Search results for 'Omega-liar' (try it on Scholar)

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  1. Cezary Cieśliński & Rafal Urbaniak (2013). Gödelizing the Yablo Sequence. Journal of Philosophical Logic 42 (5):679-695.score: 60.0
    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 Yablo (...)
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  2. 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: 60.0
    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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  3. Francesco Berto (2009). There's Something About Gödel: The Complete Guide to the Incompleteness Theorem. Wiley-Blackwell.score: 24.0
    The Gödelian symphony -- Foundations and paradoxes -- This sentence is false -- The liar and Gödel -- Language and metalanguage -- The axiomatic method or how to get the non-obvious out of the obvious -- Peano's axioms -- And the unsatisfied logicists, Frege and Russell -- Bits of set theory -- The abstraction principle -- Bytes of set theory -- Properties, relations, functions, that is, sets again -- Calculating, computing, enumerating, that is, the notion of algorithm -- Taking numbers (...)
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  4. Sean Walsh (2014). Empiricism, Probability, and Knowledge of Arithmetic. Journal of Applied Logic 12 (3):319–348.score: 24.0
    The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgements of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional philosophy (...)
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  5. Matt Leonard (2012). Burge's Contextual Theory of Truth and the Super-Liar Paradox. In Michal Pelis Vit Puncochar (ed.), The Logica Yearbook 2011. College Publications.score: 18.0
    One recently proposed solution to the Liar paradox is the contextual theory of truth. Tyler Burge (1979) argues that truth is an indexical notion and that the extension of the truth predicate shifts during Liar reasoning. A Liar sentence might be true in one context and false in another. To many, contextualism seems to capture our pre-theoretic intuitions about the semantic paradoxes; this is especially due to its reliance on the so-called Revenge phenomenon. I, however, show that Super-Liar sentences (where (...)
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  6. Richard Heck (2012). A Liar Paradox. Thought 1 (1):36-40.score: 18.0
    The purpose of this note is to present a strong form of the liar paradox. It is strong because the logical resources needed to generate the paradox are weak, in each of two senses. First, few expressive resources required: conjunction, negation, and identity. In particular, this form of the liar does not need to make any use of the conditional. Second, few inferential resources are required. These are: (i) conjunction introduction; (ii) substitution of identicals; and (iii) the inference: From ¬(p (...)
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  7. Jeff Snapper (2012). The Liar Paradox in New Clothes. Analysis 72 (2):319-322.score: 18.0
    Next SectionCharlie Pelling presents an impropriety paradox for the truth account of assertion. After solving his paradox I show that it is a version of the liar paradox. I then show that for any account of truth there is a strengthened liar-like paradox, and that for any solution to the strengthened liar paradox, there is a parallel solution to each of these “new” paradoxes.
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  8. Andrew Bacon (2013). A New Conditional for Naive Truth Theory. Notre Dame Journal of Formal Logic 54 (1):87-104.score: 18.0
    In this paper a logic for reasoning disquotationally about truth is presented and shown to have a standard model. This work improves on Hartry Field's recent results establishing consistency and omega-consistency of truth-theories with strong conditional logics. A novel method utilising the Banach fixed point theorem for contracting functions on complete metric spaces is invoked, and the resulting logic is shown to validate a number of principles which existing revision theoretic methods have heretofore failed to provide.
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  9. Michael Glanzberg (2004). A Contextual-Hierarchical Approach to Truth and the Liar Paradox. Journal of Philosophical Logic 33 (1):27-88.score: 18.0
    This paper presents an approach to truth and the Liar paradox which combines elements of context dependence and hierarchy. This approach is developed formally, using the techniques of model theory in admissible sets. Special attention is paid to showing how starting with some ideas about context drawn from linguistics and philosophy of language, we can see the Liar sentence to be context dependent. Once this context dependence is properly understood, it is argued, a hierarchical structure emerges which is neither ad (...)
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  10. J. C. Beall (ed.) (2007). Revenge of the Liar: New Essays on the Paradox. Oxford University Press.score: 18.0
    The Liar paradox raises foundational questions about logic, language, and truth (and semantic notions in general). A simple Liar sentence like 'This sentence is false' appears to be both true and false if it is either true or false. For if the sentence is true, then what it says is the case; but what it says is that it is false, hence it must be false. On the other hand, if the statement is false, then it is true, since it (...)
