Re: Exception to the rule? (Tarski´s T-scheme)

From: Jeffrey Ketland (ketland_at_ketland.fsnet.co.uk)
Date: 06/23/04 

Date: Wed, 23 Jun 2004 22:02:46 +0100

Jeffrey Ketland wrote:

> For example, Kripke's theory (Kripke 1975) is based on a
>three-valued logic with truth values {T, F, U}, where U is for "undefined",
>allows that phi and Tr("phi") always have the same truth value, even when
>phi contains the symbol Tr.
>The corresponding deductive theory (formulated by Feferman) has the
>inference rules:
>
> If you have proved phi, you can infer Tr("phi") Tr-intro
> If you have proved Tr("phi"), you can infer phi Tr-elim

Whoops. This is wrong. The Kripke-Feferman truth theory KF doesn't include
these rules (if they were added, it would be inconsistent).
A self-applicative truth theory which does include these rules is FS (for
Friedman-Sheard, based on their 1987 paper "An Axiomatic Approach to
Self-Referential Truth"), but its compositional axioms are weaker than those
of KF.

--- Jeff