I present a high-level account of the semantical distinction between count nouns and non-count nouns. The basic idea is that count nouns are semantically either singular or plural and non-count nouns are neither.

In this paper I propose and formalize a theory of the mass-count distinction in which the denotations of count nouns are built from non-overlapping generators, while the denotations of mass nouns are built from overlapping generators. Counting is counting of generators, and it will follow that counting is only correct on count denotations.I will show that the theory allows two kinds of mass nouns: mess mass nouns with denotations built from overlapping minimal generators, and neat mass nouns (...) with denotations built from overlapping generators, where the overlap is not located in the minimal generators. Prototypical mass nouns like meat and mud are of the first kind. I will argue that mass nouns like furniture and kitchenware are of the second type.I will discuss several phenomena—all involving one way or the other explicitly or implicitly individual classifiers like stuks in Dutch—that show that both distinctions mass/count and mess/neat are linguistically robust. I will show in particular that nouns like kitchenware pattern in various ways like count nouns, and not like mess mass nouns, and that these ways naturally involve the neat structure of their denotation. I will also show that they are real mass nouns: they can involve measures in the way mess mass nouns can and count nouns cannot.I will discuss grinding interpretations of count nouns, here rebaptized fission interpretations, and argue that these interpretations differ in crucial ways from the interpretations of lexical mass nouns. The paper will end with a foundational problem raised by fission interpretations, and in the course of this, atomless interpretation domains will re-enter the scene through the back door. (shrink)

The expression of attachment to the divine in certain places among different groups has been documented by anthropologists and sociologists for decades. However, the psychological processes by which this happens are not yet fully understood. This article focuses on the concept of ‘place spirituality’ as a psychological mechanism, which allows the religious believer or non-believer to achieve an organised attachment strategy, involving the interplay of place and spiritual attachment. First, place spirituality is considered as an experience that satisfies the attachment (...) relationship criteria in that geographic places and divine entities can be perceived as ‘objects’ of attachment. Second, it is proposed that the maturational aspects of the attachment repertoire in adults make the place spirituality experience possible since adults’ cognitive abilities are much wider than those of children and can include relationships to geographical spaces and invisible divine entities. Finally, the theme of place spirituality is explored to further position the concept as a relational paradigm for understanding the relationship between place experiences and spiritual attachment. (shrink)

This rejoinder acknowledges the empirical gaps and theoretical/theological disharmony highlighted in the three selected commentaries on Place Spirituality, but we defend our central argument about the developmental pathways of PS. First, we provide an overview of recent studies on PS, highlighting what has been done so far in the field. Second, we draw from the commentaries to advance the understanding of PS in relation to three world religions: Islam, Christianity and Hinduism. Third, we evaluate the normative aspects of PS as (...) a transactional versus transitional phenomenon. Finally, we defend the two contested developmental pathways to PS, involving the compensation and correspondence working models of attachment, while complementing these models using the motivational systems framework. We maintain that these models are relevant for understanding the relationship between religious attachment and place attachment among religious and non-religious people. Recommendations for further studies are made in relation to the broader implications of PS. (shrink)

The Standards' ecumenical implications are critically assessed in view of the risks which their cross-denominational or cross-faith cooperation implications on the one hand, and, on the other hand, their secular commitments to mutual learning, non-proselytizing, professionalism, and efficiency assessment might carry for chaplains' properly spiritual orientation. The problem posed by the ambiguity of language is raised as a warning that concepts like human dignity have a profoundly different meaning in secular and Christian contexts. Invoking such concepts can be seriously misleading.

