Abstract

This dissertation provides a refutation of the epistemological argument against mathematical platonism; that is, it provides an epistemology of abstract objects, in particular, of mathematical objects. ;After an introductory first chapter, I formulate what I argue is the strongest version of the epistemological argument against platonism. It is stronger than Paul Benacerraf's version because the only plausible way for a platonist to respond to it is to actually provide an epistemology of mathematical objects. ;In chapters three and four, I argue against the platonist epistemologies of Kurt Godel and Penelope Maddy, respectively. The main conclusion of these two chapters is that human beings cannot come into contact with mathematical objects, and that, indeed, it may not even by intelligible to speak in these terms, i.e., to speak of contact between spatio-temporal creatures like ourselves and an aspatial, atemporal mathematical realm. ;In chapter five, I argue that human beings don't need any contact with the mathematical realm in order to attain knowledge of that realm. The argument is based upon the fact that mathematical truths are necessarily true. ;Finally, in chapter six, I develop a second platonist epistemology, i.e., a second refutation of the epistemological argument against platonism. The argument is mostly original, but it relies at one point upon an argument of Michael Resnik's. In a nutshell, my argument is that, since platonists are free to adopt a full-blooded sort of platonism it is easy to explain how human beings could attain knowledge of the mathematical realm. For if all possible mathematical objects exist, then any consistent mathematical theory will accurately describe some collection of mathematical objects. Hence, to attain knowledge of the mathematical realm, one must simply formulate a consistent set of mathematical beliefs