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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.
Table of Contents
Notes on the Contributors xi
Philosophy of Mathematics and Its Logic: Introduction Stewart Shapiro 3
Apriority and Application: Philosophy of Mathematics in the Modern Period Lisa Shabel 28
Later Empiricism and Logical Positivism John Skorupski 51
Wittgenstein on Philosophy of Logic and Mathematics Juliet Floyd 75
The Logicism of Frege, Dedekind, and Russell William Demopoulos Peter Clark 129
Logicism in the Twenty-first Century Bob Hale Crispin Wright 166
Logicism Reconsidered Agustin Rayo 203
Formalism Michael Detlefsen 236
Intuitionism and Philosophy Carl Posy 318
Intuitionism in Mathematics D. C. McCarty 356
Intuitionism Reconsidered Roy Cook 387
Quine and the Web of Belief Michael D. Resnik 412
Three Forms of Naturalism Penelope Maddy 437
Naturalism Reconsidered Alan Weir 460
Nominalism Charles Chihara 483
Nominalism Reconsidered Gideon Rosen John P. Burgess 515
Structuralism Geoffrey Hellman 536
Structuralism Reconsidered Fraser MacBride 563
Predicativity Solomon Feferman 590
Mathematics-Application and Applicability Mark Steiner 625
Logical Consequence, Proof Theory, and Model Theory Stewart Shapiro 651
Logical Consequence From a Constructivist Point of View Dag Prawitz 671
Relevance in Reasoning Neil Tennant 696
No Requirement of Relevance John P. Burgess 727
Higher-order Logic Stewart Shapiro 751
Higher-order Logic Reconsidered Ignacio Jane 781