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Implication and the algebra of logic

Mind 21 (84):522-531 (1912)

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  1. (1 other version)C. I. Lewis.Susan Haack - 1985 - Royal Institute of Philosophy Supplement 19:215-238.
    Lewis, according to Kuklick, was ‘a private person’, of ‘unsparing honesty and … utter dedication to the rational pursuit of truth’. He was, Kuklick continues, ‘equally uncompromising in what he expected of his readers, and as a result wrote for and lectured to a tiny group of scholars’. I hope that—since I occasionally find myself borrowing from him and frequently find myself arguing with him—I may count myself as one of the ‘tiny group of scholars’ for whom Lewis wrote. And (...)
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  • Peter Simons MacColl and many-valued logic: An exclusive conjunction.an Exclusive Conjunction - 1998 - Nordic Journal of Philosophical Logic 3 (1):85-90.
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  • Modal logic and philosophy.Sten Lindström & Krister Segerberg - 2006 - In Patrick Blackburn, Johan van Benthem & Frank Wolter (eds.), Handbook of Modal Logic. Elsevier. pp. 1149-1214.
    Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the work going on in our field—a (...)
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  • Strict conditionals: A negative result.Jan Heylen & Leon Horsten - 2006 - Philosophical Quarterly 56 (225):536–549.
    Jonathan Lowe has argued that a particular variation on C.I. Lewis' notion of strict implication avoids the paradoxes of strict implication. We show that Lowe's notion of implication does not achieve this aim, and offer a general argument to demonstrate that no other variation on Lewis' notion of constantly strict implication describes the logical behaviour of natural-language conditionals in a satisfactory way.
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  • Conditionals: Inferentialism Explicated.Vincenzo Crupi & Andrea Iacona - 2024 - Erkenntnis.
    According to the view of conditionals named 'inferentialism', a conditional holds when its consequent can be inferred from its antecedent. This paper identifies some major challenges that inferentialism has to face, and uses them to assess three accounts of conditionals: one is the classical strict account, the other two have recently been proposed by Douven and Rott. As will be shown, none of the three proposals meets all challenges in a fully satisfactory way. We argue through novel formal results that (...)
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  • The Implicative Conditional.Eric Raidl & Gilberto Gomes - 2024 - Journal of Philosophical Logic 53 (1):1-47.
    This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also namedimplicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent.$${p\Rightarrow q}$$p⇒qis thus defined as$${\lnot } \Diamond {(p \wedge \lnot q) \wedge } \Diamond {p \wedge } \Diamond {\lnot q}$$¬◊(p∧¬q)∧◊p∧◊¬q. We explore the logical properties of this conditional in (...)
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  • (1 other version)Engaging Kripke with Wittgenstein: The Standard Meter, Contingent Apriori, and Beyond.Martin Gustafsson, Oskari Kuusela & Jakub Mácha (eds.) - 2023 - New York: Routledge.
    This volume draws connections between Wittgenstein's philosophy and the work of Saul Kripke, especially his Naming and Necessity. Saul Kripke is regarded as one of the foremost representatives of contemporary analytic philosophy. His most important contributions include the strict distinction between metaphysical and epistemological questions, the introduction of the notions of contingent a priori truth and necessary a posteriori truth and original accounts of names, descriptions, identity, necessity and realism. The chapters in this book elucidate the relevant connections between Kripke's (...)
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  • Possible worlds truth table task.Niels Skovgaard-Olsen, Peter Collins & Karl Christoph Klauer - 2023 - Cognition 238 (105507):1-24.
    In this paper, a novel experimental task is developed for testing the highly influential, but experimentally underexplored, possible worlds account of conditionals (Stalnaker, 1968; Lewis, 1973). In Experiment 1, this new task is used to test both indicative and subjunctive conditionals. For indicative conditionals, five competing truth tables are compared, including the previously untested, multi-dimensional possible worlds semantics of Bradley (2012). In Experiment 2, these results are replicated and it is shown that they cannot be accounted for by an alternative (...)
