FOM: Franzen on "which undecidables have determinate truth value"

Stephen G Simpson simpson at
Sat Feb 28 19:57:01 EST 1998

Charles Silver said:
 > >If Goldbach's Conjecture were proven to be formally undecidable in PA, it
 > >must then be true.

Hartry Field replied:
 > If 'finite' and 'natural number' are determinate, then the argument
 > is correct.  If they are indeterminate, then the argument is not
 > correct, for the truth of all the instances involving "genuine
 > natural numbers" doesn't guarantee the determinate truth of the
 > universal quantification over all numbers.

Sorry, I don't follow.  If GC were proven to be formally undecidable
in PA, then this would give a uniform proof of all instances of GC.
Why wouldn't this guarantee the "determinate truth" of GC?

Perhaps your reservations about Silver's argument depend on some
unusual distinction, e.g. an unusual sense of "determinate".  If so,
could you please explain the distinction in question?

-- Steve Simpson

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