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Distributive, collective and cumulative quantification

In Jeroen A. G. Groenendijk (ed.), Formal methods in the study of language. U of Amsterdam. pp. 483--512 (1981)

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  1. Collective Practical Knowledge is a Fragmented Interrogative Capacity.Joshua Habgood-Coote - 2022 - Philosophical Issues 32 (1):180-199.
    What does it take for a group of people to know how to do something? An account of collective practical knowledge ought to be compatible with the linguistic evidence about the semantics for collective knowledge-how ascriptions, be able to explain the practicality of collective knowledge, be able to explain both the connection between individual and collective know-how and the possibility of a group knowing how to do something none of its members know, and be applicable to a suitably wide range (...)
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  • Polarity in Natural Language: Predication, Quantification and Negation in Particular and Characterizing Sentences.Sebastian Löbner - 2000 - Linguistics and Philosophy 23 (3):213-308.
    The present paper is an attempt at the investigation of the nature of polarity contrast in natural languages. Truth conditions for natural language sentences are incomplete unless they include a proper definition of the conditions under which they are false. It is argued that the tertium non datur principle of classical bivalent logical systems is empirically invalid for natural languages: falsity cannot be equated with non-truth. Lacking a direct intuition about the conditions under which a sentence is false, we need (...)
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  • (1 other version)Modal set theory.Christopher Menzel - 2018 - In Otávio Bueno & Scott A. Shalkowski (eds.), The Routledge Handbook of Modality. New York: Routledge.
    This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory.
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  • Multiple reference and vague objects.Giovanni Merlo - 2017 - Synthese 194 (7):2645-2666.
    Kilimanjaro is an example of what some philosophers would call a ‘vague object’: it is only roughly 5895 m tall, its weight is not precise and its boundaries are fuzzy because some particles are neither determinately part of it nor determinately not part of it. It has been suggested that this vagueness arises as a result of semantic indecision: it is because we didn’t make up our mind what the expression “Kilimanjaro” applies to that we can truthfully say such things (...)
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  • (1 other version)Quantification and Contributing Objects to Thoughts.Michael Glanzberg - 2008 - Philosophical Perspectives 22 (1):207-231.
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  • Donkey pluralities: plural information states versus non-atomic individuals.Adrian Brasoveanu - 2008 - Linguistics and Philosophy 31 (2):129-209.
    The paper argues that two distinct and independent notions of plurality are involved in natural language anaphora and quantification: plural reference (the usual non-atomic individuals) and plural discourse reference, i.e., reference to a quantificational dependency between sets of objects (e.g., atomic/non-atomic individuals) that is established and subsequently elaborated upon in discourse. Following van den Berg (PhD dissertation, University of Amsterdam, 1996), plural discourse reference is modeled as plural information states (i.e., as sets of variable assignments) in a new dynamic system (...)
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  • Quantification as reference: Kalaallisut Q-verbs.Maria Bittner & Naja Trondhjem - 2008 - In Lisa Matthewson (ed.), Quantification: A Cross-Linguistic Perspective. Emerald. pp. 7-66.
    Formal semantics has so far focused on three categories of quantifiers, to wit, Q-determiners (e.g. 'every'), Q-adverbs (e.g. 'always'), and Q-auxiliaries (e.g. 'would'). All three can be analyzed in terms of tripartite logical forms (LF). This paper presents evidence from verbs with distributive affixes (Q-verbs) in Kalaallisut, Polish, and Bininj Gun-wok, which cannot be analyzed in terms of tripartite LFs. It is argued that a Q-verb involves discourse reference to a distributive verbal dependency, i.e. an episode-valued function that sends different (...)
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  • The Semantics of Together.Friederike Moltmann - 2004 - Natural Language Semantics 12 (4):289-318.
