Results for 'plural logic'

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  1.  46
    Advances in Contemporary Logic and Computer Science Proceedings of the Eleventh Brazilian Conference on Mathematical Logic, May 6-10, 1996, Salvador, Bahia, Brazil. [REVIEW]Walter A. Carnielli, Itala M. L. D'ottaviano & Brazilian Conference on Mathematical Logic - 1999
    This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society (co-sponsored by the Centre for Logic, Epistemology and the History of Science, State University of Campinas, Sao Paulo) in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading (...)
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  2.  84
    We Belong Together? A Plea for Modesty in Modal Plural Logic.Simon Hewitt - manuscript
    It is often assumed that pluralities are rigid, in the sense of having all and only their actual members necessarily. This assumption is operative in standard approaches to modal plural logic. I argue that a sceptical approach towards the assumption is warranted.
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  3.  88
    Plural Logic and Sensitivity to Order.Salvatore Florio & David Nicolas - 2015 - Australasian Journal of Philosophy 93 (3):444-464.
    Sentences that exhibit sensitivity to order (e.g. 'John and Mary arrived at school in that order' and 'Mary and John arrived at school in that order') present a challenge for the standard formulation of plural logic. In response, some authors have advocated new versions of plural logic based on fine-grained notions of plural reference, such as serial reference (Hewitt 2012) and articulated reference (Ben-Yami 2013). The aim of this article is to show that sensitivity to (...)
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  4.  40
    A Note on Plural Logic.Gustavo Fernández Díez - 2010 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 17 (2):150-162.
    A distinction is introduced between itemized and non-itemized plural predication. It is argued that a full-fledged system of plural logic is not necessary in order to account for the validity of inferences concerning itemized collective predication. Instead, it is shown how this type of inferences can be adequately dealt with in a first-order logic system, after small modifications on the standard treatment. The proposed system, unlike plural logic, has the advantage of preserving completeness. And (...)
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  5.  7
    Frege's Theorem in Plural Logic.Simon Hewitt - manuscript
    A version of Frege's theorem can be proved in a plural logic with pair abstraction. We talk through this and discuss the philosophical implications of the result.
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  6. Mass Nouns and Plural Logic.David Nicolas - 2008 - Linguistics and Philosophy 31 (2):211-244.
    A dilemma put forward by Schein (1993) and Rayo (2002) suggests that, in order to characterize the semantics of plurals, we should not use predicate logic, but non-singular logic, a formal language whose terms may refer to several things at once. We show that a similar dilemma applies to mass nouns. If we use predicate logic and sets, we arrive at a Russellian paradox when characterizing the semantics of mass nouns. Likewise, a semantics of mass nouns based (...)
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  7.  80
    Rigid and Flexible Quantification in Plural Predicate Logic.Lucas Champollion, Justin Bledin & Haoze Li - forthcoming - Semantics and Linguistic Theory 27.
    Noun phrases with overt determiners, such as <i>some apples</i> or <i>a quantity of milk</i>, differ from bare noun phrases like <i>apples</i> or <i>milk</i> in their contribution to aspectual composition. While this has been attributed to syntactic or algebraic properties of these noun phrases, such accounts have explanatory shortcomings. We suggest instead that the relevant property that distinguishes between the two classes of noun phrases derives from two modes of existential quantification, one of which holds the values of a variable fixed (...)
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  8.  45
    Review of Oliver & Smiley, Plural Logic, 2013. [REVIEW]David Nicolas - 2014 - Notre Dame Philosophical Reviews 2.
  9.  58
    Mass Nouns and Plural Logic (Extended Abstract).David Nicolas - 2007 - In Proceedings of the 16th Amsterdam Colloquium. Palteam. pp. 211-244.
  10.  81
    Quantified Modal Logic and the Plural De Re.Phillip Bricker - 1989 - Midwest Studies in Philosophy 14 (1):372-394.
    Modal sentences of the form "every F might be G" and "some F must be G" have a threefold ambiguity. in addition to the familiar readings "de dicto" and "de re", there is a third reading on which they are examples of the "plural de re": they attribute a modal property to the F's plurally in a way that cannot in general be reduced to an attribution of modal properties to the individual F's. The plural "de re" readings (...)
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  11.  48
    Plural Logic.Alex Oliver & Timothy Smiley - 2013 - Oxford University Press UK.
    Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.
