Search results for 'Yablo's paradox' (try it on Scholar)

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  1. Ming Hsiung (2013). Equiparadoxicality of Yablo's Paradox and the Liar. Journal of Logic, Language and Information 22 (1):23-31.score: 720.0
    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 (...)
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  2. Taishi Kurahashi (2014). Rosser-Type Undecidable Sentences Based on Yablo’s Paradox. Journal of Philosophical Logic 43 (5):999-1017.score: 720.0
    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 (...)
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  3. O. Bueno & M. Colyvan (2003). Yablo's Paradox and Referring to Infinite Objects. Australasian Journal of Philosophy 81 (3):402 – 412.score: 558.0
    The blame for the semantic and set-theoretic paradoxes is often placed on self-reference and circularity. Some years ago, Yablo [1985; 1993] challenged this diagnosis, by producing a paradox that's liar-like but does not seem to involve circularity. But is Yablo's paradox really non-circular? In a recent paper, Beall [2001] has suggested that there are no means available to refer to Yablo's paradox without invoking descriptions, and since Priest [1997] has shown that any such description is (...)
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  4. Lavinia María Picollo (2013). Yablo's Paradox in Second-Order Languages: Consistency and Unsatisfiability. Studia Logica 101 (3):601-617.score: 543.0
    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 (...)
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  5. Roy A. Sorensen (1998). Yablo's Paradox and Kindred Infinite Liars. Mind 107 (425):137-155.score: 540.0
    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 (...)
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  6. Jeffrey Ketland (2005). Yablo's Paradox and Ω-Inconsistency. Synthese 145 (3):295 - 302.score: 540.0
    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 (...)
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  7. Otávio Bueno & Mark Colyvan, Yablo's Paradox Rides Again: A Reply to Ketland.score: 540.0
    Yablo’s paradox is generated by the following (infinite) list of sentences (called the Yablo list): (s1) For all k > 1, sk is not true. (s2) For all k > 2, sk is not true. (s3) For all k > 3, sk is not true. . . . . . . . .
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  8. Jeffrey Ketland (2004). Bueno and Colyvan on Yablo's Paradox. Analysis 64 (2):165–172.score: 540.0
    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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  9. Claudio Bernardi (2009). A Topological Approach to Yablo's Paradox. Notre Dame Journal of Formal Logic 50 (3):331-338.score: 540.0
    Some years ago, Yablo gave a paradox concerning an infinite sequence of sentences: if each sentence of the sequence is 'every subsequent sentence in the sequence is false', a contradiction easily follows. In this paper we suggest a formalization of Yablo's paradox in algebraic and topological terms. Our main theorem states that, under a suitable condition, any continuous function from 2N to 2N has a fixed point. This can be translated in the original framework as follows. Consider (...)
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  10. Eduardo Alejandro Barrio (2012). Symposium on Yablo's Paradox: Introducción. Análisis Filosófico 32 (1):5-5.score: 540.0
    El contenido de la presente discusión de Análisis Filosófico surge a partir de diversas actividades organizadas por mí en SADAF y en la UBA. En primer lugar, Roy Cook dictó en SADAF el seminario de investigación intensivo On Yablo's Paradox durante la última semana de julio de 2011. En el seminario, el profesor Cook presentó el manuscrito aún sin finalizar de su libro The Yablo Paradox: An Essay on Circularity, Oxford, Oxford UP, (en prensa). Extensas y apasionantes (...)
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  11. Laureano Luna (2009). Yablo's Paradox and Beginningless Time. Disputatio 3 (26):89-96.score: 540.0
    The structure of Yablo’s paradox is analysed and generalised in order to show that beginningless step-by-step determination processes can be used to provoke antinomies, more concretely, to make our logical and our on-tological intuitions clash. The flow of time and the flow of causality are usually conceived of as intimately intertwined, so that temporal causation is the very paradigm of a step-by-step determination process. As a conse-quence, the paradoxical nature of beginningless step-by-step determina-tion processes concerns time and causality as (...)
