Kurt Godel: The writings. Université de Lille III
Kurt Godel workshop for studying his legacy and writings. Lille, France, May 19-21, 2006
My thoughts, ideas, references, comments and informal notes:
- The wheel machine, a machine for real computation which I am proposing -as a thought experiment- in a forthcoming paper on the Church-Turing thesis -Yes, one more paper on the CT thesis!- with comments on Wilfried Sieg’s paper entitled “Church Without Dogma: Axioms for Computability”
- “In case Cantor’s continuum problem should turn out to be undecidable from the accepted axioms of set theory, the question of its truth would loose its meaning, exactly as the question of the truth of Euclid’s fifth postulate in Euclidian geometry did”. Godel replies: “It has meaning anyway, as Euclid’s fifth postulate gave rise to other now accepted mathematical fields.”
- Godel Gibbs Lecture and his dicotomy on absolutely undecidable propositions and the computational power of the human mind (Turing did great work… but he was wrong when he proposed his formal theory as a model of human thought…)
- New contacts and references: Olivier Souan, Rudy Rucker, Karl Svozil
Mark van Atten’s “On Godel’s awareness of Skolem’s lecture”.
Rick Tieszen
- Herbrand on general recursive functions, letter to Godel.
- Leibniz’ influence on Godel’s arithmetization?
- Sources: Godel Editorial Project. Firestone Library, Princeton University. I.A.S. Marcia Tucker, librarian for Godel papers.
- Godel’s concept of finite procedure as the most satisfactory definition of computation. “A machine with a finite number of parts as Turing did” or “finite combinatorial procedure” as a definition of an algorithm, mechanical or computational procedure.
- Computation’s main constraints: boundness and locality (paper from Hernandez-Quiroz and Raymundo Morado).
- Aphorisms and autoreference (Gabriel Sandu and Hinttika)
- Feferman on Turing
- Is Sieg’s paper and the question of “finite machine=effective procedure” a tautology? In fact such an approach seems to be one of the most strict versions of the Turing Thesis, and even though both Church and Turing probably did propose it in such a strict sense, extensive versions of the thesis have traditionaly covered more content, but even when it is strictly stated that there is still space for a thesis, it is neither proved nor provable from my point of view, and most authors would concur, though some clearly would not. I will comment on this more extensively later, since this was one of my Master’s topics and merits a post by itself.
- Putnam’s thought experiment on cutting all sensorial inputs. Solution: It is impossible in practice. However, machines are an example in a sense, and that is why we do not recognize intelligence in them – they are deprived of sensorial capabilities.
Yes, Godel found an inconsistency in the U.S. constitution. My answer: One? Certainly a bunch. That’s why we need lawyers, who make them even worse.
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