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Functional explanation in mathematics

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posted on 26.04.2019 by Matthew Inglis, Juan P. Mejia-Ramos
Mathematical explanations are poorly understood. Although mathematicians seem to regularly suggest that some proofs are explanatory whereas others are not, none of the philosophical accounts of what such claims mean has become widely accepted. In this paper we explore Wilkenfeld’s (2014, Synthese, 191, 3367-3391) suggestion that explanations are those sorts of things that (in the right circumstances, and in the right manner) generate understanding. By considering a basic model of human cognitive architecture, we suggest that existing accounts of mathematical explanation are all derivable consequences of Wilkenfeld’s ‘functional explanation’ proposal. We therefore argue that the explanatory criteria offered by earlier accounts can all be thought of as features that make it more likely that a mathematical proof will generate understanding. On the functional account, features such as characterising properties, unification, and salience correlate with explanatoriness, but they do not define explanatoriness.

History

School

  • Science

Department

  • Mathematics Education Centre

Published in

Synthese

Citation

INGLIS, M. and MEJIA-RAMOS, J.P., 2019. Functional explanation in mathematics. Synthese, doi:10.1007/s11229-019-02234-5.

Publisher

Springer (© The Authors)

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VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/

Acceptance date

25/04/2019

Publication date

2019-05-22

Notes

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

ISSN

0039-7857

eISSN

1573-0964

Language

en

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