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 (...) and mereological sums is too weak, since it cannot characterize the “intermediary” construals that sentences containing mass nouns may receive. We then develop an account where mass nouns are treated as non-singular terms, which may refer to several things at once. This semantics is faithful to the intuition that, if there are eight pieces of silverware on a table, the speaker refers to eight things at once when he says: “The silverware that is on the table comes from Italy”. We show that this account provides a satisfactory semantics for a wide range of sentences, including cases often seen as difficult, like “The gold on the table weighs seven ounces” (Bunt 1985) and “All phosphorus is either red or black” (Roeper 1983). (shrink)

Cet ouvrage est consacre a l'etude de la distinction linguistique entre noms massifs (lait, mobilier, desordre, amour...) et noms comptables (chat, equipe, combat, chose...). Les premiers sont normalement invariables, tandis que les seconds s'emploient librement au singulier et au pluriel. Apres avoir etabli qu'il s'agit bien d'une distinction morpho-syntaxique, l'ouvrage discute la possibilite de caracteriser semantiquement cette distinction. Les recherches existantes ne tiennent compte, essentiellement, que des noms s'appliquant au domaine materiel. Ce travail, au contraire, examine en detail aussi bien (...) les noms concrets qu'abstraits. Il propose de redefinir les proprietes souvent attribuees aux noms massifs (references distributive et cumulative), grace, notamment, a une nouvelle notion de partie. Concernant les noms comptables, il montre qu'aucune propriete purement semantique n'est necessaire pour qu'un nom soit de ce type. L'ouvrage se termine par l'analyse des conversions (emplois massifs des noms comptables, et vice versa), et du role qu'y jouent les facteurs pragmatiques. (shrink)

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 (...) to be too weak. We then develop an account where mass nouns are treated as non-singular terms. This semantics is faithful to the intuition that, if there are eight pieces of silverware on a table, the speaker refers to eight things at once when he says: "The silverware that is on the table comes from Italy." We show that this account provides a satisfactory semantics for a wide range of sentences. (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)

'Mass terms', words like water, rice and traffic, have proved very difficult to accommodate in any theory of meaning since, unlike count nouns such as house or dog, they cannot be viewed as part of a logical set and differ in their grammatical properties. In this study, motivated by the need to design a computer program for understanding natural language utterances incorporating mass terms, Harry Bunt provides a thorough analysis of the problem and offers an original and detailed solution. An (...) extension of classical set theory, Ensemble Theory, is defined, and this provides the conceptual basis of a framework for the analysis of natural language meaning which Dr Bunt calls Two-level model-theoretic semantics. The validity of the framework is convincingly demonstrated by the formal analysis of a fragment of English including sentences with quantified and modified mass terms. Separate chapters of the book are devoted to an axiomatic definition of Ensemble Theory and a detailed discussion of its status as a mathematical formalism. (shrink)

Simple mass nouns are words like ‘water’, ‘furniture’ and ‘gold’. We can form complex mass noun phrases such as ‘dirty water’, ‘leaded gold’ and ‘green grass’. I do not propose to discuss the problems in giving a characterization of the words that are mass versus those that are not. For the purposes of this paper I shall make the following decrees: (a) nothing that is not a noun or noun phrase can be mass, (b) no abstract noun phrases are considered (...) mass, (c) words like ‘thing’, ‘entity’ and ‘object’ are not mass, (d) I shall not consider such words as ‘stuff’, ‘substance or ‘matter’, (e) measures on mass nouns (like ‘gallon of gasoline’, ‘blade of grass’, etc.) are not considered, (f) plurals of count terms are not considered mass. Within these limitations, we can say generally that mass noun phrases are those phrases that ‘much’ can be prefexed to, by ‘many’ cannot be prefexed to, without an0maly.l Semantically, such phrases usually have the property of collectiveness- they are true of any sum of things of which they are true ; and of divisiveness - they are true of any part (down to a certain limit) of things of which they are true. All of this, however, is only ‘generally speaking’ - I shall mostly use only the simple examples given above and ignore the problems in giving a complete characterization of mass nouns. In the paper I want to discuss some problems involved in casting English sentences containing mass nouns into some artificial language; but in order to do this we should have some anchoring framework on which to justify or reject a given proposal. The problem of finding an adequate language can be viewed as a case of translation (from English to the artificial language), where the translation relation must meet certain requirements. I shall suggest five such requirements; others could be added. (shrink)

" It is the connected presentation of Jespersen's views of the general principles of grammar based on years of studying various languages through both direct ...

