This short (10 page) paper is a draft written in late August 2000, after some discussion with Matthias Kromann at ESSLLI2000 in Birmingham. It is entirely about how quantifiers should be handled in Word Grammar, and contains no serious discussion of other approaches.
The paper starts with a discussion of the semantics of joint and distributed readings (e.g. does The students wrote an essay refer to a joint activity or to a number of separate activities each by one student?). This distinction involves two ways in which a set may be used as an argument: either as a whole, or via its individual members. In distributed readings, the argument is the individual member, but the argument set licenses a set on the parent node which has the same number as the argument set. This system is explained, with copious diagrams, for a number of examples, and finally it is applied to the semantics of ALL, SOME, NONE/NO, EVERY, EACH and ANY. The analysis for ANY is tentative and involves the same semantics as the conjunction OR.