A Counterfactual Approach to Explanation in Mathematics

Samuel Baron, Mark Colyvan, David Ripley

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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.
Original languageEnglish
Pages (from-to)1-34
Number of pages34
JournalPhilosophia Mathematica: philosophy of mathematics, its learning, and its application
Issue number1
Publication statusPublished - 1 Feb 2020


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