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  1. W. Ackermann (1962). Kahr A. S., Moore Edward F., and Wang Hao. Entscheidungsproblem Reduced to the ∀∃∀ Case. Proceedings of the National Academy of Sciences, Bd. 48 , S. 365–377. [REVIEW] Journal of Symbolic Logic 27 (2):225.
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  2. Wayne Aitken & Jeffrey A. Barrett (2008). Abstraction in Algorithmic Logic. Journal of Philosophical Logic 37 (1):23-43.
    We develop a functional abstraction principle for the type-free algorithmic logic introduced in our earlier work. Our approach is based on the standard combinators but is supplemented by the novel use of evaluation trees. Then we show that the abstraction principle leads to a Curry fixed point, a statement C that asserts C ⇒ A where A is any given statement. When A is false, such a C yields a paradoxical situation. As discussed in our earlier work, this situation leaves (...)
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  3. Wayne Aitken & Jeffrey A. Barrett (2007). Stability and Paradox in Algorithmic Logic. Journal of Philosophical Logic 36 (1):61 - 95.
    There is significant interest in type-free systems that allow flexible self-application. Such systems are of interest in property theory, natural language semantics, the theory of truth, theoretical computer science, the theory of classes, and category theory. While there are a variety of proposed type-free systems, there is a particularly natural type-free system that we believe is prototypical: the logic of recursive algorithms. Algorithmic logic is the study of basic statements concerning algorithms and the algorithmic rules of inference between such statements. (...)
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  4. Wayne Aitken & Jeffrey A. Barrett (2004). Computer Implication and the Curry Paradox. Journal of Philosophical Logic 33 (6):631-637.
    There are theoretical limitations to what can be implemented by a computer program. In this paper we are concerned with a limitation on the strength of computer implemented deduction. We use a version of the Curry paradox to arrive at this limitation.
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  5. C. Anthony Anderson (1987). Semantical Antinomies in the Logic of Sense and Denotation. Notre Dame Journal of Formal Logic 28 (1):99-114.
  6. Bradley Armour-Garb & James A. Woodbridge (2010). Truthmakers, Paradox and Plausibility. Analysis 70 (1):11-23.
    In a series of articles, Dan Lopez De Sa and Elia Zardini argue that several theorists have recently employed instances of paradoxical reasoning, while failing to see its problematic nature because it does not immediately (or obviously) yield inconsistency. In contrast, Lopez De Sa and Zardini claim that resultant inconsistency is not a necessary condition for paradoxicality. It is our contention that, even given their broader understanding of paradox, their arguments fail to undermine the instances of reasoning they attack, either (...)
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  7. F. G. Asenjo (1966). A Calculus for Antinomies. Notre Dame Journal of Formal Logic 16 (1):103-105.
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  8. F. G. Asenjo & J. Tamburino (1975). Logic of Antinomies. Notre Dame Journal of Formal Logic 16 (1):17-44.
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  9. E. J. Ashworth (1972). The Treatment of Semantic Paradoxes From 1400 to 1700. Notre Dame Journal of Formal Logic 13 (1):34-52.
  10. Andrew Bacon (2011). A Paradox for Supertask Decision Makers. Philosophical Studies 153 (2):307.
    I consider two puzzles in which an agent undergoes a sequence of decision problems. In both cases it is possible to respond rationally to any given problem yet it is impossible to respond rationally to every problem in the sequence, even though the choices are independent. In particular, although it might be a requirement of rationality that one must respond in a certain way at each point in the sequence, it seems it cannot be a requirement to respond as such (...)
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  11. K. Baier (1954). Contradiction and Absurdity. Analysis 15 (2):31 - 40.
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  12. Francesca Rivetti Barbò (1968). A Philosophical Remark on Gödel's Unprovability of Consistency Proof. Notre Dame Journal of Formal Logic 9 (1):67-74.
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  13. Eduardo Alejandro Barrio (2010). Theories of Truth Without Standard Models and Yablo's Sequences. Studia Logica 96 (3):375-391.
    The aim of this paper is to show that it’s not a good idea to have a theory of truth that is consistent but ω -inconsistent. In order to bring out this point, it is useful to consider a particular case: Yablo’s Paradox. In theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. Firstly, I exhibit some conceptual problems that follow from so introducing it. Secondly, I show (...)
