Sorting and Unsorting

In Mountain semantics mass nouns and count nouns take their denotations in different domains. This sorting underlies the semantics of constructions that involve counting, count comparison and distributivity. In Sects. 4.1, 4.2 and 4.3 I show that the sorted theory needs an elaborate machinery of shifts to cover intuitive cases where objects stand in a part-of relation, I argue that sorting leads semantic theory down the slippery slope of less and less natural part-of relations, and I propose that unsorting the theory may provide a more healthy heuristics about the part-of relation, which is: try to make your semantic theory such that it doesn’t disallow naturalistic notions of parts. In Sects. 4.4 and 4.5 I discuss two challenges for the sorted theory that will play a role throughout the book: the "supremum argument" from Chierchia (Plurality of mass nouns and the notion of semantic parameter. In: Rothstein S (ed) Events and grammar. Springer [Kluwer], Berlin, pp 52–103, 1998), which argues that definite mass DPs and corresponding definite count DPs have the same supremum, and the "portioning argument" based on Landman (Structures for semantics, Springer [Kluwer], Berlin, 1991) which concerns counting mass portions, a problem if counting takes place in a count domain. Section 4.7 shows that even mildly sorted theories like those of Rothstein (J Semantics 27:343–397, 2010) run into problems with distributive readings. I argue that the problems are compositionality problems, problems of how to keep track of the relevant information so that it is available at the right semantic level.