Russell on Gödel; Re: Odifreddi: Godel's proof of the existence of God
Alexander M Lemberg
sandylemberg at juno.com
Mon Nov 14 15:16:50 EST 2022
"Bertrand Russell expressed his profound confusion in a letter to Leon
Henkin : I realised, of course, that Godel's work is of fundamental
importance, but I was puzzled by it. If a given set of axioms leads to a
contradiction, it is clear that at least one of the axioms must be
false."
If this is true, it shows a fundamental misunderstanding of consistency
and the nature of axiomatic theories. Maybe a lapse on Russell's part, or
a lack of attention as his focus shifted in other directions.
You may be interested in the following article:
RUSSELL AND GÖDEL by ALASDAIR URQUHART
https://www.jstor.org/stable/44083314
Also, Mac Lane has 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’t covered any recent results, I asked Russell
how he related all this to Hilbert°s recent work on first order logic
and to Kurt Gödel's spectacular results with his incompleteness
theorem. There was a long silence. Finally, the chairman said, “Perhaps
someone else has a question". Fortunately, someone did.
I never met Russell again. As an undergraduate at Yale I was
mightily impressed by Principia Mathematica—Russell had been my
hero. By 1938, I realized that new ideas about logic were even more
impressive. In retrospect, I felt guilty about my question—I should
have known that Russell would not have been able to answer. In
doing so, I was too impatient to realize that he had appropriately
decided to shift his early interest from logic to other subjects—he
hadn’t kept up with current results in logic because he had been busy
working on other things. However, it is a fact that the splendid
background development in Principia made Gödel’s theorem
possible."
Sandy
On Mon, 14 Nov 2022 12:07:16 +0100 Yu Li <yu.li at u-picardie.fr> writes:
> Dear colleagues,
>
> The proof of GÃ¶del's Incompleteness Theorem has been challenged
> since
> its publication, which is compiled by John W. Dawson Jr. in his
> article
> Â«Â The reception of GÃ¶del's Incompleteness TheoremsÂ Â» ([1],
> p74-95):
> - Ernst Zermelo stated in a letter to GÃ¶del in 1931 that GÃ¶delâ€™s
> proof
> of the existence of undecidable propositions exhibits an
> Â«Â essential gapÂ Â»Â ;
> - The logician ChaÃ¯m Perelman asserted that GÃ¶del had in fact
> discovered
> an antinomy.
> - Wittgensteinâ€™s well-known comments on GÃ¶delâ€™s theorem appear
> in
> Â«Â Remarks on the Foundations of Mathematics (1938)Â Â».
> - Bertrand Russell expressed his profound confusion in a letter to
> Leon
> Henkin : I realised, of course, that GÃ¶delâ€™s work is of
> fundamental
> importance, but I was puzzled by it. [â€¦] If a given set of axioms
> leads
> to a contradiction, it is clear that at least one of the axioms must
> be
> false.
> â€¦...
>
> There is also the yet-to-be-recognized proof of Entscheidungsproblem
> proposed by Alan Turing in his paper (1936) [2], where Turing
> alluded to
> the errors made by GÃ¶del without mentioning his name and ventured
> to fix
> them.
>
> The malaise caused by GÃ¶del's proof has been continuously explored
> in
> the humanitiesÂ [3-6], even in the collision between the humanities
> and
> the natural sciences, such as the " Sokal's hoax" instigated by the
> physicist Sokal [7]; the questioning of GÃ¶del's proof from the
> perspective of human knowledge by the anthropologist Paul Jorion
> [8], â€¦...
>
> Reference :
> [1] S.G. Shanker (ed.), GÃ¶delâ€™s Theorem in Focus, Croom Helm
>
1988,Â https://pdfslide.net/documents/godels-theorem-in-focus-philosopher
s-in-focus.html
> [2] Alan Turing, Â«Â On Computable Numbers, with an Application to
> theÂ EntscheidungsproblemÂ Â»,
> https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf
> [3] Stephen Budiansky, Journey to the Edge of Reason - The Life of
> Kurt
> GÃ¶del (2021). https://wwnorton.com/books/9781324005445/overview
> [4] Rebecca Goldstein, Incompleteness: The Proof and Paradox of Kurt
> GÃ¶del).
>
https://www.essra.org.cn/upload/202102/Incompleteness%20-%20The%20Proof%2
0and%20Paradox%20of%20Kurt%20Godel%20by%20Rebecca%20Goldstein%EF%BC%88200
5%EF%BC%89.pdf
> [5] Pierre Cassou-NoguÃ¨s, Les DÃ©mons de GÃ¶del - Logique et folie
> (2007).
>
https://www.amazon.fr/D%C3%A9mons-G%C3%B6del-Logique-folie/dp/2020923394
> [6] James R Meyer, The shackles of conviction. Paperback (2022).
> https://www.amazon.com/Shackles-Conviction-James-R-Meyer/dp/1906706093
> [7] https://fr.wikipedia.org/wiki/Affaire_Sokal
> [8] Paul Jorion,Â Comment la vÃ©ritÃ© et la rÃ©alitÃ© furent
> inventÃ©esÂ (Gallimard 2009).
>
https://www.gallimard.fr/Catalogue/GALLIMARD/Bibliotheque-des-Sciences-hu
maines/Comment-la-verite-et-la-realite-furent-inventees
>
> Best regards
>
> Yu LI
>
>
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