Results for 'Banach-Tarski Paradox'

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  1. The Banach-Tarski Paradox.Ulrich Meyer - 2023 - Logique Et Analyse 261:41–53.
    Emile Borel regards the Banach-Tarski Paradox as a reductio ad absurdum of the Axiom of Choice. Peter Forrest instead blames the assumption that physical space has a similar structure as the real numbers. This paper argues that Banach and Tarski's result is not paradoxical and that it merely illustrates a surprising feature of the continuum: dividing a spatial region into disjoint pieces need not preserve volume.
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  2.  71
    Regular probability comparisons imply the BanachTarski Paradox.Alexander R. Pruss - 2014 - Synthese 191 (15):3525-3540.
    Consider the regularity thesis that each possible event has non-zero probability. Hájek challenges this in two ways: there can be nonmeasurable events that have no probability at all and on a large enough sample space, some probabilities will have to be zero. But arguments for the existence of nonmeasurable events depend on the axiom of choice. We shall show that the existence of anything like regular probabilities is by itself enough to imply a weak version of AC sufficient to prove (...)
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  3. A Continuous Movement Version Of The Banachtarski Paradox: A Solution To De Groot's Problem.Trevor M. Wilson - 2005 - Journal of Symbolic Logic 70 (3):946-952.
    In 1924 Banach and Tarski demonstrated the existence of a paradoxical decomposition of the 3-ball B, i.e., a piecewise isometry from B onto two copies of B. This article answers a question of de Groot from 1958 by showing that there is a paradoxical decomposition of B in which the pieces move continuously while remaining disjoint to yield two copies of B. More generally, we show that if n ≥ 2, any two bounded sets in.
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  4. Kant en Keus, Antinomie en Axioma: Een Ontogenese van de Paradox van Banach & Tarski.Thekla Teunis & Fa Muller - 2010 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 102 (2):81-104.
     
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  5. Tarski.Benedict Eastaugh - 2017 - In Alex Malpass & Marianna Antonutti Marfori, The History of Philosophical and Formal Logic: From Aristotle to Tarski. New York: Bloomsbury Publishing. pp. 293-313.
    Alfred Tarski was one of the greatest logicians of the twentieth century. His influence comes not merely through his own work but from the legion of students who pursued his projects, both in Poland and Berkeley. This chapter focuses on three key areas of Tarski's research, beginning with his groundbreaking studies of the concept of truth. Tarski's work led to the creation of the area of mathematical logic known as model theory and prefigured semantic approaches in the (...)
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  6. Symmetry, Invariance, and Imprecise Probability.Zachary Goodsell & Jacob M. Nebel - forthcoming - Mind.
    It is tempting to think that a process of choosing a point at random from the surface of a sphere can be probabilistically symmetric, in the sense that any two regions of the sphere which differ by a rotation are equally likely to include the chosen point. Isaacs, Hájek, and Hawthorne (2022) argue from such symmetry principles and the mathematical paradoxes of measure to the existence of imprecise chances and the rationality of imprecise credences. Williamson (2007) has argued from a (...)
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  7. A Defense of Platonic Realism In Mathematics: Problems About The Axiom Of Choice.Wataru Asanuma - unknown
    The conflict between Platonic realism and Constructivism marks a watershed in philosophy of mathematics. Among other things, the controversy over the Axiom of Choice is typical of the conflict. Platonists accept the Axiom of Choice, which allows a set consisting of the members resulting from infinitely many arbitrary choices, while Constructivists reject the Axiom of Choice and confine themselves to sets consisting of effectively specifiable members. Indeed there are seemingly unpleasant consequences of the Axiom of Choice. The non-constructive nature of (...)
     
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  8.  25
    Open sets satisfying systems of congruences.Randall Dougherty - 2001 - Journal of Mathematical Logic 1 (2):247-303.
    A famous result of Hausdorff states that a sphere with countably many points removed can be partitioned into three pieces A, B, C such that A is congruent to B, B is congruent to C, and A is congruent to B ∪ C; this result was the precursor of the BanachTarski paradox. Later, R. Robinson characterized the systems of congruences like this which could be realized by partitions of the sphere with rotations witnessing the congruences. The pieces (...)
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  9.  21
    Solutions to congruences using sets with the property of baire.Randall Dougherty - 2001 - Journal of Mathematical Logic 1 (2):221-245.
