About this topic
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
Related categories

2015 found
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1 — 50 / 2015
  1. Tarski, Frege and the Liar Paradox.Aaron Sloman - 1971 - Philosophy 46 (176):133-.
    A.1. Some philosophers, including Tarski and Russell, have concluded from a study of various versions of the Liar Paradox ‘that there must be a hierarchy of languages, and that the words “true” and “false”, as applied to statements in any given language, are themselves words belonging to a language of higher order’. In his famous essay on truth Tarski claimed that ‘colloquial’ language is inconsistent as a result of its property of ‘universality’: that is, whatever can be said at all (...)
  2. Review of Saving Truth From Paradox. [REVIEW]Jordi Abad - 2010 - Disputatio 4 (29):94-101.
  3. Saving Truth From Paradox, by Hartry Field.Jordi Valor Abad - 2010 - Disputatio.
  4. 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 (...)
  5. A Failed "Cassatio": Goldstein on the Liar.Jordi Valor Abad & José Martínez Fernández - 2009 - Proceedings of the Aristotelian Society 109 (1pt3):327 - 332.
  6. Review: E. M. Barth, R. T. P. Wiche, Problems, Functions and Semantic Roles. A Pragmatists' Analysis of Montague's Theory of Sentence Meaning. [REVIEW]Barbara Abbott - 1988 - Journal of Symbolic Logic 53 (1):317-318.
  7. Two Paradoxes of Analysis.Diana Ackerman - 1981 - Journal of Philosophy 78 (11):733-735.
  8. Analysis and its Paradoxes.Felicia Ackerman - 1992 - In Edna Ullmann-Margalit (ed.), The Scientific Enterprise. Kluwer Academic Publishers. pp. 169--178.
  9. Review: Haskell B. Curry, The Permutability of Rules in the Classical Inferential Calculus. [REVIEW]W. Ackermann - 1955 - Journal of Symbolic Logic 20 (1):66-67.
  10. Review: Haskell B. Curry, The Elimination Theorem When Modality is Present. [REVIEW]Wilhelm Ackermann - 1955 - Journal of Symbolic Logic 20 (1):67-67.
  11. Review: Haskell B. Curry, A Theory of Formal Deducibility. [REVIEW]Wilhelm Ackermann - 1951 - Journal of Symbolic Logic 16 (1):56-58.
  12. On the Physiological Generation of Antinomies and Paradoxes.Carlos Acosta - 2012 - Mind and Matter 10 (1):75 - 114.
    It is proposed that subconscious retro-predictions in conjunction with brain state update cycles are instrumental in the physiological generation of conscious sensations and perceptions, and in all abstract thought. In this paper the hypothesis is supported by conducting a detailed a re-evaluation of the self-referential statements in Set Theory and Formal Logic known as antinomies. This study concludes that the recursive behavior exhibited by abstract enigmas such as "Russell’s Paradox" is analogous to the oscillations typical of bistable perceptual phenomena.
  13. Truth Definitions Without Exponentiation and the Σ₁ Collection Scheme.Zofia Adamowicz, Leszek Aleksander Kołodziejczyk & Jeff Paris - 2012 - Journal of Symbolic Logic 77 (2):649-655.
    We prove that: • if there is a model of I∆₀ + ¬ exp with cofinal Σ₁-definable elements and a Σ₁ truth definition for Σ₁ sentences, then I∆₀ + ¬ exp +¬BΣ₁ is consistent, • there is a model of I∆₀ Ω₁ + ¬ exp with cofinal Σ₁-definable elements, both a Σ₂ and a ∏₂ truth definition for Σ₁ sentences, and for each n > 2, a Σ n truth definition for Σ n sentences. The latter result is obtained by (...)
  14. The Liar-Paradox in a Quantum Mechanical Perspective.Diederik Aerts, Jan Broekaert & Sonja Smets - 1999 - 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.
  15. Variations on the Liar's Paradox.Joseph Agassi - 1964 - 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: (...)
  16. Abstraction in Algorithmic Logic.Wayne Aitken & Jeffrey A. Barrett - 2008 - Journal of Philosophical Logic 37 (1):23-43.
    We develop a functional abstraction principle for the type-free algorithmic logic introduced in our earlier work. Our approach is based on the standard combinators but is supplemented by the novel use of evaluation trees. Then we show that the abstraction principle leads to a Curry fixed point, a statement C that asserts C ⇒ A where A is any given statement. When A is false, such a C yields a paradoxical situation. As discussed in our earlier work, this situation leaves (...)
  17. Computer Implication and the Curry Paradox.Wayne Aitken & Jeffrey A. Barrett - 2004 - Journal of Philosophical Logic 33 (6):631-637.