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  • Strict conditionals.Jan Heylen & Leon Horsten - 2022 - Croatian Journal of Philosophy 22 (64):123-131.
    Both Lowe and Tsai have presented their own versions of the theory that both indicative and subjunctive conditionals are strict conditionals. We critically discuss both versions and we find each version wanting.
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  • Guidelines for authors.[author unknown] - 2018 - Scientia et Fides 6 (1):339-344.
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  • Farewell to Suppression-Freedom.Tore Fjetland Øgaard - 2020 - Logica Universalis 14 (3):297-330.
    Val Plumwood and Richard Sylvan argued from their joint paper The Semantics of First Degree Entailment and onward that the variable sharing property is but a mere consequence of a good entailment relation, indeed they viewed it as a mere negative test of adequacy of such a relation, the property itself being a rather philosophically barren concept. Such a relation is rather to be analyzed as a sufficiency relation free of any form of premise suppression. Suppression of premises, therefore, gained (...)
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  • Reasoning About Uncertain Conditionals.Niki Pfeifer - 2014 - Studia Logica 102 (4):849-866.
    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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  • Frege’s Puzzle on the Santa Monica Beach De Jure Co-reference and the Logical Appraisal of Rational Agents.Emiliano Boccardi - 2018 - Manuscrito 41 (1):1-31.
    ABSTRACT In this paper, I argue that a number of influential Millian responses to Frege’s puzzle, which consist in denying that Frege’s data apply to natural languages, are not viable if logic is to play its role in legitimizing the logical appraisal of rational subjects. A notion of validity which does justice to the normativity of logic must make room for a distinction between valid inferences and enthymemes. I discuss the prospects of formal, relevant and manifest validity as candidates for (...)
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  • Entimemas y la tortuga de Carroll, o el problema de cómo llegar a ser determinados por reglas racionales.Miguel Angel Quintana Paz - 2005 - In Paz Miguel Angel Quintana (ed.), ¿Qué cultura?, vol. I. Ediciones SM. pp. 145-159.
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  • C. I. Lewis: History and Philosophy of Logic.John Corcoran - 2006 - Transactions of the Charles S. Peirce Society 42 (1):1-9.
    C. I. Lewis (I883-I964) was the first major figure in history and philosophy of logic—-a field that has come to be recognized as a separate specialty after years of work by Ivor Grattan-Guinness and others (Dawson 2003, 257).Lewis was among the earliest to accept the challenges offered by this field; he was the first who had the philosophical and mathematical talent, the philosophical, logical, and historical background, and the patience and dedication to objectivity needed to excel. He was blessed with (...)
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  • 2-Sequent calculus: a proof theory of modalities.Andrea Masini - 1992 - Annals of Pure and Applied Logic 58 (3):229-246.
    Masini, A., 2-Sequent calculus: a proof theory of modalities, Annals of Pure and Applied Logic 58 229–246. In this work we propose an extension of the Getzen sequent calculus in order to deal with modalities. We extend the notion of a sequent obtaining what we call a 2-sequent. For the obtained calculus we prove a cut elimination theorem.
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  • Basic Concepts in Modal Logic.Edward N. Zalta - manuscript
    These lecture notes were composed while teaching a class at Stanford and studying the work of Brian Chellas (Modal Logic: An Introduction, Cambridge: Cambridge University Press, 1980), Robert Goldblatt (Logics of Time and Computation, Stanford: CSLI, 1987), George Hughes and Max Cresswell (An Introduction to Modal Logic, London: Methuen, 1968; A Companion to Modal Logic, London: Methuen, 1984), and E. J. Lemmon (An Introduction to Modal Logic, Oxford: Blackwell, 1977). The Chellas text influenced me the most, though the order of (...)
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  • (1 other version)A survey of the life of Hugh MacColl (1837-1909).Michael Astroh, Ivor Grattan-Guinness & Stephen Read - 2001 - History and Philosophy of Logic 22 (2):81-98.