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  14. Timothy Bays (2009). Skolem's Paradox. In Edward N. Zalta (ed.), Stanford Encyclopedia of Philosophy.
    Skolem's Paradox involves a seeming conflict between two theorems from classical logic. The Löwenheim Skolem theorem says that if a first order theory has infinite models, then it has models whose domains are only countable. Cantor's theorem says that some sets are uncountable. Skolem's Paradox arises when we notice that the basic principles of Cantorian set theory—i.e., the very principles used to prove Cantor's theorem on the existence of uncountable sets—can themselves be formulated as a collection of first order sentences. (...)
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  15. Timothy Bays (2006). The Mathematics of Skolem's Paradox. In Dale Jacquette (ed.), Philosophy of Logic. North Holland. pp. 615--648.
    Over the years, Skolem’s Paradox has generated a fairly steady stream of philosophical discussion; nonetheless, the overwhelming consensus among philosophers and logicians is that the paradox doesn’t constitute a mathematical problem (i.e., it doesn’t constitute a real contradiction). Further, there’s general agreement as to why the paradox doesn’t constitute a mathematical problem. By looking at the way firstorder structures interpret quantifiers—and, in particular, by looking at how this interpretation changes as we move from structure to structure—we can give a technically (...)
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  16. Timothy Bays (2000). Reflections on Skolem's Paradox. Dissertation, University of California, Los Angeles
    The Lowenheim-Skolem theorems say that if a first-order theory has infinite models, then it has models which are only countably infinite. Cantor's theorem says that some sets are uncountable. Together, these theorems induce a puzzle known as Skolem's Paradox: the very axioms of set theory which prove the existence of uncountable sets can be satisfied by a merely countable model. ;This dissertation examines Skolem's Paradox from three perspectives. After a brief introduction, chapters two and three examine several formulations of Skolem's (...)
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  17. Francesco Berto (2007). How to Sell a Contradiction. College Publications.
    There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth – viz. that the same thing cannot at one and the same time be and not be": with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not (...)
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  18. Francesco Berto (2006). Meaning, Metaphysics, and Contradiction. American Philosophical Quarterly 43 (4):283-297.
  19. Cristina Borgoni (2008). Interpretando la Paradoja de Moore. Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 23 (2):145-161.
    RESUMEN: Este trabajo ofrece una lectura de la Paradoja de Moore que pone énfasis en su relevancia para nuestra comprensión de la racionalidad y de la interpretación lingüística. Mantiene que las oraciones que dan origen a la paradoja no necesitan entenderse en términos de ausencia de una contradicción, sino más bien en términos de ausencia de racionalidad, entendida esta como un término más amplio que el de coherencia y consistencia lógica. Se defenderá tal posición por medio de tres tesis, dos (...)
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  20. Andrew Boucher, A Comprehensive Solution to the Paradoxes.
    A solution to the paradoxes has two sides: the philosophical and the technical. The paradoxes are, first and foremost, a philosophical problem. A philosophical solution must pinpoint the exact step where the reasoning that leads to contradiction is fallacious, and then explain why it is so.
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  21. OtáVio Bueno & Mark Colyvan (2003). Paradox Without Satisfaction. Analysis 63 (2):152–156.
    Consider the following denumerably infinite sequence of sentences: (s1) For all k > 1, sk is not true. (s2) For all k > 2, sk is not true. (s3) For all k > 3, sk is not true.
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  22. Colin R. Caret & Zach Weber (2015). A Note on Contraction-Free Logic for Validity. Topoi 34 (1):63-74.
    This note motivates a logic for a theory that can express its own notion of logical consequence—a ‘syntactically closed’ theory of naive validity. The main issue for such a logic is Curry’s paradox, which is averted by the failure of contraction. The logic features two related, but different, implication connectives. A Hilbert system is proposed that is complete and non-trivial.
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  23. James Cargile (1972). Moore's Proposition $W$. Notre Dame Journal of Formal Logic 13 (1):105-117.
