Results for 'logic of paradox'

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  1.  9
    " To be an object" means" to have properties." Thus, any object has at least one property. A good formalization of this simple conclusion is a thesis of second-order logic:(1) Vx3P (Px) This formalization is based on two assumptions:(a) object variables. [REVIEW]Russell'S. Paradox - 2006 - In J. Jadacki & J. Pasniczek (eds.), The Lvov-Warsaw School: The New Generation. Reidel. pp. 6--129.
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  2. The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
  3. Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219-241.
  4. Logic of paradox revisited.Graham Priest - 1984 - Journal of Philosophical Logic 13 (2):153 - 179.
  5.  62
    Second-Order Logic of Paradox.Allen P. Hazen & Francis Jeffry Pelletier - 2018 - Notre Dame Journal of Formal Logic 59 (4):547-558.
    The logic of paradox, LP, is a first-order, three-valued logic that has been advocated by Graham Priest as an appropriate way to represent the possibility of acceptable contradictory statements. Second-order LP is that logic augmented with quantification over predicates. As with classical second-order logic, there are different ways to give the semantic interpretation of sentences of the logic. The different ways give rise to different logical advantages and disadvantages, and we canvass several of these, (...)
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  6.  45
    On Priest's logic of paradox.Alexej P. Pynko - 1995 - Journal of Applied Non-Classical Logics 5 (2):219-225.
    The present paper concerns a technical study of PRIEST'S logic of paradox [Pri 79], We prove that this logic has no proper paraconsistent strengthening. It is also proved that the mentioned logic is the largest paraconsistent one satisfaying TARSKI'S conditions for the classical conjunction and disjunction together with DE MORGAN'S laws for negation. Finally, we obtain for the logic of paradox an algebraic completeness result related to Kleene lattices.
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  7. Logic of paradoxes in classical set theories.Boris Čulina - 2013 - Synthese 190 (3):525-547.
    According to Cantor (Mathematische Annalen 21:545–586, 1883 ; Cantor’s letter to Dedekind, 1899 ) a set is any multitude which can be thought of as one (“jedes Viele, welches sich als Eines denken läßt”) without contradiction—a consistent multitude. Other multitudes are inconsistent or paradoxical. Set theoretical paradoxes have common root—lack of understanding why some multitudes are not sets. Why some multitudes of objects of thought cannot themselves be objects of thought? Moreover, it is a logical truth that such multitudes do (...)
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  8. David J. Anderson and Edward N. Zalta/Frege, Boolos, and Logical Objects 1–26 Michael Glanzberg/A Contextual-Hierarchical Approach to Truth and the Liar Paradox 27–88 James Hawthorne/Three Models of Sequential Belief Updat. [REVIEW]Max A. Freund, A. Modal Sortal Logic, R. Logic, Luca Alberucci, Vincenzo Salipante & On Modal - 2004 - Journal of Philosophical Logic 33:639-640.
     
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  9.  32
    Reassurance for the logic of paradox.Marcel Crabbé - 2011 - Review of Symbolic Logic 4 (3):479-485.
    Counterexamples to reassurance relative to a relation between models of the logic of paradox are provided. Another relation, designed to fix the problem in logic without equality, is introduced and discussed in connection with the issue of classical recapture.
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  10.  12
    Expanding the Logic of Paradox with a Difference-Making Relevant Implication.Peter Verdée - 2019 - In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency. Cham, Switzerland: Springer Verlag. pp. 507-533.
    In this paper, we aim to devise a logic that can deal with both the paradoxes that motivate dialetheism and the paradoxes related to the irrelevance of material implication. We propose the semantics and the sequent calculus of a relevant logic inspired by difference-making accounts of causation and arguably true to Graham Priest’s Logic of Paradox \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {LP}$$\end{document}: a relevant logic that validates those and only those (...)
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  11.  51
    Trivial Dialetheism and the Logic of Paradox.Jean-Yves Beziau - 2016 - Logic and Logical Philosophy 25 (1):51-56.
    In this paper we explain that the paraconsistent logic LP promoted by Graham Priest can only be supported by trivial dialetheists, i.e., those who believe that all sentences are dialetheias.
