This book uses mathematical models of language to explain why there are certain gaps in language: things that we might expect to be able to say but can't. For instance, why can we say I ran for five minutes but not *I ran all the way to the store for five minutes? Why is
five pounds of books
acceptable, but *
five pounds of book
not acceptable? What prevents us from saying *
sixty degrees of water
to express the temperature of the water in a swimming pool when
sixty inches of water
can express its depth? And why can we not say *
all the ants in my kitchen are numerous
? The constraints on these constructions involve concepts that are generally studied separately: aspect, plural and mass reference, measurement, and distributivity. In this book, Lucas Champollion provides a unified perspective on these domains, connects them formally within the framework of algebraic semantics and mereology, and uses this connection to transfer insights across unrelated bodies of literature and formulate a single constraint that explains each of the judgments above.