Mathe im Beruf Detailseite

Speaker:
Neil Barton (University of Singapore)

Abstract:

A tension seems to lie at the heart of Gödel's work on the epistemology and metaphysics of mathematics. On the one hand he seems to advocate a kind of platonism on which we have a quasi-perceptual grasp of the mathematical realm and certain axioms ``force themselves upon us as being true''. On the other hand he is famous for (allegedly) saying that kinds of platonism cannot satisfy ``any critical mind''. In this paper, I will argue that Gödel's notebooks are informative for understanding and dissolving this tension. By drawing on his remarks, I'll tentatively propose that there's a viable interpretation of Gödel on which he holds a form of representationalism about mathematics. On this view we are able to form coherent, quasi-perceptual representations of mathematical reality, but they may be better or worse. Using this, I'll argue that the use of Gödel as a kind of non-naturalistic piñata in the philosophy of mathematics is wholly unjustified, and that his work can be used as an inspiration for developing naturalist epistemologies of mathematics.