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  1. Three Dogmas of First-Order Logic and Some Evidence-Based Consequences for Constructive Mathematics of Differentiating Between Hilbertian Theism, Brouwerian Atheism and Finitary Agnosticism.Bhupinder Singh Anand - manuscript
    We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language. -/- We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'. -/- We then adopt what may (...)
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  2. A Different Approach to Logic.Mauro Avon - 2011 - Dissertation,
    The paper is about an approach to logic that differs from the standard first-order logic and other known approaches. It should be a new approach the author has created proposing to obtain a general and unifying approach to logic and a faithful model of human mathematical deductive process. We list the most relevant features of the system. In first-order logic there exist two different concepts of term and formula, in place of these two concepts in our approach we have just (...)
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  3. Higher-Order Free Logic and the Prior-Kaplan Paradox.Andrew Bacon, John Hawthorne & Gabriel Uzquiano - 2016 - Canadian Journal of Philosophy 46 (4-5):493-541.
    The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior’s paradox and Kaplan’s paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order logic. Our assessment (...)
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  4. Lógica positiva : plenitude, potencialidade e problemas (do pensar sem negação).Tomás Barrero - 2004 - Dissertation, Universidade Estadual de Campinas
    This work studies some problems connected to the role of negation in logic, treating the positive fragments of propositional calculus in order to deal with two main questions: the proof of the completeness theorems in systems lacking negation, and the puzzle raised by positive paradoxes like the well-known argument of Haskel Curry. We study the constructive com- pleteness method proposed by Leon Henkin for classical fragments endowed with implication, and advance some reasons explaining what makes difficult to extend this constructive (...)
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  5. Tableaux sin refutación.Tomás Barrero & Walter Carnielli - 2005 - Matemáticas: Enseñanza Universitaria 13 (2):81-99.
    Motivated by H. Curry’s well-known objection and by a proposal of L. Henkin, this article introduces the positive tableaux, a form of tableau calculus without refutation based upon the idea of implicational triviality. The completeness of the method is proven, which establishes a new decision procedure for the (classical) positive propositional logic. We also introduce the concept of paratriviality in order to contribute to the question of paradoxes and limitations imposed by the behavior of classical implication.
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  6. The Role of Reflexivity in Understanding Human Understanding.Steven James Bartlett - 1992 - In Steven J. Bartlett (ed.), Reflexivity: A Source-Book in Self-Reference. Amsterdam, Netherlands: Distributors for the U.S. And Canada, Elsevier Science Pub. Co.. pp. 3--18.
    The Introduction to the collection of papers, _Reflexivity: A Source-book in Self-reference_. The Introduction studies the limits of our understanding that we carry unavoidably with us. We are perpetually confined within the horizons of our conceptual structure. When this structure grows or expands, the breadth of our comprehensions enlarges, but we are forever barred from the wished-for glimpse beyond its boundaries, no matter how hard we try, no matter how much credence we invest in the substance of our learning and (...)
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  7. Involvement and Detachment: A Paradox of Practical Reasoning.Peter Baumann - 2004 - In Peter Baumann & Monika Betzler (eds.), Practical Conflicts. Cambridge University Press. pp. 244-261.
    For each of the many goals of an agent it is true that the agent wants its realization. Given further very plausible assumptions, one can show that there is no good reason for an agent not to want the realization of all of his goals. However, it seems also true that reaching all of one’s goals would be extremely boring; most human beings would consider such a life not worth living. In this respect, leading a life is like playing some (...)
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  8. Dialetheists Against Pinocchio.Jc Beall - 2011 - Analysis 71 (4):689-691.
    This paper argues that, contrary to P. Eldridge-Smith, the so-called Pinocchio paradox affords no argument against ‘simply semantic dialetheism’.
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  9. Absolute Contradiction, Dialetheism, and Revenge.Francesco Berto - 2014 - Review of Symbolic Logic 7 (2):193-207.
    Is there a notion of contradiction—let us call it, for dramatic effect, “absolute”—making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has an (...)
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  10. Adynaton and Material Exclusion.Francesco Berto - 2008 - Australasian Journal of Philosophy 86 (2):165 – 190.
    Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of the (...)
