Explanatory and Non-explanatory Proofs in Mathematics

Mark Colyvan (University of Sydney and the Ludwig-Maximilians University)

Abstract:  In this paper I look at the contrast between explanatory and non-explanatory proofs in mathematics. This is done with the aim of shedding light on what distinguishes the explanatory proofs. I argue that there may be more than one notion of explanation in operation in mathematics: there does not seem to be a single account that ties together the different explanatory proofs found in mathematics. I then attempt to give a characterisation of the different notions of explanation in play and how these sit with accounts of explanation found in philosophy of science.