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  1. Mauro Avon (2011). A Different Approach to Logic. 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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  2. Andrew Bacon, John Hawthorne & Gabriel Uzquiano (forthcoming). Higher-Order Free Logic and the Prior-Kaplan Paradox. Canadian Journal of Philosophy.
    The principle of Universal Instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior's paradox or 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 of both (...)
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  3. Tomás Barrero (2004). Lógica positiva : plenitude, potencialidade e problemas (do pensar sem negação). 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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  4. Tomás Barrero & Walter Carnielli (2005). Tableaux sin refutación. 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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  5. Peter Baumann (2004). Involvement and Detachment: A Paradox of Practical Reasoning. In Peter Baumann & Monika Betzler (eds.), Practical Conflicts. Cambridge University Press 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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  6. Francesco Berto (2014). Absolute Contradiction, Dialetheism, and Revenge. 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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  7. Francesco Berto (2008). Adynaton and Material Exclusion. 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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  8. Alexandre Billon & Marie Guillot (2014). Can Fregeans Have 'I'-Thoughts? 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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  9. Susanne Bobzien (1999). Logic: The Megarics. 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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  10. Otávio Bueno, Christopher Menzel & Edward N. Zalta (2013). Worlds and Propositions Set Free. 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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  11. Arthur W. Burks & Irving M. Copi (1950). Lewis Carroll's Barber Shop Paradox. Mind 59 (234):219-222.
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  12. John R. Cook (2005). Review of Doris Olin's Paradox. [REVIEW] 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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  13. Irving M. Copi (1971). The Theory of Logical Types. London,Routledge and K. 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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  14. John Corcoran (2011). Valor de Verdad. In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica. Editorial Trotta 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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  15. Gregor Damschen (2011). Questioning Gödel's Ontological Proof: Is Truth Positive? 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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  16. Alfredo Di Giorgio & Daniele Chiffi (eds.) (2013). Prova e Giustificazione. 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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  17. Farzad Didehvar, A Contradiction and P=NP Problem.
    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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  18. Igor Douven (2002). A New Solution to the Paradoxes of Rational Acceptability. 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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  19. Anna-Maria A. Eder (2015). No Match Point for the Permissibility Account. 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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  20. Terence Rajivan Edward, A Solution to the Surprise Exam Paradox.
    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 exam would not be a surprise on that day, but the teacher does not realize this. 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 does not result in an acceptable argument.
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  21. Terence Rajivan Edward, Another Solution to the Surprise Exam Paradox.
    I identify an assumption that the students should not rely on: if the teacher believes that the exam will 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.
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  22. P. Eldridge-Smith (2012). Pinocchio Beards the Barber. 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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  23. David Ellerman (forthcoming). On Concrete Universals: A Modern Treatment Using Category Theory. 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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  24. Hartry Field (2008). Saving Truth From Paradox. Oxford University Press Uk.
    Saving Truth from Paradox is an ambitious investigation into paradoxes of truth and related issues, with occasional forays into notions such as vagueness, the nature of validity, and the Gödel incompleteness theorems. Hartry Field presents a new approach to the paradoxes and provides a systematic and detailed account of the main competing approaches. Part One examines Tarski's, Kripke>'s, and Lukasiewicz>'s theories of truth, and discusses validity and soundness, and vagueness. Part Two considers a wide range of attempts to resolve the (...)
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  25. Bryan Frances (forthcoming). Justifying a Large Part of Philosophy. 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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  26. Danny Frederick, Decisions, Facts, Fictions and a Spurious Miners Paradox.
    Kolodny and MacFarlane claim to identify a deontic paradox in a case of some threatened miners. They propose to avoid the paradox by rejecting the logical principle of modus ponens. Other authors concur that a remedy requires rejection of classical logical principles. Graham considers a structurally similar case concerning a doctor, but he thinks that the appearance of paradox arises out of a confusion between acting rightly and not being blameworthy. I explain why Graham’s solution fails. I show that an (...)
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  27. Joseph S. Fulda (1992). Material Implications. American Mathematical Monthly 99 (5):480.
  28. Joseph S. Fulda (1991). The Paradox of the Surprise Test. 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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  29. Joseph S. Fulda (1989). Material Implication Revisited. 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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  30. Leone Gazziero (2013). Et quoniam est quis tertius homo. Argument, exégèse, contresens dans la littérature latine apparentée aux Sophistici elenchi d’Aristote. Archives D’Histoire Doctrinale Et Littéraire du Moyen Âge 80:7-48.
