Séminaire général

Nous aurons le plaisir d'accueillir Marianna Antonutti, IHPST qui interviendra sur le thème suivant :

"Mathematical Naturalism and Revisionism About Mathematics"

Anti-revisionism is a key component of all naturalistic approaches to science and mathematics. According to it, any revision to a scientific practice should come autonomously from within the practice itself, excluding ideological influences on scientific practices, but also philosophical ones. In this paper, I focus on anti-revisionism about mathematics. Recent versions of mathematical naturalism have argued that the only legitimate revisions to mathematics are those prescribed on purely mathematical, rather than scientific, grounds. After clarifying the reasons why naturalists should be anti-revisionists, I examine the proposed criterion for mathematical anti-revisionism, and I argue on the basis of case studies that this criterion is not supported by a sufficiently sharp distinction between revisions prescribed on purely mathematical grounds and other kinds of revisions. I then examine a second criterion, which maintains that we should not countenance philosophical accounts of mathematics which involve abandoning accepted theorems. I argue that while in line with naturalistic tenets, this criterion does not fully capture what is important to the mathematical naturalist. This leads to the formulation of a third criterion, which adds to the second criterion the clause that we should not abandon established mathematical methodology, and which I argue overcomes the objections to the previous two criteria.