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  12. Eduardo Alejandro Barrio (2010). Theories of Truth Without Standard Models and Yablo's Sequences. Studia Logica 96 (3):375-391.score: 480.0
    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 (...)
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  13. Eduardo Alejandro Barrio (2012). The Yablo Paradox and Circularity. Análisis Filosófico 32 (1):7-20.score: 450.0
    In this paper, I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a right representation of that paradox in first order arithmetic, there are some technical results that give rise to doubts about this possibility. Then, I present some arguments that have challenged that Yablo’s construction is non-circular. Just like that, Priest (1997) has argued that (...)
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  14. Graham Priest (1997). Yablo’s Paradox. Analysis 57 (4):236–242.score: 450.0
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  15. J. C. Beall (2001). Is Yablo’s Paradox Non-Circular? Analysis 61 (271):176–87.score: 450.0
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  16. James Hardy (1995). Is Yablo's Paradox Liar-Like? Analysis 55 (3):197 - 198.score: 450.0
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  17. Selmer Bringsjord & Bram Van Heuveln (2003). The ‘Mental Eye’ Defence of an Infinitized Version of Yablo's Paradox. Analysis 63 (277):61–70.score: 450.0
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  18. Selmer Bringsjord & Bram Van Heuveln (2003). The 'Mental Eye' Defence of an Infinitized Version of Yablo's Paradox. Analysis 63 (1):61 - 70.score: 450.0
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  19. Thomas Forster (2011). Yablo's Paradox and the Omitting Types Theorem for Propositional Languages. Logique Et Analyse 54 (215):323.score: 450.0
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  20. Hannes Leitgeb (2002). What is a Self-Referential Sentence? Critical Remarks on the Alleged Mbox(Non-)Circularity of Yablo's Paradox. Logique and Analyse 177 (178):3-14.score: 450.0
     
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  21. Cezary Cieśliński & Rafal Urbaniak (2013). Gödelizing the Yablo Sequence. Journal of Philosophical Logic 42 (5):679-695.score: 315.0
    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 (...)
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  22. P. Schlenker (2007). The Elimination of Self-Reference: Generalized Yablo-Series and the Theory of Truth. [REVIEW] Journal of Philosophical Logic 36 (3):251 - 307.score: 315.0
    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 (...)
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  23. Federico Matías Pailos (2012). About Two Objections to Cook's Proposal. Análisis Filosófico 32 (1):37-43.score: 315.0
    The main thesis of this work is as follows: there are versions of Yablo’s paradox that, if Cook is right about the non-circular character of his version of it, are truly paradoxical and genuinely non-circular, and Cook’s version of Yablo’s paradox is one of them. Here I will not evaluate the"circular" or"non-circular" side to Cook’s proposal. In fact, I think that he is right about it, and that his version of Yablo’s list is non-circular. But is it paradoxical? (...)
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  24. Laureano Luna (2011). Reasoning From Paradox. The Reasoner 5 (2):22-23.score: 261.0
    Godel's and Tarski's theorems were inspired by paradoxes: the Richard paradox, the Liar. Godel, in the 1951 Gibbs lecture argued from his metatheoretical results for a metaphysical claim: the impossibility of reducing, both, mathematics to the knowable by the human mind and the human mind to a finite machine (e.g. the brain). So Godel reasoned indirectly from paradoxes for metaphysical theses. I present four metaphysical theses concerning mechanism, reductive physicalism and time for the only purpose of suggesting how it (...)
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  25. Roy T. Cook (2006). There Are Non-Circular Paradoxes (but Yablo's Isn't One of Them!). The Monist 89 (1):118-149.score: 238.3
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  26. Cezary Cieśliński (2013). Yablo Sequences in Truth Theories. In K. Lodaya (ed.), Logic and Its Applications, Lecture Notes in Computer Science LNCS 7750. Springer. 127--138.score: 234.0
    We investigate the properties of Yablo sentences and for- mulas in theories of truth. Questions concerning provability of Yablo sentences in various truth systems, their provable equivalence, and their equivalence to the statements of their own untruth are discussed and answered.
