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  1. Sylvan's Box: A Short Story and Ten Morals.Graham Priest - 1997 - Notre Dame Journal of Formal Logic 38 (4):573-582.
    The paper contains a short story which is inconsistent, essentially so, but perfectly intelligible. The existence of such a story is used to establish various views about truth in fiction and impossible worlds.
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  • From Heaps and Gaps to Heaps of Gluts.D. Hyde - 1997 - Mind 106 (424):641-660.
    One of the few points of agreement to be found in mainstream responses to the logical and semantic problems generated by vagueness is the view that if any modification of classical logic and semantics is required at all then it will only be such as to admit underdetermined reference and truth-value gaps. Logics of vagueness including many valued logics, fuzzy logics, and supervaluation logics all provide responses in accord with this view. The thought that an adequate response might require the (...)
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  • Doubt Truth to Be a Liar.Graham Priest - 2005 - Oxford University Press.
    Dialetheism is the view that some contradictions are true. This is a view which runs against orthodoxy in logic and metaphysics since Aristotle, and has implications for many of the core notions of philosophy. Doubt Truth to Be a Liar explores these implications for truth, rationality, negation, and the nature of logic, and develops further the defense of dialetheism first mounted in Priest's In Contradiction, a second edition of which is also available.
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  • In Contradiction: A Study of the Transconsistent.Graham Priest - 2006 - Oxford University Press.
    In Contradiction advocates and defends the view that there are true contradictions, a view that flies in the face of orthodoxy in Western philosophy since Aristotle. The book has been at the center of the controversies surrounding dialetheism ever since its first publication in 1987. This second edition of the book substantially expands upon the original in various ways, and also contains the author’s reflections on developments over the last two decades. Further aspects of dialetheism are discussed in the companion (...)
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  • Entailment: The Logic of Relevance and Necessity.Alan Ross Anderson - 1975 - Princeton University Press.
  • Inconsistency Without Contradiction.Achille C. Varzi - 1997 - Notre Dame Journal of Formal Logic 38 (4):621-639.
    David Lewis has argued that impossible worlds are nonsense: if there were such worlds, one would have to distinguish between the truths about their contradictory goings-on and contradictory falsehoods about them; and this--Lewis argues--is preposterous. In this paper I examine a way of resisting this argument by giving up the assumption that ‘in so-and-so world’ is a restricting modifier which passes through the truth-functional connectives The outcome is a sort of subvaluational semantics which makes a contradiction ‘A & ~A’ false (...)
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  • A Calculus for Antinomies.F. G. Asenjo - 1966 - Notre Dame Journal of Formal Logic 16 (1):103-105.
  • A Calculus of Antinomies.F. G. Asenjo - 1966 - Notre Dame Journal of Formal Logic 7:103.
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  • Relevant Logic: A Philosophical Interpretation.Edwin D. Mares - 2004 - Cambridge University Press.
    This book introduces the reader to relevant logic and provides the subject with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles and natural language conditionals. The book ends by examining various applications of relevant logic and (...)
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  • On the Plenitude of Truth. A Defense of Trivialism.Paul Kabay - 2010
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  • Universal Logic.Ross Brady - 2006 - CSLI Publications.
    Throughout the twentieth century, the classical logic of Frege and Russell dominated the field of formal logic. But, as Ross Brady argues, a new type of weak relevant logic may prove to be better equipped to present new solutions to persistent paradoxes. _Universal Logic _begins with an overview of classical and relevant logic and discusses the limitations of both in analyzing certain paradoxes. It is the first text to demonstrate how the main set-theoretic and semantic paradoxes can be solved in (...)
     
