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3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms

[Kripke-Feferman axiomatisation of truth]

6 ideas
Kripke classified fixed points, and illuminated their use for clarifications [Kripke, by Halbach]
     Full Idea: Kripke's main contribution was …his classification of the different consistent fixed points and the discussion of their use for discriminating between ungrounded sentences, paradoxical sentences, and so on.
     From: report of Saul A. Kripke (Outline of a Theory of Truth [1975]) by Volker Halbach - Axiomatic Theories of Truth 15.1
Kripke-Feferman has truth gaps, instead of classical logic, and aims for maximum strength [Horsten]
     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.
     From: Leon Horsten (The Tarskian Turn [2011], 01.4)
Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach]
     Full Idea: The Kripke-Feferman theory KF is an axiomatisation of the fixed points of an operator, that is, of a Kripkean fixed-point semantics with the Strong Kleene evaluation schema with truth-value gluts.
     From: Volker Halbach (Axiomatic Theories of Truth [2011], 15.1)
The KF is much stronger deductively than FS, which relies on classical truth [Halbach]
     Full Idea: The Kripke-Feferman theory is relatively deductively very strong. In particular, it is much stronger than its competitor FS, which is based on a completely classical notion of truth.
     From: Volker Halbach (Axiomatic Theories of Truth [2011], 15.3)
The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach]
     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.
     From: Volker Halbach (Axiomatic Theories of Truth [2011], 16)
     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).
KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh]
     Full Idea: KF is formulated in classical logic, but describes a non-classical notion of truth. It allow truth-value gluts, making some sentences (such as the Liar) both true and not-true. Some authors add an axiom ruling out such gluts.
     From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.4)
     A reaction: [summary, which I hope is correct! Stanford is not wholly clear]