Collective quantification and the homogeneity constraint
The main theoretical claim of the paper is that a slightly revised version of the analysis of mass quantifiers proposed in Roeper 1983, Lønning 1987 and Higginbotham 1994 extends to collective quantifiers: such quantifiers denote relations between sums of entities (type e), rather than relations between sets of sums (type <e,t>). Against this background I will explain a puzzle observed by Dowty (1986) for all and generalized to all quantifiers by Winter 2002: plural quantification is not allowed with all the predicates that are traditionally classified as "collective". The Homogeneity Constraint – as well as the weaker requirement of divisiveness - will be shown to be too strong (for both collective and mass quantifiers). What is required is that the nominalization of the nuclear-scope predicate denotes a maximal sum (rather than a group). Divisiveness is a sufficient, but not a necessary condition for this to happen. Non-divisive predicates such as form a circle, which denote sets of 'extensional' groups are allowed, because extensional groups are equivalent to the maximal sum of their members. It is only intensional group predicates that block collective Qs.
Keywords: collective quantification, mass quantification, homogeneous, cumulative, divisive, groups, sums, maximality operator, plural logic