The universal scale and the semantics of comparison

Comparative constructions allow individuals to be compared according to different properties. Such comparisons form two classes, those that permit direct, comparisons (comparisons of measurements as in Seymour is taller than he is wide) and those that only allow indirect comparisons (comparisons of relative positions on separate scales as in Esme is more beautiful than Einstein is intelligent). Traditionally, these two types of comparisons have been associated with an ambiguity in the interpretations of the comparative and equative morphemes (see, Bartsch & Vennemann, 1972; Kennedy, 1999). In this thesis, I propose that there is no such ambiguity. The interpretations of the comparative and equative morphemes remain the same whether they appear in sentences that compare individuals directly or relative to two separate scales. To develop a unified account, I suggest that all comparisons involve a scale of universal degrees that are isomorphic to the rational (fractional) numbers between 0 and 1. All comparative and equative constructions are assigned an interpretation based on a comparison of such degrees. These degrees are associated with the two individuals being compared. Crucial to a unified treatment, the connection between individuals and universal degrees involves two steps. First individuals are mapped to a value on a primary scale that respects the ordering of such individuals according to the quality under consideration (whether it be height, beauty or intelligence). Second, this value on the primary scale is mapped to a universal degree that encodes the value's relative position with respect to other values. It is the ability of iv the universal degrees to encode positions on a primary scale that enables comparative and equative morphemes to either compare individuals directly or indirectly. A direct comparison results if measurements such as seven feet participate in the gradable property (as in Seven feet is tall). Such participation can sometimes result in an isomorphism between two primary scales and the ordering of measurements in a measurement system. When this occurs, comparing positions in the primary scales is equivalent to comparing measurements. If this type of isomorphism cannot be established then the sentence yields an indirect comparison
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Alan Clinton Bale (2008). A Universal Scale of Comparison. Linguistics and Philosophy 31 (1):1-55.
Alan Clinton Bale (2011). Scales and Comparison Classes. Natural Language Semantics 19 (2):169-190.

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