[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.
V.Kanovei
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