This book is a report of an investigation into the meanings of the modal auxiliaries in modern British English. The investigation took the form of a large-scale corpus-based project, looking at modal auxiliaries in both written and spoken language, and taking into account stylistic variation. The analysis of a corpus of a real language brings the analyst face-to-face with a problem which has frequently been avoided or ignored in theoretical semantics: language is not an orderly phenomenon, and, as far as meaning is concerned, indeterminacy seems to be a feature of all languages. But it is one thing to recognise the existence of indeterminacy, and another to deal with it adequately. Semantic analysis conventionally consists in distinguishing one meaning from another, in recognising discrete categories, but the acknowledgement of indeterminacy explicitly denies the existence of such discrete categories. This book examines in detail this problem and its relationship to a study of modals.