Revisiting Gödel's 1931 paper

Saunders Mac Lane (1909-2005) was an American mathematician who, together with Samuel Eilenberg, founded category theory. Mac Lane had an interesting anecdote in his autobiography: "Early in my work at Harvard, I had a confrontation with Bertrand Russell. At the time, he was visiting the United States and one of the social science departments at Harvard. The mathematics colloquium invited him to give an address on foundations, which he did: the audience that came was so large that the colloquium had to move from its regular room to a larger room normally used by physicists. Russell proceeded to give an enthusiastic lecture, which, roughly speaking, described the state of mathematical logic as it was in 1920. At the end of his talk, the chairman asked for questions. Being a little disappointed that he hadn 抰  covered any recent results, I asked Russell how he related all this to Hilbert's  recent work on first order logic and to Kurt Goel's spectacular results with his inco...

Alasdair Urquhart's article «  Russell and Gödel »   is very helpful for a comprehensive understanding of Russell's views of Gödel's theorem, where Chapitre 3 is « Russell’s response to Godel’s theorem ». Russell was very careful in his responses to Gödel's theorem, as presented in this article ([1] p.10-14), and Russell never made a simple right or wrong judgement about Gödel's theorem, but was honest in expressing his confusion and doubts : in a 1945 article, Russell described Gödel's theorem as paradox; in a 1950 article, Russell described Gödel's theorem as puzzle; in a 1963 letter to Leon Henkin, Russell expresses his puzzles about Gödel's theorem; and in a 1965 commentary, Russell said that Gödel presented a new difficulty, … Russell's attitude was consistent. In 1965 Russell was invited by Schilpp to write the following commentary on Gödel's work ([1] p.10-14) : Not long after the appearance of Principia Mathematica, G¨odel propounded a ne...