Book contents
- The Dialogical Roots of Deduction
- The Dialogical Roots of Deduction
- Copyright page
- Contents
- Figures
- Preface
- Part I The Philosophy of Deduction
- Part II The History of Deduction
- Part III Deduction and Cognition
- 8 How We Reason, Individually and in Groups
- 9 The Ontogeny of Deductive Reasoning
- 10 The Phylogeny of Deductive Reasoning
- 11 A Dialogical Account of Proofs in Mathematical Practice
- Conclusions
- References
- Index
11 - A Dialogical Account of Proofs in Mathematical Practice
from Part III - Deduction and Cognition
Published online by Cambridge University Press: 10 December 2020
- The Dialogical Roots of Deduction
- The Dialogical Roots of Deduction
- Copyright page
- Contents
- Figures
- Preface
- Part I The Philosophy of Deduction
- Part II The History of Deduction
- Part III Deduction and Cognition
- 8 How We Reason, Individually and in Groups
- 9 The Ontogeny of Deductive Reasoning
- 10 The Phylogeny of Deductive Reasoning
- 11 A Dialogical Account of Proofs in Mathematical Practice
- Conclusions
- References
- Index
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
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- Information
- The Dialogical Roots of DeductionHistorical, Cognitive, and Philosophical Perspectives on Reasoning, pp. 205 - 233Publisher: Cambridge University PressPrint publication year: 2020