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.

1. Epistemology & Nominalism.- 2. What Is Abstraction & What Is It Good For?.- 3. Beliefs About Mathematical Objects.- 5. Field & Fregean Platonism.- 5. ? in The Sky.- 6. Nominalism.- 7. The Logic of Physical Theory.- 8. Knowledge of Mathematical Objects.- 9. Physicalism, Reductionism & Hilbert.- 10. Physicalistic Platonism.- 11. Sets are Universals.- 12. Modal-Structural Mathematics.- 13. Logical & Philosophical Foundations for Arithmetical Logic.- 14. Criticisms of the Usual Rationale for Validity in Mathematics.- Contributors.- Index of Proper Names.