[FOM] Godel's Theorems

Kanovei kanovei at wmwap1.math.uni-wuppertal.de
Wed Apr 30 00:23:26 EDT 2003

>Date: Tue, 29 Apr 2003 21:55:53 -0400
>From: Harvey Friedman <friedman at math.ohio-state.edu>

>*) there is a true sentence in the language of PA which is not provable in PA.
>1. Conventional wisdom is that this is now a fully established
>theorem of mathematics (or ordinary mathematics as currently
>practiced by the overwhelming majority of mathematicians). Is there
>agreement on this?

The answer depends on the meaning of "true sentence". 
If this means: "a sentence provable in ZFC" then {*) is as 
established as any mathematical theorem.
If this refers to something external with respect to 
the system of mathematical proofs, for instance, to the 
"standard model of PA" as a phenomenon of physical existence, 
then (*) should be considered as a physical law, that is, in 
principle, a subject of change and amendments.


More information about the FOM mailing list