Why can I tell you that I 'ran for five minutes' but not that I 'ran all the way to the store for five minutes'? Why can you say that there are 'five pounds of books' in this package if it contains several books, but not 'five pounds of book' if it contains only one? What keeps you from using 'sixty degrees of water' to tell me the temperature of the water in your pool when you can use 'sixty inches of water' to tell me its height? And what goes wrong when I complain that 'all the ants in my kitchen are numerous'?
The constraints on these constructions involve concepts that semanticists usually study separately: aspect, plural and mass reference, measurement, distributivity. I will provide a unified perspective on these concepts, formalize it within algebraic semantics, and use it connection to transfer insights across unrelated bodies of literature. In particular, I will show how to generalize previous insights by Dowty, Krifka, and Schwarzschild by formulating a single constraint that explains the judgments above and improves on existing characterizations of distributivity, aspect, and measurement.