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Siblings:History/traditions: Negation
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  1. Leó Apostel (1973). Negation. Leuven,Nauwelaerts.
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  2. Jay David Atlas (1980). A Note on a Confusion of Pragmatic and Semantic Aspects of Negation. Linguistics and Philosophy 3 (3):411 - 414.
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  3. Arnon Avron (2005). A Non-Deterministic View on Non-Classical Negations. Studia Logica 80 (2-3):159 - 194.
    We investigate two large families of logics, differing from each other by the treatment of negation. The logics in one of them are obtained from the positive fragment of classical logic (with or without a propositional constant ff for “the false”) by adding various standard Gentzen-type rules for negation. The logics in the other family are similarly obtained from LJ+, the positive fragment of intuitionistic logic (again, with or without ff). For all the systems, we provide simple semantics which is (...)
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  4. Jon Barwise (1991). Review: Laurence R. Horn, A Natural History of Negation. [REVIEW] Journal of Symbolic Logic 56 (3):1103-1104.
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  5. Michael Beeson, Robert Veroff & Larry Wos (2005). Double-Negation Elimination in Some Propositional Logics. Studia Logica 80 (2-3):195 - 234.
    This article answers two questions (posed in the literature), each concerning the guaranteed existence of proofs free of double negation. A proof is free of double negation if none of its deduced steps contains a term of the formn(n(t)) for some term t, where n denotes negation. The first question asks for conditions on the hypotheses that, if satisfied, guarantee the existence of a double-negation-free proof when the conclusion is free of double negation. The second question asks about the existence (...)
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  6. W. Russell Belding (1971). Intuitionistic Negation. Notre Dame Journal of Formal Logic 12 (2):183-187.
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  7. Diane Blakemore (1989). Denial and Contrast: A Relevance Theoretic Analysis of But. [REVIEW] Linguistics and Philosophy 12 (1):15 - 37.
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  8. Robyn Carston, Metalinguistic Negation and Echoic Use.
    What I hope to achieve in this paper is some rather deeper understanding of the semantic and pragmatic properties of utterances which are said to involve the phenomenon of metalinguistic negation[FN1]. According to Laurence Horn, who has been primarily responsible for drawing our attention to it, this is a special non-truthfunctional use of the negation operator, which can be glossed as 'I object to U' where U is a linguistic utterance. This is to be distinguished from descriptive truthfunctional negation which (...)
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  9. Robyn Carston (1998). Negation, `Presupposition' and the Semantics/ Pragmatics Distinction. Journal of Linguistics 34:309-350.
    A cognitive pragmatic approach is taken to some long-standing problem cases of negation, the so-called presupposition denial cases. It is argued that a full account of the processes and levels of representation involved in their interpretation typically requires the sequential pragmatic derivation of two different propositions expressed. The first is one in which the presupposition is preserved and, following the rejection of this, the second involves the echoic (metalinguistic) use of material falling in the scope of the negation. The semantic (...)
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  10. Roberto Casati & Achille C. Varzi (2000). True and False: An Exchange. In André Chapuis & Anil Gupta (eds.), Circularity, Definition, and Truth. Indian Council of Philosophical Research. 365-370.
    Classically, truth and falsehood are opposite, and so are logical truth and logical falsehood. In this paper we imagine a situation in which the opposition is so pervasive in the language we use as to threaten the very possibility of telling truth from falsehood. The example exploits a suggestion of Ramsey’s to the effect that negation can be expressed simply by writing the negated sentence upside down. The difference between ‘p’ and ‘~~p’ disappears, the principle of double negation becomes trivial, (...)
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  11. Stephen Crain, Children's Command of Negation.
    Poverty -of-stimulus arguments have taken new ground recently, augmented by experimental findings from th e study of child language. In this paper, we briefly review two variants of the poverty-of-stimulus argument that have received empirical support from studies of child language; then we examine a third argument of this kind in more detail. The case under discussion involves the structural notion of c-command as it pertains to children’s interpretation of disjunction in the scope of negation.
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  12. Rick Dale & Nicholas D. Duran (2011). The Cognitive Dynamics of Negated Sentence Verification. Cognitive Science 35 (5):983-996.
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  13. Johan J. de Iongh, H. C. M. de Swart & L. J. M. Bergman (eds.) (1995). Perspectives on Negation: Essays in Honour of Johan J. De Iongh on His 80th Birthday. Tilburg University Press.
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  14. Michael de (2013). Empirical Negation. Acta Analytica 28 (1):49-69.
    An extension of intuitionism to empirical discourse, a project most seriously taken up by Dummett and Tennant, requires an empirical negation whose strength lies somewhere between classical negation (‘It is unwarranted that. . . ’) and intuitionistic negation (‘It is refutable that. . . ’). I put forward one plausible candidate that compares favorably to some others that have been propounded in the literature. A tableau calculus is presented and shown to be strongly complete.
