Can Proofs by Mathematical Induction Be Explanatory?
In this paper I discuss Marc Lange’s argument for the claim that inductive proofs can never be explanatory. I show that several of the assumptions on which Lange’s argument relies are problematic, and I argue that there are cases of explanatory inductive proof, providing a number of examples to back up my claim. I finish with a positive proposal on which the examples I put forward can be accounted for by Lange’s own account of mathematical explanation.
I would like to thank audiences in Cambridge, Chieti, London and Umeå for stimulating and helpful discussion. Particular thanks are due to Luke Fenton-Glynn and Marcus Giaquinto for their insightful comments on earlier versions of the paper. I worked on the paper while I was supported by grants from the UK Arts and Humanities Research Council and then the Royal Institute of Philosophy, Jacobsen Trust; my thanks to both institutions.
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