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  11. Can Fregeans Have 'I'-Thoughts?Alexandre Billon & Marie Guillot - 2014 - Revista de Filosofía de la Universidad de Costa Rica (136):97-105.
    We examine how Frege’s contrast between identity judgments of the forms “a=a” vs. “a=b” would fare in the special case where ‘a’ and ‘b’ are complex mental representations, and ‘a’ stands for an introspected ‘I’-thought. We first argue that the Fregean treatment of I-thoughts entails that they are what we call “one-shot thoughts”: they can only be thought once. This has the surprising consequence that no instance of the “a=a” form of judgment in this specific case comes out true, let (...)
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  12. Logic: The Megarics.Susanne Bobzien - 1999 - In Keimpe Algra & et al (eds.), The Cambridge History of Hellenistic Philosophy. Cambridge University Press.
    ABSTRACT: Summary presentation of the surviving logic theories of Philo the Dialectician (aka Philo of Megara) and Diodorus Cronus, including some general remarks on propositional logical elements in their logic, a presentation of their theories of the conditional and a presentation of their modal theories, including a brief suggestion for a solution of the Master Argument.
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  13. A Dutch Book for Group Decision-Making?Luc Bovens & Wlodek Rabinowicz - 2009 - In Benedikt Löwe, Eric Pacuit & Jan-Willem Romeijn (eds.), Foundations of the Formal Sciences Vi: Probabilistic Reasoning and Reasoning With Probabilities. Studies in Logic. London UK: College Publication. pp. 91-101.
    The Puzzle of the Hats is a betting arrangement which seems to show that a Dutch book can be made against a group of rational players with common priors who act in the common interest and have full trust in the other players’ rationality. But we show that appearances are misleading—no such Dutch book can be made. There are four morals. First, what can be learned from the puzzle is that there is a class of situations in which credences and (...)
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  14. Reflexivity Imagined as Art Practise.Donald Brierley - 2015 - Dissertation, Usyd
    A consideration of the relationship between conscious self-aware systems and art. I introduce my art practice and demonstrate the connections language has to self-conscious reflexivity. The document of research can be considered part of a creative practice that also uses language as a material. The specialist use and subversive manipulation of information in science and art as practiced in the service of culture are discussed to show how this informed the creation of Access Restricted-Operational Reasons as a response to my (...)
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  15. Worlds and Propositions Set Free.Otávio Bueno, Christopher Menzel & Edward N. Zalta - 2013 - Erkenntnis (4):1-24.
    The authors provide an object-theoretic analysis of two paradoxes in the theory of possible worlds and propositions stemming from Russell and Kaplan. After laying out the paradoxes, the authors provide a brief overview of object theory and point out how syntactic restrictions that prevent object-theoretic versions of the classical paradoxes are justified philosophically. The authors then trace the origins of the Russell paradox to a problematic application of set theory in the definition of worlds. Next the authors show that an (...)
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  16. Lewis Carroll's Barber Shop Paradox.Arthur W. Burks & Irving M. Copi - 1950 - Mind 59 (234):219-222.
  17. 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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  18. A Multimodal Pragmatic Treatment of the Knowability Paradox.Massimiliano Carrara, Daniele Chiffi & Davide Sergio - 2017 - In Gillman Payette & Rafal Urbaniak (eds.), Applications of Formal Philosophy. The Road Less Travelled. Berlin: Springer International Publishing AG. pp. 195-209.
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  19. Liar-Type Paradoxes and Intuitionistic Natural Deduction Systems.Seungrak Choi - 2018 - Korean Journal of Logic 21 (1):59-96.
    It is often said that in a purely formal perspective, intuitionistic logic has no obvious advantage to deal with the liar-type paradoxes. In this paper, we will argue that the standard intuitionistic natural deduction systems are vulnerable to the liar-type paradoxes in the sense that the acceptance of the liar-type sentences results in inference to absurdity (⊥). The result shows that the restriction of the Double Negation Elimination (DNE) fails to block the inference to ⊥. It is, however, not the (...)
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  20. Can Gödel's Incompleteness Theorem Be a Ground for Dialetheism?Seungrak Choi - 2017 - Korean Journal of Logic 20 (2):241-271.
