The Oxford Handbook of Philosophy of Mathematics and Logic

by Stewart Shapiro

Overview

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.

Product Details

ISBN-13:	9780195325928
Publisher:	Oxford University Press
Publication date:	06/04/2007
Series:	Oxford Handbooks
Edition description:	New Edition
Pages:	832
Product dimensions:	7.05(w) x 9.70(h) x 2.01(d)

About the Author

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

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
Index     811

Editorial Reviews

"The Oxford Handbook of the Philosophy of Mathematics and Logic is a very accessible, wide ranging work that serves not only to indicate the 'state of the art' in the given area, but, remarkably, also serves as a very fine introduction to the field. I recommend it highly, both to workers in the given field and, equally, to the 'general philosopher,' regardless of one's main area." —Notre Dame Philosophical Reviews

"The Oxford Handbook of the Philosophy of Mathematics and Logic is most certainly here to stay for a very long time. The quality of each of the contributions is reflected in the authors' stimulating writing. The handbook can add substantially to the emerging thoughts and studies on the subject."—Current Engineering Practice

From the Publisher