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Hans G. Herzberger (1982). Notes on Naive Semantics.

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  1.  6
    Guest Editors’ Introduction.Riccardo Bruni & Shawn Standefer - forthcoming - Journal of Philosophical Logic:1-9.
  2.  6
    Revision Without Revision Sequences: Self-Referential Truth.Edoardo Rivello - forthcoming - Journal of Philosophical Logic:1-29.
    The model of self-referential truth presented in this paper, named Revision-theoretic supervaluation, aims to incorporate the philosophical insights of Gupta and Belnap’s Revision Theory of Truth into the formal framework of Kripkean fixed-point semantics. In Kripke-style theories the final set of grounded true sentences can be reached from below along a strictly increasing sequence of sets of grounded true sentences: in this sense, each stage of the construction can be viewed as an improvement on the previous ones. I want to (...)
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  3.  5
    Revision Without Revision Sequences: Circular Definitions.Edoardo Rivello - forthcoming - Journal of Philosophical Logic:1-29.
    The classical theory of definitions bans so-called circular definitions, namely, definitions of a unary predicate P, based on stipulations of the form $$Px =_{\mathsf {Df}} \phi,$$where ϕ is a formula of a fixed first-order language and the definiendum P occurs into the definiensϕ. In their seminal book The Revision Theory of Truth, Gupta and Belnap claim that “General theories of definitions are possible within which circular definitions [...] make logical and semantic sense” [p. IX]. In order to sustain their claim, (...)
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  4.  25
    Truth and Generalized Quantification.Bruno Whittle - forthcoming - Australasian Journal of Philosophy:1-14.
    Kripke [1975] gives a formal theory of truth based on Kleene's strong evaluation scheme. It is probably the most important and influential that has yet been given—at least since Tarski. However, it has been argued that this theory has a problem with generalized quantifiers such as All—that is, All ϕs are ψ—or Most. Specifically, it has been argued that such quantifiers preclude the existence of just the sort of language that Kripke aims to deliver—one that contains its own truth predicate. (...)
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  5.  17
    Some Notes on Truths and Comprehension.Thomas Schindler - 2018 - Journal of Philosophical Logic 47 (3):449-479.
    In this paper we study several translations that map models and formulae of the language of second-order arithmetic to models and formulae of the language of truth. These translations are useful because they allow us to exploit results from the extensive literature on arithmetic to study the notion of truth. Our purpose is to present these connections in a systematic way, generalize some well-known results in this area, and to provide a number of new results. Sections 3 and 4 contain (...)
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  6.  30
    A Graph-Theoretic Analysis of the Semantic Paradoxes.Timo Beringer & Thomas Schindler - 2017 - Bulletin of Symbolic Logic 23 (4):442-492.
    We introduce a framework for a graph-theoretic analysis of the semantic paradoxes. Similar frameworks have been recently developed for infinitary propositional languages by Cook and Rabern, Rabern, and Macauley. Our focus, however, will be on the language of first-order arithmetic augmented with a primitive truth predicate. Using Leitgeb’s notion of semantic dependence, we assign reference graphs (rfgs) to the sentences of this language and define a notion of paradoxicality in terms of acceptable decorations of rfgs with truth values. It is (...)
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  7. Conditionals in Theories of Truth.Anil Gupta & Shawn Standefer - 2017 - Journal of Philosophical Logic 46 (1):27-63.
    We argue that distinct conditionals—conditionals that are governed by different logics—are needed to formalize the rules of Truth Introduction and Truth Elimination. We show that revision theory, when enriched with the new conditionals, yields an attractive theory of truth. We go on to compare this theory with one recently proposed by Hartry Field.
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  8. 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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  9.  65
    Axiomatizing Semantic Theories of Truth?Martin Fischer, Volker Halbach, Jönne Kriener & Johannes Stern - 2015 - Review of Symbolic Logic 8 (2):257-278.
    We discuss the interplay between the axiomatic and the semantic approach to truth. Often, semantic constructions have guided the development of axiomatic theories and certain axiomatic theories have been claimed to capture a semantic construction. We ask under which conditions an axiomatic theory captures a semantic construction. After discussing some potential criteria, we focus on the criterion of ℕ-categoricity and discuss its usefulness and limits.
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  10.  7
    Cofinally Invariant Sequences and Revision.Edoardo Rivello - 2015 - Studia Logica 103 (3):599-622.
    Revision sequences are a kind of transfinite sequences which were introduced by Herzberger and Gupta in 1982 as the main mathematical tool for developing their respective revision theories of truth. We generalise revision sequences to the notion of cofinally invariant sequences, showing that several known facts about Herzberger’s and Gupta’s theories also hold for this more abstract kind of sequences and providing new and more informative proofs of the old results.