  24. Ernst Cassirer (1923). Substance and Function. Dover Publications.
    In this double-volume work, a great modern philosopher propounds a system of thought in which Einstein's theory of relativity represents only the latest (albeit the most radical) fulfillment of the motives inherent to mathematics and the physical sciences. In the course of its exposition, it touches upon such topics as the concept of number, space and time, geometry, and energy; Euclidean and non-Euclidean geometry; traditional logic and scientific method; mechanism and motion; Mayer's methodology of natural science; Richter's definite proportions; relational (...)
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  25. Peter Cave (2011). With and Without Absurdity: Moore, Magic and McTaggart's Cat. Royal Institute of Philosophy Supplement 68 (68):125-149.
    Here is a tribute to humanity. When under dictatorial rule, with free speech much constrained, a young intellectual mimed; he mimed in a public square. He mimed a protest speech, a speech without words. People drew round to watch and listen; to watch the expressive gestures, the flicker of tongue, the mouthing lips; to listen to – silence. The authorities also watched and listened, but did nothing.
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  26. Alonzo Church (1965). Carpenter John A., Moore Omar K., Snyder Charles R., and Lisansky Edith S.. Alcohol and Higher-Order Problem Solving. Quarterly Journal of Studies on Alcohol , Vol. 22 , Pp. 183–222. [REVIEW] Journal of Symbolic Logic 30 (2):243.
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  27. Alonzo Church (1959). Moore Omar Khayyam and Anderson Scarvia B.. Modern Logic and Tasks for Experiments on Problem Solving Behavior. The Journal of Psychology, Vol. 38 , Pp. 151–160.Moore Omar Khayyam and Anderson Scarvia B.. Search Behavior in Individual and Group Problem Solving. American Sociological Review, Vol. 19 , Pp. 702–714.Anderson Scarvia B.. Problem Solving in Multiple-Goal Situations. Journal of Experimental Psychology, Vol. 54 , Pp. 297–303.Moore Omar Khayyam. Problem Solving and the Perception of Persons. Person Perception and Interpersonal Behavior, Edited by Tagiuri Renato and Petrullo Luigi, Stanford University Press, Stanford, Calif., 1958, Pp. 131–150. [REVIEW] Journal of Symbolic Logic 24 (1):86.
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  28. Alonzo Church (1954). Shannon Claude E. And Moore Edward F.. Machine Aid for Switching Circuit Design. Proceedings of the I.R.E., Vol. 41 , Pp. 1348–1351. [REVIEW] Journal of Symbolic Logic 19 (2):141.
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  29. Alonzo Church (1946). White Morton G.. A Note on the “Paradox of Analysis.” Mind, N.S. Vol. 54 , Pp. 71–72.Black Max. The “Paradox of Analysis” Again: A Reply. Mind, N.S. Vol. 54 , Pp. 272–273.White Morton G.. Analysis and Identity: A Rejoinder. Mind, N.S. Vol. 54 , Pp. 357–361.Black Max. How Can Analysis Be Informative? Philosophy and Phenomenological Research, Vol. 6 No. 4 , Pp. 628–631. [REVIEW] Journal of Symbolic Logic 11 (4):132-133.
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  30. Michael Clark (1975). Utterer's Meaning and Implications About Belief. Analysis 35 (3):105 - 108.
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  31. Marcelo E. Coniglio & Newton M. Peron (2009). A Paraconsistentist Approach to Chisholm's Paradox. Principia 13 (3):299-326.
    The Logics of Deontic (In)Consistency (LDI's) can be considered as the deontic counterpart of the paraconsistent logics known as Logics of Formal (In)Consistency. This paper introduces and studies new LDI's and other paraconsistent deontic logics with different properties: systems tolerant to contradictory obligations; systems in which contradictory obligations trivialize; and a bimodal paraconsistent deontic logic combining the features of previous systems. These logics are used to analyze the well-known Chisholm's paradox, taking profit of the fact that, besides contradictory obligations do (...)
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  32. Roy T. Cook (2009). Curry, Yablo and Duality. Analysis 69 (4):612-620.
