Towards a Uniform Strategy of Plural Quantification?
Iterative Cumulativity and the Witness Condition
 
Master Thesis Eyal Hurvitz
  
This paper relates to the question whether there is a uniform method
of collective quantification. Several approaches to plural quantification are
presented as a background for Winter's (1998) unified $dfit$ lifting strategy.
The main proposal is that so-called {\em cumulative} readings, which are known
to be non-iterative, are in fact derivable, under certain circumstances, by an
iterative procedure. Cumulativity is shown to  be one of the readings that are
generated by Winter's $dfit$  approach, which contains a {\em modificational}
component called the {\em witness condition}. However, in order to get these
readings, a cumulative operator has to be applied. This operator is needed to
overcome an under-generation effect of the witness condition. Further, it is
shown that otherwise iteration of the $dfit$ strategy generates
counter-intuitive readings. Some motivation is given for the cumulativity
operator as well as for the underlying constraints.