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 between two types of nominals has its direct correlate at the level of classifier phrases: classifier phrases like two bottles of wine are ambiguous between a counting, or individuating, reading and a measure reading. On the counting reading, this phrase has count semantics, on the measure reading it has mass semantics. (shrink)

The principal question addressed is whether there is a division among common nouns which is similar to a familiar division among noun phrases that designate particular-level individuals: the one which is captured in the relevant literature as the difference between de jure rigid and not de jure rigid singular terms. In relation with the previous philosophical literature relevant to noun rigidity it is argued that the extant positions on the matter are not defended on the basis of well-founded (...) syntactic categories and proper semantic arguments. Proper ways to argue for rigidity ascriptions to nouns are described. Then, such arguments are sought for the case of rigid/non-rigid division among count common nouns. It is shown that there are plausible, albeit inconclusive, reasons to hold that among common nouns (N-bar expressions) only simple common nouns are kind designators, and that if that is the case these simple common nouns will have to be reckoned as de jure rigid designators. (shrink)

In English, some common nouns, like 'dog', can combine with determiners like 'a' and 'many', but not with 'much', while other nouns, like 'water', can be used together with 'much', but not with 'a' and 'many'. These common nouns have been respectively called count nouns (CNs) and mass nouns (MNs). How do children learn to use CNs and MNs in the appropriate contexts? Gaining a better understanding of this is the goal of this paper. To do so, it is (...) important to first get clear on the nature of the distinction between CNs and MNs. Is it a grammatical distinction? Does the distinction apply to nouns, to their senses, or only to their occurrences within noun phrases (NPs)? Showing that the count-mass distinction really is grammatical and applies to nouns is the matter of my first part. Then the question occurs as to whether the distinction corresponds to a systematic difference in the sense of count and mass expressions. If it does, children's acquisition of the distinction may simply follow from their ability to learn the senses of these expressions and determiners. In a second part, I thus discuss various semantic characterizations that have been proposed, and make explicit the exceptions from which they suffer. Now, understanding the sense of an expression is interpreting it correctly as it occurs in an utterance. Formal characterizations of our interpretations help to clarify what is involved in learning and understanding these expressions. In my third part, I examine several formal characterizations with the purpose to specify what would be an adequate representation of the interpretations of mass and count nominal expressions. The understanding gained in these first three parts is used to identify what abilities are exercised by children when they acquire the count-mass distinction. The picture that emerges differs from earlier views of the acquisition in several respects. I thus describe these views and highlight the differences between them and my own proposal. In a final, fifth part, I critically examine the experimental evidence that proponents of some of the accounts of the acquisition of the count-mass distinction have cited in their favor. (shrink)

It is a common presupposition in ontology (metaphysics) that a so-called 'principle of individuation' amounts to a principle of counting. Against this presupposition I argue that the predicates 'x is the same individual as y' and 'x is one with y' are neither co-extensional nor co-intensional. Non-countable entities such as masses or stuffs (or the referents of nouns in classifier languages) also fulfill the requirements of individuality. I suggest that Leibniz' 'principle of the identity of indiscernibles' (PII) should be taken (...) as a principle of individuality, rather than as a principle of the individuality of countables. (shrink)

The paper argues that one distinction between concrete count nouns and concrete mass nouns is that geach's derelativization thesis is valid for the former but not valid for the latter. That is, Where 'f' is a concrete count noun 'x is (an) f' means 'for some y, X is the same f as y', But where 'f' is a concrete mass noun this is not so; rather, In this case, 'x is f' is tantamount to 'for (...) some y, X is the f of y'. It is further suggested that abstract nouns are in this respect to be grouped with concrete mass nouns. (shrink)

The word "world" has in fact many ordinary uses as a count noun; I shall discuss some of them below.(2) There is however also a distinctive philosophical use found in recent ontology (in the sense in which Quine reintroduced this term in analytic philosophy, for theories about what there is). As to this philosophical use, I shall argue that there is no reason to think that it refers to anything, if indeed it is intelligible at all.

The paper develops two approaches to mass term and count noun substantivals. One treats them on the model of adjectives, Designating phases of a more basic substratum. The other treats them in a more commonsense way, As multiply designating individuals. The two accounts are tested against two problems originally raised by aristotle and heraclitus respectively. The comparison is aimed at bringing out certain central features of one-Place predication, Or more materially, Features of the notion of kind.

