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
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2056 found
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1 — 50 / 2056
  1. Paradoxes of Logical Equivalence and Identity.Andrew Bacon - 2013 - Topoi (1):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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  2. De las pericias con que el gobernador Sancho Panza resolvió la Paradoja del Suicida.Luis Felipe Bartolo Alegre - manuscript
    This is the story of how the noble squire Sancho Panza, while governing what he thought to be an insula, ingeniously solved a paradox not unlike those of modern logic.
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  3. How to Conquer the Liar and Enthrone the Logical Concept of Truth: An Informal Exposition.Boris Culina - manuscript
    This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counter-arguments for various proposed solutions (``the revenge of the Liar''). Any solution to the paradoxes of truth necessarily establishes a certain logical concept of truth. This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through (...)
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  4. The Synthetic Concept of Truth and its Descendants.Boris Culina - manuscript
    The concept of truth has many aims but only one source. The article describes the primary concept of truth, here called the synthetic concept of truth, according to which truth is the objective result of the synthesis of us and nature in the process of rational cognition. It is shown how various aspects of the concept of truth -- logical, scientific, and mathematical aspect -- arise from the synthetic concept of truth. Also, it is shown how the paradoxes of truth (...)
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  5. The Power of Naive Truth.Hartry Field - manuscript
    While non-classical theories of truth that take truth to be transparent have some obvious advantages over any classical theory that evidently must take it as non-transparent, several authors have recently argued that there's also a big disadvantage of non-classical theories as compared to their “external” classical counterparts: proof-theoretic strength. While conceding the relevance of this, the paper argues that there is a natural way to beef up extant internal theories so as to remove their proof-theoretic disadvantage. It is suggested that (...)
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  6. Some Open Questions About Degrees of Paradoxes.Ming Hsiung - manuscript
    We can classify the (truth-theoretic) paradoxes according to their degrees of paradoxicality. Roughly speaking, two paradoxes have the same degrees of paradoxicality, if they lead to a contradiction under the same conditions, and one paradox has a (non-strictly) lower degree of paradoxicality than another, if whenever the former leads to a contradiction under a condition, the latter does so under the very condition. This paper aims at setting forth the theoretical framework of the theory of paradoxicality degree, and putting forward (...)
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  7. Meaning, Presuppositions, Truth-Relevance, Gödel's Sentence and the Liar Paradox.X. Y. Newberry - manuscript
    Section 1 reviews Strawson’s logic of presuppositions. Strawson’s justification is critiqued and a new justification proposed. Section 2 extends the logic of presuppositions to cases when the subject class is necessarily empty, such as (x)((Px & ~Px) → Qx) . The strong similarity of the resulting logic with Richard Diaz’s truth-relevant logic is pointed out. Section 3 further extends the logic of presuppositions to sentences with many variables, and a certain valuation is proposed. It is noted that, given this valuation, (...)
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  8. Cut Elimination for Systems of Transparent Truth with Restricted Initial Sequents.Carlo Nicolai - manuscript
    The paper studies a cluster of systems for fully disquotational truth based on the restriction of initial sequents. Unlike well-known alternative approaches, such systems display both a simple and intuitive model theory and remarkable proof-theoretic properties. We start by showing that, due to a strong form of invertibility of the truth rules, cut is eliminable in the systems via a standard strategy supplemented by a suitable measure of the number of applications of truth rules to formulas in derivations. Next, we (...)
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  9. Formalizing the Logical (Self-Reference) Error of the Liar Paradox.Pete Olcott - manuscript
    This paper decomposes the Liar Paradox into its semantic atoms using Meaning Postulates (1952) provided by Rudolf Carnap. Formalizing truth values of propositions as Boolean properties of these propositions is a key new insight. This new insight divides the translation of a declarative sentence into its equivalent mathematical proposition into three separate steps. When each of these steps are separately examined the logical error of the Liar Paradox is unequivocally shown.
