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  1. Making Sense of Paraconsistent Logic: The Nature of Logic, Classical Logic and Paraconsistent Logic.Koji Tanaka - 2013 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 15--25.
    Max Cresswell and Hilary Putnam seem to hold the view, often shared by classical logicians, that paraconsistent logic has not been made sense of, despite its well-developed mathematics. In this paper, I examine the nature of logic in order to understand what it means to make sense of logic. I then show that, just as one can make sense of non-normal modal logics (as Cresswell demonstrates), we can make `sense' of paraconsistent logic. Finally, I turn the tables on classical logicians (...)
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  • Impossible Worlds.Mark Jago - 2013 - Noûs 47 (3):713-728.
    Impossible worlds are representations of impossible things and impossible happenings. They earn their keep in a semantic or metaphysical theory if they do the right theoretical work for us. As it happens, a worlds-based account provides the best philosophical story about semantic content, knowledge and belief states, cognitive significance and cognitive information, and informative deductive reasoning. A worlds-based story may also provide the best semantics for counterfactuals. But to function well, all these accounts need use of impossible and as well (...)
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  • A New Introduction to Modal Logic.M. J. Cresswell & G. E. Hughes - 1996 - Routledge.
    This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: _An Introduction to Modal Logic_ and _A Companion to Modal Logic_. _A New Introduction to Modal Logic_ is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. The book takes (...)
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  • Impossible Worlds.Daniel P. Nolan - 2013 - Philosophy Compass 8 (4):360-372.
    Philosophers have found postulating possible worlds to be very useful in a number of areas, including philosophy of language and mind, logic, and metaphysics. Impossible worlds are a natural extension to this use of possible worlds, and can help resolve a number of difficulties thrown up by possible‐worlds frameworks.
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  • Impossible Worlds.Francesco Berto - 2013 - Stanford Encyclopedia of Philosophy (2013).
    It is a venerable slogan due to David Hume, and inherited by the empiricist tradition, that the impossible cannot be believed, or even conceived. In Positivismus und Realismus, Moritz Schlick claimed that, while the merely practically impossible is still conceivable, the logically impossible, such as an explicit inconsistency, is simply unthinkable. -/- An opposite philosophical tradition, however, maintains that inconsistencies and logical impossibilities are thinkable, and sometimes believable, too. In the Science of Logic, Hegel already complained against “one of the (...)
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  • Impossible Worlds: A Modest Approach.Daniel Nolan - 1997 - Notre Dame Journal of Formal Logic 38 (4):535-572.
    Reasoning about situations we take to be impossible is useful for a variety of theoretical purposes. Furthermore, using a device of impossible worlds when reasoning about the impossible is useful in the same sorts of ways that the device of possible worlds is useful when reasoning about the possible. This paper discusses some of the uses of impossible worlds and argues that commitment to them can and should be had without great metaphysical or logical cost. The paper then provides an (...)
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  • The Semantics of Entailment II.Richard Routley & Robert K. Meyer - 1972 - Journal of Philosophical Logic 1 (1):53 - 73.
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  • Simplified Semantics for Basic Relevant Logics.Graham Priest & Richard Sylvan - 1992 - Journal of Philosophical Logic 21 (2):217 - 232.
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  • Four-Valued Semantics for Relevant Logics (and Some of Their Rivals).Greg Restall - 1995 - Journal of Philosophical Logic 24 (2):139 - 160.
    This paper gives an outline of three different approaches to the four-valued semantics for relevant logics (and other non-classical logics in their vicinity). The first approach borrows from the 'Australian Plan' semantics, which uses a unary operator '⋆' for the evaluation of negation. This approach can model anything that the two-valued account can, but at the cost of relying on insights from the Australian Plan. The second approach is natural, well motivated, independent of the Australian Plan, and it provides a (...)
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  • A New Introduction to Modal Logic.G. E. Hughes & M. J. Cresswell - 1996 - Studia Logica 62 (3):439-441.
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  • Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
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  • Brouwerian Intuitionism.Michael Detlefsen - 1990 - Mind 99 (396):501-534.
    The aims of this paper are twofold: firstly, to say something about that philosophy of mathematics known as 'intuitionism' and, secondly, to fit these remarks into a more general message for the philosophy of mathematics as a whole. What I have to say on the first score can, without too much inaccuracy, be compressed into two theses. The first is that the intuitionistic critique of classical mathematics can be seen as based primarily on epistemological rather than on meaning-theoretic considerations. The (...)
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  • New Foundations for Lewis Modal Systems.E. J. Lemmon - 1957 - Journal of Symbolic Logic 22 (2):176-186.
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  • The Semantics of First Degree Entailment.R. Routley & V. Routley - 1972 - Noûs 6 (4):335-359.
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  • Semantical Analysis of Modal Logic II. Non-Normal Modal Propositional Calculi.Saul A. Kripke - 1965 - In J. W. Addison, A. Tarski & L. Henkin (eds.), The Theory of Models: Proceedings of the 1963 International Symposium at Berkeley. North Holland. pp. 206-20.
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  • New Foundations for Lewis Modal Systems.E. J. Lemmon - 1958 - Journal of Symbolic Logic 23 (3):346-347.
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  • Semantical Analysis of Modal Logic I. Normal Modal Propositional Calculi.Saul A. Kripke - 1966 - Journal of Symbolic Logic 31 (1):120-122.
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  • What is a Non-Normal World?Graham Priest - 1992 - Logique Et Analyse 35:291-302.
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