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  12. E Pluribus Unum: Plural Logic and Set Theory.John P. Burgess - 2004 - Philosophia Mathematica 12 (3):193-221.
    A new axiomatization of set theory, to be called Bernays-Boolos set theory, is introduced. Its background logic is the plural logic of Boolos, and its only positive set-theoretic existence axiom is a reflection principle of Bernays. It is a very simple system of axioms sufficient to obtain the usual axioms of ZFC, plus some large cardinals, and to reduce every question of plural logic to a question of set theory.
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  13. Monism, Emergence, and Plural Logic.Einar Duenger Bohn - 2012 - Erkenntnis 76 (2):211-223.
    In this paper I argue that we need to take irreducibly plural logic more seriously in metaphysical debates due to the fact that the verdict of many metaphysical debates hangs on it. I give two examples. The main example I focus on is the debate recently revived by Jonathan Schaffer over the fundamental cardinality of the world. I show how the three main arguments provided by Schaffer are unsound in virtue of an employment of plural logic. (...)
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  14. Burgess on Plural Logic and Set Theory.Øystein Linnebo - 2007 - Philosophia Mathematica 15 (1):79-93.
    John Burgess in a 2004 paper combined plural logic and a new version of the idea of limitation of size to give an elegant motivation of the axioms of ZFC set theory. His proposal is meant to improve on earlier work by Paul Bernays in two ways. I argue that both attempted improvements fail. I am grateful to Philip Welch, two anonymous referees, and especially Ignacio Jané for written comments on earlier versions of this paper, which have led (...)
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  15.  68
    A Note on Plural Logic.Gustavo Fernández Díez - 2010 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 17 (2):150-162.
    A distinction is introduced between itemized and non-itemized plural predication. It is argued that a full-fledged system of plural logic is not necessary in order to account for the validity of inferences concerning itemized collective predication. Instead, it is shown how this type of inferences can be adequately dealt with in a first-order logic system, after small modifications on the standard treatment. The proposed system, unlike plural logic, has the advantage of preserving completeness. And (...)
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  16.  22
    A Note on Plural Logic.G. Fernandéz Díez - 2010 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 17 (2):150-162.
    A distinction is introduced between itemized and non-itemized plural predication. It is argued that a full-fledged system of plural logic is not necessary in order to account for the validity of inferences concerning itemized collective predication. Instead, it is shown how this type of inferences can be adequately dealt with in a first-order logic system, after small modifications on the standard treatment. The proposed system, unlike plural logic, has the advantage of preserving completeness. And (...)
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  17. Plural Logic: Revised Paperback Edition.Alex Oliver & Timothy Smiley - 2015 - Oxford University Press UK.
    Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.
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  18. Plural Logic: Second Edition, Revised and Enlarged.Alex Oliver & Timothy Smiley - 2016 - Oxford University Press.
    Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.
     
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  19. Plural Logic, by Alex Oliver and Timothy Smiley: Oxford: Oxford University Press, 2013, Pp. Xiv + 336, £40. [REVIEW]Lloyd Humberstone - 2015 - Australasian Journal of Philosophy 93 (1):192-195.
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  20. Plural Quantification Logic: A Critical Appraisal.Hanoch Ben-Yami - 2009 - Review of Symbolic Logic 2 (1):208-232.
    I first show that most authors who developed Plural Quantification Logic (PQL) argued it could capture various features of natural language better than can other logic systems. I then show that it fails to do so: it radically departs from natural language in two of its essential features; namely, in distinguishing plural from singular quantification and in its use of an relation. Next, I sketch a different approach that is more adequate than PQL for capturing (...) aspects of natural language semantics and logic. I conclude with a criticism of the claim that PQL should replace natural language for specific philosophical or scientific purposes. (shrink)
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  21. Pluralities and Plural Logic.Michael Rieppel - 2015 - Analysis 75 (3):504-514.
  22. Plural Logic.Michael Rieppel - forthcoming - Analysis:anv010.
     
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  23.  3
    Burgess on Plural Logic and Set Theory.O. Linnebo - 2007 - Philosophia Mathematica 15 (1):79-93.
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  24.  33
    Book Review: Alex Oliver and Timothy Smiley, Plural Logic[REVIEW]Thomas Brouwer & Casper Storm Hansen - 2015 - Studia Logica 103 (5):1095-1100.
  25.  29
    Logic & Natural Language on Plural Reference and its Semantic and Logical Significance.Hanoch Ben-Yami - 2004 - Routledge.
