Survey of issues pertaining to the semantics of mass and plural nouns.

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)

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 (...) nouns in their mass-occurrences and those in their count-occurrences. As both the name view and the mixed view are, in my opinion, subject to serious difficulties discussed in Section III.1,I defend a version of the predicate view. Traditionally, nouns in their singular count-occurrences are also analyzed as playing the semantic role of a predicate. How, then, does the predicate view preserve the intuitive difference between nouns in their mass- and those in their count-occurrences? I suggest, in Section III.2, that there are different kinds of predicates: mass-predicates, e.g. ‘is hair’, singular count-predicates, e.g. ‘is a hair’, and plural count-predicates, e.g. ‘are hairs’. Mass-predicates and count-predicates, in my view, are not reducible to each other. The remainder of Section III takes a closer look at the differences and interrelations between these different kinds of predicates. Mass-predicates and count-predicates differ from each other truth-conditionally, and these truth-conditional differences turn out to have interesting implications, in particular concerning the part-whole relation and our practices of counting. But mass- and count-predicates are also related to each other through systematic entailment relations; these entailment relations are examined in Section III.4. (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)

The ontological question of what there is, from the perspective of common sense, is intricately bound to what can be perceived. The above observation, when combined with the fact that nouns within language can be divided between nouns that admit counting, such as ‘pen’ or ‘human’, and those that do not, such as ‘water’ or ‘gold’, provides the starting point for the following investigation into the foundations of our linguistic and conceptual phenomena. The purpose of this paper is to claim (...) that such phenomena are facilitated by, on the one hand, an intricate cognitive capacity, and on the other by the complex environment within which we live. We are, in a sense, cognitively equipped to perceive discrete instances of matter such as bodies of water. This equipment is related to, but also differs from, that devoted to the perception of objects such as this computer. Behind this difference in cognitive equipment underlies a rich ontology, the beginnings of which lies in the distinction between matter and objects. The following paper is an attempt to make explicit the relationship between matter and objects and also provide a window to our cognition of such entities. (shrink)

Polysemy has recently emerged as a popular topic in philosophy of language. While much existing research focuses on the relatedness among senses, this article introduces a novel perspective that emphasizes the continuity of sense individuation, sense regularity, and sense productivity. This new perspective has only recently gained traction, largely due to advancements in computational linguistics. It also poses a serious challenge to semantic minimalism, so I present three arguments against minimalism from the continuous perspective that touch on the minimal concept, (...) the distinction from homonymy, and the quasi‐rule‐like nature of polysemy. Last, I provide an account of polysemy that incorporates this continuous perspective. (shrink)

Most theories of concepts take concepts to be structured bodies of information used in categorization and inference. This paper argues for a version of atomism, on which concepts are unstructured symbols. However, traditional Fodorian atomism is falsified by polysemy and fails to provide an account of how concepts figure in cognition. This paper argues that concepts are generative pointers, that is, unstructured symbols that point to memory locations where cognitively useful bodies of information are stored and can be deployed to (...) resolve polysemy. The notion of generative pointers allows for unresolved ambiguity in thought and provides a basis for conceptual engineering. (shrink)

The mass-count distinction is a morpho-syntactic distinction among nouns that is generally taken to have semantic content. This content is generally taken to reflect a conceptual, cognitive, or ontological distinction and relates to philosophical and cognitive notions of unity, identity, and counting. The mass-count distinction is certainly one of the most interesting and puzzling topics in syntax and semantics that bears on ontology and cognitive science. This volume aims to contribute to some of the gaps in the research on the (...) topic, in particular the relation between the syntactic mass-count distinction and semantic and cognitive distinctions, diagnostics for mass and count, the distribution and role of numeral classifiers, abstract mass nouns, and object mass nouns (furniture, police force, clothing). (shrink)

In this paper I focus on a recently discussed phenomenon illustrated by sentences containing predicates of taste: the phenomenon of " perspectival plurality " , whereby sentences containing two or more predicates of taste have readings according to which each predicate pertains to a different perspective. This phenomenon has been shown to be problematic for (at least certain versions of) relativism. My main aim is to further the discussion by showing that the phenomenon extends to other perspectival expressions than predicates (...) of taste and by proposing a general solution to the problem raised by it on behalf of the relativist. The core claim of the solution (" multiple indexing ") is that utterances of sentences containing perspectival expressions should be evaluated with respect to (possibly infinite) sequences of perspective parameters. (shrink)

