Physicalism in Mathematics (The Western Ontario Series in Philosophy of Science, 45)

This collection of papers has its origin in a conference held at the Uni versity of Toronto in June of 1988. The theme of the conference was Physicalism in Mathematics: Recent Work in the Philosophy of Math ematics. At the conference, papers were read by Geoffrey Hellman (Minnesota), Yvon Gauthier (Montreal), Michael Hallett (McGill), Hartry Field (USC), Bob Hale (Lancaster & St Andrew's), Alasdair Urquhart (Toronto) and Penelope Maddy (Irvine). This volume supplements updated versions of six of those papers with contributions by Jim Brown (Toronto), John Bigelow (La Trobe), John Burgess (Princeton), Chandler Davis (Toronto), David Papineau (Cambridge), Michael Resnik (North Carolina at Chapel Hill), Peter Simons (Salzburg) and Crispin Wright (St Andrews & Michigan). Together they provide a vivid, expansive snapshot of the exciting work which is currently being carried out in philosophy of mathematics. Generous financial support for the original conference was provided by the Social Sciences & Humanities Research Council of Canada, the British Council, and the Department of Philosophy together with the Office of Internal Relations at the University of Toronto. Additional support for the production of this volume was gratefully received from the Social Sciences & Humanities Research Council of Canada. Front Matter....Pages i-xxvi Epistemology & Nominalism....Pages 1-15 What is abstraction & what is it good for?....Pages 17-40 Beliefs About Mathematical Objects....Pages 41-71 Field & Fregean Platonism....Pages 73-93 π in the Sky....Pages 95-120 Nominalism....Pages 121-144 The Logic of Physical Theory....Pages 145-154 Knowledge of Mathematical Objects....Pages 155-182 Physicalism, Reductionism & Hilbert....Pages 183-257 Physicalistic Platonism....Pages 259-289 Sets are Universals....Pages 291-305 Modal-Structural Mathematics....Pages 307-330 Logical & Philosophical Foundations for Arithmetical Logic....Pages 331-342 Criticisms of the Usual Rationale for Validity in Mathematics....Pages 343-356 Back Matter....Pages 357-365 Physlcallsm ln mathematlcs / edlted by A.D. Irvlne. p. cm. --(The Unlverslty of Western Ontarl0 serles ln phllosophy of sclence ; v. 45) ISBN 0-7923-0513-2 (U.S.) 1. Mathematlcs--Phllosophy--Congresses. 1. Irvlne, A. D.