Parts of a Whole: Distributivity as a Bridge Between Aspect and Measurement
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.
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