How Mathematics Can Make a DifferenceSkip other details (including permanent urls, DOI, citation information)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. Please contact email@example.com to use this work in a way not covered by the license. :
For more information, read Michigan Publishing's access and usage policy.
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.