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The Logical Analysis of Plurals and Mass Terms: A Lattice-Theoretic Approach

In P. Portner & B. H. Partee (eds.), Formal Semantics - the Essential Readings. Blackwell. pp. 127--147 (1983)

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  1. Types of plural individuals.Roger Schwarzschild - 1992 - Linguistics and Philosophy 15 (6):641 - 675.
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  • Quantifiers in Comparatives: A Semantics of Degree Based on Intervals. [REVIEW]Roger Schwarzschild & Karina Wilkinson - 2002 - Natural Language Semantics 10 (1):1-41.
    The sentence Irving was closer to me than he was to most of the others contains a quantifier, most of the other, in the scope a comparative. The first part of this paper explains the challenges presented by such cases to existing approaches to the semantics of the comparative. The second part presents a new analysis of comparatives based on intervals rather than points on a scale. This innovation is analogized to the move from moments to intervals in tense semantics. (...)
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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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  • Nip and tuck for definite description.Barry Schein - 2019 - Linguistics and Philosophy 42 (2):177-206.
    Speaking of dental floss contaminated with bacteria, I may separate the dental floss that is sterile from the dental floss that isn’t sterile. The definite description “the dental floss that isn’t sterile” contracts its reference to just the dental floss near bacteria, although it, the dental floss whole, isn’t sterile. To accommodate the definite descriptions that contract their reference, received definitions for ⌜the Φ⌝ are amended from to read as in : ⌜the Φ⌝ refers to that which any Φ is (...)
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  • Against the Russellian open future.Anders J. Schoubye & Brian Rabern - 2017 - Mind 126 (504): 1217–1237.
    Todd (2016) proposes an analysis of future-directed sentences, in particular sentences of the form 'will(φ)', that is based on the classic Russellian analysis of definite descriptions. Todd's analysis is supposed to vindicate the claim that the future is metaphysically open while retaining a simple Ockhamist semantics of future contingents and the principles of classical logic, i.e. bivalence and the law of excluded middle. Consequently, an open futurist can straightforwardly retain classical logic without appeal to supervaluations, determinacy operators, or any further (...)
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  • El dogma extensionalista de las aproximaciones veritativo-condicionales del significado.Leticia Santos Varona - 2017 - Contrastes: Revista Internacional de Filosofía 22 (2).
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  • Bare singulars and singularity in Turkish.Yağmur Sağ - 2022 - Linguistics and Philosophy 45 (4):741-793.
    This paper explores the semantics of bare singulars in Turkish, which are unmarked for number in form, as in English, but can behave like both singular and plural terms, unlike in English. While they behave like singular terms as case-marked arguments, they are interpreted number neutrally in non-case-marked argument positions, the existential copular construction, and the predicate position. Previous accounts 20:1–15, 2010; Görgülü, in: Semantics of nouns and the specification of number in Turkish, Ph.d. thesis, Simon Fraser University, 2012) propose (...)
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  • Counting, Measuring And The Semantics Of Classifiers.Susan Rothstein - 2010 - The Baltic International Yearbook of Cognition, Logic and Communication 6:1-42.
    This paper makes two central claims. The first is that there is an intimate and non-trivial relation between the mass/count distinction on the one hand and the measure/individuation distinction on the other: a defining property of mass nouns is that they denote sets of entities which can be measured, while count nouns denote sets of entities which can be counted. Crucially, this is a difference in grammatical perspective and not in ontological status. The second claim is that the mass/count distinction (...)
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  • Concealed questions and specificational subjects.Maribel Romero - 2005 - Linguistics and Philosophy 28 (6):687 - 737.
    This paper is concerned with Noun Phrases (NPs, henceforth) occurring in two constructions: concealed question NPs and NP subjects of specificational sentences. The first type of NP is illustrated in (1). The underlined NPs in (1) have been called ‘concealed questions’ because sentences that embed them typically have the same truth-conditional meaning as the corresponding versions with a full-fledged embedded interrogative clause, as illustrated in (2) (Heim 1979).