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  11. Simon Evnine, &Quot;every Proposition Asserts Itself to Be True&Quot;: A Buridanian Solution to the Liar Paradox?score: 18.0
    In this paper, I try to understand what Buridan means when he suggests that "every proposition, by its very form, signifies or asserts itself to be true." I show how one way of construing this claim - that every proposition is in fact a conjunction one conjunct of which asserts the truth of the whole conjunction - does lead to a resolution of the Liar paradox, as Buridan says, and moreover is not vulnerable to the criticism on the basis of (...)
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  12. Diederik Aerts, Jan Broekaert & Sonja Smets (1999). The Liar-Paradox in a Quantum Mechanical Perspective. Foundations of Science 4 (2):115-132.score: 18.0
    In this paper we concentrate on the nature of the liar paradox asa cognitive entity; a consistently testable configuration of properties. We elaborate further on a quantum mechanical model (Aerts, Broekaert and Smets, 1999) that has been proposed to analyze the dynamics involved, and we focus on the interpretation and concomitant philosophical picture. Some conclusions we draw from our model favor an effective realistic interpretation of cognitive reality.
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  13. Bradley Armour-Garb & James A. Woodbridge (2013). Semantic Defectiveness and the Liar. Philosophical Studies 164 (3):845-863.score: 18.0
    In this paper, we do two things. First, we provide some support for adopting a version of the meaningless strategy with respect to the liar paradox, and, second, we extend that strategy, by providing, albeit tentatively, a solution to that paradox—one that is semantic, rather than logical.
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  14. Jon Barwise (1987). The Liar: An Essay on Truth and Circularity. Oxford University Press.score: 18.0
    Bringing together powerful new tools from set theory and the philosophy of language, this book proposes a solution to one of the few unresolved paradoxes from antiquity, the Paradox of the Liar. Treating truth as a property of propositions, not sentences, the authors model two distinct conceptions of propositions: one based on the standard notion used by Bertrand Russell, among others, and the other based on J.L. Austin's work on truth. Comparing these two accounts, the authors show that while the (...)
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  15. Bradley Dowden, Liar Paradox. Internet Encyclopedia of Philosophy.score: 18.0
    The Liar Paradox is an argument that arrives at a contradiction by reasoning about a Liar Sentence. The classical Liar Sentence is the self-referential sentence “This sentence is false.”.
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  16. Greg Littmann (2012). Dialetheism and the Graphic Liar. Canadian Journal of Philosophy 42 (1):15-27.score: 18.0
    A Liar sentence is a sentence that, paradoxically, we cannot evaluate for truth in accordance with classical logic and semantics without arriving at a contradiction. For example, consider L If we assume that L is true, then given that what L says is ‘L is false,’ it follows that L is false. On the other hand, if we assume that L is false, then given that what L says is ‘L is false,’ it follows that L is true. Thus, L (...)
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  17. Lon Berk (2003). Why the Liar Does Not Matter. Journal of Philosophical Logic 32 (3):323-341.score: 18.0
    This paper develops a classical model for our ordinary use of the truth predicate (1) that is able to address the liar's paradox and (2) that satisfies a very strong version of deflationism. Since the model is a classical in the sense that it has no truth value gaps, the model is able to address Tarski's indictment of our ordinary use of the predicate as inconsistent. Moreover, since it is able to address the liar's paradox, it responds to arguments against (...)
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  18. Keith Simmons (1993). Universality and the Liar: An Essay on Truth and the Diagonal Argument. Cambridge University Press.score: 18.0
    This book is about one of the most baffling of all paradoxes--the famous Liar paradox. Suppose we say: "We are lying now." Then if we are lying, we are telling the truth; and if we are telling the truth we are lying. This paradox is more than an intriguing puzzle, since it involves the concept of truth. Thus any coherent theory of truth must deal with the Liar. Keith Simmons discusses the solutions proposed by medieval philosophers and offers his own (...)
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  19. Yann Benétreau-Dupin (forthcoming). Buridan's Solution to the Liar Paradox. History and Philosophy of Logic:1-11.score: 18.0
    Jean Buridan has offered a solution to the Liar Paradox, i.e. to the problem of assigning a truth-value to the sentence ‘What I am saying is false’. It has been argued that either (1) this solution is ad hoc since it would only apply to self-referencing sentences [Read, S. 2002. ‘The Liar Paradox from John Buridan back to Thomas Bradwardine’, Vivarium, 40 (2), 189–218] or else (2) it weakens his theory of truth, making his ‘a logic without truth’ [Klima, G. (...)
