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Stephen Yablo (1993). Paradox Without Self-Reference.

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  1.  15
    Validity, Dialetheism and Self-Reference.Federico Matias Pailos - forthcoming - Synthese.
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  2.  15
    On Paradoxes in Normal Form.Mattia Petrolo & Paolo Pistone - forthcoming - Topoi:1-13.
    A proof-theoretic test for paradoxicality was famously proposed by Tennant: a paradox must yield a closed derivation of absurdity with no normal form. Drawing on the remark that all derivations of a given proposition can be transformed into derivations in normal form of a logically equivalent proposition, we investigate the possibility of paradoxes in normal form. We compare paradoxes à la Tennant and paradoxes in normal form from the viewpoint of the computational interpretation of proofs and from the viewpoint of (...)
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  3.  24
    The Dominance Principle in Epistemic Decision Theory.R. A. Briggs - 2018 - Philosophy and Phenomenological Research 96 (3):763-775.
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  4.  27
    Axiomatic Theories of Partial Ground II.Johannes Korbmacher - 2018 - Journal of Philosophical Logic 47 (2):193-226.
    This is part two of a two-part paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truth-predicates and principles about the interaction of partial ground and truth. We show that our theory is (...)
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  5.  7
    Replies to Commentators on Accuracy and the Laws of Credence.Richard Pettigrew - 2018 - Philosophy and Phenomenological Research 96 (3):784-800.
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  6.  33
    Reference in Arithmetic.Lavinia Picollo - 2018 - Review of Symbolic Logic 11 (3):573-603.
    Self-reference has played a prominent role in the development of metamathematics in the past century, starting with Gödel’s first incompleteness theorem. Given the nature of this and other results in the area, the informal understanding of self-reference in arithmetic has sufficed so far. Recently, however, it has been argued that for other related issues in metamathematics and philosophical logic a precise notion of self-reference and, more generally, reference is actually required. These notions have been so far elusive and are surrounded (...)
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  7.  37
    The Infinity From Nothing Paradox and the Immovable Object Meets the Irresistible Force.Nicholas Shackel - 2018 - European Journal for Philosophy of Science 8 (3):417-433.
    In this paper I present a novel supertask in a Newtonian universe that destroys and creates infinite masses and energies, showing thereby that we can have infinite indeterminism. Previous supertasks have managed only to destroy or create finite masses and energies, thereby giving cases of only finite indeterminism. In the Nothing from Infinity paradox we will see an infinitude of finite masses and an infinitude of energy disappear entirely, and do so despite the conservation of energy in all collisions. I (...)
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  8.  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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  9.  41
    Yablo Without Gödel.Volker Halbach & Shuoying Zhang - 2017 - Analysis 77 (1):53-59.
    We prove Yablo’s paradox without the diagonal lemma or the recursion theorem. Only a disquotation schema and axioms for a serial and transitive ordering are used in the proof. The consequences for the discussion on whether Yablo’s paradox is circular or involves self-reference are evaluated.
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  10.  5
    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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  11.  26
    Liar-Type Paradoxes and the Incompleteness Phenomena.Makoto Kikuchi & Taishi Kurahashi - 2016 - Journal of Philosophical Logic 45 (4):381-398.
    We define a liar-type paradox as a consistent proposition in propositional modal logic which is obtained by attaching boxes to several subformulas of an inconsistent proposition in classical propositional logic, and show several famous paradoxes are liar-type. Then we show that we can generate a liar-type paradox from any inconsistent proposition in classical propositional logic and that undecidable sentences in arithmetic can be obtained from the existence of a liar-type paradox. We extend these results to predicate logic and discuss Yablo’s (...)
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  12.  2
    Some Non-Classical Approaches to the Brandenburger–Keisler Paradox.Can Başkent - 2015 - Logic Journal of the IGPL 23 (4):533-552.
  13.  25
    Two Paradoxes of Satisfaction.Peter Eldridge-Smith - 2015 - Mind 124 (493):85-119.
    There are two paradoxes of satisfaction, and they are of different kinds. The classic satisfaction paradox is a version of Grelling’s: does ‘does not satisfy itself’ satisfy itself? The Unsatisfied paradox finds a predicate, P, such that Px if and only if x does not satisfy that predicate: paradox results for any x. The two are intuitively different as their predicates have different paradoxical extensions. Analysis reduces each paradoxical argument to differing rule sets, wherein their respective pathologies lie. Having different (...)
