The Oxford Handbook of Philosophy of Mathematics and Logic

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Stewart Shapiro
Oxford University Press, USA, 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 in the Modern Period
29
3 Later Empiricism and Logical Positivism
51
4 Wittgenstein on Philosophy of Logic and Mathematics
75
5 The Logicism of Frege Dedekind and Russell
129
6 Logicism in the Twentyfirst Century
166
7 Logicism Reconsidered
203
8 Formalism
236
9 Intuitionism and Philosophy
318
16 Nominalism Reconsidered
515
17 Structuralism
536
18 Structuralism Reconsidered
563
19 Predicativity
590
20 MathematicsApplication and Applicability
625
21 Logical Consequence Proof Theory and Model Theory
651
22 Logical Consequence From a Constructivist Point of View
671
23 Relevance in Reasoning
696

10 Intuitionism in Mathematics
356
11 Intuitionism Reconsidered
387
12 Quine and the Web of Belief
412
13 Three Forms of Naturalism
437
14 Naturalism Reconsidered
460
15 Nominalism
483
24 No Requirement of Relevance
727
25 Higherorder Logic
751
26 Higherorder Logic Reconsidered
781
Index
811
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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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