    The Scottish logician Hugh MacColl is well known for his innovative contributions to modal and nonclassical logics. However, until now little biographical information has been available about his academic and cultural background, his personal and professional situation, and his position in the scientific community of the Victorian era. The present article reports on a number of recent findings.
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  • Provability logic.Rineke Verbrugge - 2008 - Stanford Encyclopedia of Philosophy.
    -/- Provability logic is a modal logic that is used to investigate what arithmetical theories can express in a restricted language about their provability predicates. The logic has been inspired by developments in meta-mathematics such as Gödel’s incompleteness theorems of 1931 and Löb’s theorem of 1953. As a modal logic, provability logic has been studied since the early seventies, and has had important applications in the foundations of mathematics. -/- From a philosophical point of view, provability logic is interesting because (...)
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  • Trouble no more: how non-truth-functionality makes the alethic indeterminacy solution to the Liar Paradox viable.Jay Newhard - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    Jay Newhard (2021) proposes a novel solution to the Liar Paradox, which he calls the alethic indeterminacy solution to the Liar Paradox. Bradley Armour-Garb (2021) raises a pair of objections to the alethic indeterminacy solution. Both objections are based upon the alethic indeterminacy solution’s alleged commitment that the truth conditions for a Liar Sentence are indeterminate, and therefore not true. In this paper, this alleged commitment is shown to be mistaken. The alethic indeterminacy solution is compatible with maintaining that the (...)
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  • Non-Boolean classical relevant logics I.Tore Fjetland Øgaard - 2019 - Synthese (8):1-32.
    Relevant logics have traditionally been viewed as paraconsistent. This paper shows that this view of relevant logics is wrong. It does so by showing forth a logic which extends classical logic, yet satisfies the Entailment Theorem as well as the variable sharing property. In addition it has the same S4-type modal feature as the original relevant logic E as well as the same enthymematical deduction theorem. The variable sharing property was only ever regarded as a necessary property for a logic (...)
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  • Inference Claims.David Hitchcock - 2011 - Informal Logic 31 (3):191-229.
    A conclusion follows from given premisses if and only if an acceptable counterfactual-supporting covering generalization of the argument rules out, either definitively or with some modal qualification, simultaneous acceptability of the premisses and non-accepta-bility of the conclusion, even though it does not rule out acceptability of the premisses and does not require acceptability of the conclusion independently of the premisses. Hence the reiterative associated conditional of an argument is true if and only it has such a covering generalization, and a (...)
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  • On Logic in the Law: "Something, but not All".Susan Haack - 2007 - Ratio Juris 20 (1):1-31.
    In 1880, when Oliver Wendell Holmes (later to be a Justice of the U.S. Supreme Court) criticized the logical theology of law articulated by Christopher Columbus Langdell (the first Dean of Harvard Law School), neither Holmes nor Langdell was aware of the revolution in logic that had begun, the year before, with Frege's Begriffsschrift. But there is an important element of truth in Holmes's insistence that a legal system cannot be adequately understood as a system of axioms and corollaries; and (...)
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  • Legal Indeterminacy and Constitutional Interpretation.José Juan Moreso - 1998 - Dordrecht, Netherland: Springer.
    In this book, I present the results of an investigation which began with an extended stay at Oxford's Balliol College during the first half of 1995. My visit to Oxford was made possible by a grant from the Spanish Ministerio de Educaci6n y Ciencia. My sincere thanks go to Joseph Raz who served as my supervisor in Oxford. For several points of the present study, conversations with Timothy Endicott in Oxford were also of great help. The book is part of (...)
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  • (1 other version)A priori, Categories and Pragmatism : C. I. Lewis’s Pathbreaking Contribution. Introduction to the French translation of “A Pragmatic Conception of the A Priori” (1923). [REVIEW]Henri Wagner - 2021 - Philosophia Scientiae 25:179-193.
