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Open Texture, Rigor, and Proof

Zayton, Benjamin (2022) Open Texture, Rigor, and Proof. [Preprint]

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Abstract

Open texture is a kind of semantic indeterminacy first systematically studied by Waismann. In this paper, extant definitions of open texture will be compared and contrasted, with a view towards the consequences of open-textured concepts in mathematics. It has been suggested that these would threaten the traditional virtues of proof, primarily the certainty bestowed by proof-possession, and this suggestion will be critically investigated using recent work on informal proof. It will be argued that informal proofs have virtues that mitigate the danger posed by open texture. Moreover, it will be argued that while rigor in the guise of formalisation and axiomatisation might banish open texture from mathematical theories through implicit definition, it can do so only at the cost of restricting the tamed concepts in certain ways.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Zayton, Benjaminbenjaminzayton@gmail.com0000-0001-9732-6303
Keywords: Mathematical Concepts; Rigor; Proof; Implicit Definition
Subjects: Specific Sciences > Mathematics > Methodology
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
Depositing User: Benjamin Zayton
Date Deposited: 01 Aug 2022 18:57
Last Modified: 01 Aug 2022 18:57
Item ID: 21008
Subjects: Specific Sciences > Mathematics > Methodology
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
Date: 1 August 2022
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/21008

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