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Full Idea
If we abandon classical logic in favour of truth-value gaps and try to strengthen the theory, this leads to the Kripke-Feferman theory of truth, and variants of it.
Gist of Idea
Kripke-Feferman has truth gaps, instead of classical logic, and aims for maximum strength
Source
Leon Horsten (The Tarskian Turn [2011], 01.4)
Book Ref
Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.8
Related Idea
Idea 15330 Friedman-Sheard theory keeps classical logic and aims for maximum strength [Horsten]
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] |