MATHEMATICAL TRUTH WITHOUT REFERENCE

According to a canonical argument for mathematical platonism, if we are to have a uniform semantics which covers both mathematical and non-mathematical language, then we must understand singular terms in mathematics as referring to objects and understand quantifiers as ranging over a domain of such objects, and so treating mathematics as literally true commits us to the existence of (mind-independent, abstract) mathematical objects. In this paper, I argue that insofar as we can provide a uniform semantics for the better part of ordinary, non-mathematical language, we can provide a uniform semantics covering both mathematical and non-mathematical language without thereby committing ourselves to the existence of mathematical objects.