Proof and the Virtues of Shared Enquiry

Philosophia Mathematica:nkw022 (forthcoming)

Abstract
This 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. I then argue that permitting results to become established on the basis of non-deductive evidence alone would lead to their deterioration. This furnishes us with a partial rational justification for mathematicians strict insistence on proof.
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DOI 10.1093/philmat/nkw022
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References found in this work BETA

Is Justified True Belief Knowledge?Edmund Gettier - 1963 - Analysis 23 (6):121-123.
After Virtue.A. MacIntyre - 1981 - Tijdschrift Voor Filosofie 46 (1):169-171.
The Morality of Happiness.Julia Annas - 1993 - Oxford University Press.
Proofs and Refutations.Imre Lakatos - 1980 - Noûs 14 (3):474-478.

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