FOM: con ZFC
kanovei at wminf2.math.uni-wuppertal.de
Fri Mar 19 02:29:58 EST 1999
>Date: Thu, 18 Mar 1999 13:59:58 -0700
>From: Randall Holmes <holmes at catseye.idbsu.edu>
> But it is not possible
>to prove certain other facts that we do believe in this language: for
>example, it is not possible to prove Con(ZFC), which can be understood
>as a fact about the natural numbers.
Con ZFC is believed to be true
not as a formal statement of any sort
but rather as a prediction that any
contradiction in ZFC will never be found in
the practical activity of mathematicians.
For instance if you succeed to prove
some A assuming Con ZFC this will
mathemtically mean that you have proved
Con ZFC --> A, but not that you have proved A.
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