Odifreddi: Godel's proof of the existence of God

[Yu Li]

Dear colleagues,

The proof of Gödel's Incompleteness Theorem has been challenged since 
its publication, which is compiled by John W. Dawson Jr. in his article 
«  The reception of Gödel's Incompleteness Theorems » ([1], p74-95):
- Ernst Zermelo stated in a letter to Gödel in 1931 that Gödel’s proof 
of the existence of undecidable propositions exhibits an « essential gap » ;
- The logician Chaïm Perelman asserted that Gödel had in fact discovered 
an antinomy.
- Wittgenstein’s well-known comments on Gödel’s theorem appear in 
« Remarks on the Foundations of Mathematics (1938) ».
- Bertrand Russell expressed his profound confusion in a letter to Leon 
Henkin : 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.
…...

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 Gödel without mentioning his name and ventured to fix 
them.

The malaise caused by Gödel's proof has been continuously explored in 
the humanities  [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 Gödel's proof from the 
perspective of human knowledge by the anthropologist Paul Jorion [8], …...

Reference :
[1] S.G. Shanker (ed.), Gödel’s Theorem in Focus, Croom Helm 
1988, https://pdfslide.net/documents/godels-theorem-in-focus-philosophers-in-focus.html
[2] Alan Turing, « On Computable Numbers, with an Application to 
the Entscheidungsproblem », 
https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf
[3] Stephen Budiansky, Journey to the Edge of Reason - The Life of Kurt 
Gödel (2021). https://wwnorton.com/books/9781324005445/overview
[4] Rebecca Goldstein, Incompleteness: The Proof and Paradox of Kurt 
Gödel). 
https://www.essra.org.cn/upload/202102/Incompleteness%20-%20The%20Proof%20and%20Paradox%20of%20Kurt%20Godel%20by%20Rebecca%20Goldstein%EF%BC%882005%EF%BC%89.pdf
[5] Pierre Cassou-Noguès, Les Démons de Gödel - 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, Comment la vérité et la réalité furent 
inventées (Gallimard 2009). 
https://www.gallimard.fr/Catalogue/GALLIMARD/Bibliotheque-des-Sciences-humaines/Comment-la-verite-et-la-realite-furent-inventees

Best regards

Yu LI