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  • Uniqueness in definite noun phrases.Craige Roberts - 2003 - Linguistics and Philosophy 26 (3):287-350.
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  • On the Identification of Quantifiers' Witness Sets: A Study of Multi-quantifier Sentences.Livio Robaldo, Jakub Szymanik & Ben Meijering - 2014 - Journal of Logic, Language and Information 23 (1):53-81.
    Natural language sentences that talk about two or more sets of entities can be assigned various readings. The ones in which the sets are independent of one another are particularly challenging from the formal point of view. In this paper we will call them ‘Independent Set (IS) readings’. Cumulative and collective readings are paradigmatic examples of IS readings. Most approaches aiming at representing the meaning of IS readings implement some kind of maximality conditions on the witness sets involved. Two kinds (...)
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  • Ontology via semantics? Introduction to the special issue on the semantics of cardinals.Craige Roberts & Stewart Shapiro - 2017 - Linguistics and Philosophy 40 (4):321-329.
    As introduction to the special issue on the semantics of cardinals, we offer some background on the relevant literature, and an overview of the contributions to this volume. Most of these papers were presented in earlier form at an interdisciplinary workshop on the topic at The Ohio State University, and the contributions to this issue reflect that interdisciplinary character: the authors represent both fields in the title of this journal.
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  • Distributivity, Collectivity, and Cumulativity in Terms of (In)dependence and Maximality.Livio Robaldo - 2011 - Journal of Logic, Language and Information 20 (2):233-271.
    This article proposes a new logical framework for NL quantification. The framework is based on Generalized Quantifiers, Skolem-like functional dependencies, and Maximality of the involved sets of entities. Among the readings available for NL sentences, those where two or more sets of entities are independent of one another are particularly challenging. In the literature, examples of those readings are known as Collective and Cumulative readings. This article briefly analyzes previous approaches to Cumulativity and Collectivity, and indicates (Schwarzschild in Pluralities. Kluwer, (...)
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  • Conservativity: a necessary property for the maximization of witness sets.L. Robaldo - 2013 - Logic Journal of the IGPL 21 (5):853-878.
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  • What we can do.Katherine Ritchie - 2020 - Philosophical Studies 177 (4):865-882.
    Plural first-person pronouns have often been ignored in the literature on indexicals and pronouns. The assumption seems to be that we is just the plural of I. So, we can focus on theorizing about singular indexicals and about non-indexical plurals then combine the results to yield a theory of plural indexicals. Here I argue that the “divide and conquer” strategy fails. By considering data involving plurals, generics, and complex demonstratives, I argue for a referential semantics on which we can refer (...)
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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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  • Pluralities and Plural Logic.Michael Rieppel - 2015 - Analysis 75 (3):504-514.
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  • Social Groups Are Concrete Material Particulars.Kevin Richardson - 2022 - Canadian Journal of Philosophy 52 (4):468-483.
    It is natural to think that social groups are concrete material particulars, but this view faces an important objection. Suppose the chess club and nature club have the same members. Intuitively, these are different clubs even though they have a common material basis. Some philosophers take these intuitions to show that the materialist view must be abandoned. I propose an alternative explanation. Social groups are concrete material particulars, but there is a psychological explanation of nonidentity intuitions. Social groups appear coincident (...)
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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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  • The descriptive content of names as predicate modifiers.Olga Poller - 2017 - Philosophical Studies 174 (9):2329-2360.
    In this paper I argue that descriptive content associated with a proper name can serve as a truth-conditionally relevant adjunct and be an additional contribution of the name to the truth-conditions. Definite descriptions the so-and-so associated by speakers with a proper name can be used as qualifying prepositional phrases as so-and-so, so sentences containing a proper name NN is doing something could be understood as NN is doing something as NN (which means as so-and-so). Used as an adjunct, the descriptive (...)
