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  1. HYPE: A System of Hyperintensional Logic.Hannes Leitgeb - 2019 - Journal of Philosophical Logic 48 (2):305-405.
    This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the (...)
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  • Theories of Truth Based on Four-Valued Infectious Logics.Damian Szmuc, Bruno Da Re & Federico Pailos - 2020 - Logic Journal of the IGPL 28 (5):712-746.
    Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at least (...)
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  • The Primacy of the Classical? Saul Kripke Meets Niels Bohr.Colin Howson - 2019 - International Studies in the Philosophy of Science 32 (3-4):141-153.
    Kripke's theory of partial truth offers a natural solution of the Liar paradox and an appealing explanation of why the Liar sentence seems to lack definite content. It seems vulnerable, however, to...
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  • How to Find an Attractive Solution to the Liar Paradox.Mark Pinder - 2018 - Philosophical Studies 175 (7):1661-1680.
    The general thesis of this paper is that metasemantic theories can play a central role in determining the correct solution to the liar paradox. I argue for the thesis by providing a specific example. I show how Lewis’s reference-magnetic metasemantic theory may decide between two of the most influential solutions to the liar paradox: Kripke’s minimal fixed point theory of truth and Gupta and Belnap’s revision theory of truth. In particular, I suggest that Lewis’s metasemantic theory favours Kripke’s solution to (...)
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  • Embracing Intensionality: Paradoxicality and Semi-Truth Operators in Fixed Point Models.Nicholas Tourville & Roy T. Cook - 2020 - Logic Journal of the IGPL 28 (5):747-770.
    The Embracing Revenge account of semantic paradox avoids the expressive limitations of previous approaches based on the Kripkean fixed point construction by replacing a single language with an indefinitely extensible sequence of languages, each of which contains the resources to fully characterize the semantics of the previous languages. In this paper we extend the account developed in Cook, Cook, Schlenker, and Tourville and Cook via the addition of intensional operators such as ``is paradoxical''. In this extended framework we are able (...)
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  • One Hundred Years of Semantic Paradox.Leon Horsten - 2015 - Journal of Philosophical Logic (6):1-15.
    This article contains an overview of the main problems, themes and theories relating to the semantic paradoxes in the twentieth century. From this historical overview I tentatively draw some lessons about the way in which the field may evolve in the next decade.
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  • What Theories of Truth Should Be Like (but Cannot Be).Hannes Leitgeb - 2007 - Philosophy Compass 2 (2):276–290.
  • Reference and Truth.Lavinia Picollo - 2020 - Journal of Philosophical Logic 49 (3):439-474.
    I apply the notions of alethic reference introduced in previous work in the construction of several classical semantic truth theories. Furthermore, I provide proof-theoretic versions of those notions and use them to formulate axiomatic disquotational truth systems over classical logic. Some of these systems are shown to be sound, proof-theoretically strong, and compare well to the most renowned systems in the literature.
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  • On Artifacts and Truth-Preservation.Shawn Standefer - 2015 - Australasian Journal of Logic 12 (3):135-158.
    In Saving Truth from Paradox, Hartry Field presents and defends a theory of truth with a new conditional. In this paper, I present two criticisms of this theory, one concerning its assessments of validity and one concerning its treatment of truth-preservation claims. One way of adjusting the theory adequately responds to the truth-preservation criticism, at the cost of making the validity criticism worse. I show that in a restricted setting, Field has a way to respond to the validity criticism. I (...)
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  • How Truth Behaves When There’s No Vicious Reference.Philip Kremer - 2010 - Journal of Philosophical Logic 39 (4):345-367.
    In The Revision Theory of Truth (MIT Press), Gupta and Belnap (1993) claim as an advantage of their approach to truth "its consequence that truth behaves like an ordinary classical concept under certain conditions—conditions that can roughly be characterized as those in which there is no vicious reference in the language." To clarify this remark, they define Thomason models, nonpathological models in which truth behaves like a classical concept, and investigate conditions under which a model is Thomason: they argue that (...)
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  • Fixed-Point Posets in Theories of Truth.Stephen Mackereth - 2019 - Journal of Philosophical Logic (1).
    We show that any coherent complete partial order is obtainable as the fixed-point poset of the strong Kleene jump of a suitably chosen first-order ground model. This is a strengthening of Visser’s result that any finite ccpo is obtainable in this way. The same is true for the van Fraassen supervaluation jump, but not for the weak Kleene jump.
