PIM’S – mardi 13 dec. 22

Geor Schiemer

“What is (implicit) structure?”

Résumé : TWO WAYS TO THINK ABOUT (IMPLICIT) STRUCTURE According to a dominant view in modern philosophy of mathematics, mathematics can be understood as the study of abstract structures.

In this talk, I will compare two ways to think about the structural content of theories of pure mathematics. According to the first approach, the implicit structure or the structural properties of mathematical objects (such as number systems, groups, vector spaces, and graphs) are specified with reference to formal languages, usually based on some notion of definability. According to the second approach, structures are determined in terms of invariance criteria. For instance, the structural properties of a given mathematical system or its objects are often said to be those properties invariant under certain transformations of the system or under mappings between similar systems. In the talk, I will further investigate these two approaches to think about implicit structure in terms of invariance and definability conditions by drawing to several examples from finite geometry. Based on this, I will give a philosophical analysis of the conceptual differences between these methods and discuss their relevance for our present understanding of structuralism.

Georg Schiemer est professeur au département de philosophie de l’université de Vienne, et il dirige l’Institut du Cercle de Vienne. Il est aussi chercheur associé au Centre de philosophie mathématique de la LMU de Munich.

Ses recherches portent sur l’histoire et la philosophie des mathématiques et sur les débuts de la philosophie analytique. Il sintéresse également à la logique, à l’histoire et à la philosophie de la logique et à la philosophie formelle des sciences.

L’adresse piétonne de l’IMéRA : 2 place Le Verrier – 13004 Marseille.

Cette place se situe sur le boulevard Camille Flammarion.

Citer ce billet
Frédéric Jaëck (2022, 7 décembre). PIM’S – mardi 13 dec. 22. Philosophie des invariants mathématiques. Consulté le 22 juin 2024, à l’adresse https://philoinvar.hypotheses.org/866