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Grasping Mathematical Reality

Legg, Catherine (2015) Grasping Mathematical Reality. Cuadernos de Sistematica Peirceana, 7. pp. 7-26. ISSN 978-958-46-4548-7

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Abstract

This paper presents a Peircean take on Wittgenstein's famous rule-following problem as it pertains to 'knowing how to go on in mathematics'. I argue that McDowell's advice that the philosophical picture of 'rules as rails' must be abandoned is not sufficient on its own to fully appreciate mathematics' unique blend of creativity and rigor. Rather, we need to understand how Peirce counterposes to the brute compulsion of 'Secondness', both the spontaneity of 'Firstness' and also the rational intelligibility of 'Thirdness'.
This is a written version of a presentation I gave at the “Peirce’s Mathematics” conference, Universidad Nacional de Colombia, November 25-27, 2015, which was organized by Professor Fernando Zalamea. The piece owes much to the inspiration of Prof. Zalamea's writings on philosophy of mathematics.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Legg, Catherinec.legg@deakin.edu.au0000-0002-0231-5415
Keywords: mathematics, necessity, Peirce, Wittgenstein, rules, firstness, secondness, thirdness
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > History of Philosophy
Specific Sciences > Mathematics > Practice
Depositing User: Dr Catherine Legg
Date Deposited: 13 Oct 2021 18:44
Last Modified: 13 Oct 2021 18:44
Item ID: 19686
Journal or Publication Title: Cuadernos de Sistematica Peirceana
Publisher: Editorial Nomos
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > History of Philosophy
Specific Sciences > Mathematics > Practice
Date: 2015
Page Range: pp. 7-26
Volume: 7
ISSN: 978-958-46-4548-7
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/19686

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