Mardi 3 juin 2025, José FERREIROS, « Conceptual Structuralism »

Dans le cadre du séminaire Histoire et Philosophie des Sciences, le CRHI, le laboratoire Dieudonné et l'axe 5 de la MSHS, sont heureux d'accueillir la conférence suivante : 

José FERREIROS (Universidad de Sevilla)

« Conceptual Structuralism »

mardi 3 juin 2025, 17h-18h30

Salle de conférence du laboratoire Dieudonné, campus Valrose

Présentation :

I will defend a conceptualistic version of structuralism as the most convincing way of elaborating a philosophical understanding of structuralism in line with the classical tradition. The argument begins with a revision of the tradition of “conceptual mathematics”, incarnated in key figures of the period 1850 to 1940 like Riemann, Dedekind, Hilbert or Noether, showing how it led to a structuralist methodology. The tension between the ‘presuppositionless’ approach of those authors, and the platonism of some recent versions of philosophical structuralism, is discussed. In order to resolve this tension, we argue for the idea of ‘semiotic objects’ as a form of minimalist realism, again in the tradition of classical authors including Peirce and Cassirer, and we introduce the basic tenets of conceptual structuralism. Finally we shall discuss the assumptions behind conceptual structuralism, and – most importantly – how the objectivity of mathematics can be explained from the adopted standpoint. This includes the idea that advanced mathematics builds on hypothetical assumptions (Riemann, Peirce, and others).