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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. 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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  3. 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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  4. 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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  5. 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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  6. 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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  7. 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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  8. 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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  9. Arthur W. Burks & Irving M. Copi (1950). Lewis Carroll's Barber Shop Paradox. Mind 59 (234):219-222.
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  10. 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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  11. 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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  12. 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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  13. 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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  14. 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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  15. 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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  16. Anna-Maria A. Eder (2015). No Match Point for the Permissibility Account. Erkenntnis:1-17.
    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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  17. 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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  18. Terence Rajivan Edward, Another Solution to the Surprise Exam Paradox.
    I identify an assumption that the students should not rely on. Even if students are entitled to assume that the teacher was sincere at the time of giving the exam announcement, there is a reason against them assuming the following: 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 does not involve doubting the moral goodness of the teacher.
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  19. 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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  20. 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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  21. Joseph S. Fulda (1992). Material Implications. American Mathematical Monthly 99 (5):480.
  22. 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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  23. 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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  24. 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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  25. Saul A. Kripke (2011). Two Paradoxes of Knowledge. In Philosophical Troubles. Collected Papers Vol I. Oxford University Press.
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  26. Saul A. Kripke (2011). A Puzzle About Time and Thought. In Philosophical Troubles. Collected Papers Vol I. Oxford University Press.
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  27. 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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  28. 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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  29. Laureano Luna (2013). Satisfiable and Unsatisfied Paradoxes. How Closely Related? The Reasoner 7 (5):56-7.
  30. 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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  31. 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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  32. Laureano Luna & William 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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  33. 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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  34. 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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  35. 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 being obligated to (...)
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  36. 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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  37. 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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  38. 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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  39. 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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  40. T. Parent, Self-Reference is Sufficient for Paradox.
    This is a much less technical argument for the same conclusion from my “Paradox with just Self-Reference,” viz., that if self-reference is unconstrained, paradox will result. I first show that in classical logic, expressions must be seen as linguistic types rather than tokens. (Otherwise, ‘this very term = this very term’ is a false instance of the Law of Identity.) But then, one can derive a contradiction from the premise ‘This sentence is not derived’, or from the premise ‘ ‘this (...)
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  41. T. Parent, A New Modal Liar.
    Montague's modal liar is thought to show that 'necessarily' cannot be treated as a predicate of sentences. However, if 'necessarily' is treated as an operator on propositions (as is standard), we can also generate paradox (and without Montague's contentious use of the necessitation rule). The reasoning of the new modal liar is not immediately obvious--however, assuming that accessibility is reflexive, one can derive a contradiction from the proposition: This very proposition is not necessary. Thus the key advantage of the operator (...)
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  42. Niki Pfeifer (2013). Reasoning About Uncertain Conditionals. Studia Logica (4):1-18.
    There is a long tradition in formal epistemology and in the psychology of reasoning to investigate indicative conditionals. In psychology, the propositional calculus was taken for granted to be the normative standard of reference. Experimental tasks, evaluation of the participants’ responses and psychological model building, were inspired by the semantics of the material conditional. Recent empirical work on indicative conditionals focuses on uncertainty. Consequently, the normative standard of reference has changed. I argue why neither logic nor standard probability theory provide (...)
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  43. David Ripley (2013). Revising Up: Strengthening Classical Logic in the Face of Paradox. Philosophers' Imprint 13 (5).
    This paper provides a defense of the full strength of classical logic, in a certain form, against those who would appeal to semantic paradox or vagueness in an argument for a weaker logic. I will not argue that these paradoxes are based on mistaken principles; the approach I recommend will extend a familiar formulation of classical logic by including a fully transparent truth predicate and fully tolerant vague predicates. It has been claimed that these principles are not compatible with classical (...)
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  44. Gonçalo Santos (2011). Unlimited Possibilities. In Michal Peliš & Vít Punčochář (eds.), The Logica Yearbook. College Publications.
    I distinguish between a metaphysical and a logical reading of Generality Relativism. While the former denies the existence of an absolutely general domain, the latter denies the availability of such a domain. In this paper I argue for the logical thesis but remain neutral in what concerns metaphysics. To motivate Generality Relativism I defend a principle according to which a collection can always be understood as a set-like collection. I then consider a modal version of Generality Relativism and sketch how (...)
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  45. Gonçalo Santos (2010). A Not So Fine Version of Generality Relativism. Theoria 25 (2):149-161.
    The generality relativist has been accused of holding a self-defeating thesis. Kit Fine proposed a modal version of generality relativism that tries to resist this claim. We discuss his proposal and argue that one of its formulations is self-defeating.
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  46. Michael J. Shaffer (2013). Epistemic Paradox and the Logic of Acceptance. Journal of Experimental and Theoretical Artificial Intelligence 25:337-353.
    Paradoxes have played an important role both in philosophy and in mathematics and paradox resolution is an important topic in both fields. Paradox resolution is deeply important because if such resolution cannot be achieved, we are threatened with the charge of debilitating irrationality. This is supposed to be the case for the following reason. Paradoxes consist of jointly contradictory sets of statements that are individually plausible or believable. These facts about paradoxes then give rise to a deeply troubling epistemic problem. (...)
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  47. David Sherry (2006). Formal Logic for Informal Logicians. Informal Logic 26 (2):199-220.
    Classical logic yields counterintuitive results for numerous propositional argument forms. The usual alternatives (modal logic, relevance logic, etc.) generate counterintuitive results of their own. The counterintuitive results create problems—especially pedagogical problems—for informal logicians who wish to use formal logic to analyze ordinary argumentation. This paper presents a system, PL– (propositional logic minus the funny business), based on the idea that paradigmatic valid argument forms arise from justificatory or explanatory discourse. PL– avoids the pedagogical difficulties without sacrificing insight into argument.
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  48. Tuomas E. Tahko (2009). The Law of Non-Contradiction as a Metaphysical Principle. Australasian Journal of Logic 7:32-47.
    The goals of this paper are two-fold: I wish to clarify the Aristotelian conception of the law of non-contradiction as a metaphysical rather than a semantic or logical principle, and to defend the truth of the principle in this sense. First I will explain what it in fact means that the law of non-contradiction is a metaphysical principle. The core idea is that the law of non-contradiction is a general principle derived from how things are in the world. For example, (...)
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  49. Joseph W. Ulatowski (2004). Paradoxes. American Catholic Philosophical Quarterly 78 (3):514-517.
  50. Joseph W. Ulatowski (2003). A Conscientious Resolution of the Action Paradox on Buridan's Bridge'. Southwest Philosophical Studies 25:85.
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