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  1. Prolog Detects Pathological Self Reference in the Gödel Sentence.P. Olcott - manuscript
    This sentence G ↔ ¬(F ⊢ G) and its negation G ↔ ~(F ⊢ ¬G) are shown to meet the conventional definition of incompleteness: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ)). They meet conventional definition of incompleteness because neither the sentence nor its negation is provable in F (or any other formal system).
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  2. Tennant’s Conjecture for Self-Referential Paradoxes and its Classical Counterexample.Seungrak Choi - 2021 - Korean Journal of Logic 1 (24):1-30.
    In his paper, “On paradox without self-reference”, Neil Tennant proposed the conjecture for self-referential paradoxes that any derivation formalizing self-referential paradoxes only generates a looping reduction sequence. According to him, the derivation of the Liar paradox in natural deduction initiates a looping reduction sequence and the derivation of the Yablo's paradox generates a spiral reduction. The present paper proposes the counterexample to Tennant's conjecture for self-referential paradoxes. We shall show that there is a derivation of the Liar paradox which generates (...)
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  3. Self-Reference and Chaos in Fuzzy Logic.Patrick Grim - 1993 - IEEE Transactions on Fuzzy Systems 1:237-253.
    The purpose of this paper is to open for investigation a range of phenomena familiar from dynamical systems or chaos theory which appear in a simple fuzzy logic with the introduction of self-reference. Within that logic, self-referential sentences exhibit properties of fixed point attractors, fixed point repellers, and full chaos on the [0, 1] interval. Strange attractors and fractals appear in two dimensions in the graphing of pairs of mutually referential sentences and appear in three dimensions in the graphing of (...)
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  4. Contradiction From the Fixed Point Lemma.T. Parent - manuscript
    Assuming that Q (Robinson arithmetic) is consistent and Church's Thesis is true, the Fixed Point Lemma enables the derivation of a contradiction, in a manner akin to the v-Curry paradox. The derivation could be blocked by excluding certain formulae from the scope of the Lemma, but this would effectively concede that the unrestricted Lemma is false. The resolution of the paradox thus remains an open question.
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  5. Vít Punčochář: Paradoxy klasické logiky. [REVIEW]Ivo Pezlar - 2020 - Filosoficky Casopis 68 (5):800-806.
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  6. Inferences and Metainferences in ST.Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij - 2020 - Journal of Philosophical Logic 49 (6):1057-1077.
    In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between metainferences holding in the strict-tolerant logic of transparent truth ST+ and inferences holding in the logic of paradox LP+. They argue that LP+ is ST+’s external logic and they question whether ST+’s solution to the semantic paradoxes is fundamentally different from LP+’s. Here we establish that by parity of reasoning, ST+ can be related to LP+’s dual logic K3+. We clarify the distinction between internal and external logic and (...)
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  7. How to Swim in Sinking Sands: The Sorites Paradox and the Nature and Logic of Vague Language.Inga Bones - 2020 - 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 sand, or neither (...)
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  8. Die Antinomien der Logik – Der Kern des Problems und seine Pragmatik.Dieter Wandschneider - 1993 - In PRAGMATIK, Bd. IV. Hamburg: pp. 320–352.
    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 actual reason for antinomic structures. It turns out to be a form (...)
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  9. 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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  10. The Liar Paradox in the Predictive Mind.Christian Michel - 2019 - Pragmatics and Cognition 26 (2-3):239-266.
    Most discussions frame the Liar Paradox as a formal logical-linguistic puzzle. Attempts to resolve the paradox have focused very little so far on aspects of cognitive psychology and processing, because semantic and cognitive-psychological issues are generally assumed to be disjunct. I provide a motivation and carry out a cognitive-computational treatment of the liar paradox based on a model of language and conceptual knowledge within the Predictive Processing framework. I suggest that the paradox arises as a failure of synchronization between two (...)
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  11. Against Philosophical Proofs Against Common Sense.Louis Doulas & Evan Welchance - forthcoming - Analysis.
