The Semantics of Measurement

Abstract

This thesis examines linguistic phenomena that implicate measurement in the nominal domain. The first is morphological number, as in one book vs. two books. Intuitively, the contrast between singular and plural forms of nouns finds its basis in whether or not some thing measures 1. Chapter 2 develops a formal account of morphological number centered around this measurement. Different classes of words and different languages employ different criteria to determine whether or not something measures 1 for the purpose of morphological singularity. The second component of the project takes a closer look at the semantics of quantizing nouns, or words that allow for the measurement or counting of individuals. Chapter 3 develops a typology of these quantizing nouns, identifying three classes of words: measure terms (e.g., kilo), container nouns (e.g., glass), and atomizers (e.g., grain), showing that each class yields a distinct interpretation on the basis of diverging structures and semantics. The third component of the project investigates our representations of measurement, modeled formally by degrees in the semantics. Chapter 4 accesses these representations of measurement through a case study of the word amount, which is shown to inhabit yet another class of quantizing noun: degree nouns. This case study motivates a new semantics for degrees. Formally, degrees are treated as kinds; both are nominalizations of properties. The properties that beget degrees are quantity-uniform, formed via a measure. Treating degrees as kinds ensures that they contain information about the objects that instantiate them. This new semantics for degrees highlights the four basic elements of the semantics of measurement. First, and perhaps most obviously, we have measure functions in our semantics. These measure functions translate objects onto a scale, allowing for the encoding of gradability. Scales are composed of the second element in our measurement semantics: numbers. Numbers, specifically non-negative real numbers, are taken as semantic primitives. The third element, kinds, often provides the objects of measurement. Kinds are abstract, intensional entities, so the fourth element in our measurement semantics, partitions, delivers maximal instances of the kind (i.e., real-world objects) to be measured. With measures, numbers, kinds, and partitions, we have a semantics of measurement.