The limiting theory

This chapter considers how the compositional theory argued for in the preceding chapters might apply to a variety of additional cases where a lexical, degree-theoretic semantics has been proposed. For example, the analysis of attitude verbs like “to want”, nouns like “idiot”, and verbs like “to cool”. The chapter suggests that, rather than diagnosing scalar structure, the kinds of data motivating lexical degree-theoretic interpretation here should be understood as diagnostic of order-theoretic properties on the relevant expression’s domain of predication. Supporting the idea of a general recipe for how such cases should be addressed, the chapter raises theoretical questions like the following: do any lexical categories natively have a degree semantics? When is a degree-theoretic treatment appropriate? Should there be morphosyntactic requirements (e.g., overt or covert “much”) for an interpretation based on degrees, or not? What alternative analyses of extant cases are available?