    Many philosophers think that common sense knowledge survives sophisticated philosophical proofs against it. Recently, however, Bryan Frances (forthcoming) has advanced a philosophical proof that he thinks common sense can’t survive. Exploiting philosophical paradoxes like the Sorites, Frances attempts to show how common sense leads to paradox and therefore that common sense methodology is unstable. In this paper, we show how Frances’s proof fails and then present Frances with a dilemma.
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  12. La paradoja de Skolem.Ariel Jonathan Roffé - 2014 - In Eduardo Alejandro Barrio (ed.), Paradojas, paradojas y más paradojas. pp. 245-260.
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  13. Zur Struktur dialektischer Begriffsentwicklung.Dieter Wandschneider - 1997 - In Das Problem der Dialektik. Bonn: pp. 114–169.
    Previous efforts to bring the Hegelian dialectic closer to a clarification give reason for skepticism. The question: "What is dialectic", according to Dieter Henrich, "has remained without an answer so far". Hegel's objective-idealistic program is, however, so much linked to the possibility of a dialectical logic that it is an urgent desideratum to gain clarity about the stringency of dialectical argumentation. But this is only possible on the basis of a theory of dialectic. Hegel's own reflection on methods cannot be (...)
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  14. Theories of Truth Based on Four-Valued Infectious Logics.Damian Szmuc, Bruno Da Re & Federico Pailos - 2020 - Logic Journal of the IGPL 28 (5):712-746.
    Infectious logics are systems that 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 as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at least (...)
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  15. Systems for Non-Reflexive Consequence.Carlo Nicolai & Lorenzo Rossi - manuscript
    Substructural logics and their application to logical and semantic paradoxes have been extensively studied, but non-reexive systems have been somewhat neglected. Here, we aim to (at least partly) ll this lacuna, by presenting a non-reexive logic and theory of naïve consequence (and truth). We also investigate the semantics and the proof-theory of the system. Finally, we develop a compositional theory of truth (and consequence) in our non-reexive framework.
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  16. How Can Buddhists Prove That Non-Existent Things Do Not Exist?Koji Tanaka - forthcoming - In Sara Bernstein & Tyron Goldschmidt (eds.), Non-Being: New Essay on the Metaphysics of Non-Existence. Oxford, UK:
    How can Buddhists prove that non-existent things do not exist? With great difficulty. For the Buddhist, this is not a laughing matter as they are largely global error theorists and, thus, many things are non-existent. The difficulty gets compounded as the Buddhist and their opponent, the non-Buddhist of various kinds, both agree that one cannot prove a thesis whose subject is non-existent. In this paper, I will first present a difficulty that Buddhist philosophers have faced in proving that what they (...)
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  17. A Two-Dimensional Logic for Two Paradoxes of Deontic Modality.Melissa Fusco & Alexander W. Kocurek - forthcoming - Review of Symbolic Logic:1-32.
    In this paper, we axiomatize the deontic logic in Fusco, which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the restrictions Fusco’s (...)
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  18. Is There A Logic of the Ineffable? Or, How Is It Possible to Talk About the Unsayable?Stephen R. Palmquist - 2017 - In Nahum Brown & J. Aaron Simmons (eds.), Contemporary Debates in Negative Theology and Philosophy. Springer. pp. 71-80.
    This chapter defends a single, fixed, definite answer to the question: Is there a logic that governs the unsayable? The proposed answer is: “Yes, and no. Or yes-but-not-yes. And/or yes-no.” Each component of this answer is examined and used to generate three laws of what I call “synthetic logic”, which correspond directly to the laws of classical (Aristotelian) logic: the law of contradiction (“A=-A”), the law of non-identity (“A≠A”), and the law of the included middle (“-(Av-A)”). We can talk about (...)
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  19. On Logic of Strictly-Deontic Modalities. A Semantic and Tableau Approach.Tomasz Jarmużek & Mateusz Klonowski - forthcoming - Logic and Logical Philosophy:1.
    Standard deontic logic (SDL) is defined on the basis of possible world semantics and is a logic of alethic-deontic modalities rather than deontic modalities alone. The interpretation of the concepts of obligation and permission comes down exclusively to the logical value that a sentence adopts for the accessible deontic alternatives. Here, we set forth a different approach, this being a logic which additionally takes into consideration whether sentences stand in relation to the normative system or to the system of values (...)
