Philosophy of Mathematics Seminar (Monday - Week 2, TT23)
Saul Kripke extended Gödel incompleteness from sentences to predicates in his second published paper, “ ‘Flexible’ predicates of formal number theory”, submitted to the Proceedings of the American Mathematical Society when he was 19, and throughout his life he made signiﬁcant contributions, both mathematical and philosophical, to the understanding of incompleteness. In my talk I will survey these contributions, but will focus on Kripke’s model-theoretic proof of incompleteness in arithmetic, for which he formulated his ingenious notion of fulﬁllability. I will give the proof in full since Kripke never published the result and his lectures on it were sketchy, and the few published accounts by others do not convey it well.
The meeting will be in person and online. Those who wish to attend via Zoom, please write to Daniel Isaacson.
Philosophy of Mathematics Seminar Convenors: Daniel Isaacson and James Studd