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  10. Minimal Type Theory (MTT).Pete Olcott - manuscript
    Minimal Type Theory (MTT) is based on type theory in that it is agnostic about Predicate Logic level and expressly disallows the evaluation of incompatible types. It is called Minimal because it has the fewest possible number of fundamental types, and has all of its syntax expressed entirely as the connections in a directed acyclic graph.
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  11. Provability with Minimal Type Theory.Pete Olcott - manuscript
    Minimal Type Theory (MTT) shows exactly how all of the constituent parts of an expression relate to each other (in 2D space) when this expression is formalized using a directed acyclic graph (DAG). This provides substantially greater expressiveness than the 1D space of FOPL syntax. -/- The increase in expressiveness over other formal systems of logic shows the Pathological Self-Reference Error of expressions previously considered to be sentences of formal systems. MTT shows that these expressions were never truth bearers, thus (...)
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  12. The Notion of Truth in Natural and Formal Languages.Pete Olcott - manuscript
    For any natural (human) or formal (mathematical) language L we know that an expression X of language L is true if and only if there are expressions Γ of language L that connect X to known facts. -/- By extending the notion of a Well Formed Formula to include syntactically formalized rules for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to neither True nor False.
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  13. Defining a Decidability Decider.Pete Olcott - manuscript
    By extending the notion of a Well Formed Formula to include syntactically formalized rules for rejecting semantically incorrect expressions we recognize and reject expressions that have the semantic error of Pathological self-reference(Olcott 2004). The foundation of this system requires the notion of a BaseFact that anchors the semantic notions of True and False. When-so-ever a formal proof from BaseFacts of language L to a closed WFF X or ~X of language L does not exist X is decided to be semantically (...)
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  14. A Cautionary Note About Self-Reference.T. Parent - manuscript
    If a semantically open language has no constraints on self-reference, one can prove an absurdity. The argument utilizes co-referring names 'a0' and 'a1', and the definition of a functional expression 'The reflection of x = y'. The definition enables a type of self-reference without deploying any semantic terminology--yet given that a0= a1, the definition implies the that 'a0' = 'a1', which is absurd. In truth, however, 'the reflection of x = y' expresses an ill-defined function. And since there is a (...)
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  15. Contradiction From a Coded Proof Predicate (Very Tentative Draft, Do Not Cite).T. Parent - manuscript
  16. Xeno Semantics for Ascending and Descending Truth.Kevin Scharp - manuscript
    As part of an approach to the liar paradox and the other paradoxes affecting truth, I have proposed replacing our concept of truth with two concepts: ascending truth and descending truth.1 I am not going to discuss why I think this is the best approach or how it solves the paradoxes; instead, I concentrate on the theory of ascending and descending truth. I formulate an axiomatic theory of ascending truth and descending truth (ADT) and provide a possible-worlds semantics for it (...)
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  17. A Quantificational Analysis of the Liar Paradox.Matheus Silva - manuscript
    It seems that the most common strategy to solve the liar paradox is to argue that liar sentences are meaningless and, consequently, truth-valueless. The other main option that has grown in recent years is the dialetheist view that treats liar sentences as meaningful, truth-apt and true. In this paper I will offer a new approach that does not belong in either camp. I hope to show that liar sentences can be interpreted as meaningful, truth-apt and false, but without engendering any (...)
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  18. Truth and Subjunctive Theories of Knwledge: No Luck?Johannes Stern - manuscript
    The paper explores applications of Kripke's theory of truth to semantics for anti-luck epistemology, that is, to subjunctive theories of knowledge. Subjunctive theories put forward modal or subjunctive conditions to rule out knowledge by mere luck as to be found in Gettier-style counterexamples to the analysis of knowledge as justified true belief. Because of the subjunctive nature of these conditions the resulting semantics turns out to be non-monotone, even if it is based on non-classical evaluation schemes such as strong Kleene (...)
