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1 results

  • 11 - A Dialogical Account of Proofs in Mathematical Practice

  • from Part III - Deduction and Cognition
  • Catarina Dutilh Novaes, Vrije Universiteit, Amsterdam
  • Book:
    The Dialogical Roots of Deduction
    Published online:
    10 December 2020
    Print publication:
    17 December 2020, pp 205-233

  • 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.