On the Innocence and Determinacy of Plural Quantification

Research output: Contribution to journalArticlepeer-review

Authors

Colleges, School and Institutes

External organisations

  • University of Oslo

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.

Details

Original languageEnglish
Pages (from-to)565-583
JournalNoûs
Volume50
Issue number3
Early online date9 Mar 2015
Publication statusPublished - Sep 2016