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  19. Inconsistency Theories: The Importance of Being Metalinguistic.Douglas Patterson - manuscript
    This is a discussion of different ways of working out the idea that the semantic paradoxes show that natural languages are somehow “inconsistent”. I take the workable form of the idea to be that there are expressions such that a necessary condition of understanding them is that one be inclined to accept inconsistent claims (an conception also suggested by Matti Eklund). I then distinguish “simple” from “complex” forms of such views. On a simple theory, such expressions are meaningless, while on (...)
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  20. Models for Liars in Bradwardine's Theory of Truth.Greg Restall - manuscript
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  21. On Berry/Russell Paradoxes.Jordan Howard Sobel - manuscript
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  22. Not Much of a Liar Paradox: An Exercise.Jordan Howard Sobel - manuscript
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  23. The Paradox of Liar and Fazil Sarab's Solution.Muhammed Ejei - unknown - Kheradnameh Sadra Quarterly 36.
    In spite of the various responses and solutions provided for the paradox of liar, different scholars and thinkers are still trying to discover some new points in this regard. We can say that this paradox has attracted the attention of a lot of philosophers due to its simplicity of formulation, long history and complexity of solution. In fact, the existing diversity in the presented solutions to this paradox is not less than the diversity in the solutions provided for the very (...)
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  24. The Riddle of the Incommensurable Root as Viewed by Some 7th Century Muslim Logicians.Ahad Gharamaleki - unknown - Kheradnameh Sadra Quarterly 7.
    A paradox in its original Greek means a statement which goes beyond the accepted opinion; a logical paradox is a statement which involves its contradictory, i.e. if asserted as true, must necessarily be false and vice versa. A classical example of such paradoxes is the Eulibides Paradox, Known as the Liar's Paradox. Eulibides, a Cretan, says that "All Cretans are liars". Is his statement true? If true, it must necessarily be false and if false, it must necessarily be true.The Liar's (...)
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  25. Something is True.Jamin Asay - forthcoming - Philosophy and Phenomenological Research.
    The thesis that nothing is true has long been thought to be a self-refuting position not worthy of serious philosophical consideration. Recently, however, the thesis of alethic nihilism—that nothing is true—has been explicitly defended (notably by David Liggins). Nihilism is also, I argue, a consequence of other views about truth that have recently been advocated, such as fictionalism about truth and the inconsistency account. After offering an account of alethic nihilism, and how it purports to avoid the self-refutation problem, I (...)
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  26. A Note on Gödel, Priest and Naïve Proof.Massimiliano Carrara - forthcoming - Logic and Logical Philosophy:1.
    In the 1951 Gibbs lecture, Gödel asserted his famous dichotomy, where the notion of informal proof is at work. G. Priest developed an argument, grounded on the notion of naïve proof, to the effect that Gödel’s first incompleteness theorem suggests the presence of dialetheias. In this paper, we adopt a plausible ideal notion of naïve proof, in agreement with Gödel’s conception, superseding the criticisms against the usual notion of naïve proof used by real working mathematicians. We explore the connection between (...)
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  27. Hegel’s Interpretation of the Liar Paradox.Franca D’Agostini & Elena Ficara - forthcoming - History and Philosophy of Logic:1-24.
    In his Lectures on the History of Philosophy, Hegel develops a subtle analysis of Megarian paradoxes: the Liar, the Veiled Man and the Sorites. In this paper, we focus on Hegel's interpretation of...
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  28. The Epistemic Consequences of Paradox.Bryan Frances - forthcoming - Cambridge: Cambridge University Press.
    By pooling together exhaustive analyses of certain philosophical paradoxes, we can prove a series of fascinating results regarding philosophical progress (yes, of a peculiar sort), agreement on substantive philosophical claims (yes, of a sort), knockdown arguments in philosophy (there are some, given here), the wisdom of philosophical belief (quite rare, because the knockdown arguments show that we philosophers have been wildly wrong about language, logic, truth, or ordinary empirical matters), the epistemic status of metaphysics (it’s not bullshit, and in one (...)
