The roots of measurement

In addition to roots for familiar classes like verb, noun, and adjective, Mayan languages have a class of roots traditionally called “positional”. Positional roots are distinct from other roots most prominently in terms of requiring derivation into stems of one of the more familiar categories to be used. The goal of this work is to show that the behavior of positionals follows from semantic facts, in particular, the fact that they denote measure functions of type 〈e,d〉. This conclusion is supported through a series of novel arguments from the Mayan language Kaqchikel that positional roots have a scalar semantics. It then argues for the type 〈e,d〉 analysis by contrasting them with gradable root adjectives, which similarly make reference to ordered degrees on a scale, but which have a relational type-namely, 〈d,et〉. I then show that a core function of positional morphology, and the morpheme that derives positional stative predicates in particular, is to take positional roots into stems of type 〈d,et〉, which will account for the fact that derived positionals behave semantically like root adjectives. In this way, this work not only presents a novel account of the Mayan data, but provide additional evidence for the proposal that even within languages there can be differences in the fine-grained compositional structure of degree-denoting expressions.