Very small or just not too big? Stratified reference and granularity

The higher-order property stratified reference is used by Champollion (this volume) to account for a variety of phenomena: aspect (conditions on the use of for-phrases), measurement (conditions on the use of measure expressions such as a kilo), and the distributivity of each and all, explaining their (in) compatibility with predicates such as meet and smile. This last extension of the use of stratified reference is highly original. One could say that Champollion’s account thus generalizes over different ‘types’ of distributivity: on the one hand distributivity as opposed to collectivity, and on the other hand a (weakened) form of distributivity (also called divisivity) as defined by Cheng (1973) (an N is distributive if and only if it applies to every subpart of something to which it applies). Stratified reference is defined as a higher-order property with two parameters. One of the parameters makes it possible to express stratified reference with respect to different dimensions, which is a great asset of the proposal. This makes it possible to generalize over temporal and spatial cases of atelicity as well as over for-phrases in the verbal domain and measure expressions in the nominal system. Champollion also makes use of the dimension parameter in order to model the different distributive readings that verbal predicates may have with respect to the referent of a particular thematic role. A thematic role is seen as “just another dimension of the abstract space in which the events live” (page 135). Note that the dimension parameter is more complex in these cases. For instance, for each, the agent of the event denoted by the VP has an atomic agent, while in the case of all the number of atomic parts in the NP is taken into account. In this way, not only the dimension introduced by the thematic role plays a role, but also the dimension introduced by the number of atomic parts in the sum denoted by the NP (see examples (58) to (65)). In my view this latter dimension is the one that is comparable to the dimension of time, space or weight in the examples with the for-phrases and measure phrases. Thus, the verb in combination with a thematic role has properties that could be compared