    The Liar paradox is the directly self-referential Liar statement: This statement is false.or : " Λ: ∼ T 1" The argument that proceeds from the Liar statement and the relevant instance of the T-schema: " T ↔ Λ" to a contradiction is familiar. In recent years, a number of variations on the Liar paradox have arisen in the literature on semantic paradox. The two that will concern us here are the Curry paradox, 2 and the Yablo paradox. 3The Curry paradox (...)
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  33. Gregor Damschen (2008). This is Nonsense. The Reasoner 2 (10):6-8.
    In his Paradoxes (1995: Cambridge University Press: 149) Mark Sainsbury presents the following pair of sentences: Line 1: The sentence written on Line 1 is nonsense. Line 2: The sentence written on Line 1 is nonsense. Sainsbury (1995: 149, 154) here makes three assertions: (1) The sentence in Line 1 is so viciously self-referential that it falls into the truth-value gap. The sentence is really nonsense. (2) The sentence in Line 2 is by contrast true. For it states precisely that (...)
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  34. George Englebretsen (1975). Trivalence and Absurdity. Philosophical Papers 4 (2):121-128.
  35. Robert Feys (1958). Review: Jean de la Harpe, La Logique de L'Assertion Pure. [REVIEW] Journal of Symbolic Logic 23 (4):442-443.
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  36. Hartry Field (2017). Disarming a Paradox of Validity. Notre Dame Journal of Formal Logic 58 (1):1-19.
    Any theory of truth must find a way around Curry’s paradox, and there are well-known ways to do so. This paper concerns an apparently analogous paradox, about validity rather than truth, which JC Beall and Julien Murzi call the v-Curry. They argue that there are reasons to want a common solution to it and the standard Curry paradox, and that this rules out the solutions to the latter offered by most “naive truth theorists.” To this end they recommend a radical (...)
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  37. Pierdaniele Giaretta (2009). The Paradox of Knowability From a Russellian Perspective. Prolegomena 8 (2):141-158.
    The paradox of knowability and the debate about it are shortly presented. Some assumptions which appear more or less tacitly involved in its discussion are made explicit. They are embedded and integrated in a Russellian framework, where a formal paradox, very similar to the Russell-Myhill paradox, is derived. Its solution is provided within a Russellian formal logic introduced by A. Church. It follows that knowledge should be typed. Some relevant aspects of the typing of knowledge are pointed out.
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  38. Patrick Girard & Luca Moretti (2014). Antirealism and the Conditional Fallacy: The Semantic Approach. Journal of Philosophical Logic 43 (4):761-783.
    The expression conditional fallacy identifies a family of arguments deemed to entail odd and false consequences for notions defined in terms of counterfactuals. The antirealist notion of truth is typically defined in terms of what a rational enquirer or a community of rational enquirers would believe if they were suitably informed. This notion is deemed to entail, via the conditional fallacy, odd and false propositions, for example that there necessarily exists a rational enquirer. If these consequences do indeed follow from (...)
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  39. André Gombay (1988). Some Paradoxes of Counterprivacy. Philosophy 63 (244):191 - 210.
    For many years G. E. Moore asked himself what was wrong with sentences like ‘I went to the pictures last Tuesday, but I don't believe that I did’, or ‘I believe that he has gone out, but he has not’. He discussed the problem in 1912 in his Ethics , and was still discussing it in 1944 in a paper to the Moral Sciences Club at Cambridge—an event we know about from a letter of Wittgenstein that I shall quote in (...)
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  40. Umberto Grandi & Ulle Endriss (2013). First-Order Logic Formalisation of Impossibility Theorems in Preference Aggregation. Journal of Philosophical Logic 42 (4):595-618.
    In preference aggregation a set of individuals express preferences over a set of alternatives, and these preferences have to be aggregated into a collective preference. When preferences are represented as orders, aggregation procedures are called social welfare functions. Classical results in social choice theory state that it is impossible to aggregate the preferences of a set of individuals under different natural sets of axiomatic conditions. We define a first-order language for social welfare functions and we give a complete axiomatisation for (...)
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  41. Patrick Greenough (2011). Truthmaker Gaps and the No-No Paradox. Philosophy and Phenomenological Research 82 (3):547 - 563.