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  • Relevance Logic.Edwin Mares - 2008 - Stanford Encyclopedia of Philosophy.
  • The AGM Theory and Inconsistent Belief Change.Koji Tanaka - 2005 - Logique Et Analyse 48 (189-192):113-150.
    The problem of how to accommodate inconsistencies has attracted quite a number of researchers, in particular, in the area of database theory. The problem is also of concern in the study of belief change. For inconsistent beliefs are ubiquitous. However, comparatively little work has been devoted to discussing the problem in the literature of belief change. In this paper, I examine how adequate the AGM theory is as a logical framework for belief change involving inconsistencies. The technique is to apply (...)
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  • Paraconsistent Logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
  • A General Characterization of Adaptive Logics.Diderik Batens - 2001 - Logique Et Analyse 173 (175):45-68.
  • 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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  • The Law of Non-Contradiction : New Philosophical Essays.Graham Priest, Jc Beall & Bradley P. Armour-Garb (eds.) - 2004 - Oxford University Press.
    The Law of Non-Contradiction - that no contradiction can be true - has been a seemingly unassailable dogma since the work of Aristotle, in Book G of the Metaphysics. It is an assumption challenged from a variety of angles in this collection of original papers. Twenty-three of the world's leading experts investigate the 'law', considering arguments for and against it and discussing methodological issues that arise whenever we question the legitimacy of logical principles. The result is a balanced inquiry into (...)
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  • An Introduction to Substructural Logics.Greg Restall - 2000 - Routledge.
    This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both (...)
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  • Intuitive Semantics for First-Degree Entailments and 'Coupled Trees'.J. Michael Dunn - 1976 - Philosophical Studies 29 (3):149-168.
  • A Paraconsistent Theory of Belief Revision.Edwin D. Mares - 2002 - Erkenntnis 56 (2):229 - 246.
    This paper presents a theory of belief revision that allows people to come tobelieve in contradictions. The AGM theory of belief revision takes revision,in part, to be consistency maintenance. The present theory replacesconsistency with a weaker property called coherence. In addition to herbelief set, we take a set of statements that she rejects. These two sets arecoherent if they do not overlap. On this theory, belief revision maintains coherence.
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  • Inconsistent Models of Arithmetic Part I: Finite Models. [REVIEW]Graham Priest - 1997 - Journal of Philosophical Logic 26 (2):223-235.
    The paper concerns interpretations of the paraconsistent logic LP which model theories properly containing all the sentences of first order arithmetic. The paper demonstrates the existence of such models and provides a complete taxonomy of the finite ones.
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  • Inference and Necessity.P. K. Schotch & R. E. Jennings - 1980 - Journal of Philosophical Logic 9 (3):327-340.
  • How a Computer Should Think.Nuel Belnap - 1977 - In G. Ryle (ed.), Contemporary Aspects of Philosophy. Oriel Press.
  • Relevant Arithmetic.Robert K. Meyer - 1976 - Bulletin of the Section of Logic 5 (4):133-135.
  • Whither Relevant Arithmetic?Harvey Friedman & Robert K. Meyer - 1992 - Journal of Symbolic Logic 57 (3):824-831.
    Based on the relevant logic R, the system R# was proposed as a relevant Peano arithmetic. R# has many nice properties: the most conspicuous theorems of classical Peano arithmetic PA are readily provable therein; it is readily and effectively shown to be nontrivial; it incorporates both intuitionist and classical proof methods. But it is shown here that R# is properly weaker than PA, in the sense that there is a strictly positive theorem QRF of PA which is unprovable in R#. (...)
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  • Dialetheism.Francesco Berto, Graham Priest & Zach Weber - 2008 - Stanford Encyclopedia of Philosophy 2018 (2018).
    A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth-bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and false.
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  • Universal Logic.Ross Brady - 2007 - Bulletin of Symbolic Logic 13 (4):544-547.
     
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  • Doubt Truth to Be a Liar.Graham Priest - 2007 - Studia Logica 87 (1):129-134.
     
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  • How to Sell a Contradiction.Francesco Berto - 2007 - 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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  • Inconsistent Models for Relevant Arithmetics.Robert K. Meyer & Chris Mortensen - 1984 - Journal of Symbolic Logic 49 (3):917-929.
  • Old Quantum Theory: A Paraconsistent Approach.Bryson Brown - 1992 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:397 - 411.
    Just what forms do (or should) our cognitive attitudes towards scientific theories take? The nature of cognitive commitment becomes particularly puzzling when scientists' commitments are) inconsistent. And inconsistencies have often infected our best efforts in science and mathematics. Since there are no models of inconsistent sets of sentences, straightforward semantic accounts fail. And syntactic accounts based on classical logic also collapse, since the closure of any inconsistent set under classical logic includes every sentence. In this essay I present some evidence (...)
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  • Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219-241.
  • The Non-Triviality of Dialectical Set Theory.Ross T. Brady - 1989 - In G. Priest, R. Routley & J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. pp. 437--470.
     
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