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  12.  30
    On the Philosophical Logic of Paradox.V. S. Bibler - 1989 - Russian Studies in Philosophy 28 (1):6-32.
    In this article I should like briefly to ground two mutually determining propositions:1. The philosophical logic that has emerged in the twentieth century and that corresponds to contemporary culture is a logic of paradox.
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  13. The logic of legitimacy: Bootstrapping paradoxes of constitutional democracy.Christopher Zurn - 2010 - Legal Theory 16 (3):191-227.
    Many have claimed that legitimate constitutional democracy is either conceptually or practically impossible, given infinite regress paradoxes deriving from the requirement of simultaneously democratic and constitutional origins for legitimate government. This paper first critically investigates prominent conceptual and practical bootstrapping objections advanced by Barnett and Michelman. It then argues that the real conceptual root of such bootstrapping objections is not any specific substantive account of legitimacy makers, such as consent or democratic endorsement, but a particular conception of the logic (...)
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  14.  30
    Automated correspondence analysis for the binary extensions of the logic of paradox.Yaroslav Petrukhin & Vasily Shangin - 2017 - Review of Symbolic Logic 10 (4):756-781.
    B. Kooi and A. Tamminga present a correspondence analysis for extensions of G. Priest’s logic of paradox. Each unary or binary extension is characterizable by a special operator and analyzable via a sound and complete natural deduction system. The present paper develops a sound and complete proof searching technique for the binary extensions of the logic of paradox.
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  15.  6
    Back to the Logic of Paradox.Vladimir S. Bibler - 2021 - Russian Studies in Philosophy 58 (5):355-356.
    The author once again offers a definition of paradox that fundamentally differs from a Hegelian notion of contradiction. In a paradox, thought should logically identify and comprehend the mental re...
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  16. Completeness via correspondence for extensions of the logic of paradox.Barteld Kooi & Allard Tamminga - 2012 - Review of Symbolic Logic 5 (4):720-730.
    Taking our inspiration from modal correspondence theory, we present the idea of correspondence analysis for many-valued logics. As a benchmark case, we study truth-functional extensions of the Logic of Paradox (LP). First, we characterize each of the possible truth table entries for unary and binary operators that could be added to LP by an inference scheme. Second, we define a class of natural deduction systems on the basis of these characterizing inference schemes and a natural deduction system for (...)
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  17.  11
    Paradoxes versus Contradictions in Logic of Sentential Operators.Michał Walicki - forthcoming - Logic and Logical Philosophy:1-44.
    Classical logic, of first or higher order, is extended with sentential operators and quantifiers, interpreted substitutionally over unrestricted substitution class. Operators mark a single layered, consistent metalanguage. Self-reference, arising from substitutional quantification over sentences, allows to express paradoxes which, unlike contradictions, do not lead to explosion. Semantics of the resulting language, using semi-kernels of digraphs, is non-explosive yet two-valued and has classical semantics as a special case for clasically consistent theories. A complete reasoning is obtained by extending LK with (...)
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  18.  74
    A Note on Freedom from Detachment in the Logic of Paradox.Jc Beall, Thomas Forster & Jeremy Seligman - 2013 - Notre Dame Journal of Formal Logic 54 (1):15-20.
    We shed light on an old problem by showing that the logic LP cannot define a binary connective $\odot$ obeying detachment in the sense that every valuation satisfying $\varphi$ and $(\varphi\odot\psi)$ also satisfies $\psi$ , except trivially. We derive this as a corollary of a more general result concerning variable sharing.
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  19.  46
    Gentzen's cut-free calculus versus the logic of paradox.Alexej P. Pynko - 2010 - Bulletin of the Section of Logic 39 (1/2):35-42.
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  20.  35
    Cajetan of Thiene on the Logic of Paradox.Miroslav Hanke - 2016 - Studia Neoaristotelica 13 (1):71-95.
