Synthese 191 (7):1-22 (2014)

Abstract
One of the standard views on plural quantification is that its use commits one to the existence of abstract objects–sets. On this view claims like ‘some logicians admire only each other’ involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates—substitutional and set-theoretic—only the latter can provide the language of plurals with the desired expressive power (given that the nominalist seems committed to the assumption that there can be at most countably many names). To counter this approach I develop a modal-substitutional semantics of plural quantification (on which plural variables, roughly speaking, range over ways names could be) and argue for its nominalistic acceptability
Keywords Plural quantification  Nominalism  Higher-order logic  Boolos  Quantifiers  Tokens  Modality
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DOI 10.1007/s11229-013-0354-5
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Philosophy of Logic.W. V. O. Quine - 1970 - Harvard University Press.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.

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