“Towards an Inflexible Semantics for Cross-Categorial Operators”
Aron Hirsch (McGill)
It is generally thought that the semantics is flexible in such a way that one operator can compose with different kinds of arguments (e.g. Montague 1973, Partee & Rooth 1983, Rooth 1985, Keenan & Faltz 1987). This flexibility seems to be required for operators such as “and”, which show a broad distribution. In (1), “and” appears to compose with truth-values in (a), quantifiers in (b), and relations in (c).
(1a) [TP John saw every student] and [TP Mary saw every professor]
(1b) John saw [DP every student] and [DP every professor].
(1c) John [V hugged] and [V pet] the dog.
In this talk, however, I argue that the semantics does not allow for this flexibility, and that “and” has a uniform meaning across its distribution: and operates on truth-values, parallel to the ^-connective of propositional logic (e.g. Schein 2017). The central case study will be data such as (1b), where and occurs between object quantifiers. First, I will argue that (1b) has a “Conjunction Reduction” parse as underlying vP conjunction. Since vPs denote truth-values, and can then compose as ^. Second, I will present data which I argue are best understood if “and” does not have the additional option to operate directly on the quantifiers. “And” is interpreted as ^, while surface cross-categoriality is created by the syntax. I will show that this view extends to another cross-categorial operator (“only”), and receives support from operators which could in principle have a cross-categorial distribution but don’t (e.g. “yesterday”).