FOM: con ZFC

Kanovei kanovei at
Fri Mar 19 02:29:58 EST 1999

>Date: Thu, 18 Mar 1999 13:59:58 -0700
>From: Randall Holmes <holmes at>

> 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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