Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no abstract entities, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. A Subject With No Object cuts through a host of technicalities that have obscured previous discussions of these projects, and presents clear, concise accounts, with minimal prerequisites, of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed.

John P. Burgess and Gideon Rosen, A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics. ...works on Nominalism have come to dominate the philosophy of mathematics, so a work that organizes the material is useful. ... It is rare to find such a comprehensive, and fair, account of a position for which the authors (on their own account) have little sympathy. ... It contains , for a little book, an astonishing amount of information about philosophy and many other things, from Einstein to Latour. * Mark Steiner, The Jerusalem Philosophical Quarterly 50 (January 2001) *
An important book. * The Economist Review *
This book has many virtues. It is concentrated on fundamental questions in the philosophy of mathematics, which it explores with an open mind - or even two open minds; it is richly informed and informative in its clear exposition of the details of nominalistic reconstruction programs ... No attempt will be made here even to summarize the rich and extensive content of this part, except to say that a great service has been performed for both students The formessexxence of the programs is clearly laid out in each case, with just enough detail to give the reader a real sense of how the program in question works but not so much as to obscure the broader picture ... it should be clear that this book is of great value and interest and that, on the whole, it exemplifies philosophy practice * Geoffrey Hellman, Philosophia Mathematica *

John Burgess is Professor of Philosophy and Gideon Rosen is Assistant Professor of Philosophy at Princeton University.