    Dialetheism is the view that there exists a true contradiction. This paper ventures to suggest that Priest’s argument for Dialetheism from Gödel’s theorem is unconvincing as the lesson of Gödel’s proof (or Rosser’s proof) is that any sufficiently strong theories of arithmetic cannot be both complete and consistent. In addition, a contradiction is derivable in Priest’s inconsistent and complete arithmetic. An alternative argument for Dialetheism is given by applying Gödel sentence to the inconsistent and complete theory of arithmetic. We argue, (...)
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  21. Review of Doris Olin's Paradox. [REVIEW]John R. Cook - 2005 - Philosophy in Review (6):422-424.
    Doris Olin's Paradox is a very helpful book for those who want to be introduced to the philosophical treatment of paradoxes, or for those who already have knowledge of the general area and would like to have a helpful resource book.
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  22. The Theory of Logical Types.Irving M. Copi - 1971 - London: Routledge and Kegan Paul.
    This reissue, first published in 1971, provides a brief historical account of the Theory of Logical Types; and describes the problems that gave rise to it, its ...
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  23. Valor de Verdad.John Corcoran - 2011 - In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica. Editorial Trotta. pp. 627--629.
    Down through the ages, logic has adopted many strange and awkward technical terms: assertoric, prove, proof, model, constant, variable, particular, major, minor, and so on. But truth-value is a not a typical example. Every proposition, even if false, no matter how worthless, has a truth-value:even “one plus two equals four” and “one is not one”. In fact, every two false propositions have the same truth-value—no matter how different they might be, even if one is self-contradictory and one is consistent. It (...)
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  24. Questioning Gödel's Ontological Proof: Is Truth Positive?Gregor Damschen - 2011 - European Journal for Philosophy of Religion 3 (1):161-169.
    In his "Ontological proof", Kurt Gödel introduces the notion of a second-order value property, the positive property P. The second axiom of the proof states that for any property φ: If φ is positive, its negation is not positive, and vice versa. I put forward that this concept of positiveness leads into a paradox when we apply it to the following self-reflexive sentences: (A) The truth value of A is not positive; (B) The truth value of B is positive. Given (...)
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  25. Prova e Giustificazione.Alfredo Di Giorgio & Daniele Chiffi (eds.) - 2013 - G. Giappichelli Editore.
    I saggi che compongono questo libro intendono presentare in maniera organica e interdisciplinare, anche se da una prospettiva fondazionale logico-filosofica, il ruolo che il concetto di prova svolge in differenti ambiti del sapere. L’elemento innovativo e caratterizzante del volume è quello di stabilire e formulare quali sono le condizioni di adeguatezza materiale e formale per una corretta esplicazione del concetto di prova nelle sue differenti applicazioni. Si cercherà, inoltre, di cogliere cosa ha qualificato storicamente e qualifica tuttora il concetto di (...)
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  26. A Contradiction and P=NP Problem.Farzad Didehvar - manuscript
    Here, by introducing a version of “Unexpected hanging paradox” first we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system could support it. Finally, we propose a claim in Theory of Computation about the consistency of this Theory. One of the major claim is:Theory of Computation and Classical Logic leads us to a contradiction.
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  27. A New Solution to the Paradoxes of Rational Acceptability.Igor Douven - 2002 - British Journal for the Philosophy of Science 53 (3):391-410.
    The Lottery Paradox and the Preface Paradox both involve the thesis that high probability is sufficient for rational acceptability. The standard solution to these paradoxes denies that rational acceptability is deductively closed. This solution has a number of untoward consequences. The present paper suggests that a better solution to the paradoxes is to replace the thesis that high probability suffices for rational acceptability with a somewhat stricter thesis. This avoids the untoward consequences of the standard solution. The new solution will (...)
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  28. No Match Point for the Permissibility Account.Anna-Maria A. Eder - 2015 - Erkenntnis 80 (3):657-673.
    In the literature, one finds two accounts of the normative status of rational belief: the ought account and the permissibility account. Both accounts have their advantages and shortcomings, making it difficult to favour one over the other. Imagine that there were two principles of rational belief or rational degrees of belief commonly considered plausible, but which, however, yielded a paradox together with one account, but not with the other. One of the accounts therefore requires us to give up one of (...)
