On the Innocence and Determinacy of Plural Quantification

Noûs 50 (3):565–583 (2016)

Authors
Øystein Linnebo
University of Oslo
Salvatore Florio
University of Birmingham
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 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.
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DOI 10.1111/nous.12091
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References found in this work BETA

Parts of Classes.David LEWIS - 1991 - Blackwell.
Plural Predication.Thomas McKay - 2006 - Oxford University Press.
Plural Logic.Alex Oliver & Timothy Smiley - 2013 - Oxford University Press UK.
Everything.Timothy Williamson - 2003 - Philosophical Perspectives 17 (1):415–465.

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Citations of this work BETA

When Do Some Things Form a Set?Simon Hewitt - 2015 - Philosophia Mathematica 23 (3):311-337.

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