    Hausdorff's paradoxical decomposition of a sphere with countably many points removed actually produced a partition of this set into three pieces A,B,C such that A is congruent to B, B is congruent to C, and A is congruent to B ∪ C. While refining the BanachTarski paradox, R. Robinson characterized the systems of congruences like this which could be realized by partitions of the sphere with rotations witnessing the congruences: the only nontrivial restriction is that the system (...)
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  10.  20
    Information-devoid routes for scale-free neurodynamics.Arturo Tozzi & James F. Peters - 2020 - Synthese 199 (1-2):2491-2504.
    Neuroscientists are able to detect physical changes in information entropy in the available neurodata. However, the information paradigm is inadequate to describe fully nervous dynamics and mental activities such as perception. This paper suggests explanations to neural dynamics that provide an alternative to thermodynamic and information accounts. We recall the BanachTarski paradox, which informally states that when pieces of a ball are moved and rotated without changing their shape, a synergy between two balls of the same volume (...)
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  11. Sur la décomposition des ensembles de points en parties respectivement congruentes.Stefan Banach & Alfred Tarski - 1924 - Fundamenta Mathematicae 6:244-277.
    Sur la décomposition des ensembles de points en parties respectivement congruentes.
     
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  12.  81
    Popper Functions, Uniform Distributions and Infinite Sequences of Heads.Alexander R. Pruss - 2015 - Journal of Philosophical Logic 44 (3):259-271.
    Popper functions allow one to take conditional probabilities as primitive instead of deriving them from unconditional probabilities via the ratio formula P=P/P. A major advantage of this approach is it allows one to condition on events of zero probability. I will show that under plausible symmetry conditions, Popper functions often fail to do what they were supposed to do. For instance, suppose we want to define the Popper function for an isometrically invariant case in two dimensions and hence require the (...)
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  13.  67
    Tarski's theorem and liar-like paradoxes.Ming Hsiung - 2014 - Logic Journal of the IGPL 22 (1):24-38.
    Tarski's theorem essentially says that the Liar paradox is paradoxical in the minimal reflexive frame. We generalise this result to the Liar-like paradox $\lambda^\alpha$ for all ordinal $\alpha\geq 1$. The main result is that for any positive integer $n = 2^i(2j+1)$, the paradox $\lambda^n$ is paradoxical in a frame iff this frame contains at least a cycle the depth of which is not divisible by $2^{i+1}$; and for any ordinal $\alpha \geq \omega$, the paradox $\lambda^\alpha$ (...)
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  14. The nature and role of intuition in mathematical epistemology.Paul Thompson - 1998 - Philosophia 26 (3-4):279-319.
    Great intuitions are fundamental to conjecture and discovery in mathematics. In this paper, we investigate the role that intuition plays in mathematical thinking. We review key events in the history of mathematics where paradoxes have emerged from mathematicians' most intuitive concepts and convictions, and where the resulting difficulties led to heated controversies and debates. Examples are drawn from Riemannian geometry, set theory and the analytic theory of the continuum, and include the Continuum Hypothesis, the Tarski-Banach Paradox, and (...)
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  15.  94
    Review: Stan Wagon, The Branch-Tarski Paradox; Stan Wagon, The Branch-Tarski Paradox[REVIEW]Matthew Foreman - 1995 - Journal of Symbolic Logic 60 (2):698-698.
  16. Tarski, Frege and the Liar Paradox.Sloman Aaron - 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 (...)
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  17.  56
    A new defense of Tarski's solution to the liar paradox.Gila Sher - 2022 - Philosophical Studies 180 (5-6):1441-1466.
    Tarski's hierarchical solution to the Liar paradox is widely viewed as ad hoc. In this paper I show that, on the contrary, Tarski's solution is justified by a sound philosophical principle that concerns the inner structure of truth. This principle provides a common philosophical basis to a number of solutions to the Liar paradox, including Tarski's and Kripke's. Tarski himself may not have been aware of this principle, but by providing a philosophical basis to (...)
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  18. Tarski on the Concept of Truth.Greg Ray - 2018 - In Michael Glanzberg, The Oxford Handbook of Truth. Oxford, United Kingdom: Oxford University Press. pp. 695-717.
    Alfred Tarski’s work on truth has played such a central role in the discourse on truth that most coming to it for the first time have probably already heard a great deal about what is said there. Unfortunately, since the work is largely technical and Tarski was only tan- gentially philosophical, a certain incautious assimilation dominates many philosophical discussions of Tarski’s ideas, and so, examining Tarski on the concept of truth is in many ways an act (...)