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  27. N. Raja (2005). A Negation-Free Proof of Cantor's Theorem. Notre Dame Journal of Formal Logic 46 (2):231-233.score: 234.0
    We construct a novel proof of Cantor's theorem in set theory.
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  28. Graham Leach-Krouse (2014). Yablifying the Rosser Sentence. Journal of Philosophical Logic 43 (5):827-834.score: 216.0
    In a recent paper , Urbaniak and Cieśliński describe an analogue of the Yablo Paradox, in the domain of formal provability. Just as the infinite sequence of Yablo sentences inherit the paradoxical behavior of the liar sentence, an infinite sequence of sentences can be constructed that inherit the distinctive behavior of the Gödel sentence. This phenomenon—the transfer of the properties of self-referential sentences of formal mathematics to their “unwindings” into infinite sequences of sentences—suggests a number of interesting logical questions. (...)
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  29. Lucas Rosenblatt (2012). On the Possibility of a General Purge of Self-Reference. Análisis Filosófico 32 (1):53-59.score: 216.0
    My aim in this paper is to gather some evident in favor of the view that a general purge of self-reference is possible. I do this by considering a modal-epistemic version of the Liar Paradox introduced by Roy Cook. Using yabloesque techniques, I show that it is possible to transform this circular paradoxical construction (and other constructions as well) into an infinitary construction lacking any sort of circularity. Moreover, contrary to Cook’s approach, I think that this can be done (...)
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  30. Laureano Luna (2010). Ungrounded Causal Chains and Beginningless Time. Logic and Logical Philosophy 18 (3-4):297-307.score: 216.0
    We use two logical resources, namely, the notion of recursively defined function and the Benardete-Yablo paradox, together with some inherent features of causality and time, as usually conceived, to derive two results: that no ungrounded causal chain exists and that time has a beginning.
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  31. Landon Rabern, Brian Rabern & Matthew Macauley (2013). Dangerous Reference Graphs and Semantic Paradoxes. Journal of Philosophical Logic 42 (5):727-765.score: 213.0
    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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  32. Philippe Schlenker (2007). How to Eliminate Self-Reference: A Précis. Synthese 158 (1):127 - 138.score: 198.0
    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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  33. Sarah Hoffman, You Can't Mean That: Yablo's Figuralist Account of Mathematics.score: 168.0
    Burgess and Rosen argue that Yablo’s figuralist account of mathematics fails because it says mathematical claims are really only metaphorical. They suggest Yablo’s view is implausible as an account of what mathematicians say and confused about literal language. I show their argument isn’t decisive, briefly exploring some questions in the philosophy of language it raises, and argue Yablo’s view may be amended to a kind of revolutionary fictionalism not refuted by Burgess and Rosen.
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  34. Lavinia Picollo (2012). The Old-Fashioned Yablo Paradox. Análisis Filosófico 32 (1):21-29.score: 144.0
    The Yablo Paradox’ main interest lies on its prima facie non-circular character, which many have doubted, specially when formulated in an extension of the language of firstorder arithmetic. Particularly, Priest (1997) and Cook (2006, forthcoming) provided contentious arguments in favor of circularity. My aims in this note are (i) to show that the notion of circularity involved in the debate so far is defective, (ii) to provide a new sound and useful partial notion of circularity and (iii) to show (...)
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  35. Roy T. Cook (2014). The Yablo Paradox: An Essay on Circularity. Oup Oxford.score: 144.0
    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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  36. Dan Marshall, Yablo's Account of Intrinsicality.score: 140.0
    An intrinsic property is roughly a property something has in virtue of how it is, as opposed to how it is related to other things. More carefully, the property of being F is intrinsic iff, necessarily, for any x that is F , x is F in virtue of how it is, as opposed to how it is related to wholly distinct things, or how wholly distinct things are. An extrinsic property, on the other hand, is any property that is (...)
