[FOM] Deflationism and the Godel phenomena
Torkel Franzen
torkel at sm.luth.se
Tue Feb 15 02:30:36 EST 2005
Neil says:
>On the contrary; the justification is given for arbitrary phi.
So let us consider the suggested justification, taking phi in
(1) Prov_S(phi)->phi
to be a logical contradiction psi&~psi. (1) then states that S is
consistent, Con_S. Applying the "intellectual reflection" to this case,
we get:
The deflationist might well wish to adopt Con_S.
After all, if he was willing to assert any sentence phi
for which he had furnished an S-proof, why not then also be
willing to assert a logical contradiction if he can furnish
a proof that S is inconsistent?
I find this baffling, and can only assume that Neil has not fully
set forth the intellectual reflection leading to Con_S.
>Actually, I don't say this. The iteration is to epsilon_(epsilon_0).
My mistake.
A correction to my earlier parenthetical remark: I should have said
that whether every arithmetical theorem of ACA is provable in some
theory in an autonomous iterated sequence of extensions of PA by
uniform reflection is a question for which I know of no answer
in the literature.
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