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 | ||||||
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| Keywords: | mathematics, necessity, Peirce, Wittgenstein, rules, firstness, secondness, thirdness | ||||||
| Subjects: | Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics > Practice |
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| 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 |
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| Date: | 2015 | ||||||
| Page Range: | pp. 7-26 | ||||||
| Volume: | 7 | ||||||
| ISSN: | 978-958-46-4548-7 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/19686 |
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