Philosophy of Mathematics Seminar


Philosophy of Mathematics seminar


Daniel Isaacson, Oxford

Kripke on Gödel incompleteness

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 very well.