Mathematical Explanation: A Contextual Approach

Abstract

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Mathematicians’ Assessments of the Explanatory Value of Proofs

“…Based on a dis.nc.on made by Salmon (1984) in the context of scien.fic explana.on, Delarivière, Frans, and Van Kerkhove (2017) dis.nguished between on5c and epistemic accounts of what it means for a proof to have explanatory value in mathema.cs: "An account of explana.on is on5c if it states:…”

Functional explanation in mathematics

“…Second, Kelp's (2016) account goes well beyond a "sense of understanding" (Trout 2002) or an "aha feeling" (Delarivière et al 2017). While these phenomenological experiences may be correlated with possessing understanding in Kelp's sense, they do not constitute understanding itself.…”

“…Recall that Delarivière et al (2017) distinguished between two broad categories of accounts of mathematical explanation: ontic and epistemic. Clearly the functional account proposed by Wilkenfeld (2014) and adopted here is an epistemic account, as it takes the generation of understanding to be the defining characteristic of an explanation.…”

“…If understanding defines explanation, then how can we characterise the mathematical properties of explanatory proofs? Delarivière et al's (2017) response to this challenge was to argue for pluralism in mathematical explanation. They suggested that the various existing accounts of mathematical explanation are all valuable, but distinct, and that therefore "there is no single account of explanation" (p. 16).…”

Explanation in mathematics: Proofs and practice

“…A very different approach to explanatory proof has been taken by Matthew Inglis and Juan Pablo Mejía‐Ramos (Inglis & Mejía‐Ramos, 2019; see also Delarivière, 2017 for a related view). Following a proposal of Daniel Wilkenfeld's (Wilkenfeld, 2014), Inglis and Mejía‐Ramos argue that a proof is explanatory precisely when and because it generates understanding (“in an appropriate manner and at an appropriate time,” p. 1).…”