FOM: truth and provability
Martin Davis
martin at eipye.com
Wed Nov 8 13:23:40 EST 2000
At 06:27 PM 11/8/00 +0100, Kanovei wrote:
> > From: Martin Davis <martin at eipye.com>
>
> > Can I be the only fom-er getting tired of this discussion going round and=
> > round in circles
>
>That you go in circles is simply because
It's not I who go around in circles.
> > following variant form of Goedel's theorem:
> >
> > For any consistent axiomatic extension T of Robinson's Q (hence certainly
> > PA and ZFC are included) there is a formula with one free variable G(x),
> > where numerals representing natural numbers may be substituted for x, such
> > that:
> > 1. for each numeral n, G(n) is provable in T.
> > 2. (Ax)G(x) is not provable in T.
>
My point which I would have thought was exquisitely clear is that this form
gives an absolutely precise sense in which, for anyone who accepts the
soundness of T (even with respect to sentences of a very simple logical
form), a sentence can be seen to be true although not provable in T.
Of course for someone who imagines that using the word "myth" will demolish
ordinary mathematical practice, none of this counts.
I will not participate any longer on this thread.
Martin
Martin Davis
Visiting Scholar UC Berkeley
Professor Emeritus, NYU
martin at eipye.com
(Add 1 and get 0)
http://www.eipye.com
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