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5.1.1.4. Distributivity
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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.

Example 32
a. De padvinders moeten een grote boomhut bouwen.
collective
  the scouts  must  a big tree cabin  build
  'The scouts must build a big tree cabin.'
b. De studenten moeten een opstel schrijven.
distributive
  the students  must  write  an essay
  'The students must write 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'.

Example 33
a. De padvinders moeten allemaal een grote boomhut bouwen.
distributive
  the scouts  must  all  a big tree cabin  build
  'The scouts must all build a big tree cabin.'
b. De studenten moeten samen een opstel schrijven.
collective
  the students  must  together  an essay  write
  'The students must write an essay 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.

Example 34
Alle padvinders moeten (*allemaal/??samen) een boomhut bouwen.
  all scouts  must     all/together  a tree cabin  build
'All scouts must build a tree cabin.'

      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).

Example 35
a. De jongens hebben het lied twee keer gezongen.
ambiguous
  the boys  have  the song  two times  sang
  'The boys sang the song twice.'
b. Alle jongens hebben het lied twee keer gezongen.
distributive
  all boys  have  the song  two times  sang
  'All boys sang the song twice.'

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.

Example 36
a. De jongens hebben twee keer het lied gezongen.
collective preferred
  the boys  have  two times  the song  sang
b. ? Alle jongens hebben twee keer het lied gezongen.
distributive
  all boys  have  two times  the song  sang
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    A free Open Access publication of the corresponding volumes of the Syntax of Dutch is available at OAPEN.org.