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What Paradoxes Depend on

Synthese:1-27 (2018)

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  1. 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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  • Dangerous Reference Graphs and Semantic Paradoxes.Landon Rabern, Brian Rabern & Matthew Macauley - 2013 - Journal of Philosophical Logic 42 (5):727-765.
    The semantic paradoxes are often associated with self-reference or referential circularity. Yablo (Analysis 53(4):251–252, 1993), however, has shown that there are infinitary versions of the paradoxes that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality. In this essay, we lay the groundwork for a general investigation into the nature of reference structures that support the semantic paradoxes and the semantic hypodoxes. We develop (...)
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  • Yablo's Paradox.Graham Priest - 1997 - Analysis 57 (4):236-242.
  • Truth and Reflection.Stephen Yablo - 1985 - Journal of Philosophical Logic 14 (3):297 - 349.
    Many topics have not been covered, in most cases because I don't know quite what to say about them. Would it be possible to add a decidability predicate to the language? What about stronger connectives, like exclusion negation or Lukasiewicz implication? Would an expanded language do better at expressing its own semantics? Would it contain new and more terrible paradoxes? Can the account be supplemented with a workable notion of inherent truth (see note 36)? In what sense does stage semantics (...)
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  • Yablo's Paradox and Kindred Infinite Liars.Roy A. Sorensen - 1998 - Mind 107 (425):137-155.
    This is a defense and extension of Stephen Yablo's claim that self-reference is completely inessential to the liar paradox. An infinite sequence of sentences of the form 'None of these subsequent sentences are true' generates the same instability in assigning truth values. I argue Yablo's technique of substituting infinity for self-reference applies to all so-called 'self-referential' paradoxes. A representative sample is provided which includes counterparts of the preface paradox, Pseudo-Scotus's validity paradox, the Knower, and other enigmas of the genre. I (...)
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  • An Entirely Non-Self-Referential Yabloesque Paradox.Jesse Butler - 2018 - Synthese 195 (11):5007-5019.
    Graham Priest has argued that Yablo’s paradox involves a kind of ‘hidden’ circularity, since it involves a predicate whose satisfaction conditions can only be given in terms of that very predicate. Even if we accept Priest’s claim that Yablo’s paradox is self-referential in this sense—that the satisfaction conditions for the sentences making up the paradox involve a circular predicate—it turns out that there are paradoxical variations of Yablo’s paradox that are not circular in this sense, since they involve satisfaction conditions (...)
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  • An Entirely Non-Self-Referential Yabloesque Paradox.Jesse Butler - 2018 - Synthese 195 (11):5007-5019.
    Graham Priest has argued that Yablo’s paradox involves a kind of ‘hidden’ circularity, since it involves a predicate whose satisfaction conditions can only be given in terms of that very predicate. Even if we accept Priest’s claim that Yablo’s paradox is self-referential in this sense—that the satisfaction conditions for the sentences making up the paradox involve a circular predicate—it turns out that there are paradoxical variations of Yablo’s paradox that are not circular in this sense, since they involve satisfaction conditions (...)
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  • Circularity and Paradox.Stephen Yablo - 2006 - In Thomas Bolander, Vincent F. Hendricks & Stig Andur Pedersen (eds.), Self-Reference. CSLI Publications. pp. 139--157.
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  • What Truth Depends On.Hannes Leitgeb - 2005 - Journal of Philosophical Logic 34 (2):155-192.
    What kinds of sentences with truth predicate may be inserted plausibly and consistently into the T-scheme? We state an answer in terms of dependence: those sentences which depend directly or indirectly on non-semantic states of affairs (only). In order to make this precise we introduce a theory of dependence according to which a sentence φ is said to depend on a set Φ of sentences iff the truth value of φ supervenes on the presence or absence of the sentences of (...)
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  • The Revision Theory of Truth.Vann McGee - 1996 - Philosophy and Phenomenological Research 56 (3):727-730.
  • On Paradox Without Self-Reference.Neil Tennant - 1995 - Analysis 55 (3):199 - 207.
  • Equiparadoxicality of Yablo’s Paradox and the Liar.Ming Hsiung - 2013 - Journal of Logic, Language and Information 22 (1):23-31.
    It is proved that Yablo’s paradox and the Liar paradox are equiparadoxical, in the sense that their paradoxicality is based upon exactly the same circularity condition—for any frame ${\mathcal{K}}$ , the following are equivalent: (1) Yablo’s sequence leads to a paradox in ${\mathcal{K}}$ ; (2) the Liar sentence leads to a paradox in ${\mathcal{K}}$ ; (3) ${\mathcal{K}}$ contains odd cycles. This result does not conflict with Yablo’s claim that his sequence is non-self-referential. Rather, it gives Yablo’s paradox a new significance: (...)
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  • How Truthlike Can a Predicate Be? A Negative Result.Vann McGee - 1985 - Journal of Philosophical Logic 14 (4):399 - 410.
  • Truth and Paradox.Anil Gupta - 1982 - Journal of Philosophical Logic 11 (1):1-60.
  • Notes on Naive Semantics.Hans G. Herzberger - 1982 - Journal of Philosophical Logic 11 (1):61 - 102.
  • How to Eliminate Self-Reference: A Précis.Philippe Schlenker - 2007 - Synthese 158 (1):127-138.
    We provide a systematic recipe for eliminating self-reference from a simple language in which semantic paradoxes (whether purely logical or empirical) can be expressed. We start from a non-quantificational language L which contains a truth predicate and sentence names, and we associate to each sentence F of L an infinite series of translations h 0(F), h 1(F), ..., stated in a quantificational language L *. Under certain conditions, we show that none of the translations is self-referential, but that any one (...)
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  • The Elimination of Self-Reference: Generalized Yablo-Series and the Theory of Truth.P. Schlenker - 2007 - Journal of Philosophical Logic 36 (3):251-307.
    Although it was traditionally thought that self-reference is a crucial ingredient of semantic paradoxes, Yablo (1993, 2004) showed that this was not so by displaying an infinite series of sentences none of which is self-referential but which, taken together, are paradoxical. Yablo's paradox consists of a countable series of linearly ordered sentences s(0), s(1), s(2),... , where each s(i) says: For each k > i, s(k) is false (or equivalently: For no k > i is s(k) true). We generalize Yablo's (...)
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  • Yablo’s Paradox.Graham Priest - 1997 - Analysis 57 (4):236–242.
  • 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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  • Is Yablo’s Paradox Non-Circular?J. Beall - 2001 - Analysis 61 (3):176-87.
  • Patterns of Paradox.Roy T. Cook - 2004 - Journal of Symbolic Logic 69 (3):767-774.
  • 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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  • Is Yablo’s Paradox Non-Circular?J. C. Beall - 2001 - Analysis 61 (3):176–87.
  • Boolean Paradoxes and Revision Periods.Ming Hsiung - 2017 - Studia Logica 105 (5):881-914.
    According to the revision theory of truth, the paradoxical sentences have certain revision periods in their valuations with respect to the stages of revision sequences. We find that the revision periods play a key role in characterizing the degrees of paradoxicality for Boolean paradoxes. We prove that a Boolean paradox is paradoxical in a digraph, iff this digraph contains a closed walk whose height is not any revision period of this paradox. And for any finitely many numbers greater than 1, (...)
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  • The 'Mental Eye' Defence of an Infinitized Version of Yablo's Paradox.S. Bringsjord & B. V. Heuveln - 2003 - Analysis 63 (1):61-70.
  • 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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  • Paradox Without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251.
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  • What is a Self-Referential Sentence? Critical Remarks on the Alleged Mbox(Non-)Circularity of Yablo's Paradox.Hannes Leitgeb - 2002 - Logique and Analyse 177 (178):3-14.
     
