On the Innocence and Determinacy of Plural Quantification

Abstract

Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the first‐order quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of non‐standard (Henkin) interpretations that confronts higher‐order logics on their more traditional, set‐based semantics. We challenge both claims. Our challenge is based on a Henkin‐style semantics for plural logic that does not resort to sets or set‐like objects to interpret plural variables, but adopts the view that a plural variable has many objects as its values. Using this semantics, we also articulate a generalized notion of ontological commitment which enables us to develop some ideas of earlier critics of the alleged ontological innocence of plural logic.