Abstract Summary
Elaine Landry (University of California, Davis) - I will use a structuralist account of mathematics to critically examine the claim, typically made against structural realists, that one cannot speak of structures without objects, because relata are prior to relations. I will argue that such priority claims result from a general conflation of mathematics with metaphysics and of metaphysics with mathematics. Specifically, I will show that many of these priority arguments arise from attempts to provide either a metamathematical or metaphysical framework for mathematical structuralism. If, however, one shifts to providing a linguistic framework, and views mathematical structuralism as a methodological stance, then one can focus on the fact that mathematical structuralism does indeed show us that it is conceptually possible to speak of structures without objects. But too, against the many pronouncements of ontic structural realists, one must be careful not to conflate what is conceptually possible with what is physically possible. Thus, accepting that mathematics is not metaphysics, one ought to adopt the more modest position of the methodological structural realist.
