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  1. Alethic Reference.Lavinia Picollo - 2020 - Journal of Philosophical Logic 49 (3):417-438.
    I put forward precise and appealing notions of reference, self-reference, and well-foundedness for sentences of the language of first-order Peano arithmetic extended with a truth predicate. These notions are intended to play a central role in the study of the reference patterns that underlie expressions leading to semantic paradox and, thus, in the construction of philosophically well-motivated semantic theories of truth.
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  2. A Theory of Structured Propositions.Andrew Bacon - manuscript
    This paper argues that the theory of structured propositions is not undermined by the Russell-Myhill paradox. I develop a theory of structured propositions in which the Russell-Myhill paradox doesn't arise: the theory does not involve ramification or compromises to the underlying logic, but rather rejects common assumptions, encoded in the notation of the $\lambda$-calculus, about what properties and relations can be built. I argue that the structuralist had independent reasons to reject these underlying assumptions. The theory is given both a (...)
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  3. The Modal Logics of Kripke-Feferman Truth.Carlo Nicolai & Johannes Stern - manuscript
    We determine the modal logic of fixed-point models of truth and their axiomatizations by Solomon Feferman via Solovay-style completeness results.
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  4. Hobson’s Conception of Definable Numbers.Zhao Fan - 2020 - History and Philosophy of Logic 41 (2):128-139.
    In this paper, I explore an intriguing view of definable numbers proposed by a Cambridge mathematician Ernest Hobson, and his solution to the paradoxes of definability. Reflecting on König’s paradox and Richard’s paradox, Hobson argues that an unacceptable consequence of the paradoxes of definability is that there are numbers that are inherently incapable of finite definition. Contrast to other interpreters, Hobson analyses the problem of the paradoxes of definability lies in a dichotomy between finitely definable numbers and not finitely definable (...)
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  5. Mechanizing Principia Logico-Metaphysica in Functional Type-Theory.Daniel Kirchner, Christoph Benzmüller & Edward N. Zalta - 2020 - Review of Symbolic Logic 13 (1):206-218.
    Principia Logico-Metaphysica contains a foundational logical theory for metaphysics, mathematics, and the sciences. It includes a canonical development of Abstract Object Theory [AOT], a metaphysical theory that distinguishes between ordinary and abstract objects.This article reports on recent work in which AOT has been successfully represented and partly automated in the proof assistant system Isabelle/HOL. Initial experiments within this framework reveal a crucial but overlooked fact: a deeply-rooted and known paradox is reintroduced in AOT when the logic of complex terms is (...)
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  6. Swyneshed, Aristotle and the Rule of Contradictory Pairs.Stephen Read - 2020 - Logica Universalis 14 (1):27-50.
    Roger Swyneshed, in his treatise on insolubles, dating from the early 1330s, drew three notorious corollaries from his solution. The third states that there is a contradictory pair of propositions both of which are false. This appears to contradict what Whitaker, in his iconoclastic reading of Aristotle’s De Interpretatione, dubbed “The Rule of Contradictory Pairs”, which requires that in every such pair, one must be true and the other false. Whitaker argued that, immediately after defining the notion of a contradictory (...)
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  7. On Hierarchical Propositions.Giorgio Sbardolini - 2020 - Journal of Philosophical Logic 49 (1):1-11.
    There is an apparent dilemma for hierarchical accounts of propositions, raised by Bruno Whittle : either such accounts do not offer adequate treatment of connectives and quantifiers, or they eviscerate the logic. I discuss what a plausible hierarchical conception of propositions might amount to, and show that on that conception, Whittle’s dilemma is not compelling. Thus, there are good reasons why proponents of hierarchical accounts of propositions did not see the difficulty Whittle raises.
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  8. Fitch's Paradox and Level-Bridging Principles.Weng Kin San - 2020 - Journal of Philosophy 117 (1):5-29.
    Fitch’s Paradox shows that if every truth is knowable, then every truth is known. Standard diagnoses identify the factivity/negative infallibility of the knowledge operator and Moorean contradictions as the root source of the result. This paper generalises Fitch’s result to show that such diagnoses are mistaken. In place of factivity/negative infallibility, the weaker assumption of any ‘level-bridging principle’ suffices. A consequence is that the result holds for some logics in which the “Moorean contradiction” commonly thought to underlie the result is (...)
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  9. Expressing Validity: Towards a Self-Sufficient Inferentialism.Ulf Hlobil - forthcoming - In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2019. London: College Publications.
