In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Dordrecht: Springer. pp. 61-76 (2013)

Michel Dufour
Université Sorbonne-Nouvelle
More or less explicitly inspired by the Aristotelian classification of arguments, a wide tradition makes a sharp distinction between argument and proof. Ch. Perelman and R. Johnson, among others, share this view based on the principle that the conclusion of an argument is uncertain while the conclusion of a proof is certain. Producing proof is certainly a major part of mathematical activity. Yet, in practice, mathematicians, expert or beginner, argue about mathematical proofs. This happens during the search for a proof, then when the proof is presented and discussed by experts, and finally when it is taught or used in didactical contexts.
Keywords Argument  Mathematics  Proof  Explanation
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Audience Role in Mathematical Proof Development.Zoe Ashton - 2020 - Synthese 198 (Suppl 26):6251-6275.

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