TY - JOUR

T1 - Functional explanation in mathematics

AU - Inglis, Matthew

AU - Mejía-Ramos, Juan Pablo

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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 (Synthese 191:3367–3391, 2014) 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.

AB - 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 (Synthese 191:3367–3391, 2014) 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.

KW - Explanation

KW - Mathematical practice

KW - Mathematics

KW - Understanding

UR - http://www.scopus.com/inward/record.url?scp=85066917096&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066917096&partnerID=8YFLogxK

U2 - 10.1007/s11229-019-02234-5

DO - 10.1007/s11229-019-02234-5

M3 - Article

AN - SCOPUS:85066917096

JO - Synthese

JF - Synthese

SN - 0039-7857

ER -