A new kind of degree

Abstract

This paper presents a case study of the English noun amount, a word that ostensibly relies on measurement in its semantics, yet stands apart from other quantizing nouns on the basis of its existential interpretation. John ate the amount of apples that Bill ate does not mean John and Bill ate the same apples, but rather that they each ate apples in the same quantity. Amount makes reference to abstract representations of measurement, that is, to degrees. Its existential interpretation evidences the fact that degrees contain information about the objects that instantiate them. Outside the domain of nominal measurement, the noun kind exhibits behavior strikingly similar to that of amount; both yield an existential interpretation. This observation motivates re-conceiving of degrees as nominalized quantity-uniform properties—the same sort of entity as kinds. Thus, the semantic machinery handling kinds also handles degrees: as nominalized properties, degrees are instantiated by objects that hold the corresponding property; when instantiated by real-world objects, degrees (and kinds) deliver the existential interpretation.