When a predicate has a positive extension and a negative extension that don't jointly cover the entire domain it gives rise to presuppositions. Are Steve and Sandro Italian? is an example involving plural predication. A simple negative answer to this question implies that neither are Italian, while a simple positive answer requires them both to be. The positive extension of are Italian includes groups of Italians and the negative extension includes groups of non-Italians, and the interrogative presupposes homogeneity: mixed groups are not considered. In this paper I extend Cooper's 1983 analysis of presupposition to cases like this one involving plural predication.
Negative and positive extensions also have a role to play in determining the assertions made with sentences containing plural predicates. Consider the sentences in (i)-(iii):
(i) Alex and Bill together weigh less than 30 kilo
(ii) Alex and Bill weigh less than 30 kilo
(iii) Alex and Bill each weigh less than 30 kilo
(i) can be paraphrased as "(ii) but not in the sense of (iii)". Previous analyses of the negative component in terms of groups and of events (Lasersohn 1990, L&P 13) is here shown to be inadequate. I propose an alternative in which together makes use of the negative extension of the predicate it attaches to.