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What inductive explanations could not be

Dougherty, John (2017) What inductive explanations could not be. Synthese. ISSN 1573-0964

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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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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Dougherty, Johnjedoughe@ucsd.edu
Keywords: mathematical explanation, proof theory, homotopy type theory, mathematical induction
Subjects: Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics
Depositing User: John Dougherty
Date Deposited: 05 Jul 2017 19:44
Last Modified: 05 Jul 2017 19:44
Item ID: 13180
Journal or Publication Title: Synthese
Publisher: Springer (Springer Science+Business Media B.V.)
Official URL: http://link.springer.com/article/10.1007/s11229-01...
DOI or Unique Handle: https://doi.org/10.1007/s11229-017-1457-1
Subjects: Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics
Date: 8 June 2017
ISSN: 1573-0964
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/13180

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