The examples in (32) show that plural definite noun phrases like de padvinders'the scouts' or de studenten'the students' can have either a collective or a distributive reading. The most prominent reading of (32a) is the collective reading, according to which the scouts will build a big tree cabin together; the noun phrase de padvinders'the scouts' is construed as referring to the scouts as a group and we are dealing with a single event of building a hut. The most plausible reading of (32b), on the other hand, is the distributive one according to which each individual student has to write an essay; the noun phrase is construed as a set of individuals and it is predicated of each of these individuals that he or she is obliged to write an essay, that is, we are dealing with multiple events of writing an essay.

In actual fact, the two examples in (32) are ambiguous; the suggested readings are simply the ones that seem most prominent or plausible given the context, but the other readings can easily be forced by adding an adverbial phrase like allemaal'all' or samen'together'.

      Recall that plural definite noun phrases refer to the complete set of entities denoted by the NP in domain D. In this respect, definite noun phrases resemble universally quantified noun phrases like alle padvinders. The latter, however, do not easily allow a collective reading, which is clear from the fact that an example such as (34) strongly disfavors a reading according to which the scouts are cooperating in building a single tree cabin; each scout has to build his own hut.

      The examples above all involve an indefinite direct object. Therefore one may think that the ambiguity between the collective and the distributive reading of the plural definite noun phrase is related to the specific/nonspecific reading of the indefinite noun phrases. Example (35a) shows that this is not the case; here, the direct object is definite, but still the sentence allows a reading according to which the song was sung only twice (by the group), or a reading where the song was sung more often (twice by each individual member of the group). Example (35b) allows only the latter reading, as predicted by the discussion of the difference between plural definite and universally quantified noun phrases; cf. example (34).

Although judgments are subtle, changing the order of the direct object and the adverbial phrase twee keer in (35a), as in (36a), seems to disfavor the distributive reading of the subject, which may be due to the fact that the direct object is in the scope of this quantified adverbial phrase. Changing the order of the direct object and the adverbial phrase in (35b), as in (36b), seems to lead to a somewhat marked result and still does not seem to allow a collective reading of the subject. Insofar as these judgments are correct, they support the claim that alle has a distributive reading only. We leave this to future research.