Methods of representing sentences containing mass terms (e.g. "gold") and amount terms (e.g. "three gallons") within the predicate calculus are given, and the semantics of the resulting sentences is discussed. the appendix sketches a way to systematically translate english sentences into the logical notation, exploiting some results of transformational grammar.

previous theories and the relevance of those criticisms to the new accounts. Additionally, we have included a new section at the end, which gives some directions to literature outside of formal semantics in which the notion of mass has been employed. We looked at work on mass expressions in psycholinguistics and computational linguistics here, and we discussed some research in the history of philosophy and in metaphysics that makes use of the notion of mass.

When philosophers talk about descriptions, usually they have in mind singular definite descriptions such as ‘the finest Greek poet’ or ‘the positive square root of nine’, phrases formed with the definite article ‘the’. English also contains indefinite descriptions such as ‘a fine Greek poet’ or ‘a square root of nine’, phrases formed with the indefinite article ‘a’ (or ‘an’); and demonstrative descriptions (also known as complex demonstratives) such as ‘this Greek poet’ and ‘that tall woman’, formed with the demonstrative articles (...) ‘this’ and ‘that’. Following the custom in philosophy, in this chapter often we use ‘description’ as short for ‘definite description’; and following the custom in linguistics, often we use ‘definite’, ‘indefinite’, and ‘demonstrative’ as shorthand nouns. For the most part we focus on definite and indefinites, although a few words about demonstratives are called for. At the centre of debates about descriptions is the matter of whether they are devices of reference or of predication (simple or higher-order), and much discussion focuses on how various proposals are to be incorporated into broader theories of the semantics of natural language. But philosophical interest goes beyond the confines of linguistics, logic, and the philosophy of language because choices made about the semantics of descriptions have repercussions elsewhere, particularly in epistemology and metaphysics. A simple match of form and meaning appears to fail.1 First, many occurrences of expressions of both forms ‘the φ’ and ‘a φ’ appear to be used to talk about particular individuals. Consider (1). (shrink)

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (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)

'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)

Branching quantifiers were first introduced by L. Henkin in his 1959 paper ‘Some Remarks on Infmitely Long Formulas’. By ‘branching quantifiers’ Henkin meant a new, non-linearly structured quantiiier-prefix whose discovery was triggered by the problem of interpreting infinitistic formulas of a certain form} The branching (or partially-ordered) quantifier-prefix is, however, not essentially infinitistic, and the issues it raises have largely been discussed in the literature in the context of finitistic logic, as they will be here. Our discussion transcends, however, the (...) resources of standard lst-order languages and we will consider the new form in the context of 1st-order logic with 1- and 2-place ‘Mostowskian` generalized quantifiers.2.. (shrink)

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.

Extension of the logical language to deliver plural reference and the logical relations that constitute knowledge of the singular and plural acquires empirical bite just in case it conforms with increasing precision to the syntax of the natural language and affords explanation of what speakers know about the distribution and meaning of plural expressions in their language. As for the syntax of natural language, this discussion, being none too precise, is guided throughout by just two considerations and their immediate consequences, (...) which is discussed at greater length in this article. The first, morpheme univocality, is that a morpheme despite its various syntactic and morphological contexts has a single meaning that supports all its occurrences. (shrink)

Questions on Form and Interpretation PdR Press Publications in Philosophy of Language.

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)