Division vs. distributivity: Is per just like each?

This paper argues that there are lexical items that conventionally express the idea of dividing one quantity by another, and per is one of them. In particular, the proposal is that there are three ratio-related senses of per: (i) a quotient function; (ii) a quotient operator; and (iii) quotient of measure functions. The ratio-based approach, which is built up here in order to handle a wider range of data than previous ratio-based approaches could, is contrasted with an opposing view, one on which per is a distributivity marker like each. Four types of evidence are used: (i) cases involving measurement of an object or an event whose measure is smaller than the unit given by per’s complement; (ii) uses in the differential argument of a comparative; (iii) uses modifying a measure function noun; and and (iv) uses modifying a gradable predicate. All of these are problematic for a distributivity- marker analysis, and support the idea that per expresses the concept of ratio. Along the way, we gain diagnostics for whether a given item conventionally expresses the concept of a ratio in a given language.