What inductive explanations could not be
 Citation data:

Synthese, ISSN: 00397857, Page: 111
 Publication Year:
 2017
 Repository URL:
 http://philsciarchive.pitt.edu/id/eprint/13180
 DOI:
 10.1007/s1122901714571
 Author(s):
 Publisher(s):
 Tags:
 Arts and Humanities; Social Sciences
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article description
Marc Lange argues that proofs by mathematical induction are generally not explanatory because inductive explanation is irreparably circular. He supports this circularity claim by presenting two putative inductive explanantia that are one anotherâ€™s explananda. On pain of circularity, at most one of this pair may be a true explanation. But because there are no relevant differences between the two explanantia on offer, neither has the explanatory high ground. Thus, neither is an explanation. I argue that there is no important asymmetry between the two cases because they are two presentations of the same explanation. The circularity argument requires a problematic notion of identity of proofs. I argue for a criterion of proof individuation that identifies the two proofs Lange offers. This criterion can be expressed in two equivalent ways: one uses the language of homotopy type theory, and the second assigns algebraic representatives to proofs. Though I will concentrate on one example, a criterion of proof identity has much broader consequences: any investigation into mathematical practice must make use of some proofindividuation principle.