Parts of a whole:
Distributivity as a Bridge
Between Aspect and Measurement

By Lucas Champollion


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 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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Relation to previous published work

This book is a substantially reworked and extended revision of my 2010 dissertation, which it supersedes. I first introduced the framework of strata theory and the concept of stratified reference in that dissertation, and I have used it in my research ever since. The book collects in one place all the work I have carried out on algebraic semantics and mereology from about 2009 to 2016, and presents it in a unified and self-contained way. It is planned and written as a coherent whole and not merely a collection of papers. I have published some parts as self-contained articles over the last few years. The revisions to the theory that resulted from peer review have been propagated through the book.

Other related materials

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