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  14.  45
    The Yablo Paradox: An Essay on Circularity By Roy T. Cook.David Ripley - 2015 - Analysis 75 (3):523-525.
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  15.  25
    A New Unified Account of Truth and Paradox.N. Tennant - 2015 - Mind 124 (494):571-605.
    I propose an anti-realist account of truth and paradox according to which the logico-semantic paradoxes are not genuine inconsistencies. The ‘global’ proofs of absurdity associated with these paradoxes cannot be brought into normal form. The account combines epistemicism about truth with a proof-theoretic diagnosis of paradoxicality. The aim is to combine a substantive philosophical account of truth with a more rigorous and technical diagnosis of the source of paradox for further consideration by logicians. Core Logic plays a central role in (...)
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  16. Semantic Paradox and Alethic Undecidability.Stephen Barker - 2014 - Analysis 74 (2):201-209.
    I use the principle of truth-maker maximalism to provide a new solution to the semantic paradoxes. According to the solution, AUS, its undecidable whether paradoxical sentences are grounded or ungrounded. From this it follows that their alethic status is undecidable. We cannot assert, in principle, whether paradoxical sentences are true, false, either true or false, neither true nor false, both true and false, and so on. AUS involves no ad hoc modification of logic, denial of the T-schema's validity, or obvious (...)
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  17.  15
    Finding Tolerance Without Gluts.Jc Beall - 2014 - Mind 123 (491):791-811.
    Weber, Colyvan, and Priest have advanced glutty approaches to the sorites, on which the truth about the penumbral region of a soritical series is inconsistent. The major benefit of a glut-based approach is maintaining the truth of all sorites premisses while none the less avoiding, in a principled fashion, the absurdity of the sorites conclusion. I agree that this is a major virtue of the target glutty approach; however, I think that it can be had without gluts. If correct, this (...)
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  18.  33
    Propositional Discourse Logic.Sjur Dyrkolbotn & Michał Walicki - 2014 - Synthese 191 (5):1-37.
    A novel normal form for propositional theories underlies the logic pdl, which captures some essential features of natural discourse, independent from any particular subject matter and related only to its referential structure. In particular, pdlallows to distinguish vicious circularity from the innocent one, and to reason in the presence of inconsistency using a minimal number of extraneous assumptions, beyond the classical ones. Several, formally equivalent decision problems are identified as potential applications: non-paradoxical character of discourses, admissibility of arguments in argumentation (...)
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  19.  36
    Self-Reference in Arithmetic I.Volker Halbach & Albert Visser - 2014 - Review of Symbolic Logic 7 (4):671-691.
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  20.  18
    Grounded Ungroundedness.Casper Storm Hansen - 2014 - Inquiry: An Interdisciplinary Journal of Philosophy 57 (2):216-243.
    A modification of Kripke’s theory of truth is proposed and it is shown how this modification solves some of the problems of expressive weakness in Kripke’s theory. This is accomplished by letting truth values be grounded in facts about other sentences’ ungroundedness.
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  21.  14
    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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  22.  18
    Rosser-Type Undecidable Sentences Based on Yablo’s Paradox.Taishi Kurahashi - 2014 - Journal of Philosophical Logic 43 (5):999-1017.
    It is widely considered that Gödel’s and Rosser’s proofs of the incompleteness theorems are related to the Liar Paradox. Yablo’s paradox, a Liar-like paradox without self-reference, can also be used to prove Gödel’s first and second incompleteness theorems. We show that the situation with the formalization of Yablo’s paradox using Rosser’s provability predicate is different from that of Rosser’s proof. Namely, by using the technique of Guaspari and Solovay, we prove that the undecidability of each instance of Rosser-type formalizations of (...)
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  23.  14
    Truth and Meaning.Ian Rumfitt - 2014 - Aristotelian Society Supplementary Volume 88 (1):21-55.
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  24.  83
    I—Truth and Meaning.Ian Rumfitt - 2014 - Aristotelian Society Supplementary Volume 88 (1):21-55.
    Should we explicate truth in terms of meaning, or meaning in terms of truth? Ramsey, Prior and Strawson all favoured the former approach: a statement is true if and only if things are as the speaker, in making the statement, states them to be; similarly, a belief is true if and only if things are as a thinker with that belief thereby believes them to be. I defend this explication of truth against a range of objections. Ramsey formalized this account (...)
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  25.  69
    Gödelizing the Yablo Sequence.Cezary Cieśliński & Rafal Urbaniak - 2013 - Journal of Philosophical Logic 42 (5):679-695.