In many languages, common nouns are divided into two morpho-syntactic subclasses, count nouns and mass nouns. Yet in certain contexts, count nouns can be used as if they were mass nouns. This linguistic phenomenon is called conversion. In this paper, we consider the conversions of count nouns into mass nouns in French. First, we identify a general semantic constraint that must be respected in these conversions, and various cases in which a count noun can be (...) used as a mass noun. Second, we examine the effects that semantic and pragmatic factors play in their interpretation. More precisely, we try to determine whether there are specific conventions for interpreting count -> mass conversions in French. Several arguments are discussed, having to do with considerations of theoretical economy, so-called "ambiguity tests", differences among languages as to what interpretations are available for conversions, and the strong feeling of conventionality of some uses. This leads us to postulate the existence of a number of specific conventions for interpreting conversions in French. (shrink)

Should objects count as necessarily having certain properties, despite their not having those properties when they do not exist? For example, should a cat that passes out of existence, and so no longer is a cat, nonetheless count as necessarily being a cat? In this essay I examine different ways of adapting Aldo Bressan’s MLν so that it can accommodate an affirmative answer to these questions. Anil Gupta, in The Logic of Common Nouns, creates a number of languages (...) that have a kinship with Bressan’s MLν , three of which are also tailored to affirmatively answering these questions. After comparing their languages, I argue that metaphysicians and philosophers of language should prefer MLν to Gupta’s languages in most applications because it can accommodate essential properties, like being a cat, while being more uniform and less cumbersome. (shrink)

Mereological entities often seem to violate ‘ordinary’ ideas of what a concrete object can be like, behaving more like sets than like Aristotelian substances. However, the mereological notions of ‘part’, ‘composition’, and ‘sum’ or ‘fusion’ appear to find concrete realisation in the actual semantics of mass nouns. Quine notes that ‘any sum of parts which are water is water’; and the wine from a single barrel can be distributed around the globe without affecting its identity. Is there here, as some (...) have claimed, a ‘natural’ or ‘innocent’ form of mereology? The claim rests on the assumption that what a mass noun such as ‘wine’ denotes — the wine from a single barrel, for example — is indeed a unit of a special type, the sum or fusion of its many ‘parts’. The assumption is, however, open to question on semantic grounds. (shrink)

The standard versions of predicativism are committed to the following two theses: proper names are count nouns in all their occurrences, and names do not refer to objects but express name-bearing properties. The main motivation for predicativism is to provide a uniform explanation of referential names and predicative names. According to predicativism, predicative names are fundamental and referential names are explained by appealing to a null determiner functioning like “the” or “that.” This paper has two goals. The first is (...) to reject the predicativists’ explanation of the two types of names. I present three syntactic counterexamples to the predicativists’ account of referential names: incorporation, modification, and measure phrase uses. The second goal is to present a novel strategy to explain the two types of names. I propose that referential names are fundamental but that there are null morphemes available for transforming a name into a count noun (and possibly into other syntactic categories). (shrink)

Names are referring expressions and interact with the determiner system only exceptionally, in stark contrast with count nouns. The-predicativists like Sloat, Matushansky, and Fara claim otherwise, maintaining that syntactic data offers indicates that names belong to a special syntactic category which differs from common count nouns only in how they interact with ‘the’. I argue that the-predicativists have incorrectly discerned the syntactic facts. They have bypassed a large range of important syntactic data and misconstrued a critical data point (...) on which they ground the-predicativism. The right data offers new compelling syntactic grounds for referentialism. (shrink)

It is unclear how children learn labels for multiple overlapping categories such as “Labrador,” “dog,” and “animal.” Xu and Tenenbaum suggested that learners infer correct meanings with the help of Bayesian inference. They instantiated these claims in a Bayesian model, which they tested with preschoolers and adults. Here, we report data testing a developmental prediction of the Bayesian model—that more knowledge should lead to narrower category inferences when presented with multiple subordinate exemplars. Two experiments did not support this prediction. Children (...) with more category knowledge showed broader generalization when presented with multiple subordinate exemplars, compared to less knowledgeable children and adults. This implies a U-shaped developmental trend. The Bayesian model was not able to account for these data, even with inputs that reflected the similarity judgments of children. We discuss implications for the Bayesian model, including a combined Bayesian/morphological knowledge account that could explain the demonstrated U-shaped trend. (shrink)

