Ideas from 'Outline of a Theory of Truth' by Saul A. Kripke [1975], by Theme Structure

[found in 'Philosophical Troubles: Papers vol. 1' by Kripke,Saul [OUP 2011,978-0-19-973015-5]].

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3. Truth / F. Semantic Truth / 2. Semantic Truth
Kripke's semantic theory has actually inspired promising axiomatic theories
                        Full Idea: Kripke has a semantic theory of truth which has inspired promising axiomatic theories of truth.
                        From: report of Saul A. Kripke (Outline of a Theory of Truth [1975]) by Leon Horsten - The Tarskian Turn 01.2
                        A reaction: Feferman produced an axiomatic version of Kripke's semantic theory.
Kripke offers a semantic theory of truth (involving models)
                        Full Idea: One of the most popular semantic theories of truth is Kripke's theory. It describes a class of models which themselves involve a truth predicate (unlike Tarski's semantic theory).
                        From: report of Saul A. Kripke (Outline of a Theory of Truth [1975]) by Leon Horsten - The Tarskian Turn 02.3
                        A reaction: The modern versions explored by Horsten are syntactic versions of this, derived from Feferman's axiomatisation of the Kripke theory.
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
Certain three-valued languages can contain their own truth predicates
                        Full Idea: Kripke showed via a fixed-point argument that certain three-valued languages can contain their own truth predicates.
                        From: report of Saul A. Kripke (Outline of a Theory of Truth [1975]) by Anil Gupta - Truth
                        A reaction: [Gupta also cites Martin and Woodruff 1975] It is an odd paradox that truth can only be included if one adds a truth-value of 'neither true nor false'. The proposed three-valued system is 'strong Kleene logic'.
The Tarskian move to a metalanguage may not be essential for truth theories
                        Full Idea: Kripke established that, contrary to the prevalent Tarskian dogma, attributions of truth do not always force a move to a metalanguage.
                        From: report of Saul A. Kripke (Outline of a Theory of Truth [1975], 5.1) by Anil Gupta - Truth
                        A reaction: [Gupta also cites Martin and Woodruff 1975]
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
Kripke classified fixed points, and illuminated their use for clarifications
                        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