    Nous traduisons, pour la première fois en langue française, l’essai célèbre de Clarence Irving Lewis (1883-1964), « A pragmatic conception of the a priori » (1923). Cette traduction est précédée d’une introduction revenant sur les deux moments argumentatifs clés de la refonte par Lewis des notions d’a priori et de catégorie : (1) la critique des conceptions traditionnelles de l’a priori et de la manière dont elles comprennent les deux éléments constitutifs du concept d’a priori, à savoir la nécessité et (...)
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  • In search of the person. Towards a real revolution.Michał Oleksowicz - 2018 - Scientia et Fides 6 (1):229-262.
    The discussion about a difference between brain and soul or mind is now at the center of the anthropological debate. It seems that the pioneers in this current polemic have a reductionistic view of human nature, inherited from the Cartesian solution to mind-body problem and the modern materialistic explanation of reality. This view – dualistic or monistic – about the opposition between material and immaterial structure of the person, claims that as a consequence of scientific progress, the human brain in (...)
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  • The Early Formation of Modal Logic and its Significance: A Historical Note on Quine, Carnap, and a Bit of Church.Adam Tamas Tuboly - 2018 - History and Philosophy of Logic 39 (3):289-304.
    The aim of the paper is to show that W. V. O. Quine's animadversions against modal logic did not get the same attention that is considered to be the case nowadays. The community of logicians focused solely on the technical aspects of C. I. Lewis’ systems and did not take Quine's arguments and remarks seriously—or at least seriously enough to respond. In order to assess Quine's place in the history, however, his relation to Carnap is considered since their notorious break (...)
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  • Proceedings of Sinn und Bedeutung 9.Emar Maier, Corien Bary & Janneke Huitink (eds.) - 2005 - Nijmegen Centre for Semantics.
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  • Modern Origins of Modal Logic.Roberta Ballarin - 2010 - Stanford Encyclopedia of Philosophy.
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  • Autoreferential semantics for many-valued modal logics.Zoran Majkic - 2008 - Journal of Applied Non-Classical Logics 18 (1):79-125.
    In this paper we consider the class of truth-functional modal many-valued logics with the complete lattice of truth-values. The conjunction and disjunction logic operators correspond to the meet and join operators of the lattices, while the negation is independently introduced as a hierarchy of antitonic operators which invert bottom and top elements. The non-constructive logic implication will be defined for a subclass of modular lattices, while the constructive implication for distributive lattices (Heyting algebras) is based on relative pseudo-complements as in (...)
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  • (1 other version)A propositional logic with subjunctive conditionals.R. B. Angell - 1962 - Journal of Symbolic Logic 27 (3):327-343.
    In this paper a formalized logic of propositions, PA1, is presented. It is proven consistent and its relationships to traditional logic, to PM ([15]), to subjunctive (including contrary-to-fact) implication and to the “paradoxes” of material and strict implication are developed. Apart from any intrinsic merit it possesses, its chief significance lies in demonstrating the feasibility of a general logic containing theprinciple of subjunctive contrariety, i.e., the principle that ‘Ifpwere true thenqwould be true’ and ‘Ifpwere true thenqwould be false’ are incompatible.
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  • Mathematical modal logic: A view of its evolution.Robert Goldblatt - 2003 - Journal of Applied Logic 1 (5-6):309-392.
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  • (1 other version)A survey of the life of Hugh MacColl (1837-1909).Michael Astroh, Ivor Grattan-Guinness & Stephen Read - 2011 - Philosophia Scientiae 15:7-29.
    Introduction Contrary to a widespread assumption the modern history of modal logic did not start with C. I. Lewis’ Survey of Symbolic Logic [Lewis 1918]. His eminent work was preceded by some 20 years by H. MacColl’s fifth article on ‘The Calculus of Equivalent Statements’. This article was read at the London Mathematical Society on 12 November 1896. Some months later it was published in the Society’s Proceedings [MacColl 1896-1897]. During the following years MacColl presented his logic prim...
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  • Ways of understanding Hugh MacColl's concept of symbolic existence.Shahid Rahman - 1998 - Nordic Journal of Philosophical Logic 3:35-58.