The proper sensible criterion of sensory individuation holds that senses are individuated by the special kind of sensibles on which they exclusively bear about (colors for sight, sounds for hearing, etc.). H. P. Grice objected to the proper sensibles criterion that it cannot account for the phenomenal difference between feeling and seeing shapes or other common sensibles. That paper advances a novel answer to Grice's objection. Admittedly, the upholder of the proper sensible criterion must bind the proper sensibles –i.e. colors– (...) to the common sensibles –i.e. shapes– so as to account for the visual phenomenal character of shapes. But, as Grice rightly objected, neither association, nor ontological dependence will do –I spend some time isolating why dependence is a bad answer here, basically because the dependence of shape on colors is generic, and that genericity is arguably not part of the phenomenal content of perception. -/- Grice is wrong, however, to think that once association and dependence have been rebutted, there is no other way to attach color to extension. The right way to connect proper and common sensibles is rather trivial, although it seems to have been widely neglected: proper sensibles FILL common ones. To see a shape, by contrast to feeling it, is to perceived as filled by some color. To feel a shape, is to perceive it as, say, filled by pressure. Filling in is the phenomenal connection between proper and common sensibles. -/- One important corollary of that proposal is that proper sensibles –color, pressure, noise, taste...– have to belong to the category of stuffs, in the sense of uncountable entities. Against the widespread view that colors are properties, which have countable instances, the last part of the paper argues that colors are phenomenal stuffs, which fill some visual area. One commits a category mistake in asking: "How many tropes/instances of this determinate redness is there on that ladybird". One should rather ask "How much of this determinate redness is there on that ladybird". (shrink)

GUM is a linguistically-motivated ontology originally developed to support natural language processing systems by offering a level of representation intermediate between linguistic forms and domain knowledge. Whereas modeling decisions for individual domains may need to be responsive to domain-specific criteria, a linguistically-motivated ontology offers a characterization that generalizes across domains because its design criteria are derived independently both of domain and of application. With respect to this mediating role, the use of GUM resembles (and partially predates) the adoption of upper (...) ontologies as tools for mediating across domains and for supporting domain modeling. This paper briefly introduces the ontology, setting out its origins, design principles and applications. The example cases for this special issue are then described, illustrating particularly some of the principal differences and similarities of GUM to non-linguistically motivated upper ontologies. (shrink)

This article introduces a new pragmatic framework for dual character concepts and their expressions, offering an alternative to the received lexical‐semantic view. On the prevalent lexical‐semantic view, expressions such as “philosopher” or “scientist” are construed as lexical polysemes, comprising both a descriptive and a normative dimension. Thereby, this view prioritizes established norms, neglecting normative expressions emerging in specific contexts. In contrast, the pragmatic view integrates pragmatic modulation as a central element in explaining context‐dependent dual character concepts and expressions. This not (...) only accounts for a wider range of phenomena but also addresses several theoretical shortcomings of the lexical view. (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)

In this paper we explore the interpretation of quantity expressions in Yudja, an indigenous language spoken in the Amazonian basin, showing that while the language allows reference to exact cardinalities, it does not generally allow reference to exact measure values. It does, however, allow non-exact comparison along continuous dimensions. We use this data to argue that the grammar of exact measurement is distinct from a grammar allowing the expression of exact cardinalities, and that the grammar of counting and the grammar (...) of measurement may use numerals with different, though related interpretations. As Yudja shows, the language of measurement is not automatically acquired along with the knowledge of exact numeral expressions. We show that the ‘gap’ between prelinguistic intuitions about quantity in terms of numerosity and counting, which is bridged by the learning of language expressing exact cardinality, is paralleled by a similar gap between prelinguistic intuitions about quantity on a continuous dimension and measuring: this gap too must be bridged by language which expresses exact measure values. Our results suggest that the enculturation process by which we develop skills to perform abstract operations in the domain of measurement is (1) language dependent and (2) distinct from the process by which we learn to perform abstract calculations in the cardinal domain. (shrink)

