Thanx, you are the first person who mentioned, that Carnap was the teacher of logic. He was not only teacher of Kurt Gödel, but further more the only one! Because the thanks Goedel gave to Hans Hahn in his ph.-thesis, had been more or less obligatory at this time in Vienna and are it until today in use. My colleague Eckehart Koehler elaborataed this conjecture in his article " Goedel und der Wiener Kreis" published in the 1st volume of the book "Kurt Goedel:Wahrheit und Beweisbarkeit" (Wien, 2002, Bundesverlag + Hölder-Pichler-Tempski-Verlag)where I am editor in chief. This book had been designed manly for the German-speeking community and especially for Austria, to understand how Goedel's ideas developed in the cultural environment of Vienna in contrary to the Göttingen school of mathematics and also in Princeton, about that Carl Menger who had been for some years the president of the AMS (American Mathematical Society) wrote " they wasted Goedel's genius". the only English booklet I can recomend, is that of John Casti and me Werner DePauli "Goedel a life of logic" Perseus books, MA 2000. But this booklet does not contain this story about Goedel and the Vienna circle.

It was a lovely and clear talk. I will push back slightly against Jean Benabou's recollection about Mac Lane's use of Gentzen's methods in categorical coherence theory. It is quite true that Mac Lane would have been aware of Gentzen's method of cut elimination. However, the realization that cut elimination methods could be adapted to study coherence problems is originally due to Joachim Lambek. Mac Lane and his co-author Max Kelly acknowledge Lambek's priority in this realization (Lambek's papers came out circa 1968, while the Kelly-Mac Lane paper Coherence in Closed Categories came out in 1971, or possibly 1972; I'd have to look it up again). The above was written before I heard Benabou's second comment, which indeed recalls Lambek's construction of free structured categories by taking equivalence classes of formal deductions in a suitable language. However, the intellectual debt that Kelly and Mac Lane owed to Lambek's seminal papers was still not made clear in this second comment.

Absolutely amazing video!

Does anyone know what paper he is reading from?

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