Talk About Stuffs & Things: The Logic of Mass and Count Nouns
Dissertation, Massachusetts Institute of Technology (
1995)
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Abstract
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.