publication . Thesis . 2017

Proof, rigour and informality : a virtue account of mathematical knowledge

Tanswell, Fenner Stanley;
Open Access English
  • Published: 08 Feb 2017
  • Publisher: University of St Andrews
  • Country: United States
Abstract
This thesis is about the nature of proofs in mathematics as it is practiced, contrasting the informal proofs found in practice with formal proofs in formal systems. In the first chapter I present a new argument against the Formalist-Reductionist view that informal proofs are justified as rigorous and correct by corresponding to formal counterparts. The second chapter builds on this to reject arguments from Gödel's paradox and incompleteness theorems to the claim that mathematics is inherently inconsistent, basing my objections on the complexities of the process of formalisation. Chapter 3 looks into the relationship between proofs and the development of the math...
Subjects
free text keywords: Proof, Rigour, Formalisation, Mathematics, Virtue epistemology, Open texture, Knowing-how, Mathematical practice, Lakatos, Paradox, Gödel's theorems, Incompleteness, Conceptual engineering, Philosophy of mathematics, QA9.54T2, Mathematics--Philosophy, Proof theory
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