    For semantic inferentialists, the basic semantic concept is validity. An inferentialist theory of meaning should offer an account of the meaning of "valid." If one tries to add a validity predicate to one's object language, however, one runs into problems like the v-Curry paradox. In previous work, I presented a validity predicate for a non-transitive logic that can adequately capture its own meta-inferences. Unfortunately, in that system, one cannot show of any inference that it is invalid. Here I extend the (...)
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  10. Lewis Carroll Inferential Paradox / O Paradoxo Inferencial de Lewis Carroll.Rodrigo Cid - 2016 - Fundamento: Revista de Filosofia 12:127-138.
    My main aim at this paper is to present Lewis Carrol’s Paradox on the justification of logical principles inasmuch as some attempts of solving it. This is important because if there are basic logical principles, it also seems necessary to exist some justification for them. By considering some observations from Ryle, Devitt and Kripke about the theme, we intend to briefly display their theories and their core critics among themselves and, mainly, the critics against adoption theory.
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  11. Modal Expansionism.Alexander Roberts - 2019 - Journal of Philosophical Logic 48 (6):1145-1170.
    There are various well-known paradoxes of modal recombination. This paper offers a solution to a variety of such paradoxes in the form of a new conception of metaphysical modality. On the proposed conception, metaphysical modality exhibits a type of indefinite extensibility. Indeed, for any objective modality there will always be some further, broader objective modality; in other terms, modal space will always be open to expansion.
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  12. Ω-Circularity of Yablo's Paradox.Ahmet Çevik - forthcoming - Logic and Logical Philosophy:1.
    In this paper, we strengthen Hardy’s [1995] and Ketland’s [2005] arguments on the issues surrounding the self-referential nature of Yablo’s paradox [1993]. We first begin by observing that Priest’s [1997] construction of the binary satisfaction relation in revealing a fixed point relies on impredicative definitions. We then show that Yablo’s paradox is ‘ω-circular’, based on ω-inconsistent theories, by arguing that the paradox is not self-referential in the classical sense but rather admits circularity at the least transfinite countable ordinal. Hence, we (...)
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  13. Wittgenstein on Cantor's Proof.Chrysoula Gitsoulis - 2018 - In Gabriele M. Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Contributions of the 41st International Wittgenstein Symposium. pp. 67-69.
    Cantor’s proof that the reals are uncountable forms a central pillar in the edifices of higher order recursion theory and set theory. It also has important applications in model theory, and in the foundations of topology and analysis. Due partly to these factors, and to the simplicity and elegance of the proof, it has come to be accepted as part of the ABC’s of mathematics. But even if as an Archimedean point it supports tomes of mathematical theory, there is a (...)
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  14. David Kaplan and Richard Montague. A Paradox Regained. Notre Dame Journal of Formal Logic, Vol. 1 , Pp. 79–90. - Martin Gardner. A New Prediction Paradox. The British Journal for the Philosophy of Science, Vol. 13 , P. 51. - K. R. Popper. A Comment on the New Prediction Paradox. The British Journal for the Philosophy of Science, Vol. 13 , P. 51. [REVIEW]James Cargile - 1965 - Journal of Symbolic Logic 30 (1):102-103.
  15. David Kaplan and Richard Montague. A Paradox Regained. Notre Dame Journal of Formal Logic, Vol. 1 , Pp. 79–90. - Martin Gardner. A New Prediction Paradox. The British Journal for the Philosophy of Science, Vol. 13 , P. 51. - K. R. Popper. A Comment on the New Prediction Paradox. The British Journal for the Philosophy of Science, Vol. 13 , P. 51. [REVIEW]James Cargile - 1965 - Journal of Symbolic Logic 30 (1):102-103.
  16. Karel Lambert. Notes on “E!“: II. Philosophical Studies , Vol. 12 , Pp. 1–5.Theodore Hailperin - 1967 - Journal of Symbolic Logic 32 (2):251.
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  17. Thomas Moro Simpson. Formas Lógicas, Realidad y Significado. With a Preface by Gregorio Klimovsky. Editorial Universitaria de Buenos Aires, Buenos Aires1964, 302 Pp. [REVIEW]Gonzalo E. Reyes - 1967 - Journal of Symbolic Logic 32 (1):112-113.
