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?
Tim
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