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