Purposive vagueness: an evaluative dimension of vague quantifying expressions

Abstract

Extending Montague's (1974) framework, Barwise and Cooper (1981) argue that some generalized expressions (which I shall call vague quantifying expressions), such as most, many ana few, correspond not to quantifiers, but to determiners within noun phrases. They argue that we need not determine the meanings of these expressions by logic; rather, we may draw upon an idea similar to the one we employ when interpreting the meaning of the quantifier Qxø(x), that is, we may appeal to an underlying topology for their interpretation (1981: 161). Similarly, they invoke one of the ‘simplifying assumptions often made in model theory’; namely, … that one has a fixed context which determines the meaning of the basic expressions. We can think of this context as providing an interpretation for non-logical determiners… We shall assume… that there is a rich context held fixed that determines the PRECISE MEANING [my emphasis here] for the basic expressions, even those like ‘most’, ‘many’ and ‘few’. We refer to this as the fixed context assumption…The fixed context assumption is our way of finessing the vagueness of non-logical determiners. We think that a theory of vagueness like that given by Kamp (1975) for other kinds of basic expressions could be superimposed on our theory (1981: 163).