Quantifier Domain Restriction and the Problem of Incomplete Quantifiers

Abstract

1. Every student passed. In a given context, 1 may be used to convey the claim that every student in Philosophy at Rutgers in 2022 passed. I assume without argument that in such cases, the sentence in context semantically expresses the relevant proposition: in the present case, that every student in Philosophy at Rutgers in 2022 passed. Given this, somehow the property of being in Philosophy at Rutgers in 2022 gets contributed to the proposition semantically expressed by 1 in context in such a case. Call this property the contextual restriction on the quantifier. The problem is that it can be that sentences such as 1 have many candidates for the contextual restriction on the quantifier, where there is no mechanism to select a unique property as the contextual restriction. Call this the problem of incomplete quantifiers. The problem of incomplete quantifiers gives rise to several worries to which I respond.