The Oxford Handbook of Philosophy of Mathematics and Logic

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Stewart Shapiro
Oxford Handbooks Online, Feb 10, 2005 - Mathematics - 833 pages
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Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.
  

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Contents

Philosophy of Mathematics and Its Logic Introduction
4
Apriority and Application Philosophy of Mathematics in the Modern Period
30
Latter Empiricism and Logical Positivism
52
Wittgenstein on Philosophy of Logic and Mathematics
76
The Logicism of Frege Debekind and Russell
130
Logicism in the Twentyfirst Century
167
Logicism Reconsidered
204
Formalism
237
Nominalism
484
Nominalism Reconsidered
516
Structuralism
537
Structuralism Reconsidered
564
Predicativity
591
MathematicsApplication and Applicability
626
Logical Consequence Proof Theory and Model Theory
652
Logical Consequence From a Constructivist Point of View
672

Intuitionism and Philosophy
319
Intuitionism in Mathematics
357
Intuitionism Reconsidered
388
Quine and the Web of Belief
413
Three Forms of Naturalism
438
Naturalism Reconsidered
461
Relevance in Reasoning
697
No Requirement of Relevance
728
Higherorder Logic
752
Higherorder Logic Reconsidered
782
Index
812
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About the author (2005)


Stewart Shapiro is O'Donnell Professor of Philosophy at The Ohio State University and Professorial Fellow at the Arche Centre, University of St. Andrews.

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