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Summary A liar paradox is generated by a sentence or proposition (or any truth bearer more generally) that says that it is false.  If we use the name 'S' for the sentence ‘S is false’, then that very sentence says of itself that it is false. We can reason intuitively that if it is true, then what it says is true, namely that it is false. So it is true that it is false, or, more directly, it is false. On the other hand, if it is false, then what it says is false, namely that it is false. So it is false that it is false, or, more directly, it is true. Thus, we derive that it is false from the assumption that it is true, and we derive that it is true from the assumption that it is false. It takes just a couple of steps from here to the claim that S is both true and false.  The above reasoning relies on the following two principles regarding truth (for some class of sentences p of which S is a member): (i) if p is true, then p, and (ii) if p, then p is true.  It also relies on principles of classical (and intuitionistic) logic.  Approaches to the liar paradox usually reject one of the principles of truth, one of the logical principles, or find some defect in S and any other sentence like it.  The liar paradox is closely related to several other paradoxes associated with truth, including Curry's paradox and Yablo's paradox.
Key works The classic work on the liar paradox in analytic philosophy is Tarski 1936. Kripke 1975 solidified the importance of logical rigor in investigations of the liar paradox. Early contextual approaches include Parsons 1974 and Burge 1979Priest 1979 and Chihara 1979 initiated the inconsistency approach. Gupta 1982 and Herzberger 1982 were the first to offer revision theories of truth. 
Introductions Introductory works include the Stanford Encyclopedia of Philosophy entry: Beall & Glanzberg 2010
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  1. Sloman Aaron (1971). Tarski, Frege and the Liar Paradox. Philosophy 46 (176):133-.
  2. Jordi Valor Abad (2008). The Inclosure Scheme and the Solution to the Paradoxes of Self-Reference. 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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  3. Diederik Aerts, Jan Broekaert & Sonja Smets (1999). The Liar-Paradox in a Quantum Mechanical Perspective. Foundations of Science 4 (2):115-132.
    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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  4. Joseph Agassi (1964). Variations on the Liar's Paradox. Studia Logica 15 (1):237 - 238.
    Line 1: The statement on line one is false. Line 2: All statements on line two are false. p and not-p Line 3: All statements on line 3 are true, or all of them are false. p and not-p Line 4: The statement on line 4 is false, or (p and not-p). Line 5: The statement on line 5 is true if and only if (p and not p). Line 6: All statements on line 6 are false. p. Line 7: (...)
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  5. Ken Akiba (2002). A Deflationist Approach to Indeterminacy and Vagueness. Philosophical Studies 107 (1):69 - 86.
    Deflationists cannot make sense ofthe notion of referential indeterminacybecause they deny the existence of substantivereference. One way for them to make sense ofthe objective existence of linguisticindeterminacy is by embracing theworldly (or objectual) view ofindeterminacy, the view that indeterminacyexists not in reference relations but in the(non-linguistic) world itself. On this view,the entire world is divided into precisified worlds, just as it is dividedinto temporal slices and (arguably) alethicpossible worlds. Supervaluationism proves tobe neutral with respect to the debate betweenthe worldly view (...)
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  6. Ken Akiba (2002). Can Deflationism Allow for Hidden Indeterminacy? Pacific Philosophical Quarterly 83 (3):223–234.
  7. Edwin B. Allaire (1975). Truth. Metaphilosophy 6 (3-4):261-276.
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  8. Robert Almeder (1990). Vacuous Truth. Synthese 85 (3):507 - 524.
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  9. William P. Alston (1996). A Realist Conception of Truth. Cornell University Press.
    William P. Alston formulates and defends a realist conception of truth, which he calls alethic realism (from "aletheia", Greek for "truth").
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  10. 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.
    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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  11. Alan Ross Anderson (1970). St. Paul'€™s Epistle to Titus. In Robert L. Martin (ed.), The Paradox of the Liar. Ridgeview.
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  12. G. Aldo Antonelli (2000). Virtuous Circles: From Fixed Points to Revision Rules. In Anil Gupta & Andre Chapuis (eds.), Circularity, Definition, and Truth. Indian Council of Philosophical Research. 1--27.
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  13. Gian Aldo Antonelli (1996). Book Review: Keith Simmons. Universality and the Liar: An Essay on Truth and the Diagonal Argument. [REVIEW] Notre Dame Journal of Formal Logic 37 (1):152-159.
