[FOM] Formalization Thesis: A second attempt
Timothy Y. Chow
tchow at alum.mit.edu
Sat May 29 22:23:47 EDT 2010
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
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