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  11.  23
    A Disquotational Theory of Truth as Strong as Z 2 −.Thomas Schindler - 2015 - Journal of Philosophical Logic 44 (4):395-410.
    T-biconditionals have often been regarded as insufficient as axioms for truth. This verdict is based on Tarski’s observation that the typed T-sentences suffer from deductive weakness. As indicated by McGee, the situation might change radically if we consider type-free disquotational theories of truth. However, finding a well-motivated set of untyped T-biconditionals that is consistent and recursively enumerable has proven to be very difficult. Moreover, some authors ) have argued that any solution to the semantic paradoxes necessarily involves ‘inflationary’ means, thus (...)
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  12. 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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  13.  28
    Solovay-Type Theorems for Circular Definitions.Shawn Standefer - 2015 - Review of Symbolic Logic 8 (3):467-487.
  14.  12
    Tarski's Theorem and Liar-Like Paradoxes.Ming Hsiung - 2014 - Logic Journal of the IGPL 22 (1):24-38.
    Tarski's theorem essentially says that the Liar paradox is paradoxical in the minimal reflexive frame. We generalise this result to the Liar-like paradox $\lambda^\alpha$ for all ordinal $\alpha\geq 1$. The main result is that for any positive integer $n = 2^i(2j+1)$, the paradox $\lambda^n$ is paradoxical in a frame iff this frame contains at least a cycle the depth of which is not divisible by $2^{i+1}$; and for any ordinal $\alpha \geq \omega$, the paradox $\lambda^\alpha$ is paradoxical in a frame (...)
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  15.  11
    Some Observations on Truth Hierarchies.P. D. Welch - 2014 - Review of Symbolic Logic 7 (1):1-30.
  16.  37
    Notes on Ω-Inconsistent Theories of Truth in Second-Order Languages.Eduardo Barrio & Lavinia Picollo - 2013 - Review of Symbolic Logic 6 (4):733-741.
    It is widely accepted that a theory of truth for arithmetic should be consistent, but -consistency is a highly desirable feature for such theories. The point has already been made for first-order languages, though the evidence is not entirely conclusive. We show that in the second-order case the consequence of adopting -inconsistent theories of truth are considered: the revision theory of nearly stable truth T # and the classical theory of symmetric truth FS. Briefly, we present some conceptual problems with (...)
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  17.  69
    Variations on a Montagovian Theme.Wolfgang Schwarz - 2013 - Synthese 190 (16):3377-3395.
    What are the objects of knowledge, belief, probability, apriority or analyticity? For at least some of these properties, it seems plausible that the objects are sentences, or sentence-like entities. However, results from mathematical logic indicate that sentential properties are subject to severe formal limitations. After surveying these results, I argue that they are more problematic than often assumed, that they can be avoided by taking the objects of the relevant property to be coarse-grained (“sets of worlds”) propositions, and that all (...)
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  18. More on 'A Liar Paradox'.Richard Heck - 2012 - Thought: A Journal of Philosophy 1 (4):270-280.
    A reply to two responses to an earlier paper, "A Liar Paradox".
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  19.  30
    Truth, Logical Validity and Determinateness: A Commentary on Field's Saving Truth From Paradox.P. D. Welch - 2011 - Review of Symbolic Logic 4 (3):348-359.
    We consider notions of truth and logical validity defined in various recent constructions of Hartry Field. We try to explicate his notion of determinate truth by clarifying the path-dependent hierarchies of his determinateness operator.
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  20.  5
    Weak Systems of Determinacy and Arithmetical Quasi-Inductive Definitions.P. D. Welch - 2011 - Journal of Symbolic Logic 76 (2):418 - 436.
    We locate winning strategies for various ${\mathrm{\Sigma }}_{3}^{0}$ -games in the L-hierarchy in order to prove the following: Theorem 1. KP+Σ₂-Comprehension $\vdash \exists \alpha L_{\alpha}\ models"\Sigma _{2}-{\bf KP}+\Sigma _{3}^{0}-\text{Determinacy}."$ Alternatively: ${\mathrm{\Pi }}_{3}^{1}\text{\hspace{0.17em}}-{\mathrm{C}\mathrm{A}}_{0}\phantom{\rule{0ex}{0ex}}$ "there is a β-model of ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17 em}}{\mathrm{\Sigma }}_{3}^{0}$ -Determinacy." The implication is not reversible. (The antecedent here may be replaced with ${\mathrm{\Pi }}_{3}^{1}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left({\mathrm{\Pi }}_{3}^{1}\right)-{\mathrm{C}\mathrm{A}}_{0}:\text{\hspace{0.17em}}{\mathrm{\Pi }}_{3}^{1}$ instances of Comprehension with only ${\mathrm{\Pi }}_{3}^{1}$ -lightface definable parameters—or even weaker theories.) Theorem 2. KP +Δ₂-Comprehension +Σ₂-Replacement + ${\mathrm{\Sigma }}_{3}^{0}\phantom{\rule{0ex}{0ex}}$ -Determinacy. (Here AQI (...)
