B INOMINAL each AS AN ANAPHORIC DETERMINER : COMPOSITIONAL ANALYSIS ∗

It could be true under thecollective interpretation of the subject, in which case the sentence expresses that the boys acted as a group and together lifted t hr e tables. It could also be true in thecumulativereading of the sentence. In this case the boys split lifting i n such a way that in total three tables were lifted for example, because there w r three boys and each of them lifted one table. Finally, the sentence could also be true if the sub ject gets thedistributiveinterpretation, in which case the sentence expresses that each boy lifted thr e tables on his own. As is well-known, the last reading can be forced by adding the distributive quantifiereach, as in the following sentence:

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