FOM: Reply to Detlefsen on consistency-completeness

Shipman, Joe x2845 shipman at
Wed Feb 4 09:52:19 EST 1998

> One last question: Do you find it unclear to say 'G's being provable in PA
> would make PA inconsistent'?

The problem people are having with this statement is the "would make".
The question is what system is your "would make" implication proved in?  

If it is ZF, then you are saying "ZF proves ((PA proves G) implies (PA 
inconsistent))."  But in ZF we know PA is consistent so this is the 
same as saying (PA does not prove G).  This seems not to be what you 

If it is PA, then you are saying "PA proves (PA proves G
implies PA inconsistent)". This is precisely stated!  
-- Joe Shipman

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