    There are theoretical limitations to what can be implemented by a computer program. In this paper we are concerned with a limitation on the strength of computer implemented deduction. We use a version of the Curry paradox to arrive at this limitation.
  18. A Deflationist Approach to Indeterminacy and Vagueness.Ken Akiba - 2002 - Philosophical Studies 107 (1):69 - 86.
    Deflationists cannot make sense of the notion of referential indeterminacy because they deny the existence of substantive reference. One way for them to make sense of the objective existence of linguistic indeterminacy is by embracing the worldly (or objectual) view of indeterminacy, the view that indeterminacy exists 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 divided into temporal slices and (arguably) alethic possible worlds. Supervaluationism (...)
  19. Can Deflationism Allow for Hidden Indeterminacy?Ken Akiba - 2002 - Pacific Philosophical Quarterly 83 (3):223–234.
    Field (2000) claims that both inflationists and deflationists can and should accept the existence of linguistic indeterminacy in their own language. This paper shows that inflationists and deflationists consider the nature of indeterminacy quite differently; in particular, deflationists’ notion of indeterminacy lacks the kind of objectivity inflationists’ notion has; as a result, while both inflationists and deflationists can and should accept the existence of manifest indeterminacy such as vagueness, only inflationists can accept the existence of hidden indeterminacy such as the (...)
  20. Münchhausen in Transzendentaler Maskerade.Hans Albert - 1985 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 16 (2):341-356.
    In this paper it is shown that the attempt by Gerhard Seel to give a positive solution to the problem of absolute justification of socalled practical sentences has failed. His attempts to explicate his central concepts and the conditions of adequacy of his fundamental practical sentence are analyzed in detail. And his proposals for the formulation of a sentence of this kind are shown to lead to absurd consequences, so that consistent fallibilism is saved from his attack.
  21. Truth.Edwin B. Allaire - 1975 - Metaphilosophy 6 (3-4):261-276.
  22. Zeno, Aristotle, the Racetrack and the Achilles: A Historical and Philosophical Investigation.Benjamin William Allen - unknown
    I reconstruct the original versions of Zeno's Racetrack and Achilles paradoxes, along with Aristotle's responses thereto. Along the way I consider some of the consequences for modern analyses of the paradoxes. It turns out that the Racetrack and the Achilles were oral two-party question-and-answer dialectical paradoxes. One consequence is that the arguments needed to be comprehensible to the average person, and did not employ theses or concepts familiar only to philosophical specialists. I rely on this fact in reconstructing the original (...)
  23. On Some Paradoxes of the Infinite.Victor Allis & Teunis Koetsier - 1991 - British Journal for the Philosophy of Science 42 (2):187-194.
    In the paper below the authors describe three super-tasks. They show that although the abstract notion of a super-task may be, as Benacerraf suggested, a conceptual mismatch, the completion of the three super-tasks involved can be defined rather naturally, without leading to inconsistency, by means of a particular kinematical interpretation combined with a principle of continuity.
  24. A Classical Prejudice?Patrick Allo - 2010 - Knowledge, Technology and Policy 23 (1-2):25-40.
    In this paper I reassess Floridi's solution to the Bar-Hillel-Carnap paradox (the information-yield of inconsistent propositions is maximal) by questioning the orthodox view that contradictions cannot be true. The main part of the paper is devoted to showing that the veridicality thesis (semantic information has to be true) is compatible with dialetheism (there are true contradictions), and that unless we accept the additional non-falsity thesis (information cannot be false) there is no reason to presuppose that there is no such thing (...)
  25. Vacuous Truth.Robert Almeder - 1990 - Synthese 85 (3):507 - 524.
  26. A Realist Conception of Truth.William P. Alston - 1996 - Cornell University Press.
    William P. Alston formulates and defends a realist conception of truth, which he calls alethic realism (from "aletheia", Greek for "truth").
  27. The Early Arabic Liar: The Liar Paradox in the Islamic World From the Mid-Ninth to the Mid-Thirteenth Centuries Ce.Ahmed Alwishah & David Sanson - 2009 - 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 (...)
  28. Review: Max Black, The Semantic Definition of Truth. [REVIEW]Alice Ambrose - 1955 - Journal of Symbolic Logic 20 (3):299-299.
  29. Review: P. F. Strawson, Truth. [REVIEW]Alice Ambrose - 1955 - Journal of Symbolic Logic 20 (3):299-299.
  30. Review: C. A. Baylis, Facts, Propositions, Exemplification and Truth. [REVIEW]Alice Ambrose - 1949 - Journal of Symbolic Logic 14 (2):133-134.
