Synthese 195 (12):5473-5483 (2018)

Authors
John Dougherty
Ludwig Maximilians Universität, München
Abstract
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 another’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 proof-individuation principle.
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Reprint years 2017, 2018
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DOI 10.1007/s11229-017-1457-1
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References found in this work BETA

Proofs and Pictures.James Robert Brown - 1997 - British Journal for the Philosophy of Science 48 (2):161-180.
Mathematical Induction and Explanation.Alan Baker - 2010 - Analysis 70 (4):681-689.

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Citations of this work BETA

Explicação Matemática.Eduardo Castro - 2020 - Compêndio Em Linha de Problemas de Filosofia Analítica.

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