How Mathematics Can Make a Difference


Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We address some objections to our approach.

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Williamson on Counterpossibles.Berto Francesco, David Ripley, Graham Priest & Rohan French - 2018 - Journal of Philosophical Logic 47 (4):693-713.
Explanation in Computational Neuroscience: Causal and Non-Causal.M. Chirimuuta - 2018 - British Journal for the Philosophy of Science 69 (3):849-880.
The Directionality of Distinctively Mathematical Explanations.Carl F. Craver & Mark Povich - 2017 - Studies in History and Philosophy of Science Part A 63:31-38.
The Narrow Ontic Counterfactual Account of Distinctively Mathematical Explanation.Mark Povich - 2019 - British Journal for the Philosophy of Science 72 (2):511-543.

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