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  21. Supervaluations Debugged.Nicholas Asher, Josh Dever & Chris Pappas - 2009 - Mind 118 (472):901-933.
    Supervaluational accounts of vagueness have come under assault from Timothy Williamson for failing to provide either a sufficiently classical logic or a disquotational notion of truth, and from Crispin Wright and others for incorporating a notion of higher-order vagueness, via the determinacy operator, which leads to contradiction when combined with intuitively appealing ‘gap principles’. We argue that these criticisms of supervaluation theory depend on giving supertruth an unnecessarily central role in that theory as the sole notion of truth, rather than (...)
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  22.  46
    Jump Liars and Jourdain’s Card Via the Relativized T-Scheme.Ming Hsiung - 2009 - Studia Logica 91 (2):239-271.
    A relativized version of Tarski's T-scheme is introduced as a new principle of the truth predicate. Under the relativized T-scheme, the paradoxical objects, such as the Liar sentence and Jourdain's card sequence, are found to have certain relative contradictoriness. That is, they are contradictory only in some frames in the sense that any valuation admissible for them in these frames will lead to a contradiction. It is proved that for any positive integer n, the n-jump liar sentence is contradictory in (...)
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  23.  90
    On the Probabilistic Convention T.Hannes Leitgeb - 2008 - Review of Symbolic Logic 1 (2):218-224.
    We introduce an epistemic theory of truth according to which the same rational degree of belief is assigned to Tr(. It is shown that if epistemic probability measures are only demanded to be finitely additive (but not necessarily σ-additive), then such a theory is consistent even for object languages that contain their own truth predicate. As the proof of this result indicates, the theory can also be interpreted as deriving from a quantitative version of the Revision Theory of Truth.
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  24.  59
    Two Types of Deflationism.Aladdin Yaqub - 2008 - Synthese 165 (1):77-106.
    It is a fundamental intuition about truth that the conditions under which a sentence is true are given by what the sentence asserts. My aim in this paper is to show that this intuition captures the concept of truth completely and correctly. This is conceptual deflationism, for it does not go beyond what is asserted by a sentence in order to define the truth status of that sentence. This paper, hence, is a defense of deflationism as a conceptual account of (...)
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  25. What Theories of Truth Should Be Like (but Cannot Be).Hannes Leitgeb - 2007 - Philosophy Compass 2 (2):276–290.
  26.  33
    The Rationale Behind Revision-Rule Semantics.Lionel Shapiro - 2006 - Philosophical Studies 129 (3):477 - 515.
    According to Gupta and Belnap, the “extensional behavior” of ‘true’ matches that of a circularly defined predicate. Besides promising to explain semantic paradoxicality, their general theory of circular predicates significantly liberalizes the framework of truth-conditional semantics. The authors’ discussions of the rationale behind that liberalization invoke two distinct senses in which a circular predicate’s semantic behavior is explained by a “revision rule” carrying hypothetical information about its extension. Neither attempted explanation succeeds. Their theory may however be modified to employ a (...)
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  27. Possible-Worlds Semantics for Modal Notions Conceived as Predicates.Volker Halbach, Hannes Leitgeb & Philip Welch - 2003 - Journal of Philosophical Logic 32 (2):179-223.
    If □ is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where □ is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics for predicates of (...)
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  28.  19
    On Revision Operators.P. D. Welch - 2003 - Journal of Symbolic Logic 68 (2):689-711.
    We look at various notions of a class of definability operations that generalise inductive operations, and are characterised as “revision operations”. More particularly we: (i) characterise the revision theoretically definable subsets of a countable acceptable structure; (ii) show that the categorical truth set of Belnap and Gupta’s theory of truth over arithmetic using \emph{fully varied revision} sequences yields a complete \Pi13 set of integers; (iii) the set of \emph{stably categorical} sentences using their revision operator ψ is similarly \Pi13 and which (...)
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  29.  24
    Dynamic Semiotics.Peter Bøgh Andersen - 2002 - Semiotica 2002 (139):161-210.