    Frege's invention of the predicate calculus has been the most influential event in the history of modern logic. The calculus' place in logic is so central that many philosophers think, in fact, of it when they think of logic. This book challenges the position in contemporary logic and philosophy of language of the predicate calculus claiming that it is based on mistaken assumptions. Ben-Yami shows that the predicate calculus is different from natural language in its fundamental (...)
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  26.  79
    A Modest Logic of Plurals.Alex Oliver & Timothy Smiley - 2006 - Journal of Philosophical Logic 35 (3):317-348.
    We present a plural logic that is as expressively strong as it can be without sacrificing axiomatisability, axiomatise it, and use it to chart the expressive limits set by axiomatisability. To the standard apparatus of quantification using singular variables our object-language adds plural variables, a predicate expressing inclusion (is/are/is one of/are among), and a plural definite description operator. Axiomatisability demands that plural variables only occur free, but they have a surprisingly important role. Plural description (...)
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  27.  80
    Sets and Plural Comprehension.Keith Hossack - 2014 - Journal of Philosophical Logic 43 (2-3):517-539.
    The state of affairs of some things falling under a predicate is supposedly a single entity that collects these things as its constituents. But whether we think of a state of affairs as a fact, a proposition or a possibility, problems will arise if we adopt a plural logic. For plural logic says that any plurality include themselves, so whenever there are some things, the state of affairs of their plural self-inclusion should be a single (...)
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  28. Logic and Plurals.Salvatore Florio & Øystein Linnebo - 2018 - In Kirk Ludwig & Marija Jankovic (eds.), The Routledge Handbook of Collective Intentionality. Routledge. pp. 451-463.
    This chapter provides an overview of the philosophical and linguistic debate about the logic of plurals. We present the most prominent singularizing analyses of plurals as well as the main criticisms that such analyses have received. We then introduce an alternative approach to plurals known as plural logic, focusing on the question whether plural logic can count as pure logic.
     
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  29.  32
    Logic and Natural Language: On Plural Reference and its Semantic and Logical Significance, by Hanoch Ben-Yami.Hans-Johann Glock - unknown
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  30. Plural Quantification Exposed.Øystein Linnebo - 2003 - Noûs 37 (1):71–92.
    This paper criticizes George Boolos's famous use of plural quantification to argue that monadic second-order logic is pure logic. I deny that plural quantification qualifies as pure logic and express serious misgivings about its alleged ontological innocence. My argument is based on an examination of what is involved in our understanding of the impredicative plural comprehension schema.
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  31. Plural Quantification.Ø Linnebo - 2008 - Stanford Encyclopedia of Philosophy.
    Ordinary English contains different forms of quantification over objects. In addition to the usual singular quantification, as in 'There is an apple on the table', there is plural quantification, as in 'There are some apples on the table'. Ever since Frege, formal logic has favored the two singular quantifiers ∀x and ∃x over their plural counterparts ∀xx and ∃xx (to be read as for any things xx and there are some things xx). But in recent decades it (...)
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  32. The Logic and Meaning of Plurals. Part II.Byeong-uk Yi - 2006 - Journal of Philosophical Logic 35 (3):239-288.
    In this sequel to "The logic and meaning of plurals. Part I", I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization (...)
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  33. The Logic and Meaning of Plurals. Part I.Byeong-Uk Yi - 2005 - Journal of Philosophical Logic 34 (5-6):459-506.
    Contemporary accounts of logic and language cannot give proper treatments of plural constructions of natural languages. They assume that plural constructions are redundant devices used to abbreviate singular constructions. This paper and its sequel, "The logic and meaning of plurals, II", aim to develop an account of logic and language that acknowledges limitations of singular constructions and recognizes plural constructions as their peers. To do so, the papers present natural accounts of the logic (...)
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  34.  58
    The Logic of Finite Order.Simon Hewitt - 2012 - Notre Dame Journal of Formal Logic 53 (3):297-318.
    This paper develops a formal system, consisting of a language and semantics, called serial logic ( SL ). In rough outline, SL permits quantification over, and reference to, some finite number of things in an order , in an ordinary everyday sense of the word “order,” and superplural quantification over things thus ordered. Before we discuss SL itself, some mention should be made of an issue in philosophical logic which provides the background to the development of SL , (...)