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  14. Gian Aldo Antonelli (1994). Non-Well-Founded Sets Via Revision Rules. Journal of Philosophical Logic 23 (6):633 - 679.
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  15. Gian Aldo Antonelli (1994). The Complexity of Revision. Notre Dame Journal of Formal Logic 35 (1):67-72.
  16. B. Armour-Garb (2012). No Consistent Way with Paradox. Analysis 72 (1):66-75.
    In ‘A Consistent Way with Paradox’, Laurence Goldstein (2009) clarifies his solution to the liar, which he touts as revenge immune . In addition, he (Ibid.) responds to one of the objections that Armour-Garb and Woodbridge (2006) raise against certain solutions to the open pair and argues that his proffered solution to the liar family of paradoxes undermines what they (Ibid.) call the dialetheic conjecture . In this paper, after critically evaluating Goldstein’s response to A-G&W, I turn to his proposed (...)
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  17. B. Armour-Garb & Jc Beall (2003). Minimalism and the Dialetheic Challenge. Australasian Journal of Philosophy 81 (3):383 – 401.
    Minimalists, following Horwich, claim that all that can be said about truth is comprised by all and only the nonparadoxical instances of (E) p is true iff p. It is, accordingly, standard in the literature on truth and paradox to ask how the minimalist will restrict (E) so as to rule out paradox-inducing sentences (alternatively: propositions). In this paper, we consider a prior question: On what grounds does the minimalist restrict (E) so as to rule out paradox-inducing sentences and, thereby, (...)
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  18. Bradley Armour-Garb (2007). Consistent Inconsistency Theories. Inquiry 50 (6):639 – 654.
    In this paper I critically evaluate a number of current "consistent inconsistency theories" and then briefly motivate a rival position. The rival position challenges a consistent inconsistency theory, by sharing many of its basic commitments without suffering the problems that such a theory appears to face.
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  19. Bradley Armour-Garb (2004). Minimalism, the Generalization Problem and the Liar. Synthese 139 (3):491 - 512.
    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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  20. Bradley Armour-Garb (2001). Deflationism and the Meaningless Strategy. Analysis 61 (4):280–289.
  21. Bradley Armour-Garb & J. C. Beall (2001). Can Deflationists Be Dialetheists? Journal of Philosophical Logic 30 (6):593-608.
    Philosophical work on truth covers two streams of inquiry, one concerning the nature (if any) of truth, the other concerning truth-related paradox, especially the Liar. For the most part these streams have proceeded fairly independently of each other. In his "Deflationary Truth and the Liar" (JPL 28:455-488, 1999) Keith Simmons argues that the two streams bear on one another in an important way; specifically, the Liar poses a greater problem for deflationary conceptions of truth than it does for inflationist conceptions. (...)
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  22. Bradley Armour-Garb & JC Beall (2002). Further Remarks on Truth and Contradiction. Philosophical Quarterly 52 (207):217-225.
    We address an issue recently discussed by Graham Priest: whether the very nature of truth (understood as in correspondence theories) rules out true contradictions, and hence whether a correspondence-theoretic notion of truth rules against dialetheism. We argue that, notwithstanding appearances to the contrary, objections from within the correspondence theory do not stand in the way of dialetheism. We close by highlighting, but not attempting to resolve, two further challenges for dialetheism which arise out of familiar philosophical theorizing about truth.
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  23. Bradley Armour-Garb & James A. Woodbridge (2013). Semantic Defectiveness and the Liar. Philosophical Studies 164 (3):845-863.
    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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  24. Bradley Armour-Garb & James A. Woodbridge (2012). Liars, Truthtellers and Naysayers: A Broader View of Semantic Pathology I. Language and Communication 32 (4):293-311.
    Semantic pathology is most widely recognized in the liar paradox, where an apparent inconsistency arises in ‘‘liar sentences’’ and their ilk. But the phenomenon of semantic pathology also manifests a sibling symptom—an apparent indeterminacy—which, while not largely discussed (save for the occasional nod to ‘‘truthteller sentences’’), is just as pervasive as, and exactly parallels, the symptom of inconsistency. Moreover, certain ‘‘dual symptom’’ cases, which we call naysayers, exhibit both inconsistency and indeterminacy and also manifest a higher-order indeterminacy between them. In (...)
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  25. Bradley Armour-Garb & James A. Woodbridge (2010). Truthmakers, Paradox and Plausibility. Analysis 70 (1):11-23.
