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

Topoi 29 (1):77-86 (2010)

Abstract
This paper explores Simon Stevin’s l’Arithmétique 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.”
Keywords Simon Stevin  Number  Ethos of geometry  Existential closure  Mathematical knowing
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DOI 10.1007/s11245-009-9068-1
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References found in this work BETA

Greek Mathematical Thought and the Origin of Algebra.Jacob Klein, Eva Brann & J. Winfree Smith - 1969 - British Journal for the Philosophy of Science 20 (4):374-375.
Domain Extension and the Philosophy of Mathematics.Kenneth Manders - 1989 - Journal of Philosophy 86 (10):553-562.

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Stevin Numbers and Reality.Karin Usadi Katz & Mikhail G. Katz - 2012 - Foundations of Science 17 (2):109-123.

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