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 ). 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