In English, some common nouns, like "cat", can be used in the singular and in the plural, while others, like "wate"r, are invariable. Moreover, nouns like "cat" can be employed with numerals like "one" and "two" and determiners like "a", "many" and "few", but neither with "much" nor "little". On the contrary, nouns like "milk" can be used with determiners like "much" and "little", but neither with "a", "one" nor "many". These two types of nouns constitute two morphosyntactic sub-classes of (...) English common nouns; cf. for instance Gillon (1992). They have been respectively called count nouns and mass nouns. In many languages, notably Romance and Germanic languages, one can similarly identify two morphosyntactic subclasses of common nouns, nouns of one class admitting singular and plural number, and nouns of the other being invariable in grammatical number. The question we want to address in this paper is one in lexical semantics: Is there anything characteristic about the meaning of a count noun? (shrink)

Portioning-out and individuation are two important semantic properties for the characterization of countability. In Mandarin, nouns are not marked with count-mass syntax, and it is controversial whether individuation is encoded in classifiers or in nouns. In the present study, we investigates the interpretation of a minimal pair of non-interrogative wh-pronominal phrases, including duo-shao-N and duo-shao-ge-N. Due to the presence/absence of the individual classifier ge, these two wh-pronominal phrases differ in how they encode portioning-out and individuation. In two experiments, we (...) used a Truth Value Judgment Task to examine the interpretation of these two wh-pronominal phrases by Mandarin-speaking adults and 4-to-6-year-old children. We found that both adults and children are sensitive to their interpretative differences with respect to the portioning-out and individuation properties. They assign either count or mass readings to the bare wh-pronominal phrase duo-shao-N depending on specific contexts, but only count readings to the classifier-bearing wh-pronominal phrase duo-shao-ge-N. Moreover, the portioning-out and individuation properties associated with the individual classifier ge emerge independently in the course of language development, with the portioning-out property taking precedence over the individuation property. Taken together, the present study provides new evidence for the view that the portioning-out and individuation properties in Mandarin are encoded in classifiers rather than in nouns, and these two semantic properties are two distinct components in our grammar. (shrink)

My thesis examines the mass/count distinction; that is, to illustrate, the distinction between the role of "hair" in "There is hair in my soup" and "There is a hair in my soup". In "hair" has a mass-occurrence; in a count-occurrence. These two kinds of noun-occurrences, I argue, can be marked off from each other largely on syntactic grounds. Along the semantic dimension, I suggest that, in order to account for the intuitive distinction between nouns in their mass-occurrences (...) and their singular count-occurrences, there must be a difference between the semantic role each of them plays. From among the available options, the most attractive one is to analyze nouns in their mass-occurrences as predicates. But, traditionally, nouns in their singular count-occurrences are also analyzed as predicates. I propose, therefore, that there are two different kinds of predicates: mass-predicates, such as "is-hair", and singular count-predicates, such as "is-a-hair". Neither kind is reducible to the other. ;Mass-predicates and singular count-predicates have something in common: they are both predicates. That is, they are related to their extension in the same way, viz. They are both true of whatever falls in their extension and the relation "is-true-of" at play here is, I conjecture, the same in both cases. The two kinds of predicates are also related to each other in a certain way, namely through a one-way entailment relation going from count to mass: everything that is a hair is also hair, but not conversely. And, finally, there are certain truth-conditional differences between them: the singular count-predicate "is-a-hair" is true only of whole individual hairs; the mass-predicate "is-hair" is true of individual hairs as well as hair-sums and hair-parts. ;These truth-conditional differences turn out to have interesting implications, in particular having to do with the part/whole relation and the act of counting. It is often held that mass-predicates are, as part of their meaning, homogeneous, while singular count-predicates are said to lack this property, as part of their meaning. I suggest, instead, that at least distributivity has to be rejected as a semantic property of mass-predicates, on the grounds that, to pick a representative example, water is not infinitely divisible into parts that are themselves water. The second kind of implication, having to do with the act of counting, is as follows. When we wish to associate, say, the world's hair with cardinal number , we need to speak of it in terms of individual hairs, the things of which the singular count-predicate "is-a-hair" is true. If, on the other hand, we are interested in amounts of hair , we need to speak of the world's hair in terms of those things of which the mass-predicate "is-hair" is true. (shrink)