This paper develops a semantic account of morphological number marking, specifically in the presence of numerals. In addition to accounting for number marking on basic nouns like _book_ in English, the account handles variation in patterns of number marking along two dimensions: cross-linguistically, between languages that either necessitate or prohibit singular morphology in the presence of numerals greater than ‘one’; and within one and the same language on the various nominal elements in English. Building off the presuppositional approach to morphological (...) number from Sauerland (Proc SALT 13:258–275, 2003), the proposed semantics accounts for both sorts of variation by assuming flexibility in the selection of the measure relevant to the one-ness presupposition of the morphological singular form. (shrink)

Most words in natural languages are polysemous; that is, they have related but different meanings in different contexts. This one‐to‐many mapping of form to meaning presents a challenge to understanding how word meanings are learned, represented, and processed. Previous work has focused on solutions in which multiple static semantic representations are linked to a single word form, which fails to capture important generalizations about how polysemous words are used; in particular, the graded nature of polysemous senses, and the flexibility and (...) regularity of polysemy use. We provide a novel view of how polysemous words are represented and processed, focusing on how meaning is modulated by context. Our theory is implemented within a recurrent neural network that learns distributional information through exposure to a large and representative corpus of English. Clusters of meaning emerge from how the model processes individual word forms. In keeping with distributional theories of semantics, we suggest word meanings are generalized from contexts of different word tokens, with polysemy emerging as multiple clusters of contextually modulated meanings. We validate our results against a human‐annotated corpus of polysemy focusing on the gradedness, flexibility, and regularity of polysemous sense individuation, as well as behavioral findings of offline sense relatedness ratings and online sentence processing. The results provide novel insights into how polysemy emerges from contextual processing of word meaning from both a theoretical and computational point of view. (shrink)

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)

According to what I call the Traditional View, there is a fundamental semantic distinction between counting and measuring, which is reflected in two fundamentally different sorts of scales: discrete cardinality scales and dense measurement scales. Opposed to the Traditional View is a thesis known as the Universal Density of Measurement: there is no fundamental semantic distinction between counting and measuring, and all natural language scales are dense. This paper considers a new argument for the latter, based on a puzzle I (...) call the Fractional Cardinalities Puzzle: if answers to ‘how many’-questions always designate cardinalities, and if cardinalities are necessarily discrete, then how can e.g. ‘2.38’ be a correct answer to the question ‘How many ounces of water are in the beaker?’? If cardinality scales are dense, then the answer is obvious: ‘2.38’ designates a fractional cardinality, contra the Traditional View. However, I provide novel evidence showing that ‘many’ is not uniformly associated with the dimension of cardinality across contexts, and so ‘how many’-questions can ask about other kinds of measures, including e.g. volume. By combining independently motivated analyses of cardinal adjectives, measure phrases, complex fractions, and degrees, I develop a semantics intended to defend the Traditional View against purported counterexamples like this and others which have received a fair amount of recent philosophical attention. (shrink)

Based on the view that “The meanings that we take most for granted are those where the complexity is best hidden”, the paper attempts to describe the complex cognitive operations at work in the pro...

C’est une voie inhabituelle que nous nous proposons d’emprunter pour analyser l’opposition noms comptables / noms massifs. Le chemin que nous allons suivre est celui où l’opposition massif / comptable rencontre, non pas les noms que la sémantique du prototype a appelés noms de base et noms subordonnés, comme c’est habituellement le cas, mais les hyperonymes qui les subsument, à savoir les noms superordonnés. Cette rencontre, comme on le verra, sans remettre en cause les principaux acquis des études sur la (...) distinction massif / comptable, débouchera sur deux résultats : premièrement, elle permettra d’éclairer certains aspects de la problématique restés jusqu’ici équivoques et, deuxièmement, tout en confirmant l’importance de la notion d’occurrence, apportera des éléments nouveaux à la fois sur la sémantique des noms qui ont une vocation à occuper le sommet des hiérarchies nominales et sur l’opposition massif / comptable elle-même. (shrink)