Gödel's Incompleteness Theorems - Ep. 6.4: Gödel's Proof

Between the end of 19th and the beginning of the 20th Century the field of mathematics and logic suffered a profound crisis. Axioms that appeared to be a priori true, such as Frege's axioms, proved to be inconsistent. Mathematicians (most notably, David Hilbert) wanted to make sure that this never happened again and set off to prove that the formal systems they were working with were consistent. In 1931, the logician Kurt Gödel published the proof of his famous incompleteness theorems, which show that this dream cannot be fulfilled. In this series of videos, which are part of a larger series of conversations, Prof. Graham Priest (CUNY) discusses this result, after setting the stage for it by introducing Russell's logicism and Hilbert's project.