    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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  31. Chien-Hsing Ho (2015). Resolving the Ineffability Paradox. 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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  32. Saul A. Kripke (2011). A Puzzle About Time and Thought. In Philosophical Troubles. Collected Papers Vol I. Oxford University Press
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  33. Saul A. Kripke (2011). Two Paradoxes of Knowledge. In Philosophical Troubles. Collected Papers Vol I. Oxford University Press
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  34. Giorgio Lando (2011). Assertion and Affirmation in the Early Wittgenstein. Wittgenstein-Studien 2 (1):21-47.
    The Tractatus rejects the sign of assertion as "logically meaningless", but the rejection of the sign did not lead Wittgenstein to reject the corresponding notion. I show the presence and the importance in the early Wittgenstein of a notion keenly similar to Fregean and Russellian logical assertion. I propose to call this notion "affirmation." The preparatory writings and the TLP present different theories about affirmation. The correct understanding of the nature and purpose of affirmation proves critical in order to confront (...)
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  35. Ken Levy (2007). The Solution to the Real Blackmail Paradox: The Common Link Between Blackmail and Other Criminal Threats. Connecticut Law Review 39:1051-1096.
    Disclosure of true but reputation-damaging information is generally legal. But threats to disclose true but reputation-damaging information unless payment is made are generally criminal. Many scholars think that this situation is paradoxical because it seems to involve illegality mysteriously arising out of legality, a criminal act mysteriously arising out of an independently legal threat to disclose conjoined with an independently legal demand for money. -/- But this formulation is not quite right. The real paradox raised by the different legal (...)
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  36. L. Luna & W. Taylor (2014). Taming the Indefinitely Extensible Definable Universe. Philosophia Mathematica 22 (2):198-208.
    In previous work in 2010 we have dealt with the problems arising from Cantor's theorem and the Richard paradox in a definable universe. We proposed indefinite extensibility as a solution. Now we address another definability paradox, the Berry paradox, and explore how Hartogs's cardinality theorem would behave in an indefinitely extensible definable universe where all sets are countable.
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  37. Laureano Luna (forthcoming). Physicalism, Truth, and the Pinocchio Paradox. Mind and Matter.
    We develop an argument sketched by Luna (2011) based on the Pinocchio paradox, which was proposed by Eldridge-Smith and Eldridge- Smith (2010). We show that, upon plausible assumptions, the claim that mental states supervene on bodily states leads to the conclusion that some proposition is both paradoxical and not paradoxical. In order to show how the presence of paradoxes can be harnessed for philosophical argumentation, we present as well a couple of related arguments.
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  38. Laureano Luna (2013). Indefinite Extensibility in Natural Language. The Monist 96 (2):295-308.
    The Monist’s call for papers for this issue ended: “if formalism is true, then it must be possible in principle to mechanize meaning in a conscious thinking and language-using machine; if intentionalism is true, no such project is intelligible”. We use the Grelling-Nelson paradox to show that natural language is indefinitely extensible, which has two important consequences: it cannot be formalized and model theoretic semantics, standard for formal languages, is not suitable for it. We also point out that object-object mapping (...)
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  39. Laureano Luna (2013). Satisfiable and Unsatisfied Paradoxes. How Closely Related? The Reasoner 7 (5):56-7.
  40. Laureano Luna (2011). Reasoning From Paradox. The Reasoner 5 (2):22-23.
    Godel's and Tarski's theorems were inspired by paradoxes: the Richard paradox, the Liar. Godel, in the 1951 Gibbs lecture argued from his metatheoretical results for a metaphysical claim: the impossibility of reducing, both, mathematics to the knowable by the human mind and the human mind to a finite machine (e.g. the brain). So Godel reasoned indirectly from paradoxes for metaphysical theses. I present four metaphysical theses concerning mechanism, reductive physicalism and time for the only purpose of suggesting how it could (...)
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  41. Laureano Luna (2010). A FailedCassatio? A Note on Valor and Martínez 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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  42. Teresa Marques (2008). The Square of Opposition and the Paradoxes. Logica Universalis 2 (1):87-105.