     
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  19. Tarski's Grelling and the T-Strategy.Greg Ray - 2006 - In Bryson Brown, Truth and Probability: Essays in Honour of Hugues Leblanc. College Publications.
    Tarski's argumentative use of the liar paradox is well-known, but officially it is the Grelling paradox that has final pride of place in Tarski's argument, not the Liar at all. Tarski explicitly gives argumentation that adverts to the liar argument, but it is an alternative argument—one he only hints at and which adverts to the Grelling—which he says has the advantage of removing any empirical element. In this paper, we will examine how the Grelling might (...)
     
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  20. A Vindication of Tarski's Claim About the Liar Paradox.Matti Eklund - 1998 - In TImothy Childers, The Logica Yearbook. Acadamy of Sciences of the Czech Republic.
  21.  11
    Truth, the Liar, and Tarski's Semantics.Gila Sher - 2002 - In Dale Jacquette, A Companion to Philosophical Logic. Malden, MA, USA: Wiley-Blackwell. pp. 143–163.
    This chapter contains sections titled: Tarski's Theory of Truth Tarski's Solution to the Liar Paradox Tarski's Method of Defining Truth for Formalized Languages Tarskian Semantics Three Criticisms of Tarski's Theory Kripke's Solution to the Liar Paradox A Reinterpretation of Tarski's Theory Truth Beyond Logic.
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  22. A minimalist critique of Tarski on truth.Paul Horwich - 2005 - In J. C. Beall & Bradley P. Armour-Garb, Deflation and Paradox. New York: Oxford University Press.
    This chapter contrasts Alfred Tarski's compositional conception (whereby the truth-values of sentences are explained in terms of the referential characteristics of their component words) unfavorably with minimalism (which relies merely on the schema, ‘(p) is true ↔ p’). First, it argues against Tarski that his approach is: (i) misdirected, insofar as it doesn't elucidate our actual concept of truth, which applies to propositions rather than sentences; (ii) ill-motivated, insofar as it reflects an insistence on explicit definitions; (iii) not (...)
     
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  23. Tarski on the Necessity Reading of Convention T.Douglas Eden Patterson - 2006 - Synthese 151 (1):1-32.
    Tarski’s Convention T is often taken to claim that it is both sufficient and necessary for adequacy in a definition of truth that it imply instances of the T-schema where the embedded sentence translates the mentioned sentence. However, arguments against the necessity claim have recently appeared, and, furthermore, the necessity claim is actually not required for the indefinability results for which Tarski is justly famous; indeed, Tarski’s own presentation of the results in the later Undecidable Theories makes (...)
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  24.  33
    Alfred Tarski: philosophy of language and logic.Douglas Patterson - 2012 - New York: Palgrave-Macmillan.
    This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence.
  25.  50
    Paradoxes and Pragmatics.Hartley Slater - 2008 - Proceedings of the Xxii World Congress of Philosophy 13:87-104.
    Tarski’s assessment that natural language is inconsistent on account of the Liar Paradox is shown to be incorrect: what Tarski’s theorem in fact shows is that Truth is not a property of sentences but of propositions. By using propositions rather than sentences as the bearers of Truth, semantic closure within the same language is easily obtained. Tarski’s contrary assessment was partly based on confusions about propositions and their grammatical expression. But more centrally it arose through blindness (...)
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  26. Gödel, Tarski, Church, and the Liar.György Serény - 2003 - Bulletin of Symbolic Logic 9 (1):3-25.
    The fact that Gödel's famous incompleteness theorem and the archetype of all logical paradoxes, that of the Liar, are related closely is, of course, not only well known, but is a part of the common knowledge of the community of logicians. Indeed, almost every more or less formal treatment of the theorem makes a reference to this connection. Gödel himself remarked in the paper announcing his celebrated result :The analogy between this result and Richard's antinomy leaps to the eye;there is (...)
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  27. The pinocchio paradox.Peter Eldridge-Smith & Veronique Eldridge-Smith - 2010 - Analysis 70 (2):212-215.
    The Pinocchio paradox, devised by Veronique Eldridge-Smith in February 2001, is a counter-example to solutions to the Liar that restrict the use or definition of semantic predicates. Pinocchio’s nose grows if and only if what he is stating is false, and Pinocchio says ‘My nose is growing’. In this statement, ‘is growing’ has its normal meaning and is not a semantic predicate. If Pinocchio’s nose is growing it is because he is saying something false; otherwise, it is not growing. (...)
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  28.  25
    Semantic Singularities: Paradoxes of Reference, Predication, and Truth.Keith Simmons - 2018 - Oxford, England: Oxford University Press.