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  37. Philip Stratton–Lake (2003). Scanlon's Contractualism and the Redundancy Objection. Analysis 63 (277):70–76.score: 135.0
    Ebbhinghaus, H., J. Flum, and W. Thomas. 1984. Mathematical Logic. New York, NY: Springer-Verlag. Forster, T. Typescript. The significance of Yablo’s paradox without self-reference. Available from http://www.dpmms.cam.ac.uk. Gold, M. 1965. Limiting recursion. Journal of Symbolic Logic 30: 28–47. Karp, C. 1964. Languages with Expressions of Infinite Length. Amsterdam.
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  38. Laurence Goldstein (2006). Fibonacci, Yablo, and the Cassationist Approach to Paradox. Mind 115 (460):867-890.score: 132.0
    A syntactically correct number-specification may fail to specify any number due to underspecification. For similar reasons, although each sentence in the Yablo sequence is syntactically perfect, none yields a statement with any truth-value. As is true of all members of the Liar family, the sentences in the Yablo sequence are so constructed that the specification of their truth-conditions is vacuous; the Yablo sentences fail to yield statements. The ‘revenge’ problem is easily defused. The solution to the semantical paradoxes offered here (...)
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  39. Anand Jayprakash Vaidya (2010). Understanding and Essence. Philosophia 38 (4):811-833.score: 99.0
    Modal epistemology has been dominated by a focus on establishing an account either of how we have modal knowledge or how we have justified beliefs about modality. One component of this focus has been that necessity and possibility are basic access points for modal reasoning. For example, knowing that P is necessary plays a role in deducing that P is essential, and knowing that both P and ¬P are possible plays a role in knowing that P is accidental. Chalmers (2002) (...)
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  40. Hartley Slater (2008). Paradoxes and Pragmatics. Proceedings of the Xxii World Congress of Philosophy 13:87-104.score: 98.0
    Tarski’s assessment that natural language is inconsistent on account of the Liar Paradox is shown to be incorrect: what Tarski’s theorem in fact shows is that Truth is not a property of sentences but of propositions. By using propositions rather than sentences as the bearers of Truth, semantic closure within the same language is easily obtained. Tarski’s contrary assessment was partly based on confusions about propositions and their grammatical expression. But more centrally it arose through blindness to pragmatic factors (...)
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  41. Kevin Scharp, Replacements for Truth.score: 90.0
    An inconsistency approach to the liar and related paradoxes takes the non-logical principles involved in the derivation of the paradoxes to be constitutive of our concept of truth. That is, it is our very competence with the concept of truth that leads us to accept the non-logical premises or inferences involved in the derivation. One who endorses an approach of this type should not be content to diagnose the problem; rather, such a theorist should propose a way of changing our (...)
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  42. Diego Tajer (2012). Anti-Realism and Infinitary Proofs. Análisis Filosófico 32 (1):45-51.score: 90.0
    In the discussion about Yablo’s Paradox, a debated topic is the status of infinitary proofs. It is usually considered that, although a realist could (with some effort) accept them, an anti-realist could not do it at all. In this paper I will argue that there are plausible reasons for an anti-realist to accept infinitary proofs and rules of inference. En la discusión sobre la Paradoja de Yablo, un tópico debatido es el estatus de las pruebas infinitarias. Se suele considerar (...)
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  43. Hansen Casper Storm (2011). New Zeno and Actual Infinity. Open Journal of Philosophy 1 (2):57.score: 90.0
    In 1964 José Benardete invented the “New Zeno Paradox” about an infinity of gods trying to prevent a traveller from reaching his destination. In this paper it is argued, contra Priest and Yablo, that the paradox must be resolved by rejecting the possibility of actual infinity. Further, it is shown that this paradox has the same logical form as Yablo’s Paradox. It is suggested that constructivism can serve as the basis of a common solution to New (...)
