Towards a Uniform Strategy of Plural Quantiication? Iterative Cumulativity and the Witness Condition

This paper relates to the question whether there is a uniform method of collective quantiication. Several approaches to plural quantiication are presented as a background for Winter's (1998) uniied df it lifting strategy. The main proposal is that so-called cumulative readings, which are known to be non-iterative, are in fact deriv-able, under certain circumstances, by an iterative procedure. Cumulativity is shown to be one of the readings that are generated by Winter's df it approach, which contains a modiicational component called the 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 eeect of the witness condition. Further, it is shown that otherwise iteration of the df it strategy generates counter-intuitive readings. Some motivation is given for the cumulativity operator as well as for the underlying constraints.