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  35. Extensionalizing Intensional Second-Order Logic.Jonathan Payne - 2015 - Notre Dame Journal of Formal Logic 56 (1):243-261.
    Neo-Fregean approaches to set theory, following Frege, have it that sets are the extensions of concepts, where concepts are the values of second-order variables. The idea is that, given a second-order entity $X$, there may be an object $\varepsilon X$, which is the extension of X. Other writers have also claimed a similar relationship between second-order logic and set theory, where sets arise from pluralities. This paper considers two interpretations of second-order logic—as being either extensional or intensional—and whether (...)
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  36. Mereological Composition and Plural Quantifier Semantics.Manuel Lechthaler & Ceth Lightfield - 2018 - Philosophia 46 (4):943-958.
    Mereological universalists and nihilists disagree on the conditions for composition. In this paper, we show how this debate is a function of one’s chosen semantics for plural quantifiers. Debating mereologists have failed to appreciate this point because of the complexity of the debate and extraneous theoretical commitments. We eliminate this by framing the debate between universalists and nihilists in a formal model where these two theses about composition are contradictory. The examination of the two theories in the model brings (...)
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  37.  69
    Plural Grundgesetze.Francesca Boccuni - 2010 - Studia Logica 96 (2):315-330.
    PG (Plural Grundgesetze) is a predicative monadic second-order system which exploits the notion of plural quantification and a few Fregean devices, among which a formulation of the infamous Basic Law V. It is shown that second-order Peano arithmetic can be derived in PG. I also investigate the philosophical issue of predicativism connected to PG. In particular, as predicativism about concepts seems rather un-Fregean, I analyse whether there is a way to make predicativism compatible with Frege’s logicism.
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  38.  54
    On the Consistency of a Plural Theory of Frege’s Grundgesetze.Francesca Boccuni - 2011 - Studia Logica 97 (3):329-345.
    PG (Plural Grundgesetze) is a predicative monadic second-order system which is aimed to derive second-order Peano arithmetic. It exploits the notion of plural quantification and a few Fregean devices, among which the infamous Basic Law V. In this paper, a model-theoretical consistency proof for the system PG is provided.
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  39. Semantics and the Plural Conception of Reality.Salvatore Florio - 2014 - Philosophers' Imprint 14:1-20.
    According to the singular conception of reality, there are objects and there are singular properties, i.e. properties that are instantiated by objects separately. It has been argued that semantic considerations about plurals give us reasons to embrace a plural conception of reality. This is the view that, in addition to singular properties, there are plural properties, i.e. properties that are instantiated jointly by many objects. In this article, I propose and defend a novel semantic account of plurals which (...)
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  40.  23
    Nominal Comparatives and Generalized Quantifiers.John Nerbonne - 1995 - Journal of Logic, Language and Information 4 (4):273-300.
    This work adopts the perspective of plural logic and measurement theory in order first to focus on the microstructure of comparative determiners; and second, to derive the properties of comparative determiners as these are studied in Generalized Quantifier Theory, locus of the most sophisticated semantic analysis of natural language determiners. The work here appears to be the first to examine comparatives within plural logic, a step which appears necessary, but which also harbors specific analytical problems examined (...)
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  41. Composition and Relative Counting.Massimiliano Carrara & Giorgio Lando - 2017 - Dialectica 71 (4):489-529.
    According to the so-called strong variant of Composition as Identity (CAI), the Principle of Indiscernibility of Identicals can be extended to composition, by resorting to broadly Fregean relativizations of cardinality ascriptions. In this paper we analyze various ways in which this relativization could be achieved. According to one broad variety of relativization, cardinality ascriptions are about objects, while concepts occupy an additional argument place. It should be possible to paraphrase the cardinality ascriptions in plural logic and, as a (...)
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  42.  48
    Reflexivity and Reciprocity with(Out) Underspecification.Sarah E. Murray - 2008 - In Alte Grønn (ed.), Proceedings of Sinn Und Bedeutung 12 (2007). ILOS. pp. 455--469.
    In languages like English, reflexivity and reciprocity are expressed by distinct proforms. However, many languages, such as Cheyenne, express reflexivity and reciprocity with a single proform. In this paper I utilize Dynamic Plural Logic (van den Berg, 1996) to a draw a semantic parallel between reflexive and reciprocal anaphors in English. I propose that they contribute overlapping but distinct requirements on the relations introduced by transitive verbs, requirements which fully specify reflexivity and reciprocity. This parallel is then extended (...)
