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

By Stuart G. Shanker | Go to book overview

CHAPTER 1

Philosophy of logic

A.D. Irvine

The relationship between evidence and hypothesis is fundamental to the advancement of science. It is this relationship-referred to as the relationship between premisses and conclusion-which lies at the heart of logic. Logic, in this traditional sense, is the study of correct inference. It is the study of formal structures and non-formal relations which hold between evidence and hypothesis, reasons and belief, or premisses and conclusion. It is the study of both conclusive (or monotonic) and inconclusive (non-monotonic or ampliative) inferences or, as it is also commonly described, the study of both entailments and inductions. Specifically, logic involves the detailed study of formal systems designed to exhibit such entailments and inductions. More generally, though, it is the study of those conditions under which evidence rightly can be said to justify, entail, imply, support, corroborate, confirm or falsify a conclusion.

In this broad sense, logic in the twentieth century has come to include, not only theories of formal entailment, but informal logic, probability theory, confirmation theory, decision theory, game theory and theories of computability and epistemic modelling as well. As a result, over the course of the century the study of logic has benefited, not only from advances in traditional fields such as philosophy and mathematics, but also from advances in other fields as diverse as computer science and economics. Through Frege and others late in the nineteenth century, mathematics helped transform logic from a merely formal discipline to a mathematical one as well, making available to it the resources of contemporary mathematics. In turn, logic opened up new avenues of investigation concerning reasoning in mathematics, thereby helping to develop new branches of mathematical research-such as set theory and category theory-relevant to the foundations of mathematics itself. Similarly, much of twentieth-century philosophy-including advances in metaphysics, epistemology, the philosophy of

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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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