Measurements from "per" without complex dimensions

To what extent is the compositional structure of quantity terms in natural language aligned with the structure of the quantity calculus commonly used in scientific practice, a calculus that critically relies on mathematical operations like division and the computation of quotients? In pioneering work, Coppock (2021) addresses this general question through a case study on the English preposition "per", as in "0.9 grams per milliliter". Coppock proposes that "per" expresses the operation of quantity division, an operation that forms quantities like 0.9g/mL by using ratios of measurements from different dimensions. Here we show that this “division theory” of "per" makes the wrong prediction with respect to statements about measures of density and concentration. We argue that these types of expressions call for an “anaphoric theory” ofper. On this analysis, anaphora allows for the composition to invoke multiple measurements in basic dimensions, creating the appearance of reference to complex quantities like 0.9g/mL, even though no such quantities are actually composed nor denoted in the formal semantics.