FOM: truth and provability
holmes@catseye.idbsu.edu
holmes at catseye.idbsu.edu
Mon Nov 6 15:59:07 EST 2000
Dear All,
The following is certainly true, and it is a consequence of Godel's
theorem. The mathematical concepts of truth and provability involved
are precise and well-known:
there is a sentence of the language of PA which is true in the standard
model of PA as defined in ZFC, not provable in PA, and true in ZFC
(because provable in ZFC).
If Kanovei disputes this, he is simply wrong; this is a well-known
result.
I have a feeling that Kanovei is actually disputing this much more
dubious assertion:
There is a sentence expressible in mathematical notation which is true
(in some metaphysical sense) and not provable (in _any_ mathematical
system).
It is perfectly possible to dispute this assertion (which is not a
consequence of Godel's theorem).
Any comments from any of the parties to the discussion?
--Randall Holmes
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