My goal in this paper is to use cross-polar anomaly as an empirical basis for motivating and developing a particular approach to the semantics of gradable adjectives and the representation of adjectival polarity. Specifically, I will argue that gradable adjectives denote relations between individuals and extents, or intervals on a scale, as in the work of Seuren 1978, 1984, von Stechow 1984b, a...