Mathematical Explanation: A Pythagorean Proposal

Abstract

Mathematics appears to play an explanatory role in science. This, in turn, is thought to pave a way toward mathematical Platonism. A central challenge for mathematical Platonists, however, is to provide an account of how mathematical explanations work. I propose a property-based account: physical systems possess mathematical properties, which either guarantee the presence of other mathematical properties and, by extension, the physical states that possess them or rule out other mathematical properties, and their associated physical states. I explain why Platonists should accept that physical systems have mathematical properties, and why a property-based account is better than existing accounts of mathematical explanation. I close by considering whether nominalists can accept the view I propose here. I argue that they cannot.