Online research in philosophy

A defense of the Frege / Russell idea of logic as a 'concept=script' or 'ideal language', and a discussion of the relationship of this project to the formalisation of mass nouns or non-count nouns.

'Philosophy may in no way interfere with the actual use of language; it can in the end only describe it. For it cannot give it any foundation either. It leaves everything as it is.' 'We must do away with all explanation, and description alone must take its place.'.

Though these expressions are often called “names of months”, there is good reason to hold that they are not names at all. Syntactically, these words behave as count nouns. They combine with determiners such as ‘every’, ‘many’, ‘exactly three’ etc. to form restricted quantifiers:3 (1) Every January I go skiing. (2) I spent many Januarys at Squaw Valley. (3) I wasted exactly three Januarys in Bakersfield. Like other count nouns, they can take relative clauses in constructions such as (1)-(3): (1a) Every January that you visited we went skiing. (2a) I spent many Januarys that I will never forget at Squaw Valley. (3a) I wasted three Januarys that seemed interminable in Bakersfield. They also combine with the copula, indefinite article and adjectival modifiers to form predicates in the way that other count nouns do: (4) The first full month I lived in Northern California was a pleasant July. Further, it is generally held that only constituents of the same syntactic category can be conjoined. And as the following example shows, ‘January’ can be conjoined with other count nouns:4 (5) All Januarys and funerals last too long. Thus distributional evidence strongly suggests that ‘January’, ‘February’, etc. are count nouns. Since in general we take count nouns to express properties, we ought to take ‘January’, ‘February’ etc. to express properties as well.5 We shall return to the question of what properties such words express below. For now, we shall stick with syntax.

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.

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.

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.

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-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.

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.

In English, some common nouns, like cat, can be used in the singular and in the plural, while others, like water, 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.1 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? This question has occupied the mind of many linguists and philosophers. It is comparable in intent to: Can one give a purely semantic definition of verbs? Four proposals have been discussed in the literature.