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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