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  18. Thomas Moro Simpson. Formas Lógicas, Realidad y Significado. With a Preface by Gregorio Klimovsky. Editorial Universitaria de Buenos Aires, Buenos Aires1964, 302 Pp. [REVIEW]Gonzalo E. Reyes - 1967 - Journal of Symbolic Logic 32 (1):112-113.
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  19. Richard M. Martin. Intension and Decision. A Philosophical Study.Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1963, Xv + 159 Pp. [REVIEW]Richard Montague - 1966 - Journal of Symbolic Logic 31 (1):98-102.
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  20. Paul R. Halmos. Naive Set Theory.D. Van Nostrand Company, Princeton1960, Vii + 104 Pp. [REVIEW]Alfons Borgers - 1969 - Journal of Symbolic Logic 34 (2):308.
  21. B. Meltzer. The Third Possibility. Mind, N.S. Vol. 73 , Pp. 430–433. - B. Meltzer and I. J. Good. Two Forms of the Prediction Paradox. The British Journal for the Philosophy of Science, Vol. 16 No. 61 , Pp. 50–51. - William H. Halberstadt. In Defence of Euclid: A Reply to B. Meltzer. Mind, N.S. Vol. 76 , P. 282. [REVIEW]Alan Ross Anderson - 1970 - Journal of Symbolic Logic 35 (3):458-459.
  22. B. Meltzer. The Third Possibility. Mind, N.S. Vol. 73 , Pp. 430–433. - B. Meltzer and I. J. Good. Two Forms of the Prediction Paradox. The British Journal for the Philosophy of Science, Vol. 16 No. 61 , Pp. 50–51. - William H. Halberstadt. In Defence of Euclid: A Reply to B. Meltzer. Mind, N.S. Vol. 76 , P. 282. [REVIEW]Alan Ross Anderson - 1970 - Journal of Symbolic Logic 35 (3):458-459.
  23. Are Backwards-Infinite Causal Sequences Possible? [REVIEW]Haidar Al-Dhalimy - forthcoming - Logic and Logical Philosophy.
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  24. Paradox Und Dereflexion: Anregungen der Logotherapie V. E. Frankls Für Religionsphilosophie Und -Psychologie.Rolf Kühn - 1988 - Archive for the Psychology of Religion 18 (1):138-153.
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  25. What is a Paraconsistent Logic?Damian Szmuc, Federico Pailos & Eduardo Barrio - 2018 - In Jacek Malinowski & Walter Carnielli (eds.), Contradictions, from Consistency to Inconsistency. Springer Verlag.
    Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic is (...)
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  26. Counterfactual Knowability Revisited.Julian J. Schlöder - 2019 - Synthese:1-15.
    Anti-realism is plagued by Fitch’s paradox: the remarkable result that if one accepts that all truths are knowable, minimal assumptions about the nature of knowledge entail that every truth is known. Dorothy Edgington suggests to address this problem by understanding p is knowable to be a counterfactual claim, but her proposal must contend with a forceful objection by Timothy Williamson. I revisit Edgington’s basic idea and find that Williamson’s objection is obviated by a refined understanding of counterfactual knowability that is (...)
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  27. Unscharfe Grenzen.Über die Haufen-Paradoxie, den Darwinismus und die rekursive Grammatik.Ulrich Pardey - 2002 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 33 (2):323-348.
    Inexact limits. On the heap-paradox, Darwinism and recursive grammar. The heap-paradox can be reinforced by a combination with the basic idea of Achilles. The logical pattern of the reinforced heap-paradox will be analysed in a new manner by distinguishing between limited and unlimited transitivity. This analysis makes explicit the constructive character of the paradox. Finally it is shown that the logical pattern of the heap-paradox is applied in popular presentations of Darwinism, in the debate about abortion and in the foundation (...)
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  28. Reference in Arithmetic.Lavinia Picollo - 2018 - Review of Symbolic Logic 11 (3):573-603.
    Self-reference has played a prominent role in the development of metamathematics in the past century, starting with Gödel’s first incompleteness theorem. Given the nature of this and other results in the area, the informal understanding of self-reference in arithmetic has sufficed so far. Recently, however, it has been argued that for other related issues in metamathematics and philosophical logic a precise notion of self-reference and, more generally, reference is actually required. These notions have been so far elusive and are surrounded (...)
