[FOM] Fwd: invitation to comment

Harvey Friedman friedman at math.ohio-state.edu
Wed May 18 23:37:32 EDT 2011

Begin forwarded message:

From: Vladimir Voevodsky <vladimir at ias.edu>
Date: May 18, 2011 4:44:13 PM EDT
To: Harvey Friedman <friedman at math.ohio-state.edu>
Cc: Vladimir Aleksandrovich Voevodsky <vladimir at ias.edu>
Subject: Re: invitation to comment

Dear Harvey,

such a comment will take some time to write ...

To put it very shortly I think that in-consistency of Peano arithmetic  
as well as in-consistency of ZFC are open and very interesting  
problems in mathematics. Consistency on the other hand is not an  
interesting problem since it has been shown by Goedel to be impossible  
to proof.


On May 17, 2011, at 2:45 PM, Harvey Friedman wrote:

> Dear Professor Voevodsky,
> I have become aware of your online videos at http://video.ias.edu/voevodsky-80th 
>  and http://video.ias.edu/univalent/voevodsky. I was particularly  
> struck by your discussion of the "possible inconsistency of Peano  
> Arithmetic". This has created a lot of attention on the FOM email  
> list. As a subscriber to that list, I would very much like you to  
> send us an account of how you view the consistency of Peano  
> Arithmetic. In particular, how you view the usual mathematical proof  
> that Peano Arithmetic is consistent, and to what extent and in what  
> sense is "the consistency of Peano Arithmetic" a genuine open  
> problem in mathematics. It would also be of interest to hear your  
> conception of what foundations of mathematics is, or should be, or  
> could be, as it appears to be very different from traditional  
> conceptions of the foundations of mathematics.
> Respectfully yours,
> Harvey M. Friedman
> Ohio State University
> Distinguished University Professor
> Mathematics, Philosophy, Computer Science

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