    This book aims to provide a solution to the semantic paradoxes. It argues for a unified solution to the paradoxes generated by our concepts of denotation, predicate extension, and truth. The solution makes two main claims. The first is that our semantic expressions 'denotes', 'extension' and 'true' are context-sensitive. The second, inspired by a brief, tantalizing remark of Godel's, is that these expressions are significant everywhere except for certain singularities, in analogy with division by zero. A formal theory of singularities (...)
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  29. Lesniewski's Early Liar, Tarski and Natural Language.Arianna Betti - 2004 - Annals of Pure and Applied Logic 127 (1-3):267-287.
    This paper is a contribution to the reconstruction of Tarski’s semantic background in the light of the ideas of his master, Stanislaw Lesniewski. Although in his 1933 monograph Tarski credits Lesniewski with crucial negative results on the semantics of natural language, the conceptual relationship between the two logicians has never been investigated in a thorough manner. This paper shows that it was not Tarski, but Lesniewski who first avowed the impossibility of giving a satisfactory theory of truth (...)
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  30. Truth, correspondence, models, and Tarski.Panu Raatikainen - 2007 - In Sami Pihlström, Panu Raatikainen & Matti Sintonen, Approaching truth: essays in honour of Ilkka Niiniluoto. London: College Publications. pp. 99-112.
    In the early 20th century, scepticism was common among philosophers about the very meaningfulness of the notion of truth – and of the related notions of denotation, definition etc. (i.e., what Tarski called semantical concepts). Awareness was growing of the various logical paradoxes and anomalies arising from these concepts. In addition, more philosophical reasons were being given for this aversion.1 The atmosphere changed dramatically with Alfred Tarski’s path-breaking contribution. What Tarski did was to show that, assuming that (...)
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  31.  23
    Logical paradoxes solution in semantically closed language.Vsevolod Ladov - 2017 - Epistemology and Philosophy of Science 52 (2):104-119.
    The author considers following question: is a consistent semantically closed language possible? The negative answer is the orthodox answer in the logic of the 20th century. It was presented in Russell's theory of types and Tarski's semantic theory of metalanguages. Nevertheless, contemporary logicians and philosophers of language return to this problem time and again, pointing to its relevance in various aspects. In particular, it is asserted that semantically closed language is a very important tool for expressing logical and philosophical (...)
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  32.  99
    Reference, paradoxes and truth.Michał Walicki - 2009 - Synthese 171 (1):195 - 226.
    We introduce a variant of pointer structures with denotational semantics and show its equivalence to systems of boolean equations: both have the same solutions. Taking paradoxes to be statements represented by systems of equations (or pointer structures) having no solutions, we thus obtain two alternative means of deciding paradoxical character of statements, one of which is the standard theory of solving boolean equations. To analyze more adequately statements involving semantic predicates, we extend propositional logic with the assertion operator and give (...)
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  33. Circularity or Lacunae in Tarski’s Truth-Schemata.Dale Jacquette - 2010 - Journal of Logic, Language and Information 19 (3):315-326.
    Tarski avoids the liar paradox by relativizing truth and falsehood to particular languages and forbidding the predication to sentences in a language of truth or falsehood by any sentences belonging to the same language. The Tarski truth-schemata stratify an object-language and indefinitely ascending hierarchy of meta-languages in which the truth or falsehood of sentences in a language can only be asserted or denied in a higher-order meta-language. However, Tarski’s statement of the truth-schemata themselves involve general truth (...)
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  34. Liar-Like Paradoxes and Metalanguage Features.Klaus Ladstaetter - 2013 - Southwest Philosophy Review 29 (1):61-70.
    In their (2008) article Liar-Like Paradox and Object Language Features C.S. Jenkins and Daniel Nolan (henceforth, JN) argue that it is possible to construct Liar-like paradox in a metalanguage even though its object language is not semantically closed. I do not take issue with this claim. I find fault though with the following points contained in JN’s article: First, that it is possible to construct Liar-like paradox in a metalanguage, even though this metalanguage is not semantically closed. (...)