    In a series of articles, Dan Lopez De Sa and Elia Zardini argue that several theorists have recently employed instances of paradoxical reasoning, while failing to see its problematic nature because it does not immediately (or obviously) yield inconsistency. In contrast, Lopez De Sa and Zardini claim that resultant inconsistency is not a necessary condition for paradoxicality. It is our contention that, even given their broader understanding of paradox, their arguments fail to undermine the instances of reasoning they attack, either (...)
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  26. Bradley Armour-Garb & James A. Woodbridge (2006). Dialetheism, Semantic Pathology, and the Open Pair. Australasian Journal of Philosophy 84 (3):395 – 416.
    Over the past 25 years, Graham Priest has ably presented and defended dialetheism, the view that certain sentences are properly characterized as true with true negations. Our goal here is neither to quibble with the tenability of true, assertable contradictions nor, really, with the arguments for dialetheism. Rather, we wish to address the dialetheist's treatment of cases of semantic pathology and to pose a worry for dialetheism that has not been adequately considered. The problem that we present seems to have (...)
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  27. Bradley Armour-Garb & James A. Woodbridge (2003). Curried Katz with Epimenidean Dilemma. Philosophical Forum 34 (3-4):351-366.
  28. D. M. Armstrong (2004). Truth and Truthmakers. Cambridge University Press.
    Truths are determined not by what we believe, but by the way the world is. Or so realists about truth believe. Philosophers call such theories correspondence theories of truth. Truthmaking theory, which now has many adherents among contemporary philosophers, is the most recent development of a realist theory of truth, and in this book D. M. Armstrong offers the first full-length study of this theory. He examines its applications to different sorts of truth, including contingent truths, modal truths, truths about (...)
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  29. Jamin Asay (forthcoming). Epistemicism and the Liar. Synthese:1-21.
    One well known approach to the soritical paradoxes is epistemicism, the view that propositions involving vague notions have definite truth values, though it is impossible in principle to know what they are. Recently, Paul Horwich has extended this approach to the liar paradox, arguing that the liar proposition has a truth value, though it is impossible to know which one it is. The main virtue of the epistemicist approach is that it need not reject classical logic, and in particular the (...)
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  30. F. G. Asenjo (1966). A Calculus for Antinomies. Notre Dame Journal of Formal Logic 16 (1):103-105.
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  31. E. J. Ashworth (1977). Thomas Bricot (D. 1516) and the Liar Paradox. Journal of the History of Philosophy 15 (3):267-280.
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  32. Richard Kenneth Atkins (2011). This Proposition is Not True: C.S. Peirce and the Liar Paradox. Transactions of the Charles S. Peirce Society 47 (4):421-444.
    Charles Sanders Peirce proposed two different solutions to the Liar Paradox. He proposed the first in 1865 and the second in 1869. However, no one has yet noted in the literature that Peirce rejected his 1869 solution in 1903. Peirce never explicitly proposed a third solution to the Liar Paradox. Nonetheless, I shall argue he developed the resources for a third and novel solution to the Liar Paradox.In what follows, I will first explain the Liar Paradox. Second, I will briefly (...)
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  33. Jody Azzouni (2007). The Inconsistency of Natural Languages: How We Live with It. Inquiry 50 (6):590 – 605.
    I revisit my earlier arguments for the (trivial) inconsistency of natural languages, and take up the objection that no such argument can be established on the basis of surface usage. I respond with the evidential centrality of surface usage: the ways it can and can't be undercut by linguistic science. Then some important ramifications of having an inconsistent natural language are explored: (1) the temptation to engage in illegitimate reductio reasoning, (2) the breakdown of the knowledge idiom (because its facticity (...)
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  34. Jody Azzouni (2003). The Strengthened Liar, the Expressive Strength of Natural Languages, and Regimentation. Philosophical Forum 34 (3-4):329–350.
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  35. Andrew Bacon (2013). Curry's Paradox and Omega Inconsistency. Studia Logica 101 (1):1-9.
    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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  36. Andrew Bacon (2013). A New Conditional for Naive Truth Theory. Notre Dame Journal of Formal Logic 54 (1):87-104.
    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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  37. Andrew Bacon (2013). Paradoxes of Logical Equivalence and Identity. Topoi:1-10.
    In this paper a principle of substitutivity of logical equivalents salve veritate and a version of Leibniz’s law are formulated and each is shown to cause problems when combined with naive truth theories.