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  • All the Superhero's Names.Olga Poller - 2016 - Studia Semiotyczne 30 (2):11-44.
    In this paper I concern myself with The Superman Puzzle. I argue that the descriptive content associated with proper names, besides determining the proper name's reference, function as truthconditionally relevant adjuncts which can be used to express a manner, reason, goal, time or purpose of action. In that way a sentence with a proper name NN is doing something could be understood as NN is doing something as NN. I argue that the substitution of names can fail on modified readings (...)
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  • Friederike Moltmann, parts and wholes in semantics.Fabio Pianesi - 2002 - Linguistics and Philosophy 25 (1):97-120.
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  • Twenty-five years of linguistics and philosophy.Francis Jeffry Pelletier & Richmond H. Thomason - 2002 - Linguistics and Philosophy 25 (5-6):507-529.
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  • Descriptive Metaphysics, Natural Language Metaphysics, Sapir-Whorf, and All That Stuff: Evidence from the Mass-Count Distinction.Francis Jeffry Pelletier - 2011 - The Baltic International Yearbook of Cognition, Logic and Communication 6:7.
    Strawson described ‘descriptive metaphysics’, Bach described ‘natural language metaphysics’, Sapir and Whorf describe, well, Sapir-Whorfianism. And there are other views concerning the relation between correct semantic analysis of linguistic phenomena and the “reality” that is supposed to be thereby described. I think some considerations from the analyses of the mass-count distinction can shed some light on that very dark topic.
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  • Updating as Communication.Sarah Moss - 2012 - Philosophy and Phenomenological Research 85 (2):225-248.
    Traditional procedures for rational updating fail when it comes to self-locating opinions, such as your credences about where you are and what time it is. This paper develops an updating procedure for rational agents with self-locating beliefs. In short, I argue that rational updating can be factored into two steps. The first step uses information you recall from your previous self to form a hypothetical credence distribution, and the second step changes this hypothetical distribution to reflect information you have genuinely (...)
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  • Children's comprehension of sentences with focus particles.Kevin B. Paterson, Simon P. Liversedge, Caroline Rowland & Ruth Filik - 2003 - Cognition 89 (3):263-294.
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  • A lot of hatred and a ton of desire: intensity in the mereology of mental states.Robert Pasternak - 2019 - Linguistics and Philosophy 42 (3):267-316.
    Certain measurement-related constructions impose a requirement that the measure function used track the part-whole structure of the domain of measurement, so that a given entity or eventuality must have a larger measurement in the chosen dimension than any of its salient proper parts. I provide evidence from English and Chinese that these constructions can be used to measure the intensity of mental states like hatred and love, indicating that in the natural language ontology of such states, intensity correlates with part-whole (...)
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  • Formal Semantics: Origins, Issues, Early Impact.Barbara H. Partee - 2010 - The Baltic International Yearbook of Cognition, Logic and Communication 6 (1).
    Formal semantics is an approach to SEMANTICS1, the study of meaning, with roots in logic, the philosophy of language, and linguistics, and since the 1980’s a core area of linguistic theory. Characteristics of formal semantics to be treated in this article include the following: Formal semanticists treat meaning as mind-independent (though abstract), contrasting with the view of meanings as concepts “in the head” (see I-LANGUAGE AND E-LANGUAGE and MEANING EXTERNALISM AND INTERNALISM); formal semanticists distinguish semantics from knowledge of semantics (Lewis (...)
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  • Formal Semantics: Origins, Issues, Early Impact.Barbara H. Partee - 2011 - The Baltic International Yearbook of Cognition, Logic and Communication 6:13.
    Formal semantics and pragmatics as they have developed since the late 1960's have been shaped by fruitful interdisciplinary collaboration among linguists, philosophers, and logicians, among others, and in turn have had noticeable effects on developments in syntax, philosophy of language, computational linguistics, and cognitive science.In this paper I describe the environment in which formal semantics was born and took root, highlighting the differences in ways of thinking about natural language semantics in linguistics and in philosophy and logic. With Montague as (...)
