Mathematical Accidents and the End of Explanation

Abstract

A conspicuous difference between “traditional” philosophy of science and “traditional” philosophy of mathematics concerns the relative importance of the notion of explanation. Explanation has long featured centrally in debates in the philosophy of science, for at least two reasons. Firstly, explanation has been viewed as playing an important role in the methodology of science, principally due to the inductive character of scientific method. This has led to a focus on giving a philosophical model of scientific explanation, whose leading candidates have included Hempel’s deductive-nomological model, the causal model promoted by Lewis, van Fraassen’s pragmatic model, and the unification models of Kitcher and Friedman. Secondly, explanatory considerations have been an important feature of philosophical debates over scientific realism and anti-realism. This has led to a focus on inference to the best explanation and the conditions under which this mode of inference can underpin robust ontological conclusions.

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