    We investigate what happens when ‘truth’ is replaced with ‘provability’ in Yablo’s paradox. By diagonalization, appropriate sequences of sentences can be constructed. Such sequences contain no sentence decided by the background consistent and sufficiently strong arithmetical theory. If the provability predicate satisfies the derivability conditions, each such sentence is provably equivalent to the consistency statement and to the Gödel sentence. Thus each two such sentences are provably equivalent to each other. The same holds for the arithmetization of the existential Yablo (...)
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  26.  49
    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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  27.  30
    Yablo's Paradox in Second-Order Languages: Consistency and Unsatisfiability.Lavinia María Picollo - 2013 - Studia Logica 101 (3):601-617.
    Stephen Yablo [23,24] introduces a new informal paradox, constituted by an infinite list of semi-formalized sentences. It has been shown that, formalized in a first-order language, Yablo’s piece of reasoning is invalid, for it is impossible to derive falsum from the sequence, due mainly to the Compactness Theorem. This result casts doubts on the paradoxical character of the list of sentences. After identifying two usual senses in which an expression or set of expressions is said to be paradoxical, since second-order (...)
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  28. 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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  29.  21
    Expressive Power of Digraph Solvability.Marc Bezem, Clemens Grabmayer & Michał Walicki - 2012 - Annals of Pure and Applied Logic 163 (3):200-213.
  30.  92
    Theories of Truth Without Standard Models and Yablo’s Sequences.Eduardo Alejandro Barrio - 2010 - Studia Logica 96 (3):375-391.
    The aim of this paper is to show that it’s not a good idea to have a theory of truth that is consistent but ω -inconsistent. In order to bring out this point, it is useful to consider a particular case: Yablo’s Paradox. In theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. Firstly, I exhibit some conceptual problems that follow from so introducing it. Secondly, I show (...)
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  31.  50
    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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  32. Truth Values, Neither-True-nor-False, and Supervaluations.Nuel Belnap - 2009 - Studia Logica 91 (3):305 - 334.
    The first section (§1) of this essay defends reliance on truth values against those who, on nominalistic grounds, would uniformly substitute a truth predicate. I rehearse some practical, Carnapian advantages of working with truth values in logic. In the second section (§2), after introducing the key idea of auxiliary parameters (§2.1), I look at several cases in which logics involve, as part of their semantics, an extra auxiliary parameter to which truth is relativized, a parameter that caters to special kinds (...)
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  33. Curry, Yablo and Duality.Roy T. Cook - 2009 - Analysis 69 (4):612-620.
    The Liar paradox is the directly self-referential Liar statement: This statement is false.or : " Λ: ∼ T 1" The argument that proceeds from the Liar statement and the relevant instance of the T-schema: " T ↔ Λ" to a contradiction is familiar. In recent years, a number of variations on the Liar paradox have arisen in the literature on semantic paradox. The two that will concern us here are the Curry paradox, 2 and the Yablo paradox. 3The Curry paradox (...)
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  34.  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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  35. The Solution to the Surprise Exam Paradox.Ken Levy - 2009 - Southern Journal of Philosophy 47 (2):131-158.
    The Surprise Exam Paradox continues to perplex and torment despite the many solutions that have been offered. This paper proposes to end the intrigue once and for all by refuting one of the central pillars of the Surprise Exam Paradox, the 'No Friday Argument,' which concludes that an exam given on the last day of the testing period cannot be a surprise. This refutation consists of three arguments, all of which are borrowed from the literature: the 'Unprojectible Announcement Argument,' the (...)
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  36.  55
    Anselm's Argument and Berry's Paradox.Philippe Schlenker - 2009 - Noûs 43 (2):214 - 223.
    We argue that Anselm’s ontological argument (or at least one reconstruction of it) is based on an empirical version of Berry’s paradox. It is invalid, but it takes some understanding of trivalence to see why this is so. Under our analysis, Anselm’s use of the notion of existence is not the heart of the matter; rather, trivalence is.
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  37.  44
    Reference, Paradoxes and Truth.Michał Walicki - 2009 - Synthese 171 (1):195 - 226.
    We introduce a variant of pointer structures with denotational semantics and show its equivalence to systems of boolean equations: both have the same solutions. Taking paradoxes to be statements represented by systems of equations (or pointer structures) having no solutions, we thus obtain two alternative means of deciding paradoxical character of statements, one of which is the standard theory of solving boolean equations. To analyze more adequately statements involving semantic predicates, we extend propositional logic with the assertion operator and give (...)