In her recent defense of predicativism for proper names, Delia Graff Fara proposes the following non-metalinguistic being-called condition for the applicability of names as predicates: A name ‘N’ is true of a thing if and only if it is called N. The BCC is supposed to hold for names only. In this essay I criticize Fara’s BCC by arguing that the word ‘called’ is ambiguous, and that the BCC holds only for the particular sense of ‘calling’ as naming. I revise (...) accordingly Fara’s BCC and propose in its place a non-metalinguistic being-named condition. I also argue, against Fara, that being-named conditions are not unique to proper names: they hold for mass nouns, common count nouns, as well as for family names, which I distinguish from surnames. Finally, I discuss honorific titles and propose a being-entitled condition according to which a title ‘T’ is true of a thing just in case it is dubbed T. I conclude the paper with pragmatic, syntactic, as well as semantic considerations in favor of the thesis that names are a subspecies of non-hereditary, honorific titles. (shrink)

In The Principles of Mathematics, Russell writes: Whatever may be an object of thought, or may occur in any true or false proposition, or can be counted as one, I call a term. This, then, is the widest word in the philosophical vocabulary. I shall use as synonymous with it the words unit, individual and entity. The first two emphasize the fact that every term is one, while the third is derived from the fact that every term has being, i.e. (...) is in some sense. A man, a moment, a number, a class, a relation, a chimera, or anything else that can be mentioned, is sure to be a term'. Now in this remark, a certain extremely general, topic-neutral use of ‘object’ is singled out, a use in which the expression is treated as equivalent to (equally neutral) uses of ‘term’, ‘entity’, ‘unit’, ‘individual’, and ‘thing’. In addition, a claim is made to the effect that the content of the expression, with its emphasis on one, is such as to be adequate to comprehend the sum-total of existence, to include whatever there may be. The paper addresses the question of what this claim means, and whether it might be true. (shrink)

I argue that the coincidence of statue and matter is a special case of a common linguistic phenomenon: the use of partitive terms to individuate uses of non-count nouns (NCNs). By marking partitives and NCNs, we can easily account for the intuition that a statue and its matter are identical.

So-called mass nouns, however precisely they are defined, are in any case a subset of non-count nouns. Count nouns are either singular or plural; to be non-count is hence to be neither singular nor plural. This is not, as such, a metaphysically significant contrast: 'pieces of furniture' is plural whereas 'furniture' itself is non-count. This contrast is simply between 'the many / few' and 'the much / little' - between counting and measuring. However not all non- (...) class='Hi'>count nouns are, like 'furniture', semantically atomic - 'wine' and 'water' are not. And here there are serious difficulties in the assignment of a range of values for variables, in a formal representation of quantified sentences involving such non-atomic non-count nouns. (shrink)

This paper explores the hypothesis that all comparative sentences— nominal, verbal, and adjectival—contain instances of a single morpheme that compositionally introduces degrees. This morpheme, sometimes pronounced much, semantically contributes a structure-preserving map from entities, events, or states, to their measures along various dimensions. A major goal of the paper is to argue that the differences in dimensionality observed across domains are a consequence of what is measured, as opposed to which expression introduces the measurement. The resulting theory has a number (...) of interesting properties. It characterizes the notion of ‘measurement’ uniformly across comparative constructions, in terms of non-trivial structure preservation. It unifies the distinctions between mass/count nouns and atelic/telic verb phrases with that between gradable and non-gradable adjectives. Finally, it affords a uniform characterization of semantically anomalous comparisons across categories. (shrink)

