[FOM] comment on the video of the lecture by Voevodsky at IAS

Andre.Rodin at ens.fr Andre.Rodin at ens.fr
Mon May 16 18:47:20 EDT 2011

I would like also to thank Juliette for posting this video.

> He stated the theorem as follows (written version, projected on the
> screen):
>    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 detail or
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 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?

Perhaps this future is not so bright indeed (as far as one sticks to a narrow
meaning of fom) but I think that at least a part of the problem is that (at
least a part of) fom community deliberately isolates itself from the rest of
mathematical community. This is harmful for the fom community at the first

Andrei Rodin

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