On the Innocence and Determinacy of Plural Quantification

Noûs 50 (3):565–583 (2016)
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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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Author Profiles

Øystein Linnebo
University of Oslo
Salvatore Florio
University of Oslo

Citations of this work

Nominalist Realism.Nicholas K. Jones - 2018 - Noûs 52 (4):808-835.
Plural quantification.Ø Linnebo - 2008 - Stanford Encyclopedia of Philosophy.
Mathematical Internal Realism.Tim Button - 2022 - In Sanjit Chakraborty & James Ferguson Conant (eds.), Engaging Putnam. Berlin, Germany: De Gruyter. pp. 157-182.

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References found in this work

Plural Logic.Alex Oliver & Timothy John Smiley - 2013 - Oxford, England: Oxford University Press UK. Edited by T. J. Smiley.
Plural predication.Thomas J. McKay - 2006 - New York: Oxford University Press.

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