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  43.  66
    Can Mereological Sums Serve as the Semantic Values of Plurals?David Nicolas - manuscript
    Abstract: Friends of plural logic—like Oliver & Smiley (2001), Rayo (2002), Yi (2005), and McKay (2006)—have argued that a semantics of plurals based on mereological sums would be too weak, and they have adduced several examples in favor of their claim. However, they have not considered various possible counter-arguments. So how convincing are their own arguments? We show that several of them are easily answered, while some others are more problematic. Overall, the case against mereological singularism—the idea that (...)
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  44.  45
    Dynamics of Reflexivity and Reciprocity.Sarah E. Murray - 2007 - In Maria Aloni, Paul Dekker & Floris Roelofsen (eds.), Proceedings of the Sixteenth Amsterdam Colloquium. ILLC/Department of Philosophy, University of Amsterdam. pp. 157--162.
    Plural reflexives and reciprocals are anaphoric not only to antecedent pluralities but also to relations between the members of those pluralities. In this paper, I utilize Dynamic Plural Logic (van den Berg 1996) to analyze reflexives and reciprocals as anaphors that elaborate on relations introduced by the verb, which can be collective, cumulative, or distributive. This analysis generalizes to languages like Cheyenne (Algonquian) where reflexivity and reciprocity are expressed by a single proform that I argue is underspecified, (...)
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  45.  53
    Composition and Identities.Manuel Lechthaler - 2017 - Dissertation, University of Otago
    Composition as Identity is the view that an object is identical to its parts taken collectively. I elaborate and defend a theory based on this idea: composition is a kind of identity. Since this claim is best presented within a plural logic, I develop a formal system of plural logic. The principles of this system differ from the standard views on plural logic because one of my central claims is that identity is a relation (...)
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  46.  57
    Modalising Plurals.Simon Hewitt - 2012 - Journal of Philosophical Logic 41 (5):853-875.
    There has been very little discussion of the appropriate principles to govern a modal logic of plurals. What debate there has been has accepted a principle I call (Necinc); informally if this is one of those then, necessarily: this is one of those. On this basis Williamson has criticised the Boolosian plural interpretation of monadic second-order logic. I argue against (Necinc), noting that it isn't a theorem of any logic resulting from adding modal axioms to the (...)
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  47.  53
    Sentence-Internal Different as Quantifier-Internal Anaphora.Adrian Brasoveanu - 2011 - Linguistics and Philosophy 34 (2):93-168.
    The paper proposes the first unified account of deictic/sentence-external and sentence-internal readings of singular different . The empirical motivation for such an account is provided by a cross-linguistic survey and an analysis of the differences in distribution and interpretation between singular different , plural different and same (singular or plural) in English. The main proposal is that distributive quantification temporarily makes available two discourse referents within its nuclear scope, the values of which are required by sentence-internal uses of (...)
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  48.  48
    Plural Quantifiers: A Modal Interpretation.Rafal Urbaniak - 2014 - Synthese 191 (7):1-22.
    One of the standard views on plural quantification is that its use commits one to the existence of abstract objects–sets. On this view claims like ‘some logicians admire only each other’ involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates—substitutional and set-theoretic—only the latter can provide the language of plurals with the desired expressive power (...)
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  49.  43
    A Critique of Frege on Common Nouns.Hanoch Ben-Yami - 2006 - Ratio 19 (2):148–155.
    Frege analyzed the grammatical subject-term 'S' in quantified subject-predicate sentences, 'q S are P', as being logically predicative. This is in contrast to Aristotelian Logic, according to which it is a logical subject-term, like the proper name 'a' in 'a is P' – albeit a plural one, designating many particulars. I show that Frege's arguments for his analysis are unsound, and explain how he was misled to his position by the mathematical concept of function. If common nouns in (...)
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  50. Consequences of Collapse.Theodore Sider - 2014 - In Donald Baxter & Aaron Cotnoir (eds.), Composition as Identity. Oxford University Press. pp. 211-221.
    "Composition as identity" is the radical claim that the whole is identical to the parts - radical because it implies that a single object can be identical to many objects. Composition as identity, together with auxiliary assumptions, implies the principle of "collapse": an object is one of some things if and only it is part of the fusion of those things. Collapse has important implications: the comprehension principle of plural logic must be restricted, plural definite descriptions such (...)
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