    The semantic function of the modifier 'together' in adnominal position has generally been considered to be that of preventing a distributive reading of the predicate. This paper will argue that this view is mistaken. The semantic function of adnominal 'together' rather is that of inducing a cumulative measurement of the group that together is associated with. The measurement-based analysis of adnominal together that I propose can also, with some modifications, be extended to adverbial occurrences of together.
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  • Weak islands and an algebraic semantics for scope taking.Anna Szabolcsi & Frans Zwarts - 1997 - In Ways of Scope Taking. Kluwer Academic Publishers.
    Modifying the descriptive and theoretical generalizations of Relativized Minimality, we argue that a significant subset of weak island violations arise when an extracted phrase should scope over some intervener but is unable to. Harmless interveners seem harmless because they can support an alternative reading. This paper focuses on why certain wh-phrases are poor wide scope takers, and offers an algebraic perspective on scope interaction. Each scopal element SE is associated with certain operations (e.g., not with complements). When a wh-phrase scopes (...)
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  • Friends and colleagues: Plurality, coordination, and the structure of DP.Caroline Heycock & Roberto Zamparelli - 2005 - Natural Language Semantics 13 (3):201-270.
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  • Relational domains and the interpretation of reciprocals.Sivan Sabato & Yoad Winter - 2012 - Linguistics and Philosophy 35 (3):191-241.
    We argue that a comprehensive theory of reciprocals must rely on a general taxonomy of restrictions on the interpretation of relational expressions. Developing such a taxonomy, we propose a new principle for interpreting reciprocals that relies on the interpretation of the relation in their scope. This principle, the Maximal Interpretation Hypothesis (MIH), analyzes reciprocals as partial polyadic quantifiers. According to the MIH, the partial quantifier denoted by a reciprocal requires the relational expression REL in its scope to denote a maximal (...)
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  • Ways of Scope Taking.Anna Szabolcsi (ed.) - 1997 - Kluwer Academic Publishers.
    Ways of Scope Taking is concerned with syntactic, semantic and computational aspects of scope. Its starting point is the well-known but often neglected fact that different types of quantifiers interact differently with each other and other operators. The theoretical examination of significant bodies of data, both old and novel, leads to two central claims. (1) Scope is a by-product of a set of distinct Logical Form processes; each quantifier participates in those that suit its particular features. (2) Scope interaction is (...)
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  • Proceedings of the Sixteenth Amsterdam Colloquium.Maria Aloni & Paul Dekker - unknown
    The 2007 edition of the Amsterdam Colloquium is the Sixteenth in a series which started in 1976. Originally, the Amsterdam Colloquium was an initiative of the Department of Philosophy of the University of Amsterdam. Since 1984 the Colloquium is organized by the Institute for Logic, Language and Computation (ILLC) of the University of Amsterdam.
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  • (1 other version)Partitioning Logical Space.Jeroen Groenendijk & Martin Stokhof - manuscript
    In the present version of these lecture notes only a number of typos and a few glaring mistakes have been corrected. Thanks to Paul Dekker for his help in this respect. No attempt has been been made to update the original text or to incorporate new insights and approaches. For a more recent overview, see our ‘Questions’ in the Handbook of Logic and Language (edited by Johan van Benthem and Alice ter Meulen, Elsevier, 1997).
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  • On the plurality of verbs.Angelika Kratzer - 2008 - In Johannes Dölling, Tatjana Heyde-Zybatow & Martin Schäfer (eds.), Event Structures in Linguistic Form and Interpretation. De Gruyter. pp. 269-300.
    This paper pursues some of the consequences of the idea that there are (at least) two sources for distributive/cumulative interpretations in English. One source is lexical pluralization: All predicative stems are born as plurals, as Manfred Krifka and Fred Landman have argued. Lexical pluralization should be available in any language and should not depend on the particular make-up of its DPs. I suggest that the other source of cumulative/distributive interpretations in English is directly provided by plural DPs. DPs with plural (...)
