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.”. (shrink)

The paper discusses legal implications of the expansion of practical uses of mathematics in social life. Taking as a starting point the omnipresence of mathematical infrastructures underlying policies, technology and markets, the paper proceeds by attending to relevant materials offered by general philosophy, legal philosophy, and the history and philosophy of mathematics. The paper suggests that the modern transformation of mathematics and its practical applications have spurred the emergence of multiple useful technologies and forms of social interaction but have impoverished (...) access to meanings originating in the lifeworld. The paper also argues that, as part of devices of interest aggregation and expert networks, mathematical infrastructures can be scrutinized by a revised form of legal practice that subjects them to legal critique and reconstruction in order to overcome conditions that have eroded the moral self-awareness of individuals and communities and their existential meanings. (shrink)

Résumé Les arts libéraux tiennent un rôle particulier dans la pensée de Simon Stevin (1548-1620). Grâce à eux, ce savant peut dévoiler dans son épistémologie d’une part ce que sont les dispositions innées de l’esprit (distinguer le vrai du faux, parler, compter) et d’autre part les fondements des objets de la Nature (le nom, le nombre, la mesure et le poids). Un art de penser associe alors l’âme et la Création et permet de codifier les différents arts et l’action vertueuse. (...) Dans cet article, nous voulons montrer le rôle que jouent la dialectique et l’arithmétique dans l’art de penser de ce mathématicien et ingénieur flamand. Nous expliciterons alors les liens entre ces deux disciplines et la mise en place grâce à eux d’outils communs comme la proportion et la méthode dans la réalisation d’un projet encyclopédique. (shrink)

The paper discusses legal implications of the expansion of practical uses of mathematics in social life. Taking as a starting point the omnipresence of mathematical infrastructures underlying policies, technology and markets, the paper proceeds by attending to relevant materials offered by general philosophy, legal philosophy, and the history and philosophy of mathematics. The paper suggests that the modern transformation of mathematics and its practical applications have spurred the emergence of multiple useful technologies and forms of social interaction but have impoverished (...) access to meanings originating in the lifeworld. The paper also argues that, as part of devices of interest aggregation and expert networks, mathematical infrastructures can be scrutinized by a revised form of legal practice that subjects them to legal critique and reconstruction in order to overcome conditions that have eroded the moral self-awareness of individuals and communities and their existential meanings. (shrink)