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  38. The Inclosure Scheme and the Solution to the Paradoxes of Self-Reference.Jordi Valor Abad - 2008 - Synthese 160 (2):183 - 202.
    All paradoxes of self-reference seem to share some structural features. Russell in 1908 and especially Priest nowadays have advanced structural descriptions that successfully identify necessary conditions for having a paradox of this kind. I examine in this paper Priest’s description of these paradoxes, the Inclosure Scheme (IS), and consider in what sense it may help us understand and solve the problems they pose. However, I also consider the limitations of this kind of structural descriptions and give arguments against Priest’s use (...)
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  39.  56
    'Hoist with His Owne Petar':1 on the Undoing of a Liar Paradox.Jordan Howard Sobel - 2008 - Theoria 74 (2):115-145.
    Abstract: A Liar would express a proposition that is true and not true. A Liar Paradox would, per impossibile, demonstrate the reality of a Liar. To resolve a Liar Paradox it is sufficient to make out of its demonstration a reductio of the existence of the proposition that would be true and not true, and to "explain away" the charm of the paradoxical contrary demonstration. Persuasive demonstrations of the Liar Paradox in this paper trade on allusive scope-ambiguities of English definite (...)
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  40.  7
    With and Without End.Peter Cave - 2007 - Philosophical Investigations 30 (2):105–126.
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  41. What Theories of Truth Should Be Like (but Cannot Be).Hannes Leitgeb - 2007 - Philosophy Compass 2 (2):276–290.
  42.  51
    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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  43.  46
    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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  44. Naturalism and the Paradox of Revisability.Mark Colyvan - 2006 - Pacific Philosophical Quarterly 87 (1):1–11.
    This paper examines the paradox of revisability. This paradox was proposed by Jerrold Katz as a problem for Quinean naturalised epistemology. Katz employs diagonalisation to demonstrate what he takes to be an inconsistency in the constitutive principles of Quine's epistemology. Specifically, the problem seems to rest with the principle of universal revisability which states that no statement is immune to revision. In this paper it is argued that although there is something odd about employing universal revisability to revise itself, there (...)
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  45.  95
    Yablo's Paradox and Ω-Inconsistency.Jeffrey Ketland - 2005 - Synthese 145 (3):295-302.
    It is argued that Yablo’s Paradox is not strictly paradoxical, but rather ‘ω-paradoxical’. Under a natural formalization, the list of Yablo sentences may be constructed using a diagonalization argument and can be shown to be ω-inconsistent, but nonetheless consistent. The derivation of an inconsistency requires a uniform fixed-point construction. Moreover, the truth-theoretic disquotational principle required is also uniform, rather than the local disquotational T-scheme. The theory with the local disquotation T-scheme applied to individual sentences from the Yablo list is also (...)
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  46.  16
    Yablo’s Paradox and Ω-Inconsistency.Jeffrey Ketland - 2005 - Synthese 145 (3):295-302.
    It is argued that Yablo's Paradox is not strictly paradoxical, but rather 'ω-paradoxical'. Under a natural formalization, the list of Yablo sentences may be constructed using a diagonalization argument and can be shown to be ω-inconsistent, but nonetheless consistent. The derivation of an inconsistency requires a uniform fixed-point construction. Moreover, the truth-theoretic disquotational principle required is also uniform, rather than the local disquotational T-scheme. The theory with the local disquotation T-scheme applied to individual sentences from the Yablo list is also (...)
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  47. Paradox by (Non-Wellfounded) Definition.Hannes Leitgeb - 2005 - Analysis 65 (4):275–278.
  48.  44
    A Berry and A Russell Without Self-Reference.Keith Simmons - 2005 - Philosophical Studies 126 (2):253-261.
    In this paper I present two new paradoxes, a definability paradox (related to the paradoxes of Berry, Richard and König), and a paradox about extensions (related to Russell’s paradox). However, unlike the familiar definability paradoxes and Russell’s paradox, these new paradoxes involve no self-reference or circularity.
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  49. Patterns of Paradox.Roy T. Cook - 2004 - Journal of Symbolic Logic 69 (3):767-774.
  50. Bueno and Colyvan on Yablo’s Paradox.Jeffrey Ketland - 2004 - Analysis 64 (2):165–172.
    This is a response to a paper “Paradox without satisfaction”, Analysis 63, 152-6 (2003) by Otavio Bueno and Mark Colyvan on Yablo’s paradox. I argue that this paper makes several substantial mathematical errors which vitiate the paper. (For the technical details, see [12] below.).
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