[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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