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Summary "Disjunction" is the technical term for the English connective "or."  As many of the entries in this leaf node attest, "or" in English means "inclusive or," i.e., "and/or."  The so-called "exclusive or," while one of the sixteen combinatorially possible binary connectives in the propositional calculus, is merely an implicature from a mutually exhaustive context or cue words whose own semantics indicate exclusivity, e.g. "else" as in "or else."  There is a "menu or" in English, but this is an n-ary connective with n not necessarily 2, and does not normally appear in ordinary declarative contexts.
Key works Aside from the book cited below, the article Barrett & Stenner 1971 is key, as are the various works by Crain and his colleagues.  I particularly recommend Crain & Khlentzos 2010.
Introductions The book  Jennings 1994, while not particularly easy reading for the neophyte, is indispensable.  It is to "Disjunction" what Horn 1989 is to "Negation."
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64 found
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  1. A Two-Dimensional Logic for Two Paradoxes of Deontic Modality.Fusco Melissa & Kocurek Alexander - forthcoming - Review of Symbolic Logic.
    In this paper, we axiomatize the deontic logic in Fusco 2015, which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the restrictions (...)
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  2. The Genealogy of ‘∨’.Landon D. C. Elkind & Richard Zach - 2022 - Review of Symbolic Logic:1-38.
    The use of the symbol ∨ for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol ∨ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or”, vel. We show that the origin of the symbol ∨ for disjunction can be traced to Whitehead (...)
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  3. The Epistemic Consequences of Paradox.Bryan Frances - 2022 - Cambridge: Cambridge University Press.
    By pooling together exhaustive analyses of certain philosophical paradoxes, we can prove a series of fascinating results regarding philosophical progress, agreement on substantive philosophical claims, knockdown arguments in philosophy, the wisdom of philosophical belief, the epistemic status of metaphysics, and the power of philosophy to refute common sense. As examples, this Element examines the Sorites Paradox, the Liar Paradox, and the Problem of the Many – although many other paradoxes can do the trick too.
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  4. Idempotent Variations on the Theme of Exclusive Disjunction.L. Humberstone - 2022 - Studia Logica 110 (1):121-163.
    An exclusive disjunction is true when exactly one of the disjuncts is true. In the case of the familiar binary exclusive disjunction, we have a formula occurring as the first disjunct and a formula occurring as the second disjunct, so, if what we have is two formula-tokens of the same formula-type—one formula occurring twice over, that is—the question arises as to whether, when that formula is true, to count the case as one in which exactly one of the disjuncts is (...)
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  5. Deontic Logic, Weakening and Decisions Concerning Disjunctive Obligations.Michael J. Shaffer - 2022 - Logos and Episteme 13 (1):93-102.
    This paper introduces two new paradoxes for standard deontic logic (SDL). They are importantly related to, but distinct from Ross' paradox. These two new paradoxes for SDL are the simple weakening paradox and the complex weakening paradox. Both of these paradoxes arise in virtue of the underlaying logic of SDL and are consequences of the fact that SDL incorporates the principle known as weakening. These two paradoxes then show that SDL has counter-intuitive implications related to disjunctive obligations that arise in (...)
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  6. Independent alternatives: Ross’s puzzle and free choice.Richard Jefferson Booth - 2021 - Philosophical Studies 179 (4):1241-1273.
    Orthodox semantics for natural language modals give rise to two puzzles for their interactions with disjunction: Ross’s puzzle and the puzzle of free choice permission. It is widely assumed that each puzzle can be explained in terms of the licensing of ‘Diversity’ inferences: from the truth of a possibility or necessity modal with an embedded disjunction, hearers infer that each disjunct is compatible with the relevant set of worlds. I argue that Diversity inferences are too weak to explain the full (...)
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  7. Agential Free Choice.Melissa Fusco - 2021 - Journal of Philosophical Logic 50 (1):57-87.
    The Free Choice effect—whereby \\) seems to entail both \ and \—has traditionally been characterized as a phenomenon affecting the deontic modal ‘may’. This paper presents an extension of the semantic account of free choice defended by Fusco to the agentive modal ‘can’, the ‘can’ which, intuitively, describes an agent’s powers. On this account, free choice is a nonspecific de re phenomenon that—unlike typical cases—affects disjunction. I begin by sketching a model of inexact ability, which grounds a modal approach to (...)