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  20. Shahid Rahman, Tero Tulenheimo & Emmanuel Genot (eds.) (2008). Unity, Truth and the Liar: The Modern Relevance of Medieval Solutions to the Liar Paradox. Springer.score: 18.0
    This volume includes a target paper, taking up the challenge to revive, within a modern (formal) framework, a medieval solution to the Liar Paradox which did ...
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  21. Gary Mar & Paul St Denis (1999). What the Liar Taught Achilles. Journal of Philosophical Logic 28 (1):29-46.score: 18.0
    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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  22. Ming Hsiung (2013). Equiparadoxicality of Yablo's Paradox and the Liar. Journal of Logic, Language and Information 22 (1):23-31.score: 18.0
    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 paradox a new significance: (...)
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  23. Ernesto Perini-Santos (2011). John Buridans Theory of Truth and the Paradox of the Liar. Vivarium 49 (1-3):184-213.score: 18.0
    The solution John Buridan offers for the Paradox of the Liar has not been correctly placed within the framework of his philosophy of language. More precisely, there are two important points of the Buridanian philosophy of language that are crucial to the correct understanding of his solution to the Liar paradox that are either misrepresented or ignored in some important accounts of his theory. The first point is that the Aristotelian formula, ` propositio est vera quia qualitercumque significat in rebus (...)
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  24. Julien Murzi (2012). On Heck's New Liar. Thought 1 (2):258-269.score: 18.0
    Richard Heck has recently drawn attention on a new version of the Liar Paradox, one which relies on logical resources that are so weak as to suggest that it may not admit of any “truly satisfying, consistent solution”. I argue that this conclusion is too strong. Heck's Liar reduces to absurdity principles that are already rejected by consistent paracomplete theories of truth, such as Kripke's and Field's. Moreover, the new Liar gives us no reasons to think that (versions of) these (...)
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  25. William Mark Stuckey, Michael Silbserstein & Michael Cifone (2008). Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox. [REVIEW] Foundations of Physics 38 (4):348-383.score: 18.0
    The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal objects. RBW is shown to provide a novel statistical interpretation of the wavefunction that deflates the measurement problem, as well as a geometric account of quantum entanglement and non-separability that satisfies locality per special relativity and is free of interpretative mystery. We present RBW’s acausal and adynamical resolution of the (...)
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  26. Aladdin Mahmūd Yaqūb (1993). The Liar Speaks the Truth: A Defense of the Revision Theory of Truth. Oxford University Press.score: 18.0
    In this book, Yaqub describes a simple conception of truth and shows that it yields a semantical theory that accommodates the whole range of our seemingly conflicting intuitions about truth. This conception takes the Tarskian biconditionals (such as "The sentence 'Johannes loved Clara' is true if and only if Johannes loved Clara") as correctly and completely defining the notion of truth. The semantical theory, which is called the revision theory, that emerges from this conception paints a metaphysical picture of truth (...)
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  27. Jordan Howard Sobel (2008). 'Hoist with His Owne Petar':1 on the Undoing of a Liar Paradox. Theoria 74 (2):115-145.score: 18.0
    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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  28. Athanassios Tzouvaras (1998). Logic of Knowledge and Utterance and the Liar. Journal of Philosophical Logic 27 (1):85-108.score: 18.0
    We extend the ordinary logic of knowledge based on the operator K and the system of axioms S₅ by adding a new operator Uφ, standing for "the agent utters φ", and certain axioms and a rule for U, forming thus a new system KU. The main advantage of KU is that we can express in it intentions of the speaker concerning the truth or falsehood of the claims he utters and analyze them logically. Specifically we can express in the new (...)
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  29. Philip Hugly & Charles Sayward (1979). The Lessons of the Liar. Theory and Decision 11 (1):55-70.score: 18.0
    The paper argues that the liar paradox teaches us these lessons about English. First, the paradox-yielding sentence is a sentence of English that is neither true nor false in English. Second, there is no English name for any such thing as a set of all and only true sentences of English. Third, ‘is true in English’ does not satisfy the axiom of comprehension.