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  15. George Englebretsen (1981). Logical Negation. Van Gorcum.
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  16. Amy Franklin & Anastasia Giannakidou (2011). Negation, Questions, and Structure Building in a Homesign System. Cognition 118 (3):398-416.
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  17. Joseph S. Fulda (2005). A Pragmatic, Truth-Functional Solution to a Logical Difficulty with Biconditionals Absent in Conditionals. Journal of Pragmatics 37 (9/12):1419-1425/2120.
    Solves what is sometimes, but not always, referred to as the third paradox of material implication. Readers downloading this piece should please also download the corrigendum. Note that "pragmatic" is here used in its original sense of context-sensitive, that is, adjacency. (This comment is made in response to an article in a student journal published in the western U.S. which claimed that I said that because something involves translation it must be pragmatic; that is so, in the original sense; only (...)
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  18. Richard M. Gale (1976). Negation and Non-Being. Blackwell.
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  19. Vibha Gaur (1990). The Navya-Nyāya Logic: With Special Reference to Raghunātha and Mathurānātha. Bharatiya Vidya Prakashan.
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  20. Stamatios Gerogiorgakis (2012). Privations, Negations and the Square: Basic Elements of a Logic of Privations. In Jean-Yves Beziau & Dale Jacquette (eds.), Around and beyond the Square of Opposition. Birkhäuser-Springer. 229--239.
    I try to explain the difference between three kinds of negation: external negation, negation of the predicate and privation. Further I use polygons of opposition as heuristic devices to show that a logic which contains all three mentioned kinds of negation must be a fragment of a Łukasiewicz-four-valued predicate logic. I show, further, that, this analysis can be elaborated so as to comprise additional kinds of privation. This would increase the truth-values in question and bring fragments of (more generally speaking) (...)
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  21. Anastasia Giannakidou, On Metalinguistic Comparatives and Negation in Greek.
    In this paper, we identify a paradigm of metalinguistic comparatives in Greek headed by the preposition para. Para clauses are lexically distinct from other comparatives clauses in Greek (headed by apo, apoti). Building on earlier intuitions, we propose a semantics of metalinguistic MORE as a contrast between two propositions in terms of how appropriate of preferred they are by some individual. Syntactically, metalinguistic comparison appears to behave like a co-ordinate structure with ellipsis in the para-clause. Our account is extended to (...)
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  22. Michael Glanzberg, Descriptions, Negation, and Focus.
    One of the mainstays of the theory of definite descriptions since Russell (1905) has been their interaction with negation. In particular, Russellians, who advocate the view that definite descriptions are a kind of quantifier, point to these interactions as evidence in favor of the their view. The argument runs roughly as follows.
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  23. B. S. Gower (1971). Conditionals. Mind 80 (319):418-420.
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  24. Jonathan Harrison (1974). Mr. Gower on Conditionals. Mind 83 (329):103-105.
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  25. Jonathan Harrison (1968). Unfulfilled Conditionals and the Truth of Their Constituents. Mind 77 (307):372-382.
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  26. Jaakko Hintikka (2002). Negation in Logic and in Natural Language. Linguistics and Philosophy 25 (5-6):585-600.
    In game-theoretical semantics, perfectlyclassical rules yield a strong negation thatviolates tertium non datur when informationalindependence is allowed. Contradictorynegation can be introduced only by a metalogicalstipulation, not by game rules. Accordingly, it mayoccur (without further stipulations) onlysentence-initially. The resulting logic (extendedindependence-friendly logic) explains several regularitiesin natural languages, e.g., why contradictory negation is abarrier to anaphase. In natural language, contradictory negationsometimes occurs nevertheless witin the scope of aquantifier. Such sentences require a secondary interpretationresembling the so-called substitutionalinterpretation of quantifiers.This interpretation is sometimes impossible,and (...)
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  27. Marco Hollenberg (1997). An Equational Axiomatization of Dynamic Negation and Relational Composition. Journal of Logic, Language and Information 6 (4):381-401.
    We consider algebras on binary relations with two main operators: relational composition and dynamic negation. Relational composition has its standard interpretation, while dynamic negation is an operator familiar to students of Dynamic Predicate Logic (DPL) (Groenendijk and Stokhof, 1991): given a relation R its dynamic negation R is a test that contains precisely those pairs (s,s) for which s is not in the domain of R. These two operators comprise precisely the propositional part of DPL.This paper contains a finite equational (...)
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  28. Laurence Horn (1989). A Natural History of Negation. University of Chicago Press.
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  29. Lloyd Humberstone (2008). Contrariety and Subcontrariety: The Anatomy of Negation (with Special Reference to an Example of J.-Y. Béziau). Theoria 71 (3):241-262.
