Vagueness in Quantity: Two Case Studies from a Linguistic Perspective

Much work on vagueness has focused on adjectives such as thin, bald and red as the paradigm case of the phenomenon. But vagueness is prevalent also in many other domains of natural language, and it is one of these other domains—namely expressions of quantity—that is the focus of the present paper. Quantificational expressions present a diverse range of examples of vagueness, imprecision and underspecification. Some quantifiers, such as many, few, much and (as will be seen below) most, are inherently vague. Others have definite but underspecified truth conditions; for example, some dogs must be at least two, but does not specify the number further. Vagueness in quantity may be signaled explicitly via modifiers such as roughly (roughly 50 books) and approximately (approximately 1000 residents). And even without modification, seemingly precise expressions such as number words may be interpreted approximately; for example, ‘there were 100 people in the audience’ is typically understood to mean ‘roughly 100’. In this paper, I examine two case studies of vagueness within the realm of quantity expressions: the vague quantifiers many, few, much and little, which pattern in some respects with gradable adjectives, but also show some illuminating differences; and the quantifier most, which along with more than half provides a minimal pair of a vague and a non-vague expression with otherwise overlapping semantics. My goal in delving into this topic for a contribution to a volume on reasoning with vague information is first of all to explore what we can learn about vagueness by examining its manifestation in the expression of quantity. I hope to show in what follows that facts from this general area are able to shed some new light on approaches and mechanisms that have been applied to the analysis of vagueness. But secondly, as I am a linguist, my contribution necessarily comes from the perspective of that field. Perhaps the most central goal of linguistics is to account for the (mostly unconscious) linguistic knowledge of native speakers of a language. This includes, among other things, knowledge about whether a string of words is or is not a grammatical sentence of the language, and about the interpretation(s) that a grammatical sentence can receive. A variety of data sources can be brought to bear on these questions, including the linguist’s own intuitions, judgments elicited from other speakers, attested