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

John Dougherty
Ludwig Maximilians Universität, München
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.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
Reprint years 2017, 2018
DOI 10.1007/s11229-017-1457-1
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 70,008
Through your library

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.

Add more references

Citations of this work BETA

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

Add more citations

Similar books and articles

Mathematical Explanations That Are Not Proofs.Marc Lange - 2018 - Erkenntnis 83 (6):1285-1302.
Explanation in Mathematical Practice.David Sandborg - 1997 - Dissertation, University of Pittsburgh
Arguing Around Mathematical Proofs.Michel Dufour - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Dordrecht: Springer. pp. 61-76.
Humean Laws and Circular Explanation.Michael Townsen Hicks & Peter van Elswyk - 2015 - Philosophical Studies 172 (2):433-443.
Induction and Reasoning to the Best Explanation.Richard A. Fumerton - 1980 - Philosophy of Science 47 (4):589-600.


Added to PP index

Total views
26 ( #438,799 of 2,505,200 )

Recent downloads (6 months)
2 ( #277,206 of 2,505,200 )

How can I increase my downloads?


My notes