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  • Anderson and Belnap’s Invitation to Sin.Alasdair Urquhart - 2010 - Journal of Philosophical Logic 39 (4):453 - 472.
    Quine has argued that modal logic began with the sin of confusing use and mention. Anderson and Belnap, on the other hand, have offered us a way out through a strategy of nominahzation. This paper reviews the history of Lewis's early work in modal logic, and then proves some results about the system in which "A is necessary" is intepreted as "A is a classical tautology.".
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  • A Relevant Logic of Questions.Vít Punčochář - 2020 - Journal of Philosophical Logic 49 (5):905-939.
    This paper introduces the inquisitive extension of R, denoted as InqR, which is a relevant logic of questions based on the logic R as the background logic of declaratives. A semantics for InqR is developed, and it is shown that this semantics is, in a precisely defined sense, dual to Routley-Meyer semantics for R. Moreover, InqR is axiomatized and completeness of the axiomatic system is established. The philosophical interpretation of the duality between Routley-Meyer semantics and the semantics for InqR is (...)
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  • (1 other version)C. I. Lewis and the Benacerraf problem.Bob Fischer - 2018 - Episteme 15 (2):154-165.
    Realists about modality offer an attractive semantics for modal discourse in terms of possible worlds, but standard accounts of the worlds—as properties, propositions, or causally-isolated concreta—invoke entities with which we can’t interact. If realism is true, how can we know anything about modal matters? Let's call this "the Benacerraf Problem." I suggest that C. I. Lewis has an intriguing answer to it. Given that we’re willing to disentangle some of Lewis’s insights from his phenomenalism, we can take the following line. (...)
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  • Peirce and Łukasiewicz on modal and multi-valued logics.Jon Alan Schmidt - 2022 - Synthese 200 (4):1-18.
    Charles Peirce incorporates modality into his Existential Graphs by introducing the broken cut for possible falsity. Although it can be adapted to various modern modal logics, Zeman demonstrates that making no other changes results in a version that he calls Gamma-MR, an implementation of Jan Łukasiewicz's four-valued Ł-modal system. It disallows the assertion of necessity, reflecting a denial of determinism, and has theorems involving possibility that seem counterintuitive at first glance. However, the latter is a misconception that arises from overlooking (...)
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  • Pursuit of the concept of validity: A dialogue.Cesare Cozzo - 2024 - Theoria 90 (5):479-491.
    This is a dialogue between Lisa and Max on Dag Prawitz's work concerning the concept of deductive validity. Lisa first explains Prawitz's criticisms of the presently prevailing non‐epistemic analyses of validity. Then Lisa describes three different ways in which Prawitz attempted to develop an epistemic concept of validity. Max asks questions for clarification, raises some objections and compares Prawitz's three approaches with other lines of thought. Two inference rules are specially discussed: disjunction introduction and ex contradictione quodlibet. Max and Lisa (...)
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  • Philosophy, Drama and Literature.Rick Benitez - 2010 - In Graham Robert Oppy, Nick Trakakis, Lynda Burns, Steven Gardner & Fiona Leigh (eds.), A companion to philosophy in Australia & New Zealand. Clayton, Victoria, Australia: Monash University Publishing. pp. 371-372.
    Philosophy and Literature is an internationally renowned refereed journal founded by Denis Dutton at the University of Canterbury, Christchurch. It is now published by the Johns Hopkins University Press. Since its inception in 1976, Philosophy and Literature has been concerned with the relation between literary and philosophical studies, publishing articles on the philosophical interpretation of literature as well as the literary treatment of philosophy. Philosophy and Literature has sometimes been regarded as iconoclastic, in the sense that it repudiates academic pretensions, (...)
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  • Constructing Concessive Conditionals: In Case of Japanese.Ai Matsui - 2009 - In Arndt Riester & Torgrim Solstad (eds.), Proceedings of Sinn Und Bedeutung 13.
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  • Preface.Matteo Pascucci & Adam Tamas Tuboly - 2019 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 26 (3):318-322.
    Special issue: "Reflecting on the Legacy of C.I. Lewis: Contemporary and Historical Perspectives on Modal Logic".