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  • Parts and Wholes in Semantics.Friederike Moltmann - 1997 - New York: Oxford University Press.
    This book present a unified semantic theory of expressions involving the notions of part and whole. It develops a theory of part structures which differs from traditional (extensional) mereological theories in that the notion of an integrated whole plays a central role and in that the part structure of an entity is allowed to vary across different situations, perspectives, and dimensions. The book presents a great range of empirical generalizations involving plurals, mass nouns, adnominal and adverbial modifiers such as 'whole', (...)
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  • Mass Nouns and Plurals.Peter Lasersohn - 2011 - In Klaus von Heusinger, Claudia Maienborn & Paul Portner (eds.), Semantics: An International Handbook of Natural Language Meaning. De Gruyter Mouton. pp. 2.
    Survey of issues pertaining to the semantics of mass and plural nouns.
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  • Part Structures in Situations: The Semantics of 'Individual' and 'Whole'.Friederike Moltmann - 2005 - Linguistics and Philosophy 28 (5):599 - 641.
    This paper presents a theory of situated part structures involving the notion of an integrated and not just a part-of relation. The theory is applied in particular to the semantics of the modifiers 'whole' and 'individual', as in 'the whole collection' and 'the individual students'. The adnominal modifiers 'whole' and 'individual' have been entirely been ignored in the linguistic and philosophical literature, even though they pose significant challenges for standard views of reference, of the semantics of referential NPs, and for (...)
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  • Groups, I.Fred Landman - 1989 - Linguistics and Philosophy 12 (5):559 - 605.
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  • The semantics of mass-predicates.Kathrin Koslicki - 1999 - Noûs 33 (1):46-91.
    Along with many other languages, English has a relatively straightforward grammatical distinction between mass-occurrences of nouns and their countoccurrences. As the mass-count distinction, in my view, is best drawn between occurrences of expressions, rather than expressions themselves, it becomes important that there be some rule-governed way of classifying a given noun-occurrence into mass or count. The project of classifying noun-occurrences is the topic of Section II of this paper. Section III, the remainder of the paper, concerns the semantic differences between (...)
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  • A remark on collective quantification.Juha Kontinen & Jakub Szymanik - 2008 - Journal of Logic, Language and Information 17 (2):131-140.
    We consider collective quantification in natural language. For many years the common strategy in formalizing collective quantification has been to define the meanings of collective determiners, quantifying over collections, using certain type-shifting operations. These type-shifting operations, i.e., lifts, define the collective interpretations of determiners systematically from the standard meanings of quantifiers. All the lifts considered in the literature turn out to be definable in second-order logic. We argue that second-order definable quantifiers are probably not expressive enough to formalize all collective (...)
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  • (1 other version)Discourse grammar and verb phrase anaphora.Hub Prüst, Remko Scha & Martin Van Den Berg - 1994 - Linguistics and Philosophy 17 (3):261-327.
    We argue that an adequate treatment of verb phrase anaphora must depart in two major respects from the standard approaches. First of all, VP anaphors cannot be resolved by simply identifying the anaphoric VP with an antecedent VP. The resolution process must establish a syntactic/semantic parallelism between larger units that the VPs occur in. Secondly, discourse structure has a significant influence on the reference possibilities of VPA. This influence must be accounted for. We propose a treatment which meets these requirements. (...)
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  • Scopeless quantity words in Shona.Elizabeth Ferch - 2013 - Natural Language Semantics 21 (4):373-400.
    In Shona , bare plurals and bare singulars seem to have different scope possibilities with respect to a class of modifiers which I term “scopeless quantity words” few’, and ose ‘all’). I argue that this is due to two factors. First, the scopeless quantity words are intersective modifiers rather than quantifying determiners, so that DPs containing them denote entities rather than generalised quantifiers. Second, transitive sentences involving plural arguments are usually interpreted using the **-operator, which gives a cumulative reading; the (...)