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  • On the DP dependence of collective interpretation with numerals.Sarah Ouwayda - 2017 - Natural Language Semantics 25 (4):263-314.
    This paper argues that, given a simple [DP VP] sentence, the availability of a collective interpretation crucially depends on the syntactic and semantic properties of the subject DP, specifically the presence versus absence of a pluralizing function that makes the collective interpretation available. In support of my claim, I present Lebanese Arabic and Western Armenian examples in which an indefinite DP contains a cardinal numeral and there is no overt distributivity operator but the interpretation of the sentence is nevertheless obligatorily (...)
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  • The Semantics of Collectives and Distributives in Papago.Almerindo E. Ojeda - 1998 - Natural Language Semantics 6 (3):245-270.
    The purpose of this paper is to propose a satisfying model-theoretic account of the notions of singularity, collective plurality, and distributive plurality expressed by both the nouns and the verbs of Papago according to Mathiot (1983). The approach will be algebraic in the sense of Link (1983). Informally, our proposal is that while English has only one form of plurality, Papago has two: one based on identity and the other on equivalence. The identity-based plural is one that Papago shares with (...)
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  • Definite descriptions and definite generics.Almerindo E. Ojeda - 1991 - Linguistics and Philosophy 14 (4):367 - 397.
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  • Questions with NPIs.Andreea C. Nicolae - 2015 - Natural Language Semantics 23 (1):21-76.
    This paper investigates how the distribution of negative polarity items can inform our understanding of the underlying semantic representation of constituent questions. It argues that the distribution of NPIs in questions is governed by the same logical properties that govern their distribution in declarative constructions. Building on an observation due to Guerzoni and Sharvit that strength of exhaustivity in questions correlates with the acceptability of NPIs, I propose a revision of the semantics of questions that can explain this link in (...)
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  • Mass nouns and plural logic (extended abstract).David Nicolas - 2007 - In Proceedings of the 16th Amsterdam Colloquium. Palteam. pp. 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 plural 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 when characterizing their semantics, we arrive at a Russellian paradox. And if we use predicate logic and mereoogical ums, the semantics turns out (...)
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  • 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 upon predicate logic (...)
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  • Mixtures and Mass Terms.David Nicolas - 2021 - Dialectica 75 (1).
    In this article, I show that the semantics one adopts for mass terms constrains the metaphysical claims one can make about mixtures. I first expose why mixtures challenge a singularist approach based on mereological sums. After discussing an alternative, non-singularist approach, I take chemistry into account and explain how it changes our perspective on these issues.
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  • 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 here.Since nominal comparatives involve (...)
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  • Mereological Ontology and Dynamic Semantics.Yasuo Nakayama - 1999 - Annals of the Japan Association for Philosophy of Science 9 (4):193-206.
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  • Measurement in the nominal and verbal domains.Kimiko Nakanishi - 2007 - Linguistics and Philosophy 30 (2):235 - 276.
    This paper examines some aspects of the grammar of measurement based on data from non-split and split measure phrase (MP) constructions in Japanese. I claim that the non-split MP construction involves measurement of individuals, while the split MP construction involves measurement of events as well as of individuals. This claim is based on the observation that, while both constructions are subject to some semantic restrictions in the nominal domain, only the split MP construction is sensitive to restrictions in the verbal (...)
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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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  • Two kinds of universals and two kinds of collections.Friederike Moltmann - 2004 - Linguistics and Philosophy 27 (6):739 - 776.
    This paper argues for an ontological distinction between two kinds of universals, 'kinds of tropes' such as 'wisdom' and properties such as 'the property of being wise'. It argues that the distinction is parallel to that between two kinds of collections, pluralities such as 'the students' and collective objects such as 'the class'. The paper argues for the priortity of distributive readings with pluralities on the basis of predicates of extent or shape, such 'large' or 'long'.