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  8. Discourse, Diversity, and Free Choice.Wolfgang Schwarz - 2021 - Australasian Journal of Philosophy 99 (1):48-67.
    ABSTRACT ‘You may have beer or wine’ suggests that you may have beer and you may have wine. Following Klinedinst, I argue that this ‘free choice’ effect is a special kind of scalar implicature, arising from the application of an unspecific predicate to a plurality. I show that the implicature can be derived from general norms of cooperative communication, without postulating new grammatical rules or hidden lexical items. The derivation calls for an extension to the classical neo-Gricean model. I give (...)
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  9. Free Choice Impossibility Results.Simon Goldstein - 2020 - Journal of Philosophical Logic 49 (2):249-282.
    Free Choice is the principle that possibly p or q implies and is implied by possibly p and possibly q. A variety of recent attempts to validate Free Choice rely on a nonclassical semantics for disjunction, where the meaning of p or q is not a set of possible worlds. This paper begins with a battery of impossibility results, showing that some kind of nonclassical semantics for disjunction is required in order to validate Free Choice. The paper then provides a (...)
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  10. Categoricity and Negation. A Note on Kripke’s Affirmativism.Constantin C. Brîncuș & Iulian D. Toader - 2019 - In The Logica Yearbook 2018. London: College Publications. pp. 57-66.
    We argue that, if taken seriously, Kripke's view that a language for science can dispense with a negation operator is to be rejected. Part of the argument is a proof that positive logic, i.e., classical propositional logic without negation, is not categorical.
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  11. Choice Points for a Modal Theory of Disjunction.Fabrizio Cariani - 2017 - Topoi 36 (1):171-181.
    This paper investigates the prospects for a semantic theory that treats disjunction as a modal operator. Potential motivation for such a theory comes from the way in which modals embed within disjunctions. After reviewing some of the relevant data, I go on to distinguish a variety of modal theories of disjunction. I analyze these theories by considering pairs of conflicting desiderata, highlighting some of the tradeoffs they must face.
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  12. Against the Unrestricted Applicability of Disjunction Elimination.Marcel Jahn - 2017 - Rerum Causae 9 (2):92-111.
    In this paper, I argue that the disjunction elimination rule presupposes the principle that a true disjunction contains at least one true disjunct. However, in some contexts such as supervaluationism or quantum logic, we have good reasons to reject this principle. Hence, disjunction elimination is restricted in at least one respect: it is not applicable to disjunctions for which this principle does not hold. The insight that disjunction elimination presupposes the principle that a true disjunction contains at least one true (...)
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  13. Conjunction and Disjunction in Infectious Logics.Hitoshi Omori & Damian Szmuc - 2017 - In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan). Berlin: Springer. pp. 268-283.
    In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that none of them discusses (...)
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  14. Expressing Permission.William B. Starr - 2016 - Semantics and Linguistic Theory 26:325-349.
    This paper proposes a semantics for free choice permission that explains both the non-classical behavior of modals and disjunction in sentences used to grant permission, and their classical behavior under negation. It also explains why permissions can expire when new information comes in and why free choice arises even when modals scope under disjunction. On the proposed approach, deontic modals update preference orderings, and connectives operate on these updates rather than propositions. The success of this approach stems from its capacity (...)
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  15. Can Questions Be Directly Disjoined? (2015).Anna Szabolcsi - 2015 - CLS Invited Talk.
    Observe that complement questions can be either directly or indirectly conjoined, but they can only be indirectly disjoined. • What theories of questions and coordination predict this difference? • Look at Partition theory (Groenendijk & Stokhof 1984) and Inquisitive Semantics (Groenendijk & Roelofsen 2009, Ciardelli et al. 2012).
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  16. What Do Quantifier Particles Do?Anna Szabolcsi - 2015 - Linguistics and Philosophy 38 (2):159-204.
    In many languages, the same particles that form quantifier words also serve as connectives, additive and scalar particles, question markers, roots of existential verbs, and so on. Do these have a unified semantics, or do they merely bear a family resemblance? Are they aided by silent operators in their varied roles―if yes, what operators? I dub the particles “quantifier particles” and refer to them generically with capitalized versions of the Japanese morphemes. I argue that both MO and KA can be (...)