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  35.  33
    Francesca Rivetti Barbò. L'antinomia del mentitore nel pensiero contemporaneo, da Peirce a Tarski. Studi - testi - bibliografia. Pubblicazioni dell'Università Cattolica del Sacro Cuore, serie terza, scienze filosofiche, 5. Vita e Pensiero, Milano1961, XLIII + 744 pp. - Charles Sanders Peirce. Ristampa di un brano da 283, con versione italiana a fronte. Ivi, pp. 334–339. - Charles Sanders Peirce. Ristampa di un breve commento da Collected papers 2.352, con versione italiana a fronte. Ivi, pp. 338, 339. - Charles Sanders Peirce. Ristampa di un brano di The regenerated logic , con versione italiana a fronte. Ivi, pp. 338–341. - Charles Sanders Peirce. Insolubilia. Ristampa di 2813, con versione italiana a fronte. Ivi, pp. 340–343. - Ernst Schröder. Ristampa di un brano di 4210, con versione italiana a fronte. Ivi, pp. 342–345. - Bertrand Russell. Les paradoxes de la logique. Ristampa di brani di 11114, con versione italiana a fronte. Ivi, pp. 346–353. - Bertrand Russell. Mathematical logi. [REVIEW]Amedeo G. Conte - 1966 - Journal of Symbolic Logic 31 (2):283-284.
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  36.  55
    The paradox of belief instability and a revision theory of belief.Byeong D. Lee - 1998 - Pacific Philosophical Quarterly 79 (4):314-328.
    The epistemic paradox of 'belief instability' has recently received notable attention from many philosophers. Understanding this paradox is very important because belief is a central notion of psychologically motivated semantic theories in philosophy, linguistics, and cognitive science, and this paradox poses serious problems for these theories. In this dissertation I criticize previous proposals and offer a new proposal, which I call a 'revision theory of belief'. ;My revision theory of belief is in many respects an application of (...)
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  37. There is No Paradox of Logical Validity.Roy T. Cook - 2014 - Logica Universalis 8 (3-4):447-467.
    A number of authors have argued that Peano Arithmetic supplemented with a logical validity predicate is inconsistent in much the same manner as is PA supplemented with an unrestricted truth predicate. In this paper I show that, on the contrary, there is no genuine paradox of logical validity—a completely general logical validity predicate can be coherently added to PA, and the resulting system is consistent. In addition, this observation lead to a number of novel, and important, insights into the (...)
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  38.  24
    The paradox of belief instability and a revision theory of belief.Byeong D. Lee - 1998 - Dissertation, Indiana University, Bloomington
    The epistemic paradox of 'belief instability' has recently received notable attention from many philosophers. Understanding this paradox is very important because belief is a central notion of psychologically motivated semantic theories in philosophy, linguistics, and cognitive science, and this paradox poses serious problems for these theories. In this dissertation I criticize previous proposals and offer a new proposal, which I call a 'revision theory of belief'. -/- My revision theory of belief is in many respects an application (...)
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  39.  53
    An Update of Tarski: Two Usages of the Word “True”.Zhen Zhao - 2022 - Journal of Logic, Language and Information 31 (3):505-523.
    This paper is based on Tarski’s theory of truth. The purpose of this paper is to solve the liar paradox (and its cousins) and keep both of the deductive power of classical logic and the expressive power of the word “true” in natural language. The key of this paper lies in the distinction between the predicate usage and the operator usage of the word “true”. The truth operator is primarily used for characterizing the semantics of the language. Then, (...)
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  40.  72
    Reasoning from paradox.Laureano Luna - 2011 - The Reasoner 5 (2):22-23.
    Godel's and Tarski's theorems were inspired by paradoxes: the Richard paradox, the Liar. Godel, in the 1951 Gibbs lecture argued from his metatheoretical results for a metaphysical claim: the impossibility of reducing, both, mathematics to the knowable by the human mind and the human mind to a finite machine (e.g. the brain). So Godel reasoned indirectly from paradoxes for metaphysical theses. I present four metaphysical theses concerning mechanism, reductive physicalism and time for the only purpose of suggesting how (...)
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  41.  74
    Paradoxes of validity.Keith Simmons - 2021 - Philosophical Studies 179 (2):383-403.
    Consider the following argument written on the board in room 227: 1 = 1. So, the argument on the board in room 227 is not valid. This argument generates a paradox. The aim of this paper is to present a resolution of this paradox and related paradoxes of validity, including a version of the Curry paradox. The proposal stresses the close connections between these validity paradoxes and paradoxes of truth and paradoxes of denotation. So a more general (...)
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  42. Liar-like paradox and object language features.C. S. Jenkins & Daniel Nolan - 2008 - American Philosophical Quarterly 45 (1):67 - 73.