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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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  • Tarski Hierarchies.Volker Halbach - 1995 - Erkenntnis 43 (3):339 - 367.
    The general notions of object- and metalanguage are discussed and as a special case of this relation an arbitrary first order language with an infinite model is expanded by a predicate symbol T0 which is interpreted as truth predicate for . Then the expanded language is again augmented by a new truth predicate T1 for the whole language plus T0. This process is iterated into the transfinite to obtain the Tarskian hierarchy of languages. It is shown that there are natural (...)
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  • Ultramaximalist minimalism!A. Weir - 1996 - Analysis 56 (1):10-22.
  • Disquotation and Infinite Conjunctions.Lavinia Picollo & Thomas Schindler - 2017 - Erkenntnis (5):1-30.
    One of the main logical functions of the truth predicate is to enable us to express so-called ‘infinite conjunctions’. Several authors claim that the truth predicate can serve this function only if it is fully disquotational, which leads to triviality in classical logic. As a consequence, many have concluded that classical logic should be rejected. The purpose of this paper is threefold. First, we consider two accounts available in the literature of what it means to express infinite conjunctions with a (...)
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  • Can a Many-Valued Language Functionally Represent its Own Semantics?Jeffrey Ketland - 2003 - Analysis 63 (4):292–297.
    Tarski’s Indefinability Theorem can be generalized so that it applies to many-valued languages. We introduce a notion of strong semantic self-representation applicable to any (sufficiently rich) interpreted many-valued language L. A sufficiently rich interpreted many-valued language L is SSSR just in case it has a function symbol n(x) such that, for any f Sent(L), the denotation of the term n(“f”) in L is precisely ||f||L, the semantic value of f in L. By a simple diagonal construction (finding a sentence l (...)
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  • Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.
    In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn’t automatically solved by solving c-curry. A unified treatment of curry paradox thus calls for a unified treatment of both c-Curry and v-Curry. If, as is often thought, c-Curry paradox is to be solved via non-classical logic, then v-Curry may require a lesson about the structure—indeed, the substructure—of the validity relation itself.
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  • Truth: Do We Need It?Dorothy Grover - 1981 - Philosophical Studies 40 (1):69-103.
  • Truth: Do We Need It? [REVIEW]Dorothy L. Grover - 1981 - Philosophia (Misc.) 40 (1):225-252.
  • A Comparative Taxonomy of Medieval and Modern Approaches to Liar Sentences.C. Dutilh Novaes - 2008 - History and Philosophy of Logic 29 (3):227-261.
    Two periods in the history of logic and philosophy are characterized notably by vivid interest in self-referential paradoxical sentences in general, and Liar sentences in particular: the later medieval period (roughly from the 12th to the 15th century) and the last 100 years. In this paper, I undertake a comparative taxonomy of these two traditions. I outline and discuss eight main approaches to Liar sentences in the medieval tradition, and compare them to the most influential modern approaches to such sentences. (...)
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  • New Grounds for Naive Truth Theory.Stephen Yablo - 2004 - In J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox. Clarendon Press. pp. 312-330.
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  • Property Theory: The Type-Free Approach V. The Church Approach.George Bealer - 1994 - Journal of Philosophical Logic 23 (2):139 - 171.
    In a lengthy review article, C. Anthony Anderson criticizes the approach to property theory developed in Quality and Concept (1982). That approach is first-order, type-free, and broadly Russellian. Anderson favors Alonzo Church’s higher-order, type-theoretic, broadly Fregean approach. His worries concern the way in which the theory of intensional entities is developed. It is shown that the worries can be handled within the approach developed in the book but they remain serious obstacles for the Church approach. The discussion focuses on: (1) (...)
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  • Fixed-Point Models for Theories of Properties and Classes.Greg Restall - 2017 - Australasian Journal of Logic 14 (1).
    There is a vibrant community among philosophical logicians seeking to resolve the paradoxes of classes, properties and truth by way of adopting some non-classical logic in which trivialising paradoxical arguments are not valid. There is also a long tradition in theoretical computer science|going back to Dana Scott's fixed point model construction for the untyped lambda-calculus of models allowing for fixed points. In this paper, I will bring these traditions closer together, to show how these model constructions can shed light on (...)
