Parsimony and inference to the best mathematical explanation

Alan Baker

pp. 333-350

in: Daniele Molinini, Fabrice Pataut, Andrea Sereni (eds), Indispensability and explanation, Synthese 193 (2), 2016.

Abstract

Indispensability-based arguments for mathematical platonism are typically motivated by drawing an analogy between abstract mathematical objects and concrete scientific posits. In this paper, I argue that mathematics can sometimes help to reduce our concrete ontological, ideological, and structural commitments. My focus is on optimization explanations, and in particular the case study involving periodical cicadas. I argue that in this case, stronger mathematical apparatus yields explanations that have fewer concrete commitments. The nominalist cannot accept these more parsimonious explanations without embracing the stronger mathematics, and this poses a challenge for the nominalist position.