R: [FOM] 31st Novembertagung 2020

Timothy Y. Chow tchow at math.princeton.edu
Sun Apr 26 10:26:53 EDT 2020

On Sun, 26 Apr 2020, Antonino Drago wrote:
> By incidence, it is fortunate for us that von Neumann, as he said to 
> Goedel, the day before Goedel's first communication had realize to be 
> unsuccessful in his last attempt for proving the completeness; otherwise 
> no one had conceded attention to the young mathematician. In previous 
> years Von Neumann had already publicly announced to have obtained the 
> proof.

This account surprises me.  What does "proving the completeness" mean 
here?  I'm not aware of any such announcement by von Neumann.  Various 
*consistency* proofs had been announced earlier, a more limited result by 
von Neumann and more general ones by Ackermann.  There was a problem with 
one of Ackermann's proofs; von Neumann wrote on March 10, 1931: "I think 
that this answers the question, which we recently discussed when going 
through Ackermann's modified proof, namely whether an estimate of the 
length of the correction process can be made uniformly and independently 
of numerical substituends, in the negative.  At this point the proof of 
termination of the procedure (for the next higher degree, i.e., 3) has a 
gap."  (See for example "The Practice of Finitism: Epsilon Calculus and 
Consistency Proofs in Hilbert's Program" by Richard Zach.)  But March 1931 
was *after* Goedel's results had been announced and understood.

I'm wondering if you can give more details about what von Neumann said to 
Goedel "the day before Goedel's first communication"---I assume this would 
have been in August or September 1930?


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