Mathematical explanation and epistemology: Please mind the gap

Samuel Baron

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

© 2015 John Wiley & Sons Ltd. 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.
Original languageEnglish
Pages (from-to)149-167
JournalRatio
Volume29
Issue number2
DOIs
Publication statusPublished - 2016

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