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  29. Paradoxes of Demonstrability.Sten Lindström - 2009 - In Lars-Göran Johansson, Jan Österberg & Ryszard Sliwinski (eds.), Logic, Ethics and all that Jazz: Essays in Honour of Jordan Howard Sobel. Uppsala, Sverige: 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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  30. Theories of Truth Based on Four-Valued Infectious Logics.Damian Szmuc, Bruno Da Re & Federico Pailos - forthcoming - Logic Journal of the IGPL.
    Infectious logics are systems which have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated (i) as a way to treat different pathological sentences (like the Liar and the Truth-Teller) differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps, and (ii) as a way to (...)
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  31. Indicative Conditionals, Restricted Quantification, and Naive Truth.Hartry Field - 2016 - Review of Symbolic Logic 9 (1):181-208.
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  32. Paradoxos da lógica deôntica: Indícios de um equívoco.Ricardo Tavares da Silva - 2017 - Kriterion: Journal of Philosophy 58 (138):673-690.
    RESUMO De acordo com a teoria das funções de verdade, a verdade/falsidade de uma proposição é computável a partir da verdade/falsidade das suas proposições “internas”: para cada proposição há uma função entre valores de verdade. Aplicada a proposições modais, origina a semântica dos mundos possíveis e, aplicada a proposições normativas, origina uma semântica que reduz os conceitos normativos aos conceitos modais, a semântica modal. Esta redução fica posta em questão com a existência dos chamados ‘paradoxos da lógica deôntica’. Estes não (...)
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  33. A Yabloesque Paradox in Epistemic Game Theory.Can Başkent - 2018 - Synthese 195 (1):441-464.
    The Brandenburger–Keisler paradox is a self-referential paradox in epistemic game theory which can be viewed as a two-person version of Russell’s Paradox. Yablo’s Paradox, according to its author, is a non-self referential paradox, which created a significant impact. This paper gives a Yabloesque, non-self-referential paradox for infinitary players within the context of epistemic game theory. The new paradox advances both the Brandenburger–Keisler and Yablo results. Additionally, the paper constructs a paraconsistent model satisfying the paradoxical statement.
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  34. Prospects for a Naive Theory of Classes.Hartry Field, Harvey Lederman & Tore Fjetland Øgaard - 2017 - Notre Dame Journal of Formal Logic 58 (4):461-506.
    The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are identical. In (...)
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  35. The Philosophical Significance of Stein’s Paradox.Olav Vassend, Elliott Sober & Branden Fitelson - 2017 - European Journal for Philosophy of Science 7 (3):411-433.
    Charles Stein discovered a paradox in 1955 that many statisticians think is of fundamental importance. Here we explore its philosophical implications. We outline the nature of Stein’s result and of subsequent work on shrinkage estimators; then we describe how these results are related to Bayesianism and to model selection criteria like AIC. We also discuss their bearing on scientific realism and instrumentalism. We argue that results concerning shrinkage estimators underwrite a surprising form of holistic pragmatism.
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  36. Curry's Paradox.Lionel Shapiro & Jc Beall - 2017 - Edward N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. CSLI Publications.
    “Curry’s paradox”, as the term is used by philosophers today, refers to a wide variety of paradoxes of self-reference or circularity that trace their modern ancestry to Curry (1942b) and Löb (1955). The common characteristic of these so-called Curry paradoxes is the way they exploit a notion of implication, entailment or consequence, either in the form of a connective or in the form of a predicate. Curry’s paradox arises in a number of different domains. Like Russell’s paradox, it can take (...)
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  37. Paradoxes and Diagonalization.Timm Lampert - 2007 - In Proceedings of the GAP Conference. Paderborn: Mentis. pp. 50-59.
    In this paper Richard’s Paradox and the Proof of Cantor’s Theorem are compared. It is argued that there is no conclusive reason to treat them differently such as to call the one a Paradox and the other a Proof.
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  38. Hierarchical Propositions.Bruno Whittle - 2017 - Journal of Philosophical Logic 46 (2):215-231.
    The notion of a proposition is central to philosophy. But it is subject to paradoxes. A natural response is a hierarchical account and, ever since Russell proposed his theory of types in 1908, this has been the strategy of choice. But in this paper I raise a problem for such accounts. While this does not seem to have been recognized before, it would seem to render existing such accounts inadequate. The main purpose of the paper, however, is to provide a (...)
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  39. A Variant of the 'Heterological' Paradox: A Further Note.J. L. Mackie - 1953 - Analysis 14 (6):146.