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  30. Avrum Stroll (1988). The Liar: What Paradox? [REVIEW] Argumentation 2 (1):63-75.score: 18.0
    Most philosophers believe that the Liar Paradox is semantical in character, and arises from difficulties in the predicate “true.” The author argues that the paradox is pragmatic, not semantic, and arises from violations of essential conditions that define statement-making speech acts. The author shows that his solution to the paradox will not only handle the classical Liar sentences that are “necessarily” or “intrinsically” paradoxical, but also sets of Kripke-sentences that are “contingently” paradoxical.
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  31. Björn Lundgren (forthcoming). The Information Liar Paradox: A Problem for Floridi's RSDI Definition. Philosophy and Technology:1-5.score: 18.0
    In this commentary, I discuss the effects of the liar paradox on Floridi’s definition on semantic information. In particular, I show that there is at least one sentence that creates a contradictory result for Floridi’s definition of semantic information that does not affect the standard definition.
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  32. Mark Pinder (forthcoming). The Cognitivist Account of Meaning and the Liar Paradox. Philosophical Studies:1-22.score: 18.0
    A number of theorists hold that literal, linguistic meaning is determined by the cognitive mechanism that underpins semantic competence. Borg and Larson and Segal defend a version of the view on which semantic competence is underpinned by the cognition of a truth-conditional semantic theory—a semantic theory which is true. Let us call this view the “cognitivist account of meaning”. In this paper, I discuss a surprisingly serious difficulty that the cognitivist account of meaning faces in light of the liar paradox. (...)
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  33. Klaas Pieter Hart (1989). Ultrafilters of Character $Omega_1$. Journal of Symbolic Logic 54 (1):1-15.score: 18.0
    Using side-by-side Sacks forcing, it is shown that it is consistent that $2^\omega$ be large and that there be many types of ultrafilters of character $\omega_1$.
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  34. Matti Eklund (2007). The Liar Paradox, Expressibility, Possible Languages. In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox. Oxford University Press.score: 15.0
    Here is the liar paradox. We have a sentence, (L), which somehow says of itself that it is false. Suppose (L) is true. Then things are as (L) says they are. (For it would appear to be a mere platitude that if a sentence is true, then things are as the sentence says they are.) (L) says that (L) is false. So, (L) is false. Since the supposition that (L) is true leads to contradiction, we can assert that (L) is (...)
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  35. Keith Simmons (1999). Deflationary Truth and the Liar. Journal of Philosophical Logic 28 (5):455-488.score: 15.0
  36. Michael Scriven (1963). The Supercomputer as Liar. British Journal for the Philosophy of Science 13 (February):313-314.score: 15.0
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  37. Mark Isalan (2009). Gene Networks and Liar Paradoxes. Bioessays 31 (10):1110-1115.score: 15.0
  38. Robert L. Martin (ed.) (1984). Recent Essays on Truth and the Liar Paradox. Oxford University Press.score: 15.0
     
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  39. Robert L. Martin (ed.) (1970). The Paradox of the Liar. New Haven [Conn.]Yale University Press.score: 15.0
     
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  40. Douglas Patterson (2007). Understanding the Liar. In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox. Oxford University Press. 197.score: 15.0
    (Beall ed. The Revenge of the Liar, forthcoming from Oxford University Press) > The main presentation of my approach to the semantic paradoxes. I take them to show that understanding a natural language is sharing a cognitive relation to a logically false semantic theory with other speakers.
     
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  41. Andrew Bacon (2013). Curry's Paradox and Omega Inconsistency. Studia Logica 101 (1):1-9.score: 12.0
    In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, but (...)
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  42. Ahmed Alwishah & David Sanson (2009). The Early Arabic Liar: The Liar Paradox in the Islamic World From the Mid-Ninth to the Mid-Thirteenth Centuries Ce. Vivarium (1):97-127.score: 12.0
    We describe the earliest occurrences of the Liar Paradox in the Arabic tradition. e early Mutakallimūn claim the Liar Sentence is both true and false; they also associate the Liar with problems concerning plural subjects, which is somewhat puzzling. Abharī (1200-1265) ascribes an unsatisfiable truth condition to the Liar Sentence—as he puts it, its being true is the conjunction of its being true and false—and so concludes that the sentence is not true. Tūsī (1201-1274) argues that self-referential sentences, like the (...)
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  43. Graham Priest (2006). Doubt Truth to Be a Liar. Oxford University Press.score: 12.0
    Dialetheism is the view that some contradictions are true. This is a view which runs against orthodoxy in logic and metaphysics since Aristotle, and has implications for many of the core notions of philosophy. Doubt Truth to Be a Liar explores these implications for truth, rationality, negation, and the nature of logic, and develops further the defense of dialetheism first mounted in Priest's In Contradiction, a second edition of which is also available.