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  • Pluractional comparisons.Sigrid Beck - 2012 - Linguistics and Philosophy 35 (1):57-110.
    This paper develops a semantic analysis of data like It is getting colder and colder. Their meaning is argued to arise from a combination of a comparative with pluractionality. The analysis is embedded in a general theory of plural predication and pluractionality. It supports a semantic theory involving a family of syntactic plural operators.
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  • Two kinds of distributivity.Hanna de Vries - 2017 - Natural Language Semantics 25 (2):173-197.
    This paper argues that lexical and operator-based analyses of distributivity are not in conflict, but are both necessary components of any theory of distributivity that aims to account for all the relevant data. I use several contrasts between plural definites and group NPs to show that we need an operator-based analysis of distributivity; this kind of distributivity is available with plural definites but not with group subjects, which can be explained under the common assumption that group NPs denote atoms rather (...)
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  • Comparing pluralities.Gregory Scontras, Peter Graff & Noah D. Goodman - 2012 - Cognition 123 (1):190-197.
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  • Reciprocals are Definites.Sigrid Beck - 2001 - Natural Language Semantics 9 (1):69-138.
    This paper proposes that elementary reciprocal sentences have four semantic readings: a strongly reciprocal interpretation, a weakly reciprocal interpretation, a situation-based weakly reciprocal reading, and a collective reading. Interpretational possibilities of reciprocal sentences that have been discussed in the literature are identified as one of these four. A compositional semantic analysis of all of these readings is provided in which the reciprocal expression is uniformly represented as 'the other ones among them' (recasting Heim, Lasnik and May 1991a, b). A reciprocal (...)
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  • Dependent Plurals and Plural Meaning.Eytan Zweig - 2008 - Dissertation, Nyu
    While writing this thesis, there were many things I wanted to get right. I wanted to get the data right. I wanted to get my analysis of the data right. I certainly wanted to get all my citations right, which can get pretty tricky when one is trying to finish a chapter at 2am. But if an error did creep in somewhere in the body of the thesis, that is not a disaster. Sooner or later, I will get a chance (...)
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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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  • Syntax and semantics: an overview.Arnim von Stechow - 2011 - In Klaus von Heusinger, Claudia Maienborn & Paul Portner (eds.), Semantics: An International Handbook of Natural Language Meaning. De Gruyter Mouton.
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  • A unified semantic treatment of singular NP coordination.Yoad Winter - 1996 - Linguistics and Philosophy 19 (4):337 - 391.
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  • Types of plural individuals.Roger Schwarzschild - 1992 - Linguistics and Philosophy 15 (6):641 - 675.
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  • Discourse grammar and verb phrase anaphora.Hub Prüst, Remko Scha & Martin Berg - 1994 - Linguistics and Philosophy 17 (3):261-327.
    We argue that an adequate treatment of verb phrase anaphora must depart in two major respects from the standard approaches. First of all, VP anaphors cannot be resolved by simply identifying the anaphoric VP with an antecedent VP. The resolution process must establish a syntactic/semantic parallelism between larger units that the VPs occur in. Secondly, discourse structure has a significant influence on the reference possibilities of VPA. This influence must be accounted for.We propose a treatment which meets these requirements. It (...)
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  • Generalized conjunction and temporal modification.Peter Lasersohn - 1992 - Linguistics and Philosophy 15 (4):381 - 410.
    Argues for an assimilation of sentential and predicate conjunction to collective conjunction, based on modification of predicates by adverbs such as 'alternately'.
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  • Beyond the Frege boundary.Edward L. Keenan - 1992 - Linguistics and Philosophy 15 (2):199-221.
    In sentences like Every teacher laughed we think of every teacher as a unary (=type (1)) quantifier - it expresses a property of one place predicate denotations. In variable binding terms, unary quantifiers bind one variable. Two applications of unary quantifiers, as in the interpretation of No student likes every teacher, determine a binary (= type (2)) quantifier; they express properties of two place predicate denotations. In variable binding terms they bind two variables. We call a binary quantifier Fregean (or (...)
