Can Proofs by Mathematical Induction Be Explanatory?

In Gabriele Pulcini & Mario Piazza, Truth, Existence and Explanation: Filmat 2016 Studies in the Philosophy of Mathematics. Cham, Switzerland: Springer. pp. 163-188 (2018)
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Abstract

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.

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