A conventionalist account of distinctively mathematical explanation

Abstract

Distinctively mathematical explanations (DMEs) explain natural phenomena primarily by appeal to mathematical facts. One important question is whether there can be an ontic account of DME. An ontic account of DME would treat the explananda and explanantia of DMEs as ontic items (ontic objects, properties, structures, etc.) and the explanatory relation between them as an ontic relation (e.g., Pincock, 2015; Povich, 2021). Here I present a conventionalist account of DME, defend it against objections, and argue that it should be considered ontic. Notably, if indeed it is ontic, the conventionalist account seems to avoid a convincing objection to other ontic accounts (Kuorikoski, 2021).