*Variables in natural language
A central goal of generative linguistics is to determine what constitutes a possible grammar of a natural language. This thesis works toward that goal in positing a constraint on the possible semantic types of variables in natural language. Specifically, I argue here that the logical forms (LFs) of natural languages do not contain higher-type variables, i.e., variables of a type higher than that of an individual, type e (see Chierchia (1984) and Baker (2003) for similar proposals). I refer to this constraint as the No Higher-Type Variables constraint (NHTV).
Assuming that the domain of individuals, D, includes at least objects, kinds, events, event-kinds, degrees, situations, worlds, times, and locations, all of which have been independently argued to be necessary members of D, what NHTV predicts not to occur are object language expressions that vary over, e.g., generalized quantifiers, relations, or properties. While NHTV thus predicts a very restricted inventory of variable denoting expressions, I argue that it accounts for a surprisingly wide range of data in characterizing which variable-denoting expressions do and do not occur.
I motivate NHTV based primarily on data from English, and to a lesser extent, German and Polish. I focus empirically on two types of expressions that are commonly analyzed as involving variables: (i) (overt) pro-forms, and (ii) A'-movement gaps. In particular, I look closely at pro-forms and gaps that have the syntactic distribution of items that are commonly taken to be of a higher-type, namely, APs, AdvPs, VPs, and NPs. While all of these expressions are commonly taken to denote properties of individuals, I argue that pro-forms and gaps that have the distribution of these categories should not be analyzed as property variables, but instead either (i) vary over individuals, or (ii) do not involve variables at all.
The bulk of the thesis is devoted to backing up NHTV by (i) showing that hypothetical higher-type variables are systematically missing, and (ii) looking closely at potential counterexamples on a case-by-case basis.