • Chapter 8 - Chance, Cause and Conduct: Probability Theory and the Explanation of Human Action 266
  • Chapter 9 - Cybernetics 292
  • Bibliography 313
  • Chapter 10 - Descartes' Legacy: the Mechanist/Vitalist Debates 315
  • Notes 366
  • Glossary 376
  • Index 444
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