A Subject With No Object Strategies for Nominalistic Interpretation of Mathematics

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 such objects, 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 Burgess is Professor of Philosophy at Princeton University, where he has taught since 1975. He has published widely on the philosophy of mathematics and logic. Gideon Rosen is Assistant Professor of Philosophy at Princeton University. He was previously Assistant Professor at the University of Michigan and a Visiting Lecturer at the University of Auckland, New Zealand.