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  44. Catarina Dutilh Novaes (2011). Lessons on Truth From Mediaeval Solutions to the Liar Paradox. Philosophical Quarterly 61 (242):58-78.score: 12.0
    Some fourteenth-century treatises on paradoxes of the liar family offer a promising starting-point for the formulation of full-fledged theories of truth with systematic relevance in their own right. In particular, Bradwardine's thesis that sentences typically say more than one thing gives rise to a quantificational approach to truth, and Buridan's theory of truth based on the notion of suppositio allows for remarkable metaphysical parsimony. Bradwardine's and Buridan's theories both have theoretical advantages, but fail to provide a satisfactory account of truth (...)
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  45. Patrick Greenough (2001). Free Assumptions and the Liar Paradox. American Philosophical Quarterly 38 (2):115 - 135.score: 12.0
    A new solution to the liar paradox is developed using the insight that it is illegitimate to even suppose (let alone assert) that a liar sentence has a truth-status (true or not) on the grounds that supposing this sentence to be true/not-true essentially defeats the telos of supposition in a readily identifiable way. On that basis, the paradox is blocked by restricting the Rule of Assumptions in Gentzen-style presentations of the sequent-calculus. The lesson of the liar is that not all (...)
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  46. Ruth Kastner (2010). The Quantum Liar Experiment in Cramer's Transactional Interpretation. Studies in History and Philosophy of Science Part B 41 (2):86-92.score: 12.0
    Cramer's Transactional Interpretation (TI) is applied to the ``Quantum Liar Experiment'' (QLE). It is shown how some apparently paradoxical features can be explained naturally, albeit nonlocally (since TI is an explicitly nonlocal interpretation). At the same time, it is proposed that in order to preserve the elegance and economy of the interpretation, it may be necessary to consider offer and confirmation waves as propagating in a ``higher space'' of possibilities.
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  47. Emil Badici (2008). The Liar Paradox and the Inclosure Schema. Australasian Journal of Philosophy 86 (4):583 – 596.score: 12.0
    In Beyond the Limits of Thought [2002], Graham Priest argues that logical and semantic paradoxes have the same underlying structure (which he calls the Inclosure Schema ). He also argues that, in conjunction with the Principle of Uniform Solution (same kind of paradox, same kind of solution), this is sufficient to 'sink virtually all orthodox solutions to the paradoxes', because the orthodox solutions to the paradoxes are not uniform. I argue that Priest fails to provide a non-question-begging method to 'sink (...)
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  48. Lionel Shapiro (2011). Expressibility and the Liar's Revenge. Australasian Journal of Philosophy 89 (2):297-314.score: 12.0
    There is a standard objection against purported explanations of how a language L can express the notion of being a true sentence of L. According to this objection, such explanations avoid one paradox (the Liar) only to succumb to another of the same kind. Even if L can contain its own truth predicate, we can identify another notion it cannot express, on pain of contradiction via Liar-like reasoning. This paper seeks to undermine such ‘revenge’ by arguing that it presupposes a (...)
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  49. Bradley Armour-Garb (2004). Minimalism, the Generalization Problem and the Liar. Synthese 139 (3):491 - 512.score: 12.0
    In defense of the minimalist conception of truth, Paul Horwich(2001) has recently argued that our acceptance of the instances of the schema,`the proposition that p is true if and only if p', suffices to explain our acceptanceof truth generalizations, that is, of general claims formulated using the truth predicate.In this paper, I consider the strategy Horwich develops for explaining our acceptance of truth generalizations. As I show, while perhaps workable on its own, the strategy is in conflictwith his response to (...)
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  50. Lon A. Berk (2004). The Liar, Context and Logical Form. Journal of Logic, Language and Information 13 (3):267-286.score: 12.0
    This essay attempts to give substance to the claim that the liar''sparadox shows the truth predicate to be context sensitive. The aim ismodest: to provide an account of the truth predicate''s contextsensitivity (1) that derives from a more general understanding ofcontext sensitivity, (2) that does not depend upon a hierarchy ofpredicates and (3) that is able to address the liar''s paradox. Theconsequences of achieving this goal are not modest, though. Perhapssurprisingly, for reasons that will be discussed in the last section (...)
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