FOM: Franzen on "which undecidables have determinate truth value"
hf18 at is4.nyu.edu
Fri Feb 27 12:30:39 EST 1998
I have two different answers, depending on the determinacy of 'finite', or
equivalently of 'natural number'. (On the view argued in the paper, their
determinacy depends on empirical assumptions). 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.
(There's actually an extra complication here, for 'formally undecidable'
would itself become indeterminate. But I don't think that this alters
things in the end.)
Regards, Hartry Field
At 09:27 AM 2/27/1998 -0500, you wrote:
>To Hartry Field:
> Would you want to refute the following argument (why or why not?):
>If Goldbach's Conjecture were proven to be formally undecidable in PA, it
>must then be true. The reason it must be true is that if it were false,
>then some even number could be found that was not the sum of two primes
>(and thus it wouldn't be undecidable).
> Any clarification would be appreciated.
> Thank you,
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