    In the first half of the fifteenth century, the Italian logician, natural philosopher, and doctor of medicine Cajetan of Thiene wrote a commentary on William Heytesbury’s Regulae solvendi sophismata, which later became a part of the printed edition of Heytesbury’s treatises. Several late fifteenth century reprints sustained its circulation and further influence. Following Heytesbury, Cajetan listed four alternative treatments of paradoxes, where the first three were formulated in general logico-semantic terms and the last one in terms of obligationes. The present (...)
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  21.  68
    Logic of Simpson paradox.Jacek Malinowski - 2005 - Logic and Logical Philosophy 14 (2):203-210.
    The main aim of this paper is to elucidate, from a logical point of view, the phenomenon of Simpson reversal — the paradox of a statistical reasoning. We define a binary relation of supporting in the following way: a sentence A supports a sentence B if and only if the probability of B is higher when A is true, than when A is false. It appears that a statistical argument occurring in Simpson paradox cannot be formalized by means (...)
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  22.  85
    The logic of Simpson’s paradox.Prasanta S. Bandyoapdhyay, Davin Nelson, Mark Greenwood, Gordon Brittan & Jesse Berwald - 2011 - Synthese 181 (2):185 - 208.
    There are three distinct questions associated with Simpson's paradox, (i) Why or in what sense is Simpson's paradox a paradox? (ii) What is the proper analysis of the paradox? (iii) How one should proceed when confronted with a typical case of the paradox? We propose a "formar" answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding Simpson's paradox. Our account contrasts sharply with Pearl's causal (and questionable) (...)
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  23.  63
    Logic of the preface paradox.Dale Jacquette - 2008 - Principia: An International Journal of Epistemology 12 (2):203-216.
    The preface paradox is the apparent pragmatic inconsistency that occurs when the author of a book declares in its preface that despite believing that it is highly probable that everything the book maintains is true it is also highly probable that the book contains at least some errors. The preface paradox has often been presented as an example of a logically inconsistent belief that it is nevertheless rational to accept, supporting the suggestion that rationality has nothing immediately to (...)
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  24.  31
    The logic of Simpson’s paradox.Prasanta S. Bandyoapdhyay, Davin Nelson, Mark Greenwood, Gordon Brittan & Jesse Berwald - 2011 - Synthese 181 (2):185-208.
    There are three distinct questions associated with Simpson’s paradox. Why or in what sense is Simpson’s paradox a paradox? What is the proper analysis of the paradox? How one should proceed when confronted with a typical case of the paradox? We propose a “formal” answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding Simpson’s paradox. Our account contrasts sharply with Pearl’s causal account of the first two (...)
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  25.  11
    The Mechanism of Paradox in the Structures of Logic, Mathematics, and Physics.Douglas C. Gill - 2023 - Open Journal of Philosophy 13 (2):155-170.
    This paper presents a model for the structure of universal frameworks in logic, mathematics, and physics that are closed to logical conclusion by the mechanism of paradox across a dualism of elements. The prohibition takes different forms defined by the framework of observation inherent to the structure. Forms include either prohibition to conclusion on the logical relationship of internal elements or prohibition to conclusion based on the existence of an element not included in the framework of a first (...)
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  26.  68
    Logic of the preface paradox.Dale Jacquette - 2008 - Principia 12 (2):203-216.
    http://dx.doi.org/10.5007/1808-1711.2008v12n2p203 The preface paradox is the apparent pragmatic inconsistency that occurs when the author of a book declares in its preface that despite believing that it is highly probable that everything the book maintains is true it is also highly probable that the book contains at least some errors. The preface paradox has often been presented as an example of a logically inconsistent belief that it is nevertheless rational to accept, supporting the suggestion that rationality has nothing immediately (...)
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  27. Rituals-from the principle of order to the logic of paradoxes-theoretical reference points.A. Piette - 1992 - Cahiers Internationaux de Sociologie 92:163-179.
  28.  8
    Introduction: Logics of transparency in late modernity: Paradoxes, mediation and governance.Mikkel Flyverbom, Lars Thøger Christensen & Hans Krause Hansen - 2015 - European Journal of Social Theory 18 (2):117-131.