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  17. Focus and Uninformativity in Yucatec Maya Questions.Scott AnderBois - 2012 - Natural Language Semantics 20 (4):349-390.
    Crosslinguistically, questions frequently make crucial use of morphosyntactic elements which also occur outside of questions. Chief among these are focus, disjunctions, and wh-words with indefinite semantics. This paper provides a compositional account of the semantics of wh-, alternative, and polar questions in Yucatec Maya (YM), which are composed primarily of these elements. Key to the account is a theory of disjunctions and indefinites (extending work by others) which recognizes the inherently inquisitive nature of these elements. While disjunctions and indefinites are (...)
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  18. Connectives Without Truth Tables.Nathan Klinedinst & Daniel Rothschild - 2012 - Natural Language Semantics 20 (2):137-175.
    There are certain uses of and and or that cannot be explained by their normal meanings as truth-functional connectives, even with sophisticated pragmatic resources. These include examples such as The cops show up, and a fight will break out (‘If the cops show up, a fight will break out’), and I have no friends, or I would throw a party (‘I have no friends. If I did have friends, I would throw a party.’). We argue that these uses are indeed (...)
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  19. Failures of Categoricity and Compositionality for Intuitionistic Disjunction.Jack Woods - 2012 - Thought: A Journal of Philosophy 1 (4):281-291.
    I show that the model-theoretic meaning that can be read off the natural deduction rules for disjunction fails to have certain desirable properties. I use this result to argue against a modest form of inferentialism which uses natural deduction rules to fix model-theoretic truth-conditions for logical connectives.
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  20. The Logic Instinct.Stephen Crain & Drew Khlentzos - 2010 - Mind and Language 25 (1):30-65.
    We present a series of arguments for logical nativism, focusing mainly on the meaning of disjunction in human languages. We propose that all human languages are logical in the sense that the meaning of linguistic expressions corresponding to disjunction (e.g. English or , Chinese huozhe, Japanese ka ) conform to the meaning of the logical operator in classical logic, inclusive- or . It is highly implausible, we argue, that children acquire the (logical) meaning of disjunction by observing how adults use (...)
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  21. Logic for Dogs.Andrew Aberdein - 2008 - In Steven D. Hales (ed.), What Philosophy Can Tell You About Your Dog. Open Court. pp. 167-181.
    Imagine a dog tracing a scent to a crossroads, sniffing all but one of the exits, and then proceeding down the last without further examination. According to Sextus Empiricus, Chrysippus argued that the dog effectively employs disjunctive syllogism, concluding that since the quarry left no trace on the other paths, it must have taken the last. The story has been retold many times, with at least four different morals: (1) dogs use logic, so they are as clever as humans; (2) (...)
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  22. Disjunction.Ray Jennings - 2008 - Stanford Encyclopedia of Philosophy.
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  23. On the Interpretation of Disjunction: Asymmetric, Incremental, and Eager for Inconsistency. [REVIEW]Raj Singh - 2008 - Linguistics and Philosophy 31 (2):245-260.
    Hurford’s Constraint (Hurford, Foundations of Language, 11, 409–411, 1974) states that a disjunction is infelicitous if its disjuncts stand in an entailment relation: #John was born in Paris or in France. Gazdar (Pragmatics, Academic Press, NY, 1979) observed that scalar implicatures can obviate the constraint. For instance, sentences of the form (A or B) or (Both Aand B) are felicitous due to the exclusivity implicature of the first disjunct: A or B implicates ‘not (A and B)’. Chierchia, Fox, and Spector (...)
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  24. The Relevance of a Relevantly Assertable Disjunction for Material Implication.Liza Verhoeven - 2007 - Journal of Philosophical Logic 36 (3):339-366.
    In this paper Grice's requirements for assertability are imposed on the disjunction of Classical Logic. Defining material implication in terms of negation and disjunction supplemented by assertability conditions, results in the disappearance of the most important paradoxes of material implication. The resulting consequence relation displays a very strong resemblance to Schurz's conclusion-relevant consequence relation.