    We argue that it would seem to be a mistake to blame Liar-like paradox on certain features of the object language, since the effect can be created with very minimal object languages that contain none of the usual suspects (truth-like predicates, reference to their own truth-bearers, negation, etc.).
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  43. Paradoxes of Demonstrability.Sten Lindström - 2009 - In Lars-Göran Johansson, Jan Österberg & Rysiek Śliwiński, Logic, Ethics and All That Jazz: Essays in Honour of Jordan Howard Sobel. Uppsala: Dept. Of Philosophy, Uppsala University. pp. 177-185.
    In this paper I consider two paradoxes that arise in connection with the concept of demonstrability, or absolute provability. I assume—for the sake of the argument—that there is an intuitive notion of demonstrability, which should not be conflated with the concept of formal deducibility in a (formal) system or the relativized concept of provability from certain axioms. Demonstrability is an epistemic concept: the rough idea is that a sentence is demonstrable if it is provable from knowable basic (“self-evident”) premises by (...)
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  44. Paradoxes and the Foundations of Semantics and Metaphysics.Matti Eklund - 2000 - Dissertation, Massachusetts Institute of Technology
    Numerous philosophical problems, otherwise quite different in character, are of the following form. Certain claims which seem not only obviously true, but even constitutive of the meanings of the expressions employed, can be shown to lead to absurdity when taken together. All such problems can justly be called paradoxes. The paradoxes I examine are the liar paradox, the sorites paradox, and the personal identity paradox posed by the fission problem. ;I argue that in these cases, the claims (...)
     
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  45.  55
    From Paradoxicality to Paradox.Ming Hsiung - 2024 - Erkenntnis 89 (7):2545-2569.
    In various theories of truth, people have set forth many definitions to clarify in what sense a set of sentences is paradoxical. But what, exactly, is _a_ paradox per se? It has not yet been realized that there is a gap between ‘being paradoxical’ and ‘being a paradox’. This paper proposes that a paradox is a minimally paradoxical set meeting some closure property. Along this line of thought, we give five tentative definitions based upon the folk notion (...)
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  46.  74
    Two Fallacies in Proofs of the Liar Paradox.Peter Eldridge-Smith - 2020 - Philosophia 48 (3):947-966.
    At some step in proving the Liar Paradox in natural language, a sentence is derived that seems overdetermined with respect to its semantic value. This is complemented by Tarski’s Theorem that a formal language cannot consistently contain a naive truth predicate given the laws of logic used in proving the Liar paradox. I argue that proofs of the Eubulidean Liar either use a principle of truth with non-canonical names in a fallacious way or make a fallacious use (...)
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  47. Liar paradox.Bradley Dowden - 2001 - Internet Encyclopedia of Philosophy.
    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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  48.  41
    The Liar Paradox and Methods for its Solution.A. I. Uemov - 1977 - Russian Studies in Philosophy 15 (4):92-106.
    There is no need to prove the significance to philosophy of the famous liar paradox. Attempts to solve it have not ceased over the course of many centuries, from hoary antiquity to our own day. The failure of attempts undertaken within the bounds of everyday, natural languages has led many philosophers, particularly of the positivist trend, to pessimistic conclusions with respect to the potentials of such languages. This is very clearly evident, for example, in the statement of A. (...), who writes: "The liar paradox made its first appearance in our discussions as a kind of evil force possessed of great destructive energy. It compels us to reject all attempts to explicate the notion of truth for natural languages and to confine ourselves to the formalized languages of scientific reasoning." Tarski's viewpoint has been repeatedly criticized. We should prefer not to cast doubt on the significance of that highly valuable criticism. However, we cannot fail to observe that Tarski's notion retains its force so long as its basic argument - the insolubility of the liar paradox within the confines of natural languages - remains standing. (shrink)
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  49. Lies, half-truths, and falsehoods about Tarski’s 1933 “liar” antinomies.John Corcoran & Joaquin Miller - 2012 - Bulletin of Symbolic Logic 18 (1):140-141.
    We discuss misinformation about “the liar antinomy” with special reference to Tarski’s 1933 truth-definition paper [1]. Lies are speech-acts, not merely sentences or propositions. Roughly, lies are statements of propositions not believed by their speakers. Speakers who state their false beliefs are often not lying. And speakers who state true propositions that they don’t believe are often lying—regardless of whether the non-belief is disbelief. Persons who state propositions on which they have no opinion are lying as much as those (...)
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  50.  25
    Anatomy of a Nonidentity Paradox.Dale Jacquette - 2016 - South American Journal of Logic 2 (1):119-125.
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