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  29.  43
    The logic of relative modality and the paradoxes of deontic logic.John Bryant - 1980 - Notre Dame Journal of Formal Logic 21 (1):78-88.
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  30. The logic of permission and obligation in the framework of ALX3: how to avoid the paradoxes of deontic logic.Zhisheng Huang & Michael Masuch - 1997 - Logique Et Analyse 149:55-74.
  31. Epistemic Paradox and the Logic of Acceptance.Michael J. Shaffer - 2013 - Journal of Experimental and Theoretical Artificial Intelligence 25:337-353.
    Paradoxes have played an important role both in philosophy and in mathematics and paradox resolution is an important topic in both fields. Paradox resolution is deeply important because if such resolution cannot be achieved, we are threatened with the charge of debilitating irrationality. This is supposed to be the case for the following reason. Paradoxes consist of jointly contradictory sets of statements that are individually plausible or believable. These facts about paradoxes then give rise to a deeply troubling (...)
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  32.  11
    The Political Logic of Experience and the Paradox of Expression.Rajiv Kaushik - 2024 - Research in Phenomenology 54 (1):131-137.
  33.  38
    Kierkegaarad and the Paradoxical Logic of Worldly Faith.Ronald L. Hall - 1995 - Faith and Philosophy 12 (1):40-53.
    I argue here that Kierkegaardian faith is essentially, albeit paradoxically, worldly---that Kierkegaardian faith is a form of world-affirmation. A correlate of this claim is that faithlessness of any kind is ultimately a form of aesthetic resignation grounded in a deep seated world-alienation. The paradox of faith’s worldliness is found in the fact that, for Kierkegaard, faith both excludes and includes resignation in itself. I make sense of this paradox by appealing to Kierkegaard’s idea of “an annulled possibility,” and (...)
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  34.  31
    Focault, the Logic of Psychiatric Power, and Its Paradoxes.John Iliopoulos - 2012 - Philosophy, Psychiatry, and Psychology 19 (1):67-69.
  35. Skolem’s “paradox” as logic of ground: The mutual foundation of both proper and improper interpretations.Vasil Penchev - 2020 - Epistemology eJournal (Elsevier: SSRN) 13 (19):1-16.
    A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality. Its investigation needs philosophical (...)
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  36.  6
    A formalization of the Protagoras court paradox in a temporal logic of epistemic and normative reasons.Meghdad Ghari - 2024 - Artificial Intelligence and Law 32 (2):325-367.
    We combine linear temporal logic (with both past and future modalities) with a deontic version of justification logic to provide a framework for reasoning about time and epistemic and normative reasons. In addition to temporal modalities, the resulting logic contains two kinds of justification assertions: epistemic justification assertions and deontic justification assertions. The former presents justification for the agent’s knowledge and the latter gives reasons for why a proposition is obligatory. We present two kinds of semantics for (...)
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  37.  9
    The Logics Meta-Logic and Paradoxes of Nuclear Deterrence.Jonathan F. Galloway - 1989 - Social Philosophy Today 2:205-216.
  38. Explaining the Paradoxes of Logic – The Nub of the Matter and its Pragmatics.Dieter Wandschneider - 1993 - In PRAGMATIK, Vol. IV. Hamburg:
    [[[ (Here only the chapters 3 – 8, see *** ) First I argue that the prohibition of linguistic self-reference as a solution to the antinomy problem contains a pragmatic contradiction and is thus not only too restrictive, but just inconsistent (chap.1). Furthermore, the possibilities of non-restrictive strategies for antinomy avoidance are discussed, whereby the explicit inclusion of the – pragmatically presuposed – consistency requirement proves to be the optimal strategy (chap.2). ]]] The central question here is that about the (...)
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  39.  33
    The logics, meta-logic and paradoxes of nuclear deterrence.Jonathan F. Galloway - 1987 - Journal of Social Philosophy 18 (2):33-41.
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  40.  10
    Universal aspects of paradoxical logic in Nishida Kitaro’s philosophy.Agnieszka Kozyra - 2004 - Rocznik Orientalistyczny 57 (1).