This book reimagines the compositional semantics of comparative sentences using words such as more, as, too, and others. The book's central thesis entails a rejection of a fundamental assumption of degree semantic frameworks: that gradable adjectives like tall lexicalize functions from individuals to degrees, i.e., measure functions. I argue that comparative expressions in English themselves introduce “measure functions”; this is the case whether that morphology targets adjectives, as in *taller* or *more intelligent*; nouns, as in *more coffee*, *more coffees*; verbs, (...) such as *run more*, *jump more*; or expressions of other categories. Furthermore, she suggests that expressions that comfortably and meaningfully appear in the comparative form should be distinguished from those that do not in terms of a general notion of "measurability": a measurable predicate has a domain of application with non-trivial structure. This notion unifies the independently motivated distinctions between, for example, gradable and non-gradable adjectives, mass and count nouns, singular and plural noun phrases, and telic and atelic verb phrases. Based on careful examination of the distribution of dimensions for comparison within the class of measurable predicates, I tie the selection of measure functions to the specific nature and structure of the domain entities targeted for measurement. The book ultimately explores how, precisely, we should understand semantic theories that invoke the "nature" of domain entities: does the theory depend for its explanation on features of metaphysical reality, or something else? Such questions are especially pertinent in light of a growing body of research in cognitive science exploring the understanding and acquisition of comparative sentences. (shrink)

There are predicates that I call “stubbornly distributive” based on what happens when they are combined with plural count noun phrases. I will use these stubbornly distributive predicates to identify and analyze a certain subset of mass nouns which I call “multi-participant nouns”. Traffic and rubble are multi-participant nouns but furniture and luggage turn out not to be. Importantly, ‘typical’ mass nouns like water are multiparticipant nouns.

I argue that common nouns should be analyzed as variables, rather than as predicates which take variables as arguments. This necessitates several unusual features to the analysis, such as allowing variables to be modally non-rigid, and assigning their values compositionally. However, treating common nouns as variables offers a variety of theoretical and empirical advantages over a more traditional analysis: It predicts the conservativity of nominal quantification, simplifies the analysis of articleless languages, derives the weak reading of sentences with donkey anaphora, (...) solves the proportion problem presented by quantifiers like ‘most’, improves the analysis of the temperature paradox, allows a more unified analysis of bare plurals, and regularizes the correspondence between syntactic categories and semantic types. (shrink)

Terms such as 'wisdom' or 'happiness' are commonly held to refer to abstract objects that are properties. On the basis of a greater range of linguistic data and with the support of some ancient and medieval philosophical views, I argue that such terms do not stand for objects, but rather for kinds of tropes, entities that do not have the status of objects, but only play a role as semantic values of terms and as arguments of predicates. Such ‘non-objects’ crucially (...) differ from objects in that they are not potential bearers of properties. (shrink)

English mass noun phrases & count noun phrases differ only minimally grammatically. The basis for the difference is ascribed to a difference in the features +/-CT. These features serve the morphosyntactic function of determining the available options for the assigment of grammatical number, itself determined by the features +/-PL: +CT places no restriction on the available options, while -CT, in the unmarked case, restricts the available options to -PL. They also serve the semantic function of determining the (...) sort of denotation associated with demonstrative & quantified noun phrases. The feature -CT requires that the associated denotation be the set whose sole member is the greatest aggregate of which the noun phrase or noun is true; the feature +CT requires that the associated denotation be the set whose members are all & only those minimal aggregates of which the noun phrase or noun is true. At the same time, neither mass NPs nor count NPs that are arguments of a predicate have their predicate evaluated with respect to their denotations. Rather, the predicate is evaluated with respect to an aggregation, a set of aggregates constructed from the denotation of the noun phrase that is an argument of the predicate. 3 Tables, 4 Figures, 74 References. AA. (shrink)

In this research work I take into account the relation of indistinguishability. This relation seems to be prima facie reflexive, symmetric and transitive; in short, an equivalence relation. However, there are some cases where the relation under consideration fails to be transitive. In this thesis I will discuss two of those cases: vagueness of gradabale adjectives and count nouns, and identity criteria involving perceptual phenomena. My research attempts to answer the following question: how is it possible to communicate and (...) to make meaningful judgments using vague terms and non-transitive identity criteria? This thesis presents an analysis of vagueness and identity criteria that shows that speakers always consider the elements which vague expressions refer to or whose names compose identity statements within a context and from a certain level of precision. I also attempt to provide a formal treatment of vague adjectives and count nouns on the one hand, and of identity criteria on the other. I employ two key concepts in both the treatments: context dependence and granularity. (shrink)

The book series Linguistische Arbeiten (LA) publishes high-quality work in linguistics that addresses current issues in synchrony and diachrony, theoretically or empirically oriented.

