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Title: Functional explanation in mathematics
Authors: Inglis, Matthew
Mejia-Ramos, Juan P.
Issue Date: 2019
Publisher: Springer © The Authors
Citation: INGLIS, M. and MEJIA-RAMOS, J.P., 2019. Functional explanation in mathematics. Synthese, doi:10.1007/s11229-019-02234-5.
Abstract: 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.
Description: 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.
Version: Published
DOI: 10.1007/s11229-019-02234-5
URI: https://dspace.lboro.ac.uk/2134/37657
Publisher Link: https://doi.org/10.1007/s11229-019-02234-5
ISSN: 0039-7857
Appears in Collections:Published Articles (Mathematics Education Centre)

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