The Role of the Prover in Mathematical Practice

If all men are mortal, and Socrates is a man, then it must be that Socrates is mortal. What could be more obvious? Well, sometimes obviousness serves to conceal philosophical difficulties. There’s more going on in this simple deduction than we tend to recognize. For one thing, we are not being asked to assess whether all men are, indeed, mortal. Nor are we asking whether Socrates is indeed a man. Instead, we’re focusing on the logical relation that obtains between those two claims and the third. We claim that the third statement “follows from” the combination of the first two, or that the third is “entailed by” them. But what, exactly, is that?

Despite the obviousness of deduction, questions abound. In her new book, The Dialogical Roots of Deduction: Historical, Cognitive, and Philosophical Perspectives on Reasoning (Cambridge University Press 2021), Catarina Dutilh Novaes argues that deduction arises out of social practices of dialogue.

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