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  29. An Ancient Paradox Applied to the Difference Principle (with the Help of Cryptocurrencies).Terence Rajivan Edward - manuscript
    John Rawls’s difference principle says that we should change our economy if doing so is better for the worst-off group, on the condition that certain basic rights are secured. This paper presents a kind of case that challenges the principle. If we modify the principle to cope with the challenge, we open the way to a Sorites paradox.
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  30. The Surprise Exam Paradox: A Note on Formulating It and a Solution to It.Terence Rajivan Edward - manuscript
    Some formulations of the surprise paradox involve a pair of unnecessary and controversial assumptions. After casting doubt on these assumptions, I propose a solution to the paradox.
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  31. A Value-Based Solution to the Surprise Exam Paradox.Terence Rajivan Edward - 2018 - Philosophical Pathways (221):1-2.
    I identify an assumption that the students should not rely on: if the teacher believes that the exam would not be a surprise on a certain day, the teacher will not give the exam on that day. The reason I present for not making this assumption does not involve doubting the moral goodness of the teacher. But it does involve making a value judgment.
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  32. A Solution to the Surprise Exam Paradox.Terence Rajivan Edward - 2017 - Filozofia 72 (4):325-327.
    The students’ argument against the possibility of a surprise exam assumes that the following would not occur: the teacher decides to give the exam on a certain day; the teacher believes that the exam would be a surprise on that day; but, actually, the exam would not be a surprise on that day. I give a reason to reject this assumption, and I point out that an attempt to reformulate the surprise exam paradox in order to allow for the assumption (...)
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  33. Pinocchio Beards the Barber.P. Eldridge-Smith - 2012 - Analysis 72 (4):749-752.
    The Pinocchio paradox poses one dialetheia too many for semantic dialetheists (Eldridge-Smith 2011). However, Beall (2011) thinks that the Pinocchio scenario is merely an impossible story, like that of the village barber who shaves just those villagers who do not shave themselves. Meanwhile, Beall maintains that Liar paradoxes generate dialetheia. The Barber scenario is self-contradictory, yet the Pinocchio scenario requires a principle of truth for a contradiction. In this and other respects the Pinocchio paradox is a version of the Liar, (...)
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  34. On Concrete Universals: A Modern Treatment Using Category Theory.David Ellerman - 2014 - AL-MUKHATABAT.
    Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid-20th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this category-theoretic treatment of concrete universals (...)
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  35. Saving Truth From Paradox.Hartry H. Field - 2008 - Oxford University Press.
    A selective background -- Broadly classical approaches -- Paracompleteness -- More on paracomplete solutions -- Paraconsistent dialetheism.
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  36. What Russell Should Have Said to Burali–Forti.Salvatore Florio & Graham Leach-Krouse - 2017 - Review of Symbolic Logic 10 (4):682-718.
    The paradox that appears under Burali-Forti’s name in many textbooks of set theory is a clever piece of reasoning leading to an unproblematic theorem. The theorem asserts that the ordinals do not form a set. For such a set would be—absurdly—an ordinal greater than any ordinal in the set of all ordinals. In this article, we argue that the paradox of Burali-Forti is first and foremost a problem about concept formation by abstraction, not about sets. We contend, furthermore, that some (...)
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  37. Justifying a Large Part of Philosophy.Bryan Frances - forthcoming - Think.
    I explain why research in non-applied, non-interdisciplinary, non-historical philosophy is worthwhile. The key move in the explanation is the realization that many philosophical problems can be put in the form of a set of highly plausible yet apparently jointly inconsistent claims regarding a fundamental notion.
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  38. A Spurious Paradox.Danny Frederick - manuscript
    Niko Kolodny and John MacFarlane claim that a situation involving some trapped miners involves a deontic paradox the resolution of which requires rejecting the logical law of modus ponens. I show that the appearance of paradox results from confusion and that the miners case supplies no cogent reason for impugning modus ponens.
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  39. Risk, Ignorance, and What We Ought to Do.Danny Frederick - manuscript
    I consider cases in which risk or ignorance create barriers to our discovery of what we ought to do. I argue that neither expected utility theory, nor the maximin principle, nor a timid gambling temperament, is relevant to discovering what we ought to do in one-off or infrequently recurring types of decisions involving risk, or to decisions involving ignorance. I argue, contra Kolodny and MacFarlane, that the miners case does not require us to give up any classical logical principle in (...)
