Conceptual Structuralism

Présentation :

Pour rappel, les thématiques du séminaire d'histoire et de philosophie des sciences sont à l’intersection entre philosophie et sciences contemporaines. Les développements les plus récents en sciences font en effet apparaître que les réflexions sur l’ontologie, les analyses conceptuelles, les interrogations générales sur le rôle et la nature des théories font partie intégrante de l’activité scientifique et de la réflexion.
 

Résumé de l'intervention :

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).

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