An Epistemic View of Mathematical Explanation and Its Ontological Import

Abstract

Some mathematical realists attempt to establish that there are legitimate mathematical explanations of empirical phenomena. They argue that if there are such explanations, and if they are our best explanations of relevant phenomena, we ought to be ontologically committed to mathematical facts or objects. Expectably, some mathematical nominalists reject the legitimacy of mathematical explanation. In this paper, I argue that this entire debate is based upon a unsustainable or narrow conception of explanation, the ontic conception of explanation. This leads us to the conclusion that, when we adopt an epistemic conception of explanation, accommodating legitimate mathematical explanations no longer necessitates our ontological commitment to mathematical facts or objects.