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  40. Material Implications.Joseph S. Fulda - 1992 - American Mathematical Monthly 99 (5):480.
  41. The Paradox of the Surprise Test.Joseph S. Fulda - 1991 - The Mathematical Gazette 75 (474):419-421.
    Presents a /simple/ epistemic solution to the paradox of the surprise test, suitable for undergraduates. Given the Gazette's audience, recalcitrant versions, such as Sorenson's, would have been inappropriate to even mention. It is also classified under "logical paradoxes," because it can be argued that given the existence of logical, rather than epistemic, solutions, so also the paradox is logical, rather than epistemic. -/- The author was not sent proofs, because the /Gazette/ was then run on a "shoestring budget"; the 2009 (...)
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  42. Material Implication Revisited.Joseph S. Fulda - 1989 - American Mathematical Monthly 96 (3):247-250.
    Demonstrates that the "paradoxes of material implication" are only apparent, sticking entirely within the confines of classical logic.
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  43. Our Incorrigible Ontological Relations and Categories of Being.Julian M. Galvez Bunge (ed.) - 2017 - Buenos Aires: Amazon.
    The object of this book is to present a radical novel conception of the ontological categories, their nature and epistemic importance. A conception that constitutes a challenge to the prevailing tenets, if not paradigms, of ontology today. The arguments and observations are given without addressing nor directly contesting the current theories on the subject. However, its author emphasises some of the main conclusions that entail from the new perspective, in particular regarding the role of philosophy among the sciences. Departing from (...)
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  44. Et quoniam est quis tertius homo. Argument, exégèse, contresens dans la littérature latine apparentée aux Sophistici elenchi d’Aristote.Leone Gazziero - 2013 - Archives D’Histoire Doctrinale Et Littéraire du Moyen Âge 80 (1):7-48.
    Les commentateurs latins ont rencontré pour la première fois le « Troisième homme » d’Aristote dans le chapitre vingt-deux des Sophistici elenchi. Cette rencontre illustre bien à la fois leur respect de la lettre et la radicalité de certaines de leurs innovations. Influencée par la traduction de Boèce, leur exégèse de l’argument a tenu compte de l’ensemble des indications du texte tout en lui conférant une tournure inédite.
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  45. Göodel's Theorems and the Epsilon Calculus.Slater Hartley - 2016 - SOUTH AMERICAN JOURNAL OF LOGIC 2 (1):83-90.
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  46. The Cut‐Free Approach and the Admissibility‐Curry.Ulf Hlobil - 2018 - Thought: A Journal of Philosophy 7 (1):40-48.
    The perhaps most important criticism of the nontransitive approach to semantic paradoxes is that it cannot truthfully express exactly which metarules preserve validity. I argue that this criticism overlooks that the admissibility of metarules cannot be expressed in any logic that allows us to formulate validity-Curry sentences and that is formulated in a classical metalanguage. Hence, the criticism applies to all approaches that do their metatheory in classical logic. If we do the metatheory of nontransitive logics in a nontransitive logic, (...)
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  47. Resolving the Ineffability Paradox.Chien-Hsing Ho - 2015 - Bloomsbury Academic.
    A number of contemporary philosophers think that the unqualified statement “X is unspeakable” faces the danger of self-referential absurdity: if this statement is true, it must simultaneously be false, given that X is speakable by the predicate word “unspeakable.” This predicament is in this chapter formulated as an argument that I term the “ineffability paradox.” After examining the Buddhist semantic theory of apoha (exclusion) and an apoha solution to the issue, I resort to a few Chinese Buddhist and Hindu philosophical (...)
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  48. Anatomy of a Nonidentity Paradox.Dale Jacquette - 2016 - SOUTH AMERICAN JOURNAL OF LOGIC 2 (1):119-125.
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  49. A Puzzle About Time and Thought.Saul A. Kripke - 2011 - In Philosophical Troubles. Collected Papers Vol I. Oxford University Press.
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  50. Two Paradoxes of Knowledge.Saul A. Kripke - 2011 - In Philosophical Troubles. Collected Papers Vol I. Oxford University Press.
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