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11 - A Dialogical Account of Proofs in Mathematical Practice

from Part III - Deduction and Cognition

Published online by Cambridge University Press:  10 December 2020

Catarina Dutilh Novaes
Catarina Dutilh Novaes
Affiliation:
Vrije Universiteit, Amsterdam
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Summary

This chapter investigates deductive practices in what is arguably their main current instantiation, namely practices of mathematical proofs. The dialogical hypothesis delivers a compelling account of a number of features of these practices; indeed, the fictive characters Prover and Skeptic can be viewed as embodied by real-life mathematicians. The chapter includes a discussion of the ontological status of proofs, the functions of proofs, practices of mathematicians such as peer review and collaboration, and a brief discussion of probabilistic and computational proofs. It also discusses three case studies: the reception of Gödel’s incompleteness results, a failed proof of the inconsistency of Peano Arithmetic, and a purported proof of the ABC conjecture.

Keywords

mathematicsmathematical proofspeer reviewcollaborationfunctions of proofsprobabilistic proofscomputational proofsProverSkepticdeduction
Type
Chapter
Information
The Dialogical Roots of Deduction
Historical, Cognitive, and Philosophical Perspectives on Reasoning
 , pp. 205 - 233
Publisher: Cambridge University Press
Print publication year: 2020

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