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  1. Revenge of the Liar: New Essays on the Paradox.J. C. Beall (ed.) - 2007 - Oxford, England: Oxford University Press.
    The Liar paradox raises foundational questions about logic, language, and truth (and semantic notions in general). A simple Liar sentence like 'This sentence is false' appears to be both true and false if it is either true or false. For if the sentence is true, then what it says is the case; but what it says is that it is false, hence it must be false. On the other hand, if the statement is false, then it is true, since it (...)
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  • The Revision Theory of Truth.Vann Mcgee - 1996 - Philosophy and Phenomenological Research 56 (3):727-730.
  • A Revenge-Immune Solution to the Semantic Paradoxes.Hartry Field - 2003 - Journal of Philosophical Logic 32 (2):139-177.
    The paper offers a solution to the semantic paradoxes, one in which we keep the unrestricted truth schema “True↔A”, and the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in “ordinary” contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True with A within the (...)
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  • The Revision Theory of Truth.A. Gupta & N. Belnap - 1993 - MIT Press.
    In this rigorous investigation into the logic of truth Anil Gupta and Nuel Belnap explain how the concept of truth works in both ordinary and pathological..
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  • The Consistency of The Naive Theory of Properties.Hartry Field - 2004 - Philosophical Quarterly 54 (214):78-104.
    If properties are to play a useful role in semantics, it is hard to avoid assuming the naïve theory of properties: for any predicate Θ(x), there is a property such that an object o has it if and only if Θ(o). Yet this appears to lead to various paradoxes. I show that no paradoxes arise as long as the logic is weakened appropriately; the main difficulty is finding a semantics that can handle a conditional obeying reasonable laws without engendering paradox. (...)
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  • Games for Truth.P. D. Welch - 2009 - Bulletin of Symbolic Logic 15 (4):410-427.
    We represent truth sets for a variety of the well known semantic theories of truth as those sets consisting of all sentences for which a player has a winning strategy in an infinite two person game. The classifications of the games considered here are simple, those over the natural model of arithmetic being all within the arithmetical class of $\Sum_{3}^{0}$.
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  • Axiomatizing Kripke's Theory of Truth.Volker Halbach & Leon Horsten - 2006 - Journal of Symbolic Logic 71 (2):677 - 712.
    We investigate axiomatizations of Kripke's theory of truth based on the Strong Kleene evaluation scheme for treating sentences lacking a truth value. Feferman's axiomatization KF formulated in classical logic is an indirect approach, because it is not sound with respect to Kripke's semantics in the straightforward sense: only the sentences that can be proved to be true in KF are valid in Kripke's partial models. Reinhardt proposed to focus just on the sentences that can be proved to be true in (...)
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  • Naive Semantics and the Liar Paradox.Hans G. Herzberger - 1982 - Journal of Philosophy 79 (9):479-497.
  • Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
    A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.
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  • Notes on Naive Semantics.Hans G. Herzberger - 1982 - Journal of Philosophical Logic 11 (1):61 - 102.
  • On the Metatheory of Field's `Solving the Paradoxes, Escaping Revenge'.Hannes Leitgeb - 2007 - In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox. Oxford University Press.
     
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  • Ultimate Truth Vis- À- Vis Stable Truth.P. D. Welch - 2008 - Review of Symbolic Logic 1 (1):126-142.
    We show that the set of ultimately true sentences in Hartry Field's Revenge-immune solution model to the semantic paradoxes is recursively isomorphic to the set of stably true sentences obtained in Hans Herzberger's revision sequence starting from the null hypothesis. We further remark that this shows that a substantial subsystem of second-order number theory is needed to establish the semantic values of sentences in Field's relative consistency proof of his theory over the ground model of the standard natural numbers: -CA0 (...)
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  • Hypermachines.Sy-David Friedman & P. D. Welch - 2011 - Journal of Symbolic Logic 76 (2):620 - 636.
    The Infinite Time Turing Machine model [8] of Hamkins and Kidder is, in an essential sense, a "Σ₂-machine" in that it uses a Σ₂ Liminf Rule to determine cell values at limit stages of time. We give a generalisation of these machines with an appropriate Σ n rule. Such machines either halt or enter an infinite loop by stage ζ(n) = df μζ(n)[∃Σ(n) > ζ(n) L ζ(n) ≺ Σn L Σ(n) ], again generalising precisely the ITTM case. The collection of (...)
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  • Solving the Paradoxes, Escaping Revenge.Hartry Field - 2007 - In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox. Oxford University Press.
    It is “the received wisdom” that any intuitively natural and consistent resolution of a class of semantic paradoxes immediately leads to other paradoxes just as bad as the first. This is often called the “revenge problem”. Some proponents of the received wisdom draw the conclusion that there is no hope of any natural treatment that puts all the paradoxes to rest: we must either live with the existence of paradoxes that we are unable to treat, or adopt artificial and ad (...)
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