Re: Godel's Theorem and Model Theory
- From: stevendaryl3016@xxxxxxxxx (Daryl McCullough)
- Date: 27 Jul 2007 08:05:17 -0700
Keith Ramsay says...
It seems to be a common problem, however, to get
stuck imagining that the concept of truth is
dependent on the concept of "model". If one then
tries to retrace one's steps, to work out a
logical sequence of definitions of terms, one
keeps getting stuck wondering how it's possible
to specify a model while being unable to talk
about truth of any kind (but only provability).
Very good point. Actually, even if you want to
be a formalist about it and say that the only
meaningful statements are of the form "Phi is
provable in theory T", you are still relying on
the *truth* (not just provability) of statements
of the form "X is a proof of Y from axioms Z".
--
Daryl McCullough
Ithaca, NY
.
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