Magicicada, Mathematical Explanation and Mathematical Realism
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Baker (2005) claims to provide an example of mathematical explanation of an empirical phenomenon which leads to ontological commitment to mathematical objects. This is meant to show that the positing of mathematical entities is necessary for satisfactory scientific explanations and thus that the application of mathematics to science can be used, at least in some cases, to support mathematical realism. In this paper I show that the example of explanation Baker considers can actually be given without postulating mathematical objects and thus cannot be used by the mathematical realist. I also show that, despite this, mathematics keeps playing an important methodological role in the explanation and does not reduce to a merely computational or descriptive framework.
I wish to thank Alan Baker, Sorin Bangu, Mary Leng and David Liggins for helpful comments on previous drafts of this paper. Its clarity and structure have also benefited from valuable suggestions and remarks from two anonymous referees.
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