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  38. Emil Badici (2008). The Liar Paradox and the Inclosure Schema. Australasian Journal of Philosophy 86 (4):583 – 596.
    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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  39. Emil Badici & Kirk Ludwig (2007). The Concept of Truth and the Semantics of the Truth Predicate. Inquiry 50 (6):622 – 638.
    We sketch an account according to which the semantic concepts themselves are not pathological and the pathologies that attend the semantic predicates arise because of the intention to impose on them a role they cannot fulfill, that of expressing semantic concepts for a language that includes them. We provide a simplified model of the account and argue in its light that (i) a consequence is that our meaning intentions are unsuccessful, and such semantic predicates fail to express any concept, and (...)
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  40. Y. Bar-Hillel (1957). New Light on the Liar. Analysis 18 (1):1 - 6.
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  41. Dorit Bar-On, Claire Horisk & William G. Lycan (2000). Deflationism, Meaning and Truth-Conditions. Philosophical Studies 101 (1):1-28.
    Some deflationists about truth maintain that such deflationism undercuts truth-condition theories of meaning. We offer a deductive argument designed to show that meaning must at least include truth-condition. Deflationist replies are considered and rebutted. We conclude that either deflationism is false or it is not, after all, incompatible with truth-condition theories of meaning.
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  42. Juan Barba (1998). Construction of Truth Predicates: Approximation Versus Revision. Bulletin of Symbolic Logic 4 (4):399-417.
  43. John Barker (2009). Disquotation, Conditionals, and the Liar. Polish Journal of Philosophy 3 (1):5-21.
    In this paper I respond to Jacquette’s criticisms, in (Jacquette, 2008), of my (Barker, 2008). In so doing, I argue that the Liar paradox is in fact a problem about the disquotational schema, and that nothing in Jacquette’s paper undermines this diagnosis.
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  44. Stephen Barker (2014). Semantic Paradox and Alethic Undecidability. 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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  45. Stephen Barker (2003). Truth and Conventional Implicature. Mind 112 (445):1-34.
    Are all instances of the T-schema assertable? I argue that they are not. The reason is the presence of conventional implicature in a language. Conventional implicature is meant to be a component of the rule-based content that a sentence can have, but it makes no contribution to the sentence's truth-conditions. One might think that a conventional implicature is like a force operator. But it is not, since it can enter into the scope of logical operators. It follows that the semantic (...)
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  46. Eduardo Alejandro Barrio (2012). The Yablo Paradox and Circularity. Análisis Filosófico 32 (1):7-20.
    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 such formalization (...)
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  47. Jon Barwise (1987). The Liar: An Essay on Truth and Circularity. Oxford University Press.
    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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  48. Arvid Båve (2013). Formulating Deflationism. Synthese 190 (15):3287-3305.
    I here argue for a particular formulation of truth-deflationism, namely, the propositionally quantified formula, (Q) “For all p, ${\langle \text{p}\rangle}$ is true iff p”. The main argument consists of an enumeration of the other (five) possible formulations and criticisms thereof. Notably, Horwich’s Minimal Theory is found objectionable in that it cannot be accepted by finite beings. Other formulations err in not providing non-questionbegging, sufficiently direct derivations of the T-schema instances. I end by defending (Q) against various objections. In particular, I (...)
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  49. Arvid Båve (2012). On Using Inconsistent Expressions. Erkenntnis 77 (1):133-148.
    The paper discusses the Inconsistency Theory of Truth (IT), the view that “true” is inconsistent in the sense that its meaning-constitutive principles include all instances of the truth-schema (T). It argues that (IT) entails that anyone using “true” in its ordinary sense is committed to all the (T)-instances and that any theory in which “true” is used in that sense entails the (T)-instances (which, given classical logic, entail contradictions). More specifically, I argue that theorists are committed to the meaning-constitutive principles (...)
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  50. J. C. Beal & B. Armour-Garb (eds.) (2006). Deflationism and Paradox. Clarendon.
    Deflationist accounts of truth are widely held in contemporary philosophy: they seek to show that truth is a dispensable concept with no metaphysical depth. However, logical paradoxes present problems for deflationists that their work has struggled to overcome. In this volume of fourteen original essays, a distinguished team of contributors explore the extent to which, if at all, deflationism can accommodate paradox. The volume will be of interest to philosophers of logic, philosophers of language, and anyone working on truth. Contributors (...)
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