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  20. Axiomatizing Norms Across Time and the 'Paradox of the Court'.Daniela Glavanicova & Matteo Pascucci - forthcoming - In DEON 2021. College Publications.
    In normative reasoning one typically refers to intervals of time across which norms are intended to hold, as well as to alternative possibilities representing hypothetical developments of a given scenario. Thus, deontic modalities are naturally intertwined with temporal and metaphysical ones. Furthermore, contemporary debates in philosophy suggest that a proper understanding of fundamental ethical principles, such as the Ought-Implies-Can thesis, requires a simultaneous analysis of these three families of concepts. In the present article we propose a general formal framework which (...)
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  21. 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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  22. 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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  23. 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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  24. 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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  25. 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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  26. 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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  27. (I Can't Get No) Antisatisfaction.Pablo Cobreros, Elio La Rosa & Luca Tranchini - forthcoming - Synthese:1-15.
    Substructural approaches to paradoxes have attracted much attention from the philosophical community in the last decade. In this paper we focus on two substructural logics, named ST and TS, along with two structural cousins, LP and K3. It is well known that LP and K3 are duals in the sense that an inference is valid in one logic just in case the contrapositive is valid in the other logic. As a consequence of this duality, theories based on either logic are (...)
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  28. 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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  29. 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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  30. Expressing Validity: Towards a Self-Sufficient Inferentialism.Ulf Hlobil - 2020 - In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2019. London: College Publications. pp. 67-82.
    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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  31. 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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  32. 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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  33. 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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  34. 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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  35. Syntactic Proofs for Yablo’s Paradoxes in Temporal Logic.Ahmad Karimi - forthcoming - Logic and Logical Philosophy:1.
    Temporal logic is of importance in theoretical computer science for its application in formal verification, to state requirements of hardware or software systems. Linear temporal logic is an appropriate logical environment to formalize Yablo’s paradox which is seemingly non-self-referential and basically has a sequential structure. We give a brief review of Yablo’s paradox and its various versions. Formalization of these paradoxes yields some theorems in Linear Temporal Logic (LTL) for which we give syntactic proofs using an appropriate axiomatization of LTL.
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  36. 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.
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  37. Abraham A. Fraenkel and Yehoshua Bar-Hillel. Foundations of Set Theory. Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Company, Amsterdam1958, X + 415 Pp. [REVIEW]J. R. Shoenfield - 1964 - Journal of Symbolic Logic 29 (3):141.
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  38. 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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  39. K. Jaakko J. Hintikka. Identity, Variables, and Impredicative Definitions. The Journal of Symbolic Logic, Vol. 21 , Pp. 225–245. - K. Jaakko J. Hintikka. Vicious Circle Principle and the Paradoxes. The Journal of Symbolic Logic, Vol. 22 , Pp. 245–249. [REVIEW]Ronald Jensen - 1967 - Journal of Symbolic Logic 32 (2):258-259.
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  40. 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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  41. 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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  42. 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.
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  43. The Labours of Zeno – a Supertask Indeed?Barbara M. Sattler - 2019 - Ancient Philosophy Today 1 (1):1-17.
    It is usually supposed that, with his dichotomy paradox, Zeno gave birth to the modern so-called supertask debate – the debate of whether carrying out an infinite sequence of actions or operations...
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  44. Are Backwards-Infinite Causal Sequences Possible? [REVIEW]Haidar Al-Dhalimy - 2019 - Logic and Logical Philosophy 28 (2).
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  45. 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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  46. 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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  47. Counterfactual Knowability Revisited.Julian J. Schlöder - 2019 - Synthese (2):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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  48. The End of Mystery.Sam Baron & Mark Colyvan - 2019 - American Philosophical Quarterly 56 (3):247-264.
    Tim travels back in time and tries to kill his grandfather before his father was born. Tim fails. But why? Lewis's response was to cite "coincidences": Tim is the unlucky subject of gun jammings, banana peels, sudden changes of heart, and so on. A number of challenges have been raised against Lewis's response. The latest of these focuses on explanation. This paper diagnoses the source of this new disgruntlement and offers an alternative explanation for Tim's failure, one that Lewis would (...)
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  49. 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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  50. 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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