Début du module 13/12/2022
Date limite d'inscription 8/12/2022
Lieu IMeRA, Maison des Astronomes 2 place Le Verrier
Observations Le séminaire « Philosophie des invariants mathématiques » vous est proposé en inscription à la séance.
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13/12/2022 : Les exposés du séminaire offrent une exploration extensive du thème de l'invariance selon plusieurs axes. Les exposés proposés par des spécialistes internationaux de premier plan sont adaptés à un public non spécialiste de mathématiques, mais intéressé par des questions philosophiques liées à la notion d'invariance.

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 is professor at the Department of Philosophy, University of Vienna and external fellow at the Munich Center for Mathematical Philosophy at LMU Munich.
His research focuses on the history and philosophy of mathematics and early analytic philosophy. He is also interested in logic, the history and philosophy of logic and formal philosophy of science.
Catégorie Séminaires disciplinaires et transdisciplinaires - Formations scientifiques
Mots clés Philosophie, Mathématiques, Physique, Arts, interdisciplinarité
Organisation des sessions
Nombre d'heures : 2
Participants
Inscrits : 2
Min participants : 5
Max participants : 20
Public
Public prioritaire : Aucun
Public concerné : Tout doctorant de Aix-Marseille
Contact
Direction de la Formation Doctorale AMU