Philosophy of Mathematics Seminar (Monday - Week 8, HT26)

Abstract: When we accept a formal system S, we are implicitly committed also to statements partially or fully expressing the soundness of S in the language of S. This claim is a simple version of the Implicit Commitment Thesis (ICT). A paradigmatic example of a statement partially expressing soundness is the arithmetized consistency claim for Peano arithmetic with PA as S. I will try to sharpen ICT. In particular, I will investigate what exactly these additional statements are, what their relative strengths are, and what supports the claim that we are implicitly committed to them. I will consider less familiar systems as base theory S and present cases where the addition of soundness statements to an arithmetically sound system S leads to an inconsistency. Finally, I will consider the overall plausibility of ICT.

Registration: If you do not hold a University card which gives access to the upper floors of the Schwarzman Centre, please write to admin@philosophy.ox.ac.uk copied to daniel.isaacson@philosophy.ox.ac.uk at least two working days before a seminar to register your attendance.

Please note: A notice will be sent out for each talk with the Zoom link.