    We discuss aspects of the logic of negation bearing on an issue raised by Jean-Yves Béziau, recalled in §1. Contrary- and subcontrary-forming operators are introduced in §2, which examines some of their logical behaviour, leading on naturally to a consideration in §3 of dual intuitionistic negation (as well as implication), and some further operators related to intuitionistic negation. In §4, a historical explanation is suggested as to why some of these negation-related connectives have attracted more attention than others. The remaining (...)
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  30. Thomas Kroedel (2012). Implicit Definition and the Application of Logic. Philosophical Studies 158 (1):131-148.
    The paper argues that the theory of Implicit Definition cannot give an account of knowledge of logical principles. According to this theory, the meanings of certain expressions are determined such that they make certain principles containing them true; this is supposed to explain our knowledge of the principles as derived from our knowledge of what the expressions mean. The paper argues that this explanation succeeds only if Implicit Definition can account for our understanding of the logical constants, and that fully (...)
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  31. N. Kurbis (2007). Pluralism and the Logical Basis of Metaphysics. In Logica Yearbook.
    I argue for a kind of logical pluralism on the basis of a difficulty with defining the meaning of negation in the framework of Dummett's and Prawitz' proof-theoretic semantics.
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  32. Nils Kürbis (forthcoming). Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality. Journal of Philosophical Logic:1-15.
    This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett’s and Dag Prawitz’ philosophical motivations and give precise characterisations of the crucial notions of harmony and stability, placed in the context of proving normalisation results in systems of natural deduction. I point out a problem for defining the meaning of negation in this framework and prospects for an account of the meanings of (...)
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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. Robert K. Meyer (2008). Ai, Me and Lewis (Abelian Implication, Material Equivalence and C I Lewis 1920). Journal of Philosophical Logic 37 (2):169 - 181.
    C I Lewis showed up Down Under in 2005, in e-mails initiated by Allen Hazen of Melbourne. Their topic was the system Hazen called FL (a Funny Logic), axiomatized in passing in Lewis 1921. I show that FL is the system MEN of material equivalence with negation. But negation plays no special role in MEN. Symbolizing equivalence with → and defining ∼A inferentially as A→f, the theorems of MEN are just those of the underlying theory ME of pure material equivalence. (...)
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  35. Grigori Mints (2006). Notes on Constructive Negation. Synthese 148 (3):701 - 717.
    We put together several observations on constructive negation. First, Russell anticipated intuitionistic logic by clearly distinguishing propositional principles implying the law of the excluded middle from remaining valid principles. He stated what was later called Peirce’s law. This is important in connection with the method used later by Heyting for developing his axiomatization of intuitionistic logic. Second, a work by Dragalin and his students provides easy embeddings of classical arithmetic and analysis into intuitionistic negationless systems. In the last section, we (...)
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  36. Ernesto Napoli (2006). Negation. Grazer Philosophische Studien 72 (1):233-252.
    The paper is concerned with negation in artificial and natural languages. "Negation" is an ambiguous word. It can mean three different things: An operation(negating), an operator (a sign of negation), the result of an operation. The threethings, however, are intimately linked. An operation such as negation, is realizedthrough an operator of negation, i.e. consists in adding a symbol of negation to an entity to obtain an entity of the same type; and which operation it is dependson what it applies to (...)
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  37. T. Nyan (1999). Simplement, as a Metalinguistic Operator. Argumentation 13 (3):275-295.
    This paper aims to provide a description of a metalinguistic use of simplement, one which occurs primarily in ce n'est pas que P simplement Q constructions. The two main points that will be raised concern the nature and function of the negation preceding P, and the meaning of simplement, which, following Anscombre and Ducrot, I will construe in procedural terms.
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  38. Niki Pfeifer (2012). Experiments on Aristotle's Thesis: Towards an Experimental Philosophy of Conditionals. The Monist 95 (2):223-240.
    Two experiments (N1 = 141, N2 = 40) investigate two versions of Aristotle’s Thesis for the first time. Aristotle’s Thesis is a negated conditional, which consists of one propositional variable with a negation either in the antecedent (version 1) or in the consequent (version 2). This task allows to infer if people interpret indicative conditionals as material conditionals or as conditional events. In the first experiment I investigate between-participants the two versions of Aristotle’s Thesis crossed with abstract versus concrete task (...)
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  39. Graham Priest (2006). Doubt Truth to Be a Liar. 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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  40. Graham Priest (1999). Negation as Cancellation, and Connexive Logic. Topoi 18 (2):141-148.
    Of the various accounts of negation that have been offered by logicians in the history of Western logic, that of negation as cancellation is a very distinctive one, quite different from the explosive accounts of modern "classical" and intuitionist logics, and from the accounts offered in standard relevant and paraconsistent logics. Despite its ancient origin, however, a precise understanding of the notion is still wanting. The first half of this paper offers one. Both conceptually and historically, the account of negation (...)