  31. Review: A. J. Ayer, Thinking and Meaning. [REVIEW]Alice Ambrose - 1948 - Journal of Symbolic Logic 13 (3):145-146.
  32. Review: Yehoshua Bar-Hillel, Analysis of "Correct" Language. [REVIEW]Alice Ambrose - 1947 - Journal of Symbolic Logic 12 (1):23-24.
  33. St. Paul'€™s Epistle to Titus.Alan Ross Anderson - 1970 - In Robert L. Martin (ed.), The Paradox of the Liar. Ridgeview.
  34. Thomson J.F.. On Some Paradoxes. Analytical Philosophy, Edited by Butler R. J., Barnes & Noble, Inc., New York 1962, Pp. 104–119. [REVIEW]Alan Ross Anderson - 1964 - Journal of Symbolic Logic 29 (3):139-140.
  35. A Choice-Semantical Approach to Theoretical Truth.Holger Andreas & Georg Schiemer - 2016 - Studies in History and Philosophy of Science Part A 58:1-8.
  36. Perun's Revenge: Understanding Theduxovnaja Kul'tura.Irving H. Anellis - 1984 - Studies in East European Thought 27 (1):1-24.
  37. The Complexity of Revision, Revised.G. Aldo Antonelli - 2002 - Notre Dame Journal of Formal Logic 43 (2):75-78.
    The purpose of this note is to acknowledge a gap in a previous paper, "The complexity of revision," and to provide a corrected version of the argument.
  38. Virtuous Circles: From Fixed Points to Revision Rules.G. Aldo Antonelli - 2000 - In Anil Gupta & Andre Chapuis (eds.), Circularity, Definition, and Truth. Indian Council of Philosophical Research. pp. 1--27.
  39. What's in a Function?Gian Aldo Antonelli - 1996 - Synthese 107 (2):167 - 204.
    In this paper we argue that Revision Rules, introduced by Anil Gupta and Nuel Belnap as a tool for the analysis of the concept of truth, also provide a useful tool for defining computable functions. This also makes good on Gupta's and Belnap's claim that Revision Rules provide a general theory of definition, a claim for which they supply only the example of truth. In particular we show how Revision Rules arise naturally from relaxing and generalizing a classical construction due (...)
  40. Book Review: Keith Simmons. Universality and the Liar: An Essay on Truth and the Diagonal Argument. [REVIEW]Gian Aldo Antonelli - 1996 - Notre Dame Journal of Formal Logic 37 (1):152-159.
  41. The Complexity of Revision.Gian Aldo Antonelli - 1994 - Notre Dame Journal of Formal Logic 35 (1):67-72.
    In this paper we show that the Gupta-Belnap systems S# and S* are П12. Since Kremer has independently established that they are П12-hard, this completely settles the problem of their complexity. The above-mentioned upper bound is established through a reduction to countable revision sequences that is inspired by, and makes use of a construction of McGee.
  42. Non-Well-Founded Sets Via Revision Rules.Gian Aldo Antonelli - 1994 - Journal of Philosophical Logic 23 (6):633 - 679.
  43. Barwise and Etchemendy's Theory of Truth.Hiroshi Aoyama - unknown
  44. This is the Title of This Thesis.Hiroshi Aoyama - 1988 - Dissertation, University of Illinois at Urbana-Champaign
    This thesis is a study of the Liar paradox and the notion of truth and consists of two parts, a philosophical part and a technical part. ;In the philosophical part , the Liar paradox and a solution to it are considered. Ch. 1 presents an overview of logical and semantical paradoxes, including the Liar paradox. Ch. 2 presents some discussions of Kripke's solution to the Liar paradox and it is argued that although Kripke's view that the Liar sentence is neither (...)
  45. The Priest on the Campus.J. A. Appleyard - 1969 - Thought: A Journal of Philosophy 44 (4):546-564.
    If the priest is always a sign of transcendence in some form or other, what is his function in the academic community for which he labors?
  46. Revenge Is Mine, I Will Repay.Ruben G. Apressyan - 2009 - Russian Studies in Philosophy 48 (2):8-27.
    By placing Jesus's commandment not to "resist evil" in its textual and religious context, the author demonstrates that it should not be interpreted in an absolute sense. Christianity does not condemn vengeance as such but makes it a divine prerogative. A critique is presented of Tolstoy's doctrine of nonviolence.
  47. No Consistent Way with Paradox.B. Armour-Garb - 2012 - 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 (...)
  48. Minimalism and the Dialetheic Challenge.B. Armour-Garb & Jc Beall - 2003 - 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, (...)
  49. Spandrels of Truth * By JC BEALL.B. Armour-Garb & L. Goldstein - 2010 - Analysis 70 (3):586-589.
    (No abstract is available for this citation).
  50. The Relevance of the Liar.Bradley Armour-Garb (ed.) - forthcoming - Oxford University Press.
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