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  • Some Supervaluation-Based Consequence Relations.Philip Kremer & Michael Kremer - 2003 - Journal of Philosophical Logic 32 (3):225-244.
    In this paper, we define some consequence relations based on supervaluation semantics for partial models, and we investigate their properties. For our main consequence relation, we show that natural versions of the following fail: upwards and downwards Lowenheim-Skolem, axiomatizability, and compactness. We also consider an alternate version for supervaluation semantics, and show both axiomatizability and compactness for the resulting consequence relation.
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  • Supervaluation Fixed-Point Logics of Truth.Philip Kremer & Alasdair Urquhart - 2008 - Journal of Philosophical Logic 37 (5):407-440.
    Michael Kremer defines fixed-point logics of truth based on Saul Kripke’s fixed point semantics for languages expressing their own truth concepts. Kremer axiomatizes the strong Kleene fixed-point logic of truth and the weak Kleene fixed-point logic of truth, but leaves the axiomatizability question open for the supervaluation fixed-point logic of truth and its variants. We show that the principal supervaluation fixed point logic of truth, when thought of as consequence relation, is highly complex: it is not even analytic. We also (...)
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  • The Truth is Sometimes Simple.Philip Kremer - manuscript
    Philip Kremer, Department of Philosophy, McMaster University Note: The following version of this paper does not contain the proofs of the stated theorems. A longer version, complete with proofs, is forthcoming. §1. Introduction. In "The truth is never simple" and its addendum, Burgess conducts a breathtakingly comprehensive survey of the complexity of the set of truths which arise when you add a truth predicate to arithmetic, and interpret that predicate according to the fixed point semantics or the revision-theoretic semantics for (...)
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  • Comparing Fixed-Point and Revision Theories of Truth.Philip Kremer - 2009 - Journal of Philosophical Logic 38 (4):363-403.
    In response to the liar’s paradox, Kripke developed the fixed-point semantics for languages expressing their own truth concepts. Kripke’s work suggests a number of related fixed-point theories of truth for such languages. Gupta and Belnap develop their revision theory of truth in contrast to the fixed-point theories. The current paper considers three natural ways to compare the various resulting theories of truth, and establishes the resulting relationships among these theories. The point is to get a sense of the lay of (...)
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  • Does Truth Behave Like a Classical Concept When There is No Vicious Reference?Philip Kremer - unknown
    §1. Introduction. When truth-theoretic paradoxes are generated, two factors seem to be at play: the behaviour that truth intuitively has; and the facts about which singular terms refer to which sentences, and so on. For example, paradoxicality might be partially attributed to the contingent fact that the singular term, "the italicized sentence on page one", refers to the sentence, The italicized sentence on page one is not true. Factors of this second kind might be represented by a ground model: an (...)
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  • Guest Editors’ Introduction.Riccardo Bruni & Shawn Standefer - 2019 - Journal of Philosophical Logic 48 (1):1-9.
  • The Paradox of the Believer.Sven Ove Hansson - 1991 - Philosophia 21 (1-2):25-30.
  • On Meaningfulness and Truth.BrianEdison McDonald - 2000 - Journal of Philosophical Logic 29 (5):433-482.
    We show how to construct certain L M, T -type interpreted languages, with each such language containing meaningfulness and truth predicates which apply to itself. These languages are comparable in expressive power to the L T -type, truth-theoretic languages first considered by Kripke, yet each of our L M, T -type languages possesses the additional advantage that, within it, the meaninglessness of any given meaningless expression can itself be meaningfully expressed. One therefore has, for example, the object level truth (and (...)
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  • Truth as Translation – Part A.Hannes Leitgeb - 2001 - Journal of Philosophical Logic 30 (4):281-307.
    This is the second part of a paper dealing with truth and translation. In Part A a revised version of Tarski's Convention T has been presented, which explicitly refers to a translation mapping from the object language to the metalanguage; the vague notion of a translation has been replaced by a precise definition. At the end of Part A it has been shown that interpreted languages exist, which allow for vicious self-reference but which nevertheless contain their own truth predicate - (...)
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  • Tarskian and Kripkean Truth.Volker Halbach - 1997 - Journal of Philosophical Logic 26 (1):69-80.