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  29. In Search of an Integrated Logic of Conviction and Intention.Prof em Dr Hans-Ulrich Hoche - forthcoming - Philosophical Explorations.
    According to a two-level criterion for combination tests in the field of ordinary language, moral 'ought'-sentences may be taken to imply 'I intend'-sentences partly semantically and partly pragmatically. If so, a trenchant linguistic analysis of the concept of moral obligation cannot do without a non-classical logic which allows to model these important kinds of ordinary-language implications by means of purely syntactical derivations. For this purpose, an integrated logic of conviction and intention has been tentatively devised by way of a doxastically, (...)
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  30. Wittgenstein Und Die Philosophie der Mathematik.Bromand Joachim & Reichert Bastian (eds.) - forthcoming - Mentis Verlag.
    Ludwig Wittgenstein selbst hielt seine Überlegungen zur Mathematik für seinen bedeutendsten Beitrag zur Philosophie. So beabsichtigte er zunächst, dem Thema einen zentralen Teil seiner Philosophischen Untersuchungen zu widmen. Tatsächlich wird kaum irgendwo sonst in Wittgensteins Werk so deutlich, wie radikal die Konsequenzen seines Denkens eigentlich sind. Vermutlich deshalb haben Wittgensteins Bemerkungen zur Mathematik unter all seinen Schriften auch den größten Widerstand provoziert: Seine Bemerkungen zu den Gödel’schen Unvollständigkeitssätzen bezeichnete Gödel selbst als Nonsens, und Alan Turing warf Wittgenstein vor, dass aufgrund (...)
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  31. Grim Variations.Fabio Lampert & John Waldrop - forthcoming - Faith and Philosophy.
    Patrick Grim advances arguments meant to show that the doctrine of divine omniscience—the classical doctrine according to which God knows all truths—is false. In particular, we here have in mind to focus on two such arguments: the set theoretic argument and the semantic argument. These arguments due to Grim run parallel to, respectively, familiar paradoxes in set theory and naive truth theory. It is beyond the purview of this article to adjudicate whether or not these are successful arguments against the (...)
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  32. The Liar Without Relativism.Poppy Mankowitz - forthcoming - Erkenntnis:1-22.
    Some in the recent literature have claimed that a connection exists between the Liar paradox and semantic relativism: the view that the truth values of certain occurrences of sentences depend on the contexts at which they are assessed. Sagi :913–928, 2017) argues that contextualist accounts of the Liar paradox are committed to relativism, and Rudnicki and Łukowski propose a new account that they classify as relativist. I argue that a full understanding of how relativism is conceived within theories of natural (...)
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  33. Not Wanted: On Scharp’s Solution to the Liar.Mark Pinder - forthcoming - Erkenntnis:1-18.
    Kevin Scharp argues that the concept of truth is defective, and is therefore unable to play its intended role in natural language truth-conditional semantics. As such, for this theoretical purpose, Scharp constructs two replacements: ascending truth and descending truth. Scharp applies the resultant theory, AD semantics, to the liar sentence, thereby obtaining a novel solution to the liar paradox. The aim of the present paper is fourfold. First, I show that, contrary to Scharp’s claims, AD semantics in fact yields an (...)
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  34. Scharp on Inconsistent Concepts and Their Engineered Replacements, Or: Can We Mend These Broken Things?Mark Pinder - forthcoming - Tandf: Inquiry:1-22.
    Kevin Scharp’s influential work on the alethic paradoxes combines an extensively developed inconsistency theory with a substantial conceptual engineering project. I argue that Scharp’s inconsistency theory is in tension with his conceptual engineering project: the inconsistency theory includes an account of concepts that implies that the conceptual engineering project will fail. I recommend that Scharp revises his account of concepts, and show how doing so allows him to resolve the tension. The discussion is important for ongoing work on conceptual engineering. (...)
