Parts of a Whole

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 <em>five pounds of books</em> acceptable but *<em>five pounds of book </em>not acceptable? What prevents us from saying *<em>sixty degrees of water</em> to express the temperature of the water in a swimming pool when <em>sixty inches of water </em>can express its depth? And why can we not say *<em>all the ants in my kitchen are numerous</em>? 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.<br>