Prospects for a Syntactic Analysis of Conservativity

The model theoretic tradition in semantic analysis maintains that determiners denote functions from properties to sets of properties, where in an extensional model a property is a set of individuals. For a determiner d and properties p and q I write ‘d(p,q)’ for ‘[d(p)](q)’ and refer to p as d’s ‘restrictor’ and to q as its ‘nuclear scope’. Barwise and Cooper (1981) and Keenan and Stavi (1986) claim that natural language determiners denote ‘conservative’ functions. The denotation of a conservative determiner function is insensitive to that portion of the nuclear scope that is not included in the restrictor. Keenan and Stavi define conservativity as in (1a). Put another way, conservative determiners display the equivalency in (1b) for any choice of p and q.