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Full Idea
KF is useful for explicating Peano arithmetic, but it certainly does not come to close to being a theory that contains its own truth predicate.
Gist of Idea
The KF theory is useful, but it is not a theory containing its own truth predicate
Source
Volker Halbach (Axiomatic Theories of Truth [2011], 16)
Book Ref
Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.229
A Reaction
Since it is a type-free theory, its main philosophical aspiration was to contain its own truth predicate, so that is bad news (for philosophers).
| 16328 | Kripke classified fixed points, and illuminated their use for clarifications [Kripke, by Halbach] |
| 15331 | Kripke-Feferman has truth gaps, instead of classical logic, and aims for maximum strength [Horsten] |
| 16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach] |
| 16331 | The KF is much stronger deductively than FS, which relies on classical truth [Halbach] |
| 16332 | The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach] |
| 19130 | KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh] |