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  44. Ignacio Ojea (2012). The Structural Collapse Approach Reconsidered. Análisis Filosófico 32 (1):61-68.score: 90.0
    I will argue that Roy Cook’s (forthcoming) reformulation of Yablo’s Paradox in the infinitary system D is a genuinely non-circular paradox, but for different reasons than the ones he sustained. In fact, the first part of the job will be to show that his argument regarding the absence of fixed points in the construction is insufficient to prove the noncircularity of it; at much it proves its non-self referentiality. The second is to reconsider the structural collapse approach Cook (...)
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  45. Nicholas Shackel (2005). The Form of the Benardete Dichotomy. British Journal for the Philosophy of Science 56 (2):397-417.score: 81.0
    Benardete presents a version of Zeno's dichotomy in which an infinite sequence of gods each intends to raise a barrier iff a traveller reaches the position where they intend to raise their barrier. In this paper, I demonstrate the abstract form of the Benardete Dichotomy. I show that the diagnosis based on that form can do philosophical work not done by earlier papers rejecting Priest's version of the Benardete Dichotomy, and that the diagnosis extends to a paradox not normally (...)
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  46. T. Parent, Paradox with Just Self-Reference.score: 78.0
    If a semantically open language allows self-reference, one can show there is a predicate which is both satisfied and unsatisfied by a self-referring term. The argument requires something akin to diagonalization on substitution instances of a definition-scheme (*): ‘x is Lagadonian iff, in the g(t)th substitution instance of (*), x = t’. (Given a substitution instance of (*), let t be the term replacing 'x' and let g(t) be the Godel code for t.) Assuming an appropriate enumeration of the instances, (...)
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  47. Peter Hawke (2011). Van Inwagen's Modal Skepticism. Philosophical Studies 153 (3):351-364.score: 70.0
    In this paper, the author defends Peter van Inwagen’s modal skepticism. Van Inwagen accepts that we have much basic, everyday modal knowledge, but denies that we have the capacity to justify philosophically interesting modal claims that are far removed from this basic knowledge. The author also defends the argument by means of which van Inwagen supports his modal skepticism, offering a rebuttal to an objection along the lines of that proposed by Geirrson. Van Inwagen argues that Stephen Yablo’s recent and (...)
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  48. Andrej Jandrić (2014). “The King of France is Bald” Reconsidered: A Case Against Yablo. Philosophical Studies 169 (2):173-181.score: 70.0
    Stephen Yablo has argued for metaontological antirealism: he believes that the sentences claiming or denying the existence of numbers (or other abstract entities or mereological sums) are inapt for truth valuation, because the reference failure of a numerical singular term (or a singular term for an abstract entity or a mereological sum) would not produce a truth value gap in any sentence containing that term. At the same time, Yablo believes that nothing similar applies to singular terms that aim to (...)
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  49. Sara Worley (1997). Determination and Mental Causation. Erkenntnis 46 (3):281-304.score: 62.0
    Yablo suggests that we can understand the possibility of mental causation by supposing that mental properties determine physical properties, in the classic sense of determination according to which red determines scarlet. Determinates and their determinables do not compete for causal relevance, so if mental and physical properties are related as determinable and determinates, they should not compete for causal relevance either. I argue that this solution won''t work. I first construct a more adequate account of determination than that provided by (...)
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  50. Marcus Rossberg (forthcoming). Somehow Things Do Not Relate: On the Interpretation of Polyadic Second-Order Logic. Journal of Philosophical Logic:1-10.score: 61.7
    Boolos has suggested a plural interpretation of second-order logic for two purposes: (i) to escape Quine’s allegation that second-order logic is set theory in disguise, and (ii) to avoid the paradoxes arising if the second-order variables are given a set-theoretic interpretation in second-order set theory. Since the plural interpretation accounts only for monadic second-order logic, Rayo and Yablo suggest an new interpretation for polyadic second-order logic in a Boolosian spirit. The present paper argues that Rayo and Yablo’s interpretation does not (...)
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