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  • Monotonicity and collective quantification.Gilad Ben-avi & Yoad Winter - 2003 - Journal of Logic, Language and Information 12 (2):127-151.
    This article studies the monotonicity behavior of plural determinersthat quantify over collections. Following previous work, we describe thecollective interpretation of determiners such as all, some andmost using generalized quantifiers of a higher type that areobtained systematically by applying a type shifting operator to thestandard meanings of determiners in Generalized Quantifier Theory. Twoprocesses of counting and existential quantification thatappear with plural quantifiers are unified into a single determinerfitting operator, which, unlike previous proposals, both capturesexistential quantification with plural determiners and respects theirmonotonicity (...)
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  • Reference by proxy.Michael Rieppel - 2022 - Synthese 200 (3):1-18.
    Formal semantic theories are generally thought to make contact with pre-theoretic semantic notions of aboutness and reference. The nature of that contact is, however, not always straightforward. This paper addresses two debates where that issue assumes a significant role. I begin with Simchen’s recent argument that Lewisian Interpretationism succumbs to referential indeterminacy. I develop a proposal about the relationship between the theoretical notion of a term’s semantic value and the pre-theoretic notion of reference, and argue that the indeterminacy Simchen identifies (...)
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  • Dependent plurals and three levels of multiplicity.Serge Minor - 2022 - Linguistics and Philosophy 45 (3):431-509.
    The paper focuses on the semantics of distributivity, grammatical number, and cardinality predicates. I argue that constructions involving so-called ‘dependent plurals’, i.e. plurals lacking cardinality predicates occurring in the scope of certain quantificational items such as all and most, pose a challenge to familiar semantic frameworks that distinguish between two sources of multiplicity: mereological plurality and distributive quantification. I argue that dependent plural readings should be analysed as distinct both from cumulative readings and distributive readings, in the classical sense. I (...)
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  • On The Interpretation of Wide-scope Indefinites.Lisa Matthewson - 1998 - Natural Language Semantics 7 (1):79-134.
    This paper argues, on the basis of data from St'át'imcets (Lillooet Salish), for a theory of wide-scope indefinites which is similar, though not identical, to that proposed by Kratzer (1998). I show that a subset of S'át'imcets indefinites takes obligatory wide scope with respect to if-clauses, negation, and modals, and is unable to be distributed over by quantificational phrases. These wide-scope effects cannot be accounted for by movement, but require an analysis involving choice functions (Reinhart 1995, 1997). However, Reinhart's particular (...)
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  • Aspect, quantification and plurality.Lucas Champollion - unknown
    The goal of this dissertation is twofold. First, we aim to identify the source of distributivity in natural language. Our hypothesis is that throughout the grammar, distributivity can be tracked down to a single operator. Two converging lines of reasoning help us identify this operator. One line emerges as a result of generalizing and unifying previously disparate treatments of distributivity in the domain of nominal quantifiers. The other line comes from analyzing the meaning of durative adverbials, with special attention to (...)
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  • Distributivity and Dependency.Yoad Winter - 2000 - Natural Language Semantics 8 (1):27-69.
    Sentences with multiple occurrences of plural definites give rise to certain effects suggesting that distributivity should be modeled by polyadic operations. Yet in this paper it is argued that the simpler treatment of distributivity using unary universal quantification should be retained. Seemingly polyadic effects are claimed to be restricted to definite NPs. This fact is accounted for by the special anaphoric (dependent) use of definites. Further evidence concerning various plurals, island constraints, and cumulative quantification is shown to support this claim. (...)
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  • Induction and comparison.Paul Pietrowski - 2007 - University of Maryland Working Papers in Linguistics 15:154-188.