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  35. Precis: the world philosophy made.Scott Soames - forthcoming - Philosophical Studies:1-5.
    Understanding Truth aims to illuminate the notion of truth, and the role it plays in our ordinary thought, as well as in our logical, philosophical, and scientific theories. Part one is concerned with substantive background issues: the identification of the bearers of truth, the basis for distinguishing truth from other notions, like certainty, with which it is often confused, and the formulation of positive responses to well-known forms of philosophical skepticism about truth. Part two explicates the formal theories of Alfred (...)
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  36. Classical Logic and the Liar.Yannis Stephanou - forthcoming - Logic and Logical Philosophy:1.
    The liar and kindred paradoxes show that we can derive contradictions when we reason in accordance with classical logic from the schema (T) about truth: S is true iff p, where ‘p’ is to be replaced with a sentence and ‘S’ with a name of that sentence. The paper presents two arguments to the effect that the blame lies not with (T) but with classical logic. The arguments derive contradictions using classical logic, but instead of appealing to (T), they invoke (...)
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  37. Review of Wright & Pedersen (Eds.), New Waves in Truth. [REVIEW]Andreas Stokke - forthcoming - Notre Dame Philosophical Reviews.
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  38. The Consistency of a Certain Medieval-Like Solution to the Liar Paradox. Proof Given by Bolesław Sobociński.Kordula Świętorzecka - forthcoming - History and Philosophy of Logic:1-9.
    In Formale Logik, published in 1956, J. M. Bocheński presented his first proposal for the solution to the liar paradox, which he related to Paul of Venice's argumentation from Logica Magna. A forma...
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  39. Proof-Theoretic Semantics, Paradoxes and the Distinction Between Sense and Denotation.Luca Tranchini - forthcoming - Journal of Logic and Computation 2014.
    In this paper we show how Dummett-Prawitz-style proof-theoretic semantics has to be modified in order to cope with paradoxical phenomena. It will turn out that one of its basic tenets has to be given up, namely the definition of the correctness of an inference as validity preservation. As a result, the notions of an argument being valid and of an argument being constituted by correct inference rules will no more coincide. The gap between the two notions is accounted for by (...)
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  40. Truth, Hierarchy and Incoherence.Bruno Whittle - forthcoming - In Bradley Armour-Garb (ed.), Reflections on the Liar. Oxford University Press.
    Approaches to truth and the Liar paradox seem invariably to face a dilemma: either appeal to some sort of hierarchy, or declare apparently perfectly coherent concepts incoherent. But since both options lead to severe expressive restrictions, neither seems satisfactory. The aim of this paper is a new approach, which avoids the dilemma and the resulting expressive restrictions. Previous approaches tend to appeal to some new sort of semantic value for the truth predicate to take. I argue that such approaches inevitably (...)
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  41. Exceptional Logic.Bruno Whittle - forthcoming - Review of Symbolic Logic:1-37.
    The aim of the paper is to argue that all—or almost all—logical rules have exceptions. In particular, it is argued that this is a moral that we should draw from the semantic paradoxes. The idea that we should respond to the paradoxes by revising logic in some way is familiar. But previous proposals advocate the replacement of classical logic with some alternative logic. That is, some alternative system of rules, where it is taken for granted that these hold without exception. (...)
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  42. Review of Nuel Belnap, Michael Perloff, and Ming Xu's Facing the Future. [REVIEW]S. Wölfl - forthcoming - Notre Dame Philosophical Reviews.
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  43. Abharī’s Solution to the Liar Paradox: A Logical Analysis.Mohammad Saleh Zarepour - forthcoming - Tandf: History and Philosophy of Logic:1-16.
  44. Inferential Role and the Ideal of Deductive Logic.Thomas Hofweber - unknown - The Baltic International Yearbook of Cognition, Logic and Communication 5.
