A Counterfactual Approach to Explanation in Mathematics. Issue 1 (2nd December 2019) - Baron, Sam; Colyvan, Mark; Ripley, David
ABSTRACT: Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.