Mathematical Explanation and Epistemology: Please Mind the Gap.

This paper draws together two strands in the debate over the existence of mathematical objects. The first strand concerns the notion of extra-mathematical explanation: the explanation of physical facts, in part, by facts about mathematical objects. The second strand concerns the access problem for platonism: the problem of how to account for knowledge of mathematical objects. I argue for the following conditional: if there are extra-mathematical explanations, then the core thesis of the access problem is false. This has implications for nominalists and platonists alike. Platonists can make a case for epistemic access to mathematical objects by providing evidence in favour of the existence of extra-mathematical explanations. Nominalists, by contrast, can use the access problem to cast doubt on the idea that mathematical objects play a substantive role in scientific explanation. [ABSTRACT FROM AUTHOR]