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  41.  17
    A formalization of the Protagoras court paradox in a temporal logic of epistemic and normative reasons.Meghdad Ghari - 2023 - Artificial Intelligence and Law 31:1-43.
    We combine linear temporal logic (with both past and future modalities) with a deontic version of justification logic to provide a framework for reasoning about time and epistemic and normative reasons. In addition to temporal modalities, the resulting logic contains two kinds of justification assertions: epistemic justification assertions and deontic justification assertions. The former presents justification for the agent’s knowledge and the latter gives reasons for why a proposition is obligatory. We present two kinds of semantics for (...)
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  42.  28
    The paradoxical logic of Europe in turkey: Where does Europe end?Banu Helvaçioğlu - 1999 - The European Legacy 4 (3):18-34.
  43.  61
    Truth, Vagueness, and Paradox: An Essay on the Logic of Truth.Vann McGee - 1990 - Indianapolis, IN, USA: Hackett.
    Awarded the 1988 Johnsonian Prize in Philosophy. Published with the aid of a grant from the National Endowment for the Humanities.
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  44.  87
    Revising Up: Strengthening Classical Logic in the Face of Paradox.David Ripley - 2013 - Philosophers' Imprint 13.
    This paper provides a defense of the full strength of classical logic, in a certain form, against those who would appeal to semantic paradox or vagueness in an argument for a weaker logic. I will not argue that these paradoxes are based on mistaken principles; the approach I recommend will extend a familiar formulation of classical logic by including a fully transparent truth predicate and fully tolerant vague predicates. It has been claimed that these principles are (...)
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  45. Benardete’s paradox and the logic of counterfactuals.Michael Caie - 2018 - Analysis 78 (1):22-34.
    I consider a puzzling case presented by Jose Benardete, and by appeal to this case develop a paradox involving counterfactual conditionals. I then show that this paradox may be leveraged to argue for certain non-obvious claims concerning the logic of counterfactuals.
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  46. Patterns of paradox.Roy T. Cook - 2004 - Journal of Symbolic Logic 69 (3):767-774.
    We begin with a prepositional languageLpcontaining conjunction (Λ), a class of sentence names {Sα}αϵA, and a falsity predicateF. We (only) allow unrestricted infinite conjunctions, i.e., given any non-empty class of sentence names {Sβ}βϵB,is a well-formed formula (we will useWFFto denote the set of well-formed formulae).The language, as it stands, is unproblematic. Whether various paradoxes are produced depends on which names are assigned to which sentences. What is needed is a denotation function:For example, theLPsentence “F(S1)” (i.e.,Λ{F(S1)}), combined with a denotation functionδsuch (...)
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  47. Moore’s paradox and the logic of belief.Andrés Páez - 2020 - Manuscrito 43 (2):1-15.
    Moore’s Paradox is a test case for any formal theory of belief. In Knowledge and Belief, Hintikka developed a multimodal logic for statements that express sentences containing the epistemic notions of knowledge and belief. His account purports to offer an explanation of the paradox. In this paper I argue that Hintikka’s interpretation of one of the doxastic operators is philosophically problematic and leads to an unnecessarily strong logical system. I offer a weaker alternative that captures in a (...)
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  48. Truth, Vagueness, and Paradox. An Essay on the Logic of Truth.Vann Mcgee & Giovanni Sommaruga-Rosolemos - 1993 - Critica 25 (73):83-108.
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  49.  38
    How to Swim in Sinking Sands: The Sorites Paradox and the Nature and Logic of Vague Language.Inga Bones - 2021 - Paderborn, Deutschland: Mentis.
    This book examines philosophical approaches to linguistic vagueness, a puzzling feature of natural language that gives rise to the ancient Sorites paradox and challenges classical logic and semantics. -/- The Sorites, or Paradox of the Heap, consists in three claims: (1) One grain of sand does not make a heap. (2) One billion grains of sand do make a heap. (3) For any two amounts of sand differing by at most one grain: either both are heaps of (...)
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  50. Truth, Vagueness and Paradox. An Essay on the Logic of Truth.Vann Mcgee - 1992 - Studia Logica 51 (2):340-341.
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