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

[Karlis Podnieks]

-----Original Message-----
From: Charles Silver <csilver at sophia.smith.edu>
Date: 27-FEB 19:43
Subject: Re: FOM: Franzen on "which undecidables have
determinate truth value"


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).
...

KP> Paul Lévy used this argument in 1926:


"... il est possible que le theoreme de Fermat soit
indemontrable, mais on ne demontrera jamais qu'il est
indemontrable.Au contraire, il n'est pas absurde d'imaginer
qu'on demontre qu'on ne soura jamais si la constante d'Euler est
algebrique ou transcendente."

See: P. Lévy. Sur le principe du tiers exclu et sur les
théoremes non susceptibles de démonstration. "Revue de
Métaphysique et de Morale", 1926, vol. 33, N2, pp.253-258.

Best wishes,
K.Podnieks
podnieks at cclu.lv
http://sisenis.com.latnet.lv/~podnieks/
University of Latvia
Institute of Mathematics and Computer Science