Michel Dufour
Université Sorbonne-Nouvelle
Inferential communities are communities using specific substantial argumentative schemes. The religious or scientific communities are examples. I discuss the status of the mathematical community as it appears through the position held by the French mathematician Henri Poincaré during his famous ar-guments with Russell, Hilbert, Peano and Cantor. The paper focuses on the status of complete induction and how logic and psychology shape the community of mathematicians and the teaching of mathematics.
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Carnap and Logical Truth.Willard van Orman Quine - 1960 - Synthese 12 (4):350--74.
Mathematical Logic as Based on the Theory of Types.Bertrand Russell - 1908 - American Journal of Mathematics 30 (3):222-262.
Posterior Analytics. Aristotle - 1994 - Clarendon Press.

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