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  30.  33
    On Gupta-Belnap Revision Theories of Truth, Kripkean Fixed Points, and the Next Stable Set.P. D. Welch - 2001 - Bulletin of Symbolic Logic 7 (3):345-360.
    We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.
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  31.  33
    Property Theory and the Revision Theory of Definitions.Francesco Orilia - 2000 - Journal of Symbolic Logic 65 (1):212-246.
    Russell’s type theory has been the standard property theory for years, relying on rigid type distinctions at the grammatical level to circumvent the paradoxes of predication. In recent years it has been convincingly argued by Bealer, Cochiarella, Turner and others that many linguistic and ontological data are best accounted for by using a type-free property theory. In the spirit of exploring alternatives and “to have as many opportunities as possible for theory comparison”, this paper presents another type-free property theory, to (...)
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  32.  71
    What the Liar Taught Achilles.Gary Mar & Paul St Denis - 1999 - Journal of Philosophical Logic 28 (1):29-46.
    Zeno's paradoxes of motion and the semantic paradoxes of the Liar have long been thought to have metaphorical affinities. There are, in fact, isomorphisms between variations of Zeno's paradoxes and variations of the Liar paradox in infinite-valued logic. Representing these paradoxes in dynamical systems theory reveals fractal images and provides other geometric ways of visualizing and conceptualizing the paradoxes.
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  33.  33
    Construction of Truth Predicates: Approximation Versus Revision.Juan Barba - 1998 - Bulletin of Symbolic Logic 4 (4):399-417.
  34.  45
    Non-Well-Founded Sets Via Revision Rules.Gian Aldo Antonelli - 1994 - Journal of Philosophical Logic 23 (6):633 - 679.
  35.  54
    Dynamic Semantics and Circular Propositions.Willem Groeneveld - 1994 - Journal of Philosophical Logic 23 (3):267 - 306.
  36.  18
    Belief Representation in a Deductivist Type-Free Doxastic Logic.Francesco Orilia - 1994 - Minds and Machines 4 (2):163-203.
    Konolige''s technical notion of belief based on deduction structures is briefly reviewed and its usefulness for the design of artificial agents with limited representational and deductive capacities is pointed out. The design of artificial agents with more sophisticated representational and deductive capacities is then taken into account. Extended representational capacities require in the first place a solution to the intensional context problems. As an alternative to Konolige''s modal first-order language, an approach based on type-free property theory is proposed. It considers (...)
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  37.  1
    Annual Meeting of the Association for Symbolic Logic, Pittsburgh, 1991.Carl Jockusch - 1992 - Journal of Symbolic Logic 57 (1):352-365.
  38.  4
    Spring Meeting of the Association for Symbolic Logic, San Francisco, 1991.Penelope Maddy - 1992 - Journal of Symbolic Logic 57 (1):366-371.
  39.  72
    Semantics and Supervenience.Daniel Bonevac - 1991 - Synthese 87 (3):331 - 361.
  40.  36
    Denotation and Description in Free Logic.Frederick W. Kroon - 1991 - Theoria 57 (1-2):17-41.
  41.  34
    Paradoxes of Fulfillment.Daniel Bonevac - 1990 - Journal of Philosophical Logic 19 (3):229 - 252.
  42. Semantics and Property Theory.Gennaro Chierchia & Raymond Turner - 1988 - Linguistics and Philosophy 11 (3):261 - 302.
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  43.  19
    A Theory of Properties.Ray Turner - 1987 - Journal of Symbolic Logic 52 (2):455-472.
  44. Meeting of the Association for Symbolic Logic: Stanford, California, 1985.Jon Barwise, Solomon Feferman & David Israel - 1986 - Journal of Symbolic Logic 51 (3):832-862.
  45.  94
    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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  46.  44
    Some Remarks on Extending and Interpreting Theories with a Partial Predicate for Truth.William N. Reinhardt - 1986 - Journal of Philosophical Logic 15 (2):219 - 251.
  47.  77
    Die Logik der Unbestimmtheiten Und Paradoxien.Ulrich Blau - 1985 - Erkenntnis 22 (1-3):369 - 459.
  48.  84
    How Truthlike Can a Predicate Be? A Negative Result.Vann McGee - 1985 - Journal of Philosophical Logic 14 (4):399 - 410.
  49.  70
    Four Valued Semantics and the Liar.Albert Visser - 1984 - Journal of Philosophical Logic 13 (2):181 - 212.
  50.  34
    Paradox, Truth and Logic Part I: Paradox and Truth. [REVIEW]Peter W. Woodruff - 1984 - Journal of Philosophical Logic 13 (2):213 - 232.