Determiners, Conservativity, Witnesses

Abstract

A cherished semantic universal is that determiners are conservative (Barwise & Cooper 1981; Keenan & Stavi 1986). Well-known problem cases are only (if it has determiner uses) and certain uses of proportional determiners like many (Westerståhl 1985). Fortuny (2017), in a retracted contribution to this journal, proposed a new constraint (the Witness Set Constraint) to replace Conservativity. He claimed that his constraint is satisfied by only and the Westerståhl-many, thus correctly allowing the existence of these non-conservative determiners, whilst it is not satisfied by unattested non-conservative determiners (such as allnon). In fact, we show here that only does not satisfy Fortuny’s Witness Set Constraint (nor does Westerståhl-many, which we leave to the readers to convince themselves of). Upon reflection, it turns out that the reason is simple: the Witness Set Constraint is in fact equivalent to Conservativity. There simply cannot be non-conservative determiners that satisfy the Witness Set Constraint. We consider further weakening of the Witness Set Constraint but show that this would allow unattested determiners.