    Can an appeal to the difference between contrary and contradictory statements, generated by a non-uniform behaviour of negation, deal adequately with paradoxical cases like the sorites or the liar? This paper offers a negative answer to the question. This is done by considering alternative ways of trying to construe and justify in a useful way (in this context) the distinction between contraries and contradictories by appealing to the behaviour of negation only. There are mainly two ways to try to do (...)
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  43. Alessandra Marra (2014). For a Dynamic Semantics of Necessity Deontic Modals. In Fabrizio Cariani, Davide Grossi, Joke Meheus & Xavier Parent (eds.), Deontic Logic and Normative Systems. Springer 124-138.
    Traditional approaches in deontic logic have focused on the so-called reportative reading of obligation sentences, by providing truth-functional semantics based on a primitive ideality order between possible worlds. Those approaches, however, do not take into account that, in natural language, obligation sentences primarily carry a prescriptive effect. The paper focuses precisely on that prescriptive character, and shows that the reportative reading can be derived from the prescriptive one. A dynamic, non truth-functional semantics for necessity deontic modals is developed, in which (...)
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  44. Paul McNamara (2004). Agential Obligation as Non-Agential Personal Obligation Plus Agency. Journal of Applied Logic 2:117-152.
    I explore various ways of integrating the framework for predeterminism, agency, and ability in[P.McNamara, Nordic J. Philos. Logic 5 (2)(2000) 135] with a framework for obligations. However,the agential obligation operator explored here is defined in terms of a non-agential yet personal obligation operator and a non-deontic (and non-normal) agency operator. This is contrary to the main current trend, which assumes statements of personal obligation always take agential complements. Instead, I take the basic form to be an agent’s (...)
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  45. Christopher Menzel (2012). Sets and Worlds Again. Analysis 72 (2):304-309.
    Bringsjord (1985) argues that the definition W of possible worlds as maximal possible sets of propositions is incoherent. Menzel (1986a) notes that Bringsjord’s argument depends on the Powerset axiom and that the axiom can be reasonably denied. Grim (1986) counters that W can be proved to be incoherent without Powerset. Grim was right. However, the argument he provided is deeply flawed. The purpose of this note is to detail the problems with Grim’s argument and to present a sound alternative argument (...)
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  46. Christopher Menzel (1986). On Set Theoretic Possible Worlds. Analysis 46 (2):68 - 72.
  47. John D. Norton, Paradoxes of Sailing.
    Paradoxes have long been a driving force in philosophy. They compel us to think more clearly about what we otherwise take for granted. In Antiquity, Zeno insisted that a runner could never complete the course because he’d first need to go half way, and then half way again; and so on indefinitely. Zeno also argued that matter could not be infinitely divisible, else it would be made of parts of no size at all. Even infinitely many nothings combined still measure (...)
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  48. G. Oppy (1997). Countable Fusion Not yet Proven Guilty: It May Be the Whiteheadian Account of Space Whatdunnit. Analysis 57 (4):249-253.
    I criticise a paper by Peter Forrest in which he argues that a principle of unrestricted countable fusion has paradoxical consequences. I argue that the paradoxical consequences that he exhibits may be due to his Whiteheadean assumptions about the nature of spacetime rather than to the principle of unrestricted countable fusion.
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  49. Federico Matías Pailos (2012). About Two Objections to Cook's Proposal. Análisis Filosófico 32 (1):37-43.
    The main thesis of this work is as follows: there are versions of Yablo’s paradox that, if Cook is right about the non-circular character of his version of it, are truly paradoxical and genuinely non-circular, and Cook’s version of Yablo’s paradox is one of them. Here I will not evaluate the"circular" or"non-circular" side to Cook’s proposal. In fact, I think that he is right about it, and that his version of Yablo’s list is non-circular. But is it paradoxical? In order (...)
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  50. T. Parent, Paradox with Just Self-Reference.
    If a semantically open language allows self-reference, one can show there is a predicate which is both satisfied and unsatisfied by a self-referring term. The argument requires something akin to diagonalization on substitution instances of a definition-scheme for the predicate "x is Lagadonian." (The term 'Lagadonian' is adapted from David Lewis). Briefly, a self-referring term is counted as “Lagadonian” if the initial variable in the schema is replaced with the term itself. But the same term is not counted as Lagadonian (...)
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