A Scheme Foiled: A Critique of Baron’s Account of Extra-mathematical Explanation

Abstract

Abstract Extra-mathematical explanations explain natural phenomena primarily by appeal to mathematical facts. Philosophers disagree about whether there are extra-mathematical explanations, the correct account of them if they exist, and their implications (for example, for the philosophy of scientific explanation and for the metaphysics of mathematics) (Baker 2005, 2009; Bangu 2008; Colyvan 1998; Craver and Povich 2017; Lange 2013, 2016, 2018; Mancosu 2008; Povich 2019, 2020; Steiner 1978). In this discussion, I present three desiderata for any account of extra-mathematical explanation and argue that Baron’s (2020) U-Counterfactual theory fails to meet each of them. I conclude with some reasons for pessimism that a successful account will be forthcoming.