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How to Define a Number? A General Epistemological Account of Simon Stevin's Art of Defining

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Naets, Jurgen

This paper explores Simon Stevin's l'Arithm,tique of 1585, where we find a novel understanding of the concept of number. I will discuss the dynamics between his practice and philosophy of mathematics, and put it in the context of his general epistemological attitude. Subsequently, I will take a close look at his justificational concerns, and at how these are reflected in his inductive, a postiori and structuralist approach to investigating the numerical field. I will argue that Stevin's renewed conceptualisation of the notion of number is a sort of "existential closure" of the numerical domain, founded upon the practice of his predecessors and contemporaries. Accordingly, I want to make clear that l'Aritmetique have to be read not as an ontological analysis or exploration of the numerical field, but as an explication of a mathematical ethos. In this sense, this article also intends to make a specific contribution to the broader issue of the "ethics of geometry.".

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2010
Language Anglais
Journal information "Topoi : an international review of philosophy" - Vol. 29, no. 1, p. 77-86 (2010)
Peer reviewed yes
Publisher Springer (Dordrecht)
issn 0167-7411
e-issn 1572-8749
Publication status Publié
Affiliation UCL
Keywords Simon Stevin ; Number ; Ethos of geometry ; Existential closure ; Mathematical knowing
Links
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Bibliographic reference Naets, Jurgen. How to Define a Number? A General Epistemological Account of Simon Stevin's Art of Defining. In: Topoi : an international review of philosophy, Vol. 29, no. 1, p. 77-86 (2010)
Permanent URL http://hdl.handle.net/2078.1/34950