Baron, S., Colyvan, M. & Ripley, D. (2017). How mathematics can make a difference. Philosophers' Imprint,17(3), 1-19. United States of America: University of Michigan Press.
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 (in part) 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.
Dianoia Institute of Philosophy
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