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  25. The Bush Disjunction.Paul Keeling - 2005 - Philosophy Now 52:29-31.
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  26. The Ambiguity of Quantifiers.Francesco Paoli - 2005 - Philosophical Studies 124 (3):313-330.
    In the tradition of substructural logics, it has been claimed for a long time that conjunction and inclusive disjunction are ambiguous:we should, in fact, distinguish between ‘lattice’ connectives (also called additive or extensional) and ‘group’ connectives (also called multiplicative or intensional). We argue that an analogous ambiguity affects the quantifiers. Moreover, we show how such a perspective could yield solutions for two well-known logical puzzles: McGee’s counterexample to modus ponens and the lottery paradox.
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  27. On the Exclusivity Implicature of ‘Or’ or on the Meaning of Eating Strawberries.Liza Verhoeven & Leon Horsten - 2005 - Studia Logica 81 (1):19-24.
    This paper is a contribution to the program of constructing formal representations of pragmatic aspects of human reasoning. We propose a formalization within the framework of Adaptive Logics of the exclusivity implicature governing the connective 'or'.
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  28. Linguistic-Pragmatic Factors in Interpreting Disjunctions.Ira A. Noveck, Gennaro Chierchia, Florelle Chevaux, Raphaelle Guelminger & Emmanuel Sylvestre - 2002 - Thinking and Reasoning 8 (4):297 – 326.
    The connective or can be treated as an inclusive disjunction or else as an exclusive disjunction. Although researchers are aware of this distinction, few have examined the conditions under which each interpretation should be anticipated. Based on linguistic-pragmatic analyses, we assume that interpretations are initially inclusive before either (a) remaining so, or (b) becoming exclusive by way of an implicature ( but not both ). We point to a class of situations that ought to predispose disjunctions to inclusive interpretations and (...)
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  29. Disjunction and Alternatives.M. Simmons - 2002 - Linguistics and Philosophy 25.
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  30. Hungarian Disjunctions and Positive Polarity.Anna Szabolcsi - 2002 - In Istvan Kenesei & Peter Siptar (eds.), Approaches to Hungarian, Vol. 8. Univ. of Szeged.
    The de Morgan laws characterize how negation, conjunction, and disjunction interact with each other. They are fundamental in any semantics that bases itself on the propositional calculus/Boolean algebra. This paper is primarily concerned with the second law. In English, its validity is easy to demonstrate using linguistic examples. Consider the following: (3) Why is it so cold in here? We didn’t close the door or the window. The second sentence is ambiguous. It may mean that I suppose we did not (...)
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  31. Disjunction and Alternativeness.Mandy Simons - 2001 - Linguistics and Philosophy 24 (5):597-619.
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  32. Why the Disjunction in Quantum Logic is Not Classical.Diederik Aerts, Ellie D'Hondt & Liane Gabora - 2000 - Foundations of Physics 30 (9):1473-1480.
    The quantum logical `or' is analyzed from a physical perspective. We show that it is the existence of EPR-like correlation states for the quantum mechanical entity under consideration that make it nonequivalent to the classical situation. Specifically, the presence of potentiality in these correlation states gives rise to the quantum deviation from the classical logical `or'. We show how this arises not only in the microworld, but also in macroscopic situations where EPR-like correlation states are present. We investigate how application (...)
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  33. The Genealogy of Disjunction R. E. Jennings New York and Oxford: Oxford University Press, 1994, X + 344 Pp., $66.95. [REVIEW]Charles B. Daniels - 1997 - Dialogue 36 (1):208-210.
  34. Tūsī on Avicenna's Logical Connectives∗.Tony Street - 1995 - History and Philosophy of Logic 16 (2):257-268.
    T?s?, a thirteenth century logician writing in Arabic, uses two logical connectives to build up molecular propositions: ?if-then?, and ?either-or?. By referring to a dichotomous Tree, T?s? shows how to choose the proper disjunction relative to the terms in the disjuncts. He also discusses the disjunctive propositions which follow from a conditional proposition.
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  35. The or of Free Choice Permission.R. E. Jennings - 1994 - Topoi 13 (1):3-10.