In §54 of the Grundlagen, Frege advances an interesting proposal on how to distinguish among different sorts of concepts, only some of which he thinks can be associated with number. This paper is devoted to an analysis of the two criteria he offers, isolation and non-arbitrary division. Both criteria say something about the way in which a concept divides its extension; but they emphasize different aspects. Isolation ensures that a concept divides its extension into discrete units. I offer two construals (...) of this: isolation as discreteness, i.e. absence of overlap, between the objects to be counted; and isolation as the drawing of conceptual boundaries. Non-arbitrary division concerns the internal structure of the units we count: it makes sure that we cannot go on dividing them arbitrarily and still find more units of the kind. Non-arbitrary division focuses not only on how long something can be divided into parts of the same kind; it also speaks to the way in which these divisions are made, arbitrarily or non-arbitrarily, as well as to the compositional structure of the objects divided. (shrink)

The mass/count distinction attracts a lot of attention among cognitive scientists, possibly because it involves in fundamental ways the relation between language (i.e. grammar), thought (i.e. extralinguistic conceptual systems) and reality (i.e. the physical world). In the present paper, I explore the view that the mass/count distinction is a matter of vagueness. While every noun/concept may in a sense be vague, mass nouns/concepts are vague in a way that systematically impairs their use in counting. This idea has (...) never been systematically pursued, to the best of my knowledge. I make it precise relying on supervaluations (more specifically, ‘data semantics’) to model it. I identify a number of universals pertaining to how the mass/count contrast is encoded in the languages of the world, along with some of the major dimensions along which languages may vary on this score. I argue that the vagueness based model developed here provides a useful perspective on both. The outcome (besides shedding light on semantic variation) seems to suggest that vagueness is not just an interface phenomenon that arises in the interaction of Universal Grammar (UG) with the Conceptual/Intentional System (to adopt Chomsky’s terminology), but it is actually part of the architecture of UG. (shrink)

This paper documents the number-related properties of Dëne Sųłiné (Athapaskan). Dëne Sųłiné has neither number inflection nor numeral classifiers. Nouns are bare, occur as such in argument positions, and combine directly with numerals. With these traits, Dëne Sųłiné represents a type of language that is little considered in formal typologies of number and countability. The paper critiques one influential proposal, that of Chierchia (in: Rothstein (ed.) Events and grammar, 1998a; Natural Language Semantics 6: 339–405, 1998b), and presents an alternative number (...) typology, which introduces variation in the semantics of numerals. It will be shown that bare nouns in Dëne Sųłiné can be mass or count. Hence, the difference between count and mass cannot be expressed in terms of number, as in Chierchia. Instead, I express it in terms of atomicity. Mass nouns have nonatomic denotations, bare count nouns have atomic denotations that comprise singularities and pluralities. I also propose that numerals contain a function that accesses the singularities in a noun’s denotation. Hence they are compatible with bare count nouns, but not with mass nouns. In classifier languages, numerals denote a cardinality only; singularity-accessing functions are expressed in separate elements: the classifiers. Thus, languages like Chinese require classifiers because the numerals are semantically deficient, and not, as is assumed by Chierchia and others, the bare nouns. (shrink)

A semantic analysis of mass nouns is given in terms of a logic of classes as many. In previous work it was shown that plural reference and predication for count nouns can be interpreted within this logic of classes as many in terms of the subclasses of the classes that are the extensions of those count nouns. A brief review of that account of plurals is given here and it is then shown how the same kind of interpretation (...) can also be given for mass nouns. (shrink)

Common nouns and noun phrases have usually been analyzed semantically as predicates. In quantified sentences, these predicates take variables as arguments. This paper develops and defends an analysis in which common nouns and noun phrases themselves are treated as variables, rather than as predicates taking variables as arguments. Several apparent challenges for this view will be addressed, including the modal non-rigidity of common nouns. Two major advantages to treating common nouns as variables will be presented: Such an analysis (...) predicts that all nominal quantification is conservative, rather than requiring conservativity to be stipulated as a constraint on determiner denotations; and it makes possible some improvements to the analysis of the temperature paradox, allowing for quantificational examples without adding a spurious layer of modal variability. (shrink)