Mathematical Explanations that are Not Proofs

Erkenntnis 83 (6):1285-1302 (2018)
  Copy   BIBTEX

Abstract

Explanation in mathematics has recently attracted increased attention from philosophers. The central issue is taken to be how to distinguish between two types of mathematical proofs: those that explain why what they prove is true and those that merely prove theorems without explaining why they are true. This way of framing the issue neglects the possibility of mathematical explanations that are not proofs at all. This paper addresses what it would take for a non-proof to explain. The paper focuses on a particular example of an explanatory non-proof: an argument that mathematicians regard as explaining why a given theorem holds regarding the derivative of an infinite sum of differentiable functions. The paper contrasts this explanatory non-proof with various non-explanatory proofs of the same theorem. The paper offers an account of what makes the given non-proof explanatory. This account is motivated by investigating the difficulties that arise when we try to extend Mark Steiner’s influential account of explanatory proofs to cover this explanatory non-proof.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,593

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Explanation in Mathematical Practice.David Sandborg - 1997 - Dissertation, University of Pittsburgh
Mathematical Fit: A Case Study.Manya Raman-Sundström & Lars-Daniel Öhman - forthcoming - Philosophia Mathematica:nkw015.
What is a Proof?Reinhard Kahle - 2015 - Axiomathes 25 (1):79-91.
Arguing Around Mathematical Proofs.Michel Dufour - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Dordrecht: Springer. pp. 61-76.
On automating diagrammatic proofs of arithmetic arguments.Mateja Jamnik, Alan Bundy & Ian Green - 1999 - Journal of Logic, Language and Information 8 (3):297-321.
Outlines of a theory of structural explanations.Philippe Huneman - 2018 - Philosophical Studies 175 (3):665-702.
Why do mathematicians re-prove theorems?John W. Dawson Jr - 2006 - Philosophia Mathematica 14 (3):269-286.

Analytics

Added to PP
2017-09-26

Downloads
63 (#231,470)

6 months
7 (#175,814)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Marc Lange
University of North Carolina, Chapel Hill

References found in this work

Mathematical explanation.Mark Steiner - 1978 - Philosophical Studies 34 (2):135 - 151.
Mathematical Explanation beyond Explanatory Proof.William D’Alessandro - 2017 - British Journal for the Philosophy of Science 71 (2):581-603.
What Are Mathematical Coincidences ?M. Lange - 2010 - Mind 119 (474):307-340.

View all 7 references / Add more references