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  • Reciprocals and Same/Different: Towards a Semantic Analysis.Friederike Moltmann - 1992 - Linguistics and Philosophy 15 (4):411 - 462.
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  • Measure adverbials.Friederike Moltmann - 1991 - Linguistics and Philosophy 14 (6):629 - 660.
    This papers argues that the apparent constraint of adverbials like 'for two hours' (or 'throughout the house') should not be viewed as a restriction to telic events or event predicates, but should be explained entirely in terms of the quantificational status of such adverials, acting as quantifiers over (contextually individuated) parts of a time interval (or spatial region).
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  • Intensional verbs and quantifiers.Friederike Moltmann - 1997 - Natural Language Semantics 5 (1):1-52.
    This paper discusses the semantics of intensional transitive verbs such as 'need', 'want','recognize', 'find', and 'hire'. It proposes new linguistic criteria for intensionality and defends two semantic analyses for two different classes of intensional verbs. The paper also includes a systematic classification of intensional verbs according to the type of lexical meaning they involve.
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  • Exception sentences and polyadic quantification.Friederike Moltmann - 1995 - Linguistics and Philosophy 18 (3):223 - 280.
    In this paper, I have proposed a compositional semantic analysis of exception NPs from which three core properties of exception constructions could be derived. I have shown that this analysis overcomes various empirical and conceptual shortcomings of prior proposals of the semantics of exception sentences. The analysis was first formulated for simple exception NPs, where the EP-complement was considered a set-denoting term and the EP-associate was a monadic quantifier. It was then generalized in two steps: first, in order to account (...)
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  • The English resultative perfect and its relationship to the experiential perfect and the simple past tense.Anita Mittwoch - 2008 - Linguistics and Philosophy 31 (3):323-351.
    A sentence in the Resultative perfect licenses two inferences: (a) the occurrence of an event (b) the state caused by this event obtains at evaluation time. In this paper I show that this use of the perfect is subject to a large number of distributional restrictions that all serve to highlight the result inference at the expense of the event inference. Nevertheless, only the event inference determines the truth conditions of this use of the perfect, the result inference being a (...)
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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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  • Evidence for three distinct nominal classes in Plains Cree.Jeff Mühlbauer - 2007 - Natural Language Semantics 15 (2):167-186.
    I argue for three basic classes of nominals, based on the (non)-relation they encode; (i) alienable nouns, which have no inherent relation, but gain an underspecified ‘R’ relation when possessed (Higginbotham, Linguistic Inquiry, 14, 305–420, 1983); (ii) relational nouns, which have an inherent relation, defined as an ‘R’ relation restricted by the lexical meaning of the head noun (Barker, Possessive descriptions. CSLI: California, USA, 1995; Burton, Six issues to consider when choosing a husband. Doctoral Dissertation, Rutgers, New Brunswick, New Jersey, (...)
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  • Reference to ad hoc kinds.Jon Ander Mendia - 2020 - Linguistics and Philosophy 43 (6):589-631.
    Although there is no consensus about what kinds are, there is a common understanding that kinds can be regarded as collections of objects that share certain properties. What these properties exactly are is often left unspecified. This paper explores the semantics of ad hoc kind-referring terms, where the determination of the relevant set of shared properties does not rely on “natural” properties or world knowledge. Rather, information provided by a nominal modifier, typically a relative clause, is used to impute the (...)
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  • Reference to ad hoc kinds.Jon Ander Mendia - 2020 - Linguistics and Philosophy 43 (6):589-631.
    Although there is no consensus about what kinds are, there is a common understanding that kinds can be regarded as collections of objects that share certain properties. What these properties exactly are is often left unspecified. This paper explores the semantics of ad hoc kind-referring terms, where the determination of the relevant set of shared properties does not rely on “natural” properties or world knowledge. Rather, information provided by a nominal modifier, typically a relative clause, is used to impute the (...)
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