The examples in (35) show that plural definite noun phrases like de padvindersthe scouts or de studententhe students can have either a collective or a distributive reading. The most prominent reading of (35a) is the collective reading, according to which the scouts will build a big tree house together; the noun phrase de padvindersthe scouts is construed as referring to the scouts as a group, and we are dealing with a single event of building a tree house. The most plausible reading of (35b), 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, i.e. we are dealing with multiple events of writing an essay.

In fact, the two examples in (35) are ambiguous; the suggested readings are simply the ones that seem most salient or plausible given the context, but the other readings can easily be forced by adding an adverbial phrase like allemaalall or samentogether.

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 such as alle padvinders. The latter, however, do not lend themselves easily to a collective reading, as can be seen from the fact that an example such as (37) strongly disfavors a reading according to which the scouts cooperate in building a single tree house; each scout has to build his own tree house.

The above examples all involve an indefinite direct object. Therefore, one might think that the ambiguity between the collective and distributive readings of the plural definite noun phrase is related to the specific/non-specific reading of the indefinite noun phrases. Example (38a) shows that this is not the case; here the direct object is definite, but the sentence still allows a reading according to which the song was sung only twice (by the group), or a reading according to which the song was sung more often (twice by each individual member of the group). Example (38b) allows only the latter reading, as predicted by the discussion of the difference between plural definite and universally quantified noun phrases; cf. example (37).

Although the judgments are subtle, changing the order of the direct object and the adverbial phrase twee keer in (38a), as in (39a), 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 (38b), as in (39b), 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 only a distributive reading. We leave this to future research.