It is argued that the usual proposals for dealing with mass-Quantification--All x is f--Are inadequate with the predicate is complex or when multiple quantification is considered. Mass-Quantification is seen as a generalisation of ordinary (thing) quantification in that the specialising assumption that the domain of quantification is atomic is not made. It is suggested that the semantic values of predicates are complete ideals of the boolean algebra consisting of the quantity which is the domain of quantification and all its sub-Quantities, (...) While logical connectives are represented by operations on complete ideals. (shrink)

Comparative judgments for mass and count nouns yield two generalizations. First, all words that can be used in both mass and count syntax always denote individuals when used in count syntax but never when used in mass syntax. Second, some mass nouns denote individuals while others do not. In this article, we show that no current theory of mass–count semantics can capture these two facts and argue for an alternative theory that can. We propose that lexical roots are not specified (...) as mass or count. Rather, a root becomes a mass noun or count noun by combining with a functional head. Some roots have denotations with individuals while others do not. The count head is interpreted as a function that maps denotations without individuals to those with individuals. The mass head is interpreted as an identity function making the interpretation of a mass noun equivalent to the interpretation of the root. As a result, all count nouns have individuals in their denotation, whereas mass counterparts of count nouns do not. Also, some roots that have individuals in their denotations can be used as mass nouns to denote individuals. (shrink)

The goal of semantics is the insightful identification of the set of meanings that human language can express - the construction of what has been called the metaphysics of natural language. A formal attempt to construct such a metaphysics has generally involved identifying a set of individuals referred to as the universe of discourse. Until recently, however, semanticists have had little to say about the structure of this set. Ojeda argues that the structure of the set of linguistic individuals is (...) a mereology, that is, the domain of discourse is made up of kinds and the instantiations of kinds. His argument forms the four main sections of this work. The first examines the semantics of countability (countable stems, number inflection, adjectives of measure, and determiners); the second explores the semantics of uncountability (the individuation of reference, the reversibility of countability, cumulative and distributive reference, and non-Boolean mass predicates); the third takes up the semantics of nominality (the mereological homogeneity of nouns and the constraints on nouns in classifier languages); and the last investigates the semantics of the conceptional neuter, a pronominal category discussed by Otto Jesperson. Ojeda's investigations contribute to the characterization of linguistic individuals and provide for a new basis for the semantics of individuation. (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)

This chapter is concerned with representing the semantics of natural language plurals and mass terms in property theory; a weak first-order theory of Truth, Propositions and Properties with fine-grained intensionality (Turner 1990, Turner 1992, Aczel 1980). The theory allows apparently coreferring items to corefer without inconsistency. This is achieved by using property modifiers which keep track of the property used to refer to a term, much like Landman’s roles (Landman 1989). We can thus predicate apparently contradictory properties of “the judge” (...) and “the cleaner,” for example, even if they turn out to be the same individual. The same device can also be used to control distribution into mereological terms: when we say “the dirty water is liquid,” we can infer that those parts that are dirty water are liquid without inferring that the dirt is liquid. The theory shows how we can formalise some aspects of natural language semantics without being forced to make certain ontological commitments. This is achieved in part by adopting an axiomatic methodology. Axioms are proposed that are just strong enough to support intuitively acceptable inferences, whilst being weak enough for some ontological choices to be avoided (such as whether or not the extensions of mass terms should be homogeneous or atomic). The axioms are deliberately incomplete, just as in basic PT, where incomplete axioms are used to avoid the logical paradoxes. The axioms presented are deliberately too weak to say much about ”non-denoting’ definite descriptors. For example, we cannot erroneously prove that they are all equal. Neither can we prove that predication of such definites results in a proposition. This means that we cannot question the truth of sentences such as “the present king of France is bald.”. (shrink)