This book develops both a philosophical and a formal, model-theoretic account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. Extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases: a person can be tall with respect to male accountants and not tall (even short) with respect to professional basketball players. The main feature of the author's account is that the extensions (and anti-extensions) of vague terms also vary in the course of a conversation, even after the external contextual features, such as the comparison class, are fixed. A central thesis is that in some cases, a competent speaker of the language can go either way in the borderline area of a vague predicate without sinning against the meaning of the words and the non-linguistic facts. Shapiro calls thisopen texture, borrowing the term from Friedrich Waismann. The formal model theory has a similar structure to the supervaluationist approach, employing the notion of a sharpening of a base interpretation. In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. The ultimate goal of the technical aspects of the work is to delimit a plausible notion of logical consequence, and to explore what happens with the sorites paradox. Later chapters deal with what passes for higher-order vagueness — vagueness in the notions of ‘determinacy’ and ‘borderline’ — and with vague singular terms, or objects. In each case, the philosophical picture is developed by extending and modifying the original account. This is followed with modifications to the model theory and the central meta-theorems. In this book, vagueness is seen as a linguistic phenomenon, due to the kinds of languages that humans speak. But vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. Vagueness is also due to the kinds of beings we are.