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  40. Présuppositions linguistiques et enjeux philosophiques des paralogismes liés à la forme de l’expression dans les Réfutations sophistiques d’Aristote.Leone Gazziero - 2016 - In Béatrice Godart-Wendling & Layla Raïd (eds.), B. Godart-Wendling et L. Raïd (éd.), A la recherche de la présupposition, London, Iste Editions, 2016. London: Iste. pp. 33-52.
    Pour des raisons essentiellement liées à la vocation des textes où la notion de présupposition a fait son apparition, c’est la présupposition d’existence qui s’est imposée la première à l’attention des philosophes du langage. Elle a également déterminé l’orientation des débats en les focalisant sur quelques problèmes traditionnels, au premier chef desquels le problème de l’absence de référence de certaines expressions et celui des imperfections du langage naturel. Contrairement aux noms propres et aux descriptions définies, les termes qui signifient des (...)
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  41. The Paradox of Useful Research.Sven Ove Hansson - 2017 - Theoria 83 (1):1-3.
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  42. The Paradox of the Question.Alexander D. Scott - 1999 - Analysis 59 (4):331-335.
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  43. On an Alleged Paradox of Consistency and Material Implication.Edward S. Robinson - 1970 - Critica 4 (11/12):111-122.
  44. We Have Always Been Mixed Up: Aristotle at the Heart of the ‘Composite Age’.Hélène Mialet - 2001 - Studies in History and Philosophy of Science Part A 32 (1):193-202.
  45. Parfits "Paradox der blossen Hinzufügung": Anstoss für eine untypische version des Utilitarismus.Fabian Fricke - 2002 - Grazer Philosophische Studien 64 (1):175-207.
    Parfit's Mere Addition Paradox seems to show that we must give up one of three very plausible beliefs about the relative goodness of certain outcomes, which would put a strong damper on our hopes of finding an acceptable theory of benevolence dealing with issues of procreation. I shall argue that such a result can be avoided if we challenge some basic assumptions about moral reasoning which underlie Parfit's argument. An alternative account of the nature of moral reasoning will be given, (...)
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  46. John Mair on Semantic Paradoxes: Alethic and Correspondence Paradoxes II.Miroslav Hanke - 2012 - Studia Neoaristotelica 9 (2):154-183.
    John Mair was an influential post-medieval scholar. This paper focuses on his Tractatus insolubilium, in which he proposed semantic analysis of self-referential phenomena, in particular on his solution to alethic and correspondence paradoxes and his treatment of their general semantic aspects as well as particular applications. His solution to paradoxes is based on the so-called “network evaluation”, i.e. on a semantics which defines the concepts of truth and correspondence with reality in contextual terms. Consequently, the relation between semantic valuation, synonymy (...)
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  47. Rescuing Poincaré From Richard’s Paradox.Laureano Luna - 2017 - History and Philosophy of Logic 38 (1):57-71.
    Poincaré in a 1909 lecture in Göttingen proposed a solution to the apparent incompatibility of two results as viewed from a definitionist perspective: on the one hand, Richard’s proof that the definitions of real numbers form a countable set and, on the other, Cantor’s proof that the real numbers make up an uncountable class. Poincaré argues that, Richard’s result notwithstanding, there is no enumeration of all definable real numbers. We apply previous research by Luna and Taylor on Richard’s paradox, indefinite (...)
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  48. Appendix 1. The Twelve-Coin Puzzle and The Paradox of the Heap.Andrew Lawless - 2005 - In Plato's Sun: An Introduction to Philosophy. University of Toronto Press. pp. 247-250.
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  49. The Paradox of Majoritarianism.Richard B. Hall - 1979 - Philosophy Research Archives 5:25-34.
    A democrat who finds himself in the minority on some political issue is compelled to judge that the policy favored by the majority ought to be implemented even though he believes that same policy ought not to be implemented because it does not represent the best social policy. I argue that this paradox does not reduce to a mere conflict of prima facie judgments ; that to view the paradox as a conflict of desires rather than of principles makes it (...)
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  50. Conditionals and Curry.Daniel Nolan - 2016 - Philosophical Studies 173 (10):2629-2647.
    Curry's paradox for "if.. then.." concerns the paradoxical features of sentences of the form "If this very sentence is true, then 2+2=5". Standard inference principles lead us to the conclusion that such conditionals have true consequents: so, for example, 2+2=5 after all. There has been a lot of technical work done on formal options for blocking Curry paradoxes while only compromising a little on the various central principles of logic and meaning that are under threat. -/- Once we have a (...)
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