A dialogical conception of explanation in mathematical proofs
In this chapter, I argue that the issue of explanatoriness in mathematical proofs can be fruitfully addressed within the dialogical conceptualization of proofs that I have been developing in recent years. The key idea is to emphasize the observation that a proof is a piece of discourse aimed at an intended audience, with the intent to produce explanatory persuasion. This approach explains both why explanatory proofs are to be preferred over non- or less explanatory ones, and why explanatoriness is an audience-relative property of a proof. This account is also able to clarify a number of features of mathematical practice.
Dutilh Novaes, C. (2018)., A dialogical conception of explanation in mathematical proofs, in P. Ernest (ed.), The philosophy of mathematics education today, Dordrecht, Springer, pp. 81-98.
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