    A theory of the transfinite Tarskian hierarchy of languages is outlined and compared to a notion of partial truth by Kripke. It is shown that the hierarchy can be embedded into Kripke's minimal fixed point model. From this results on the expressive power of both approaches are obtained.
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  • Truth and Paradox.Anil Gupta - 1982 - Journal of Philosophical Logic 11 (1):1-60.
  • Grounding, Dependence, and Paradox.Steve Yablo - 1982 - Journal of Philosophical Logic 11 (1):117 - 137.
  • Truth. [REVIEW]Dorothy L. Grover - 1981 - Philosophia 10 (3-4):225-252.
  • Gupta's Rule of Revision Theory of Truth.Nuel D. Belnap - 1982 - Journal of Philosophical Logic 11 (1):103-116.
    Gupta’s Rule of Revision theory of truth builds on insights to be found in Martin and Woodruff and Kripke in order to permanently deepen our understanding of truth, of paradox, and of how we work our language while our language is working us. His concept of a predicate deriving its meaning by way of a Rule of Revision ought to impact significantly on the philosophy of language. Still, fortunately, he has left me something to.
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  • A Fixed Point Theorem for the Weak Kleene Valuation Scheme.Anil Gupta & Robert L. Martin - 1984 - Journal of Philosophical Logic 13 (2):131 - 135.
  • Assertion, Denial, and the Liar Paradox.Terence Parsons - 1984 - Journal of Philosophical Logic 13 (2):137 - 152.
  • Contraction and Revision.Shawn Standefer - 2016 - Australasian Journal of Logic 13 (3):58-77.
    An important question for proponents of non-contractive approaches to paradox is why contraction fails. Zardini offers an answer, namely that paradoxical sentences exhibit a kind of instability. I elaborate this idea using revision theory, and I argue that while instability does motivate failures of contraction, it equally motivates failure of many principles that non-contractive theorists want to maintain.
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  • A Paradox Involving Representational States and Activities.Blake Myers - 2019 - Thought: A Journal of Philosophy 8 (2):96-100.
    In this paper, I present a novel paradox that pertains to a variety of representational states and activities. I begin by proving that there are certain contingently true propositions that no one can occurrently believe. Then, I use this to develop a further proof by which I derive a contradiction, thus giving us the paradox. Next, I differentiate the paradox from the Liar Paradox, and I show how a common response to the different variations of the Liar Paradox fails to (...)
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  • The Truth is Never Simple.John P. Burgess - 1986 - Journal of Symbolic Logic 51 (3):663-681.
    The complexity of the set of truths of arithmetic is determined for various theories of truth deriving from Kripke and from Gupta and Herzberger.
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  • Meeting of the Association for Symbolic Logic, Chicago, 1989.Kenneth Manders - 1990 - Journal of Symbolic Logic 55 (1):436-445.
  • Classicality Lost: K3 and LP After the Fall.Matthias Jenny - 2017 - Thought: A Journal of Philosophy 6 (1):43-53.
    It is commonly held that the ascription of truth to a sentence is intersubstitutable with that very sentence. However, the simplest subclassical logics available to proponents of this view, namely K3 and LP, are hopelessly weak for many purposes. In this article, I argue that this is much more of a problem for proponents of LP than for proponents of K3. The strategies for recapturing classicality offered by proponents of LP are far less promising than those available to proponents of (...)
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  • Toward Useful Type-Free Theories. I.Solomon Feferman - 1984 - Journal of Symbolic Logic 49 (1):75-111.
  • A Guide to Truth Predicates in the Modern Era.Michael Sheard - 1994 - Journal of Symbolic Logic 59 (3):1032-1054.
  • On Meaningfulness and Truth.Brian Edison McDonald - 2000 - Journal of Philosophical Logic 29 (5):433 - 482.
    We show how to construct certain " $[Unrepresented Character]_{M,T}$ -type" interpreted languages, with each such language containing meaningfulness and truth predicates which apply to itself. These languages are comparable in expressive power to the $[Unrepresented Character]_{T}$ -type, truth-theoretic languages first considered by. Kripke, yet each of our $[Unrepresented Character]_{M,T}$ -type languages possesses the additional advantage that, within it, the meaninglessness of any given meaningless expression can itself be meaningfully expressed. One therefore has, for example, the object level truth (and meaningfulness) (...)
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  • Stenius on the Paradoxes.Fred Kroon - 1984 - Theoria 50 (2-3):178-211.