[FOM] Formalization Thesis: A second attempt

[Timothy Y. Chow]

On Thu, 27 May 2010, Vladimir Sazonov wrote:
>Here I am in a shock since such restricting mathematics to ZFC 
>(even tentatively) or to anything like that seems to me absolutely 
>inappropriate. I highly agree on the extraordinary importance of 
>ZFC, but not to such a degree. 

Let me once again draw your attention back to one of my main motivating 
applications, namely explaining why Goedel's 2nd theorem is relevant to 
Hilbert's program of proving the consistency of mathematics.  It is widely 
believed that Hilbert's program is essentially hopeless, because of 
Goedel's 2nd theorem.  Do you share this point of view?  If mathematics is 
as open-ended as you seem to be arguing, then isn't Hilbert's program 
still wide open?  Tomorrow someone may complete Hilbert's program by 
publishing a perfectly acceptable mathematical proof that mathematics is 
consistent.  The proof will presumably not be formalizable in ZFC, but so 
what?

Tim