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  41. Marie la Palme Reyes, John Macnamara, Gonzalo E. Reyes & And Houman Zolfaghari (1994). The Non-Boolean Logic of Natural Language Negation. Philosophia Mathematica 2 (1):45-68.
    Since antiquity two different negations in natural languages have been noted: predicate negation (not honest) and predicate term negation (dishonest). The extensive literature offers no models. We propose category-theoretic models with two distinct negation operators, neither of them in general Boolean. We study combinations of the two (not dishonest) and sentential counterparts of each. We emphasize the relevance of our work for the theory of cognition.
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  42. David Ripley (2011). Negation, Denial, and Rejection. Philosophy Compass 6 (9):622-629.
    At least since [Frege, 1960] and [Geach, 1965], there has been some consensus about the relation between negation, the speech act of denial, and the attitude of rejection: a denial, the consensus has had it, is the assertion of a negation, and a rejection is a belief in a negation. Recently, though, there have been notable deviations from this orthodox view. Rejectivists have maintained that negation is to be explained in terms of denial or rejection, rather than vice versa. Some (...)
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  43. David Ripley, Weak Negations and Neighborhood Semantics.
    As we’ve seen in the last chapter, there is good linguistic reason to categorize negations (and negative operators in general) by which De Morgan laws they support. The weakest negative operators (merely downward monotonic) support only two De Morgan laws;1 medium-strength negative operators support a third;2 and strong negative operators support all four. As we’ve also seen, techniques familiar from modal logic are of great use in giving unifying theories of negative operators. In particular, Dunn’s (1990) distributoid theory allows us (...)
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  44. David Ripley, Embedding Denial.
    Suppose Alice asserts p, and the Caterpillar wants to disagree. If the Caterpillar accepts classical logic, he has an easy way to indicate this disagreement: he can simply assert ¬p. Sometimes, though, things are not so easy. For example, suppose the Cheshire Cat is a paracompletist who thinks that p ∨ ¬p fails (in familiar (if possibly misleading) language, the Cheshire Cat thinks p is a gap). Then he surely disagrees with Alice's assertion of p, but should himself be unwilling (...)
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  45. Gabriel Sandu (1994). Some Aspects of Negation in English. Synthese 99 (3):345 - 360.
    I introduce a formal language called the language of informational independence (IL-language, for short) that extends an ordinary first-order language in a natural way. This language is interpreted in terms of semantical games of imperfect information. In this language, one can define two negations: (i) strong or dual negation, and (ii) weak or contradictory negation. The latter negation, unlike the former, can occur only sentence-initially. Then I argue that, to a certain extent, the two negations match the distinction existing in (...)
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  46. Walter J. Schroyens, Walter Schaeken & G. (2001). The Processing of Negations in Conditional Reasoning: A Meta-Analytic Case Study in Mental Model and/or Mental Logic Theory. Thinking and Reasoning 7 (2):121 – 172.
    We present a meta-analytic review on the processing of negations in conditional reasoning about affirmation problems (Modus Ponens: "MP", Affirmation of the Consequent "AC") and denial problems (Denial of the Antecedent "DA", and Modus Tollens "MT"). Findings correct previous generalisations about the phenomena. First, the effects of negation in the part of the conditional about which an inference is made, are not constrained to denial problems. These inferential-negation effects are also observed on AC. Second, there generally are reliable effects of (...)
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  47. Peter Sells, Three Aspects of Negation in Korean.
    Studies 6, 1–15. Korean has three forms that express negation: short-form negation, long-form negation and inherently lexical verbs. The goal of this paper is to argue that there are three separate notions related to the expression and interpretation of negation in Korean, which must be kept separate. They are the notions of a negative clause, of the surface c-command domain of a negative element, and of the semantic scope of a negative element. The main arguments derive from the interactions of (...)
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  48. Howard James Simmons, 'Austere' Sentential Logic: Double Negation Collapse Without Excluded Middle.
    This paper describes and defends a system of sentential logic in which both contradictions and instances of excluded middle are treated as incoherent.
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  49. Neil Sinclair (2011). Moral Expressivism and Sentential Negation. Philosophical Studies 152 (3):385-411.
    This paper advances three necessary conditions on a successful account of sentential negation. First, the ability to explain the constancy of sentential meaning across negated and unnegated contexts (the Fregean Condition). Second, the ability to explain why sentences and their negations are inconsistent, and inconsistent in virtue of the meaning of negation (the Semantic Condition). Third, the ability of the account to generalize regardless of the topic of the negated sentence (the Generality Condition). The paper discusses three accounts of negation (...)
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  50. Michael P. Slattery (1967). Descriptions as Negations. Philosophical Studies 16:193-209.
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