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

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. [ABSTRACT FROM AUTHOR]