Abstract
We explore the prospects of a monist account of explanation for both non-causal explanations in science and pure mathematics. Our starting point is the counterfactual theory of explanation (CTE) for explanations in science, as advocated in the recent literature on explanation. We argue that, despite the obvious differences between mathematical and scientific explanation, the CTE can be extended to cover both non-causal explanations in science and mathematical explanations. In particular, a successful application of the CTE to mathematical explanations requires us to rely on counterpossibles. We conclude that the CTE is a promising candidate for a monist account of explanation in both science and mathematics.
Highlights
Since the late 1980s the attention of philosophers interested in theories of explanation has been almost entirely on causal explanations and causal theories of scientific explanation
We believe that this development constitutes progress in the debate on scientific explanation. (We will provide a detailed exposition of the counterfactual theory of explanation (CTE) below.) But even if the CTE is an adequate theory of scientific explanations, the question arises whether it can be expanded to cover explanations in pure mathematics
What is the source of the problem of applying the CTE to explanations in pure mathematics? According to Lange, the problem rests on the kind of necessity attached to the explanatory assumptions in mathematical explanation: “they possess an especially strong variety of necessity and have an especially strong resistance to being changed” (Lange 2016: 88)
Summary
Since the late 1980s the attention of philosophers interested in theories of explanation has been almost entirely on causal explanations and causal theories of scientific explanation. The key idea of the CTE is that causal as well as non-causal explanations provide information about how the explanandum counterfactually depends on the explanans We believe that this development constitutes progress in the debate on scientific explanation. Lange suggests that the CTE cannot capture non-causal explanations in pure mathematics Lange’s Challenge: Proponents of the CTE must show that their theory of explanation is applicable to explanations in pure mathematics. We provide evidence for the claim that mathematicians do appeal to counterpossibles in their reasoning This evidence lends additional support to our proposal of extending the CTE from scientific to mathematical explanations.
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