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  • The Yablo Paradox: An Essay on Circularity.Roy T. Cook - 2014 - Oxford University Press.
    Roy T Cook examines the Yablo paradox--a paradoxical, infinite sequence of sentences, each of which entails the falsity of all others that follow it. He focuses on questions of characterization, circularity, and generalizability, and pays special attention to the idea that it provides us with a semantic paradox that involves no circularity.
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  • Semantics and the Liar Paradox.Albert Visser - 1989 - Handbook of Philosophical Logic 4 (1):617--706.
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  • Axiomatic Theories of Truth.Volker Halbach - 2008 - Stanford Encyclopedia of Philosophy.
    Definitional and axiomatic theories of truth -- Objects of truth -- Tarski -- Truth and set theory -- Technical preliminaries -- Comparing axiomatic theories of truth -- Disquotation -- Classical compositional truth -- Hierarchies -- Typed and type-free theories of truth -- Reasons against typing -- Axioms and rules -- Axioms for type-free truth -- Classical symmetric truth -- Kripke-Feferman -- Axiomatizing Kripke's theory in partial logic -- Grounded truth -- Alternative evaluation schemata -- Disquotation -- Classical logic -- Deflationism (...)
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  • Discovering Modern Set Theory II: Set-Theoretic Tools for Every Mathematician.W. Just & M. Weese - forthcoming - Amer. Math. Soc., Providence, Ri.
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