[FOM] comment on the video of the lecture by Voevodsky at IAS
neilt at mercutio.cohums.ohio-state.edu
Mon May 16 15:56:12 EDT 2011
Thank you for the link to Voevodsky's lecture video.
I would be most interested to know whether other fom-ers are as
unimpressed--indeed, dismayed--as I am by his inexact presentation of
Goedel's Second Incompleteness Theorem.
He stated the theorem as follows (written version, projected on the
It is impossible to prove the consistency of any formal reasoning
system which is at least as strong as the standard axiomatization
of elementary number theory ("first order arithmetic").
So he failed to inform his audience that the impossibility that Goedel
actually established was the impossibility of proof-in-S of a sentence
expressing the consistency of S, for any consistent and sufficiently
strong system S.
This cavalier inattention to detail marred the subsequent dialectic,
expecially concerning the "choices" supposedly open to us in dealing with
what he called "Goedel's paradox" (verbatim quote follows, again from
what was on the screen):
We know that the first order arithmetic is consistent.
It can be proved that it is impossible to prove that the first order
arithmetic is consistent.
If a Fields Medallist working in algebraic geometry and homotopy theory
is able to give an account of GII at only such an amateurish level, what
hope is there for the future of fom in Departments of Mathematics?
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