Mathematical Explanation and Epistemology: Please Mind the Gap. (2nd June 2015) - Baron, Sam
Abstract: 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.1