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Proof and the Virtues of Shared Enquiry†

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ABSTRACTThis paper investigates an important aspect of mathematical practice: that proof is required for a finished piece of mathematics. If follows that non-deductive arguments — however convincing — are never sufficient. I explore four aspects of mathematical research that have facilitated the impressive success of the discipline. These I call the ‘Practical Virtues’: Permanence, Reliability, Autonomy, and Consensus (PRAC). I then argue that permitting results to become established on the basis of non-deductive evidence alone would lead to their deterioration (with some possible exceptions). This furnishes us with a partial rational justification for mathematicians’ strict insistence on proof.

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News source: Philosophia Mathematica Current Issue

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