[FOM] Re: Godel's Theorems
Torkel Franzen
torkel at sm.luth.se
Thu May 1 01:12:28 EDT 2003
V. Kanovei says:
>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.
These are strange alternatives. How would you interpret "If T
is consistent, then the Godel sentence for T is true" in a case
where we have no idea whether or not T is consistent?
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Torkel Franzen
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