[FOM] comment on the video of the lecture by Voevodsky at IAS
joeshipman at aol.com
joeshipman at aol.com
Mon May 16 21:46:43 EDT 2011
I must strongly disagree with Rodin and Messing here. Tennant's
technical criticisms are not the main problem with Voevodsky's lecture.
The real howler was Voevodsky's presentation of 3 alternatives as
exhaustive, completely overlooking the obvious 4th alternative of a
hierarchy of systems of increasing strength, such that the strongest
system acceptable to him is stronger than Peano Arithmetic and proves
Voevodsky acted like his failure to see the well-orderedness of
epsilon_0 as an acceptably obvious axiom was all there was to say,
ignoring the existence of second order arithmetic, even weak forms of
which prove the consitency of PA. Even if Voevodsky's own work is
entirely formalizable in PA, which I doubt, I am certain that he has
read (and even refereed), and approved of as valid with no
reservations, mathematical proofs which assume some principle of
induction or set theory sufficient to prove the consistency of PA. If
those papers had included as a corollary Con(PA) wouldhe have rejected
them? if he wouldnot have, how can he say that the consistency of
arithmetic cannot be proven?
Or does he not even understand the distinction between firstand second
From: Andre.Rodin at ens.fr
To: Foundations of Mathematics <fom at cs.nyu.edu>
Sent: Mon, May 16, 2011 6:47 pm
Subject: Re: [FOM] comment on the video of the lecture by Voevodsky at
I would like also to thank Juliette for posting this video.
> 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.
He didn't mention this detail but I cannot see that it changed the
sense of the
theorem. Do you seriously think Voevodsky is not aware about this
that the detail is too subtle so he's unable to understand it?
> This cavalier inattention to detail marred the subsequent dialectic,
is "dialectic" a course word in your language?
> If a Fields Medallist working in algebraic geometry and homotopy
> is able to give an account of GII at only such an amateurish level,
> hope is there for the future of fom in Departments of Mathematics?
Perhaps this future is not so bright indeed (as far as one sticks to a
meaning of fom) but I think that at least a part of the problem is that
least a part of) fom community deliberately isolates itself from the
mathematical community. This is harmful for the fom community at the
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