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

Arnon Avron aa at tau.ac.il
Tue May 17 01:48:34 EDT 2011

Quoting Andre.Rodin at ens.fr:

>> 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.

So you too do not understand the sense of the  theorem. The above formulation
is simply FALSE (and totally misleading).

> 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?

I think he has not done the effort to really understand it, or for ideological
reasons has chosen to ignore/hide the real content (and sense) of the theorem.
And yes, there is also the possibility that he really does not understand it.
Mathematicians nowadays have become rather careless about rigor,
precision, deep understanding, and avoiding mistakes. One can trust *nobody*.

Arnon Avron

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