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  • Reference Processes in Intensional Contexts.Francesca Delogu - 2009 - In Arndt Riester & Torgrim Solstad (eds.), Proceedings of Sinn Und Bedeutung 13.
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  • Fehldeutungen der klassischen Aussagenlogik.Werner Loh - 1986 - Dialectica 40 (2):157-162.
    ZusammenfassungDie klassische Aussagenlogik wird falsch gedeutet. Korrigiert man die Deutungen, dann ist sie eine epistemische Möglichkeitenlogik, die sich aus assertorischen und kon‐tingenten Aussagen zusammensetzt. Da sie nicht modalitatenneutral ist, dürfen andere Logiken nicht auf ihr ohne diese Einschrankung aufbauen. Sie bedarf zur sinnvollen Deutung einer handlungstheoretischen Einbettung und ist insofern selbst schon ein Stück pragmatische Logik. Der Gebrauch der Negation dyadischer Aussagen beruht auf einer willkürlichen Festlegung, die durch die Abstraktion vom epistemisch‐hand‐lungstheoretischen Zusammenhang ermöglicht wird.
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  • Findlay’s Hegel: Idealism as Modal Actualism.Paul Redding - 2017 - Critical Horizons 18 (4):359-377.
    Here, I suggest a hitherto relatively unexplored way beyond the opposed Aristotelian realist and Kantian idealist approaches that divide recent interpretations of the categories or “thought determinations” of Hegel’s Logic, by locating his idealism within the terrain of recent debates in modal metaphysics. In particular, I return to the outlook of the first philosopher to attempt to bring Hegel into the analytic conversation, John Niemeyer Findlay, and consider Hegel’s idealism as instantiating the metaphysical position that, following the work of Findlay’s (...)
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  • Anomalies of Classical Logic in View of Relevant Logic.Akihiro Yoshimitsu - 2012 - Kagaku Tetsugaku 45 (2):65-81.
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  • (1 other version)C. I. Lewis.Susan Haack - 1985 - Royal Institute of Philosophy Lectures 19:215-238.
    Lewis's account of the role of sensory experience in empirical knowledge rests on the theses: (1) that one's apprehension of what is given in sensory experience is certain; (2) that unless there were such certain apprehension of the given, No knowledge would be possible; (3) that justification of one's other justified empirical beliefs always derives from one's apprehension of the given. I show that all three theses are false. That they are false provides further motivation for the theory of justification (...)
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  • (1 other version)A priori, catégories et pragmatisme : la percée de C. I. Lewis. Présentation de la traduction française de « A pragmatic conception of the a priori ». [REVIEW]Henri Wagner - 2021 - Philosophia Scientiae 25:179-193.
    Nous traduisons, pour la première fois en langue française, l’essai célèbre de Clarence Irving Lewis, « A pragmatic conception of the a priori ». Cette traduction est précédée d’une introduction revenant sur les deux moments argumentatifs clés de la refonte par Lewis des notions d’a priori et de catégorie : la critique des conceptions traditionnelles de l’a priori et de la manière dont elles comprennent les deux éléments constitutifs du concept d’a priori, à savoir la nécessité et l’indépendance à l’égard (...)
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  • Possibilistic reasoning—a mini-survey and uniform semantics.Churn-Jung Liau & Bertrand I.-Peng Lin - 1996 - Artificial Intelligence 88 (1-2):163-193.
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  • On relevance and justification of legal decisions.J. J. Moreso - 1996 - Erkenntnis 44 (1):73 - 100.
    The author discusses a question related to a certain aspect of justification of legal decisions, often so-called internal justification-a legal decision is internally justified if and only if it can be deduced from the norm(s) applicable to the case, and from the statement(s) describing the facts of the case. According to this notion, infinite irrelevant logical consequences are justified. To avoid this counterintuitive conclusion, the author analyzes three notions of relevance: Sperber-Wilson's notion, Anderson-Belnap's notion, and Schurz's notion. The author presents (...)
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