    Although there is a prima facie strong case for a close connection between the meaning and inferential role of certain expressions, this connection seems seriously threatened by the semantic and logical paradoxes which rely on these inferential roles. Some philosophers have drawn radical conclusions from the paradoxes for the theory of meaning in general, and for which sentences in our language are true. I criticize these overreactions, and instead propose to distinguish two conceptions of inferential role. This distinction is closely (...)
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  45. Machine-Believers Learning Faiths & Knowledges: The New Gospel of Artificial Intelligence.Virgil W. Brower - 2021 - Internationales Jahrbuch Für Medienphilosophie 7 (1):97-121.
    One is occasionally reminded of Foucault's proclamation in a 1970 interview that "perhaps, one day this century will be known as Deleuzian." Less often is one compelled to update and restart with a supplementary counter-proclamation of the mathematician, David Lindley: "the twenty-first century would be a Bayesian era..." The verb tenses of both are conspicuous. // To critically attend to what is today often feared and demonized, but also revered, deployed, and commonly referred to as algorithm(s), one cannot avoid the (...)
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  46. Taylor Swift's Liar Paradox.Theresa Helke - 2021 - Philosophy Now 145:34-37.
    With the help of renowned logician Taylor Swift, Theresa Helke introduces four fundamental paradoxes: the Liar, Epimenides’, the Truth-Teller, and the No-No.
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  47. Limits of Abductivism About Logic.Ulf Hlobil - 2021 - Philosophy and Phenomenological Research 103 (2):320-340.
    I argue against abductivism about logic, which is the view that rational theory choice in logic happens by abduction. Abduction cannot serve as a neutral arbiter in many foundational disputes in logic because, in order to use abduction, one must first identify the relevant data. Which data one deems relevant depends on what I call one's conception of logic. One's conception of logic is, however, not independent of one's views regarding many of the foundational disputes that one may hope to (...)
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  48. Menzogna o verità? Il rovescio della medaglia.Giorgio Marchetti & Pier Celeste Marchetti - 2021 - 02100 Rieti RI, Italia: PlaceBook Publishing.
    Per quanto la disprezziamo e condanniamo, la menzogna accompagna da sempre e inevitabilmente la nostra vita. Mentiamo sin da bambini e continuiamo a mentire da adulti. Mentiamo a tutti, alle persone più care come agli sconosciuti e ancor di più ai nostri nemici. Mentiamo persino a noi stessi. Mentiamo in mille modi: quando raccontiamo una bugia, quando illudiamo noi stessi e gli altri, quando truffiamo, imbrogliamo e fingiamo. Mentiamo a parole e gesti. Mentiamo per far del male ma anche a (...)
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  49. The Intoxicating Effects of Conciliatory Omniscience.David McElhoes - 2021 - Philosophical Studies 178 (7):2151-2167.
    The coherence of omniscience is sometimes challenged using self-referential sentences like, “No omniscient entity knows that which this very sentence expresses,” which suggest that there are truths which no omniscient entity knows. In this paper, I consider two strategies for addressing these challenges: The Common Strategy, which dismisses such self-referential sentences as meaningless, and The Conciliatory Strategy, which discounts them as quirky outliers with no impact on one’s status as being omniscient. I argue that neither strategy succeeds. The Common Strategy (...)
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  50. Fix, Express, Quantify: Disquotation After Its Logic.Carlo Nicolai - 2021 - Mind 130 (519):727-757.
    Truth-theoretic deflationism holds that truth is simple, and yet that it can fulfil many useful logico-linguistic roles. Deflationism focuses on axioms for truth: there is no reduction of the notion of truth to more fundamental ones such as sets or higher-order quantifiers. In this paper I argue that the fundamental properties of reasonable, primitive truth predicates are at odds with the core tenets of classical truth-theoretic deflationism that I call fix, express, and quantify. Truth may be regarded as a broadly (...)
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