    Frege proved an important result, concerning the relation of arithmetic to second-order logic, that bears on several issues in linguistics. Frege’s Theorem illustrates the logic of relations like PRECEDES(x, y) and TALLER(x, y), while raising doubts about the idea that we understand sentences like ‘Carl is taller than Al’ in terms of abstracta like heights and numbers. Abstract paraphrase can be useful—as when we say that Carl’s height exceeds Al’s—without reflecting semantic structure. Related points apply to causal relations, and even (...)
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  • Vector space semantics: A model-theoretic analysis of locative prepositions. [REVIEW]Joost Zwarts & Yoad Winter - 2000 - Journal of Logic, Language and Information 9 (2):169-211.
    This paper introduces a compositional semantics of locativeprepositional phrases which is based on a vector space ontology.Model-theoretic properties of prepositions like monotonicity andconservativity are defined in this system in a straightforward way.These notions are shown to describe central inferences with spatialexpressions and to account for the grammaticality of prepositionmodification. Model-theoretic constraints on the set of possibleprepositions in natural language are specified, similar to the semanticuniversals of Generalized Quantifier Theory.
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  • Choice functions and the scopal semantics of indefinites.Yoad Winter - 1997 - Linguistics and Philosophy 20 (4):399-467.
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  • Quantifier scope: How labor is divided between QR and choice functions. [REVIEW]Tanya Reinhart - 1997 - Linguistics and Philosophy 20 (4):335-397.
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  • Plurals, presuppositions and the sources of distributivity.Roger Schwarzschild - 1993 - Natural Language Semantics 2 (3):201-248.
    This paper begins with a discussion ofcumulativity (e.g., ‘P(a) & P(b) implies P(a+b)’), formalized using a verb phrase operator. Next, the meanings of distributivity markers such aseach and non-distributivity indicators such astogether are considered. An existing analysis ofeach in terms of quantification over parts of a plurality is adopted. However,together is problematic, for it involves a cancellation or negation of the quantification associated witheach. (The four boys together owned exactly three cars could not be true if each of the boys (...)
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  • Pragmatic identification of the witness sets.Livio Robaldo & Jakub Szymanik - 2012 - Proceeding of the 8th Conference on Language Resources and Evaluation.
    Among the readings available for NL sentences, those where two or more sets of entities are independent of one another are particularly challenging from both a theoretical and an empirical point of view. Those readings are termed here as ‘Independent Set (IS) readings'. Standard examples of such readings are the well-known Collective and Cumulative Readings. (Robaldo, 2011) proposes a logical framework that can properly represent the meaning of IS readings in terms of a set-Skolemization of the witness sets. One of (...)
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  • Genericity and logical form.Kathrin Koslicki - 1999 - Mind and Language 14 (4):441–467.
    In this paper I propose a novel treatment of generic sentences, which proceeds by means of different levels of analysis. According to this account, all generic sentences (I-generics and D-generics alike) are initially treated in a uniform manner, as involving higher-order predication (following the work of George Boolos, James Higginbotham and Barry Schein on plurals). Their non-uniform character, however, re-emerges at subsequent levels of analysis, when the higher-order predications of the first level are cashed out in terms of quantification over (...)
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  • (1 other version)Quantification and Contributing Objects to Thoughts.Michael Glanzberg - 2008 - Noûs 42 (1):207 - 231.
    In this paper, I shall explore a determiner in natural language which is ambivalent as to whether it should be classified as quantificational or objectdenoting: the determiner both. Both in many ways appears to be a paradigmatic quantifier; and yet, I shall argue, it can be interpreted as having an individual—an object—as semantic value. To show the significance of this, I shall discuss two ways of thinking about quantifiers. We often think about quantifiers via intuitions about kinds of thoughts. Certain (...)
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  • Group action and spatio-temporal proximity.Peter Lasersohn - 1990 - Linguistics and Philosophy 13 (2):179 - 206.
    Presents a unified semantics for various readings of 'together', using event mereology.
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