0: Ok last we left off, Gödel arrived on the scene. > Steve Kleene: Then Gödel arrived on the scene and there must have been discussions between Church and Gödel, and I don't know how ready Gödel was to embrace the thesis that this was all effectively calculable functions but Church of course is the one that certainly came out explicitly with this. > Steve Kleene: Then Gödel arrived in the Fall or Spring of the year 1933-34. Gödel was giving his lectures. Gödel had this notion of General Recursive Functions, and the question came up, y'know, well, does this embrace all effectively calculable functions and is it equivalent to lambda definability. > Steve Kleene: I left Princeton in June of 1935, and of course we already had Church's Thesis in, it must have been the late spring of '34. That's when Gödel was talking about his General Recursive Functions. > Steve Kleene: You don't happen to have a copy of Introduction to Metamathematics do you? > Steve Kleene: Well, what Herbrand did in General Recursive Functions as presented by Gödel giving credit for ideas of Herbrand, is something I understand more than what Herbrand published. It was a little note of Herbrand's or a little, y'know, it was something short but whether it was a short note or just a short piece on the end of something else. > > _(Kleene thumbs through his book Introduction to Metamathematics: The "frighteningly technical" book mentioned earlier.)_ > > Gerald Sacks: It's hard to remember everything in that book. > > _(Everyone laughs.)_ > > Some Famous Logician: I knew it for a week or two when I had to take my exams. But I must say a few have slipped my mind. > > Steve Kleene: It helps to have written it. > > C. C. Chang: I don't even remember what's in _Model Theory_ anymore. 1: What's _Model Theory_? 0: A part of foundations of mathematics. But in this case it's a book that guy wrote. ![[chang-forgets-whats-in-model-theory.png]] > Gerald Sacks: Rosser made me go through it. > > Steve Kleene: _(Continues thumbing through his book.)_ I thought I'd get a reference here to Gödel having claimed that resolvability in this particular system was independent of the system... Let me see... "Remarks contributed to a discussion of _(In a French accent mixed with German, correctness unclear)_ _Une discussion sur Grundlagen der Mathematik."_ It comes from that conference. I'll have to look it up to see which one it was in. --- ## Mr Why TODO: 1 should say something about how we need to cover who Godel's history like we did for Church. TODO: 0 should be reluctant to cover this stuff because of how often it's covered elsewhere. TODO: 1 convinces 0. TODO: Write a dialogue that includes an important subset of the pictures below in Anti-gist format. ![[godel-goldstein-00.jpg|400]] ![[godel-goldstein-01.png]] ![[godel-goldstein-02.png]] ![[godel-goldstein-03.png]] ![[godel-goldstein-04.png]] ![[godel-goldstein-05.png]] ![[godel-goldstein-06.png]] ![[godel-goldstein-07.png]] ![[godel-goldstein-08.png]] ![[godel-goldstein-09.png]] ![[godel-goldstein-10.png]] ![[godel-goldstein-11.png]] ![[godel-goldstein-12.png]] ![[godel-goldstein-13.png]] ![[godel-goldstein-14.png]] ![[godel-goldstein-15.png]] ![[godel-goldstein-16.png]] ![[godel-goldstein-17.png]] ![[godel-goldstein-18.png]] ![[godel-goldstein-19.png]] ![[godel-goldstein-20.png]] ![[godel-goldstein-21.png]] ![[godel-goldstein-22.png]] ![[godel-goldstein-23.png]] ![[godel-goldstein-24.png]] ![[godel-goldstein-25.png]] ![[godel-goldstein-26.png]] ![[godel-goldstein-27.png]] ![[godel-goldstein-28.png]] ![[godel-goldstein-29.png]] ![[godel-goldstein-30.png]] ![[godel-goldstein-31.png]] ![[godel-goldstein-32.png]] ![[godel-goldstein-33.png]] ![[godel-goldstein-34.png]] ![[godel-goldstein-35.png]] ![[godel-goldstein-36.png]] ![[godel-goldstein-37.png]] ![[godel-goldstein-38.png]] ![[godel-goldstein-39.png]] ![[godel-goldstein-40.png]] ![[godel-goldstein-41.png]] ![[godel-goldstein-42.png]] ![[godel-goldstein-43.png]] ![[godel-goldstein-44.png]] ![[godel-goldstein-45.png]] ![[godel-goldstein-46.png]] ![[godel-goldstein-47.png]] ![[godel-goldstein-48.png]] ![[godel-goldstein-49.png]] ![[godel-goldstein-50.png]] ![[godel-goldstein-51.png]] ![[godel-goldstein-52.png]] ![[godel-goldstein-53.png]] ![[godel-goldstein-54.png]] ![[godel-goldstein-55.png]] ![[godel-goldstein-56.png]] ![[godel-goldstein-57.png]] ![[godel-goldstein-58.png]] ![[godel-goldstein-59.png]] ![[godel-goldstein-60.png]] ![[godel-goldstein-61.png]] ![[godel-goldstein-62.png]] ![[godel-goldstein-63.png]] ![[godel-goldstein-64.png]] ![[godel-goldstein-65.png]] --- This goes at the end of the file. > Steve Kleene: Well as I say, I don't know how firmly convinced Gödel was that his General Recursive Functions represented all effectively calculable functions. > > Gerald Sacks: He seemed very skeptical. > > Steve Kleene: I think he was skeptical. And it may well be that Turing's presentation was what brought Gödel around. > > Someone: Actually he said that in print somewhere. I remember I read that in the last year or two. 0: Perfect timing. Next file. 1: But you didn't even _explain_ what general recursive functions ar--- 0: Almost there. Follow me. goto: [[2/5|Turing]]