Philosophy of Mathematics Seminar (Monday - Week 1, MT19)

Philosophy of Mathematics Seminar

What is a good predicate of provability? In my talk, I will discuss the Kreisel approach to this question, the Hilbert-Bernays-Löb approach and the Feferman approach. I provide some separating examples. I will demonstrate how, in the case of sequential theories with full induction, we can sidestep these approaches and define provability in a way that does not use any design choices like choice of Gödel numbering and deductive system. I will also discuss the construction of predicates that satisfy the Kreisel condition even in the case where the given theory is substantially unsound.

See the seminar webpage for titles and abstracts of other speakers as available.

Philosophy of Mathematics Seminar Convenors: Daniel Isaacson and Volker Halbach