Russell on Gödel; Re: Odifreddi: Godel's proof of the existence of God (FOM Digest, Vol 239, Issue 13)

[Alexander M Lemberg]

I cited the Alasdair Urquhart article because I had just come across it
and was interested because I hold Urquhart in high regard.

Now that I have read the article, I enthusiastically recommend it to
anyone on this list serve who is interested in Russell or Godel. It
contains detailed background to the quote from the letter to Henkin
(which apparently is authentic) and the quote from Mac Lane. There is
quite a bit of information from Russell himself about his state of mind
at various stages of his life.

Urquhart clearly put a lot of effort into this article and the result is
an excellent and important piece of scholarship.

Sandy

ps

can anyone suggest what I can do to prevent my computer from introducing
unwanted characters, as shown in the rendering of the text below? Thanks


On Fri, 18 Nov 2022 19:58:36 +0100 Yu Li <franceliuyu at gmail.com> writes:
> Thank you so much for the article RUSSELL AND GOEL [1] ! It is very 
> helpful for a fuller understanding of Russell's views of Gödel'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.
> 
> It can be seen from Russell's 1965 comments, Russell did not 
> question Gödel's incompleteness conclusion, that is, the existence 
> of undecidable propositions in formal systems, for Russell said: « 
> I had always supposed that there are propositions in mathematical 
> logic which can be stated, but neither proved nor disproved. » ([1] 
> p.14) Russell was questioning Gödel's proof of the incompleteness 
> conclusion, for Gödel took the liar's paradox as a premise and 
> argued that this paradox was a true but unprovable proposition in 
> the formal system. Perhaps this is why Russell says: «  I realised, 
> of course, that Gödel’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. » 
> 
> Maybe we can also ask ourselves :
> - What do we think of incompleteness conclusion ?
> - Are we puzzled by Godel’s proof of the incompleteness conclusion 
> ?
> 
> Best regards
> 
> Yu 
> 
> Reference:
> [1] Alasdair Urquhart, Russell and Gödel. 
> https://www.academia.edu/27310325/Russell_and_G%C3%B6del 
> <https://www.academia.edu/27310325/Russell_and_G%C3%B6del>=