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- Title
Proof and the Virtues of Shared Enquiry?
- Authors
Berry, Don
- Abstract
This paper investigates an important aspect of mathematical practice: that proof is required for a finished piece of mathematics. If follows that nondeductive 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.
- Subjects
MATHEMATICAL proofs; MATHEMATICAL research; PRACTICAL reason; ANALOGY; GOLDBACH conjecture
- Publication
Philosophia Mathematica, 2018, Vol 26, Issue 1, p112
- ISSN
0031-8019
- Publication type
Article
- DOI
10.1093/philmat/nkw022