What is (implicit) structure? - Cycle PIMS « Philosophie des invariants mathématiques »

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, Georg Schiemer 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, Georg Schiemer 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, Georg Schiemer will give a philosophical analysis of the conceptual differences between these methods and discuss their relevance for our present understanding of structuralism.


Ce séminaire est organisé dans le cadre du cycle PIMS « Philosophie des invariants mathématiques » organisé par Frédéric Jaëck, AMU Fellow / chercheur en résidence à l'Institut d'études avancées d'Aix-Marseille Université (Iméra), dans le cadre du programme Explorations interdisciplinaires dirigé par Gabriella Crocco.


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

Cette place se situe sur le boulevard Camille Flammarion.