    I argue that the conjunctive distribution of permissibility over or, which is a puzzling feature of free-choice permission is just one instance of a more general class of conjunctive occurrences of the word, and that these conjunctive uses are more directly explicable by the consideration that or is a descendant of oper than by reference to the disjunctive occurrences which logicalist prejudices may tempt us to regard as semantically more fundamental. I offer an account of how the disjunctive uses of (...)
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  36. The Genealogy of Disjunction.Raymond Earl Jennings - 1994 - Oxford and New York: Oxford University Press.
    This is a comprehensive study of the English word 'or', and the logical operators variously proposed to present its meaning. Although there are indisputably disjunctive uses of or in English, it is a mistake to suppose that logical disjunction represents its core meaning. 'Or' is descended from the Anglo-Saxon word meaning second, a form which survives in such expressions as "every other day." Its disjunctive uses arise through metalinguistic applications of an intermediate adverbial meaning which is conjunctive rather than disjunctive (...)
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  37. Algebraic Logic for Classical Conjunction and Disjunction.J. M. Font & V. Verdú - 1993 - Studia Logica 52 (1):181.
    In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent calculus. (...)
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  38. Exclusive Disjunction and the Biconditional: An Even-Odd Relationship.Joseph S. Fulda - 1993 - Mathematics Magazine 66 (2):124.
    Proves two simple identities relating the biconditional and exclusive disjunction. -/- The PDF has been made available gratis by the publisher.
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  39. Coordination and Comparatives.Friederike Moltmann - 1992 - Dissertation, MIT
  40. Algebraic Logic for Classical Conjunction and Disjunction.Josep M. Font & Ventura Verdú - 1991 - Studia Logica 50 (3-4):391 - 419.
    In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent calculus. (...)
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  41. 'Or' and 'And/Or':A Discussion.Thomas J. Richards & Roderic A. Girle - 1989 - History and Philosophy of Logic 10 (1):29-45.
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  42. The Punctuational Sources of the Truth-Functional 'Or'.R. E. Jennings - 1986 - Philosophical Studies 50 (2):237-259.
  43. Disjunction.Stephen Read - 1982 - Journal of Semantics 1 (3-4):275-285.
    In relevant logics one can formally distinguish two logical operators, symbolised as ┌A ∨ B┐ and ┌A + B┐. Addition holds for ‘ ∨ ’ and Disjunctive Syllogism for ‘ + ’, but not vice versa. The question arises, whether this distinction between two different formal notions of disjunction can be found in natural reasoning. First it is necessary to rebut Quinean objections to any rival to classical logic, Crice's claim that an intensional disjunction is not needed to explain the (...)
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  44. On the Verifiers of Disjunction.Bogus law Wolniewicz - 1980 - Bulletin of the Section of Logic 9 (2):57-59.
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  45. On the Verifiers of Disjunction.Boguslaw Wolniewicz - 1980 - Bulletin of the Section of Logic 9 (2):57-59.
    In a letter David Makinson has pointed out to me a clear-cut coun- terexample to the formula T3: S = M in [ S()), propounded in [1] for objective of disjunction. As he says: let p; q be independent E- propositions and put = p ^ q, = p^ q. Since p is an E-proposition, S = fug for some u in SE. Then S = S _ ) = S = fug; but u 62 V () [ V () (...)
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  46. Disjunctions and Questions.Vera Peetz - 1978 - Philosophy 53 (204):264 - 269.
    Mr B. H. Slater distinguishes between various pairs of questions: 1 Did they agree either that they would go to the pictures or that they would go out for a meal? 1 Did they agree that either they would go to the pictures or they would go out for a meal? 2 Is it known either that Jones was guilty or that Smith was guilty? 2 Is it known that either Jones was guilty or Smith was guilty? 3 Did he (...)
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  47. A Grammatical Point About Disjunction.B. H. Slater - 1976 - Philosophy 51 (196):226 - 228.
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  48. Exclusive or Inclusive Disjunction.James R. Hurford - 1974 - Foundations of Language 11 (3):409-411.
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  49. The Myth of the Exclusive `Or'.Robert B. Barrett & Alfred J. Stenner - 1971 - Mind 80 (317):116-121.
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  50. The Exclusive 'Or'.L. Goddard - 1959 - Analysis 20 (5):97.
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