Luca Incurvati: On the Concept of Finitism

Grolog lecture by Luca Incurvati (ILLC - UvA)

At the most general level, the concept of finitism is typically characterized by saying that finitistic mathematics is that part of mathematics which does not appeal to completed infinite totalities and is endowed with some epistemological property that makes it secure or privileged. This paper argues that this characterization can in fact be sharpened in various ways, giving rise to different conceptions of finitism. This talk investigates these conceptions and shows that they sanction different portion of mathematics as finitistic.