    Consider the following sentences: The neighbouring sentence is not true. The neighbouring sentence is not true. Call these the no-no sentences. Symmetry considerations dictate that the no-no sentences must both possess the same truth-value. Suppose they are both true. Given Tarski’s truth-schema—if a sentence S says that p then S is true iff p—and given what they say, they are both not true. Contradiction! Conclude: they are not both true. Suppose they are both false. Given Tarski’s falsity-schema—if a sentence S (...)
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  42. Patrick Greenough (2001). Free Assumptions and the Liar Paradox. American Philosophical Quarterly 38 (2):115 - 135.
    A new solution to the liar paradox is developed using the insight that it is illegitimate to even suppose (let alone assert) that a liar sentence has a truth-status (true or not) on the grounds that supposing this sentence to be true/not-true essentially defeats the telos of supposition in a readily identifiable way. On that basis, the paradox is blocked by restricting the Rule of Assumptions in Gentzen-style presentations of the sequent-calculus. The lesson of the liar is that not all (...)
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  43. Joseph Y. Halpern & Yoram Moses (1986). Taken by Surprise: The Paradox of the Surprise Test Revisited. [REVIEW] Journal of Philosophical Logic 15 (3):281 - 304.
    A teacher announced to his pupils that on exactly one of the days of the following school week (Monday through Friday) he would give them a test. But it would be a surprise test; on the evening before the test they would not know that the test would take place the next day. One of the brighter students in the class then argued that the teacher could never give them the test. "It can't be Friday," she said, "since in that (...)
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  44. Michael Hand & Jonathan L. Kvanvig (1999). Tennant on Knowability. Australasian Journal of Philosophy 77 (4):422 – 428.
    The knowability paradox threatens metaphysical or semantical antirealism, the view that truth is epistemic, by revealing an awful consequence of the claim [i] that all truths are knowable. Various attempts have been made to find a way out of the paradox.
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  45. Frederik Herzberg & Daniel Eckert (2012). Impossibility Results for Infinite-Electorate Abstract Aggregation Rules. Journal of Philosophical Logic 41 (1):273-286.
    Following Lauwers and Van Liedekerke (1995), this paper explores in a model-theoretic framework the relation between Arrovian aggregation rules and ultraproducts, in order to investigate a source of impossibility results for the case of an infinite number of individuals and an aggregation rule based on a free ultrafilter of decisive coalitions.
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  46. Claus Janew (2011). Laws of Form: Why Spencer-Brown is Missing the Point. Journal of Consciousness Exploration and Research 2 (6):885-886.
    What George Spencer-Brown wants to rationalize out of existence is alternation itself – the prerequisite of his whole operation. By that he simplifies (identifies) more than he says. And he does not say all that is important.
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  47. Ansten Klev (2016). A Proof‐Theoretic Account of the Miners Paradox. Theoria 82 (4):351-369.
    By maintaining that a conditional sentence can be taken to express the validity of a rule of inference, we offer a solution to the Miners Paradox that leaves both modus ponens and disjunction elimination intact. The solution draws on Sundholm's recently proposed account of Fitch's Paradox.
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  48. Jonathan L. Kvanvig (2009). ``Restriction Strategies for Knowability: Lessons in False Hope&Quot. In Joseph Salerno (ed.), New Essays on Knowability. Oxford: Oxford University Press. pp. 205-222.
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  49. Laureano (2010). A Failed Cassatio? A Note on Valor and Martinez on Goldstein. Proceedings of the Aristotelian Society 110 (3pt3):383-386.
    I address the claim by Valor and Martínez that Goldstein's cassationist approach to Liar-like paradoxes generates paradoxes it cannot solve. I argue that these authors miss an essential point in Goldstein's cassationist approach, namely the thesis that paradoxical sentences are not able to make the statement they seem to make.
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  50. Ken Levy (2009). The Solution to the Surprise Exam Paradox. Southern Journal of Philosophy 47 (2):131-158.
    The Surprise Exam Paradox continues to perplex and torment despite the many solutions that have been offered. This paper proposes to end the intrigue once and for all by refuting one of the central pillars of the Surprise Exam Paradox, the 'No Friday Argument,' which concludes that an exam given on the last day of the testing period cannot be a surprise. This refutation consists of three arguments, all of which are borrowed from the literature: the 'Unprojectible Announcement Argument,' the (...)
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