On plural reference and elementary set theory

Synthese 96 (2):201 - 254 (1993)
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The view that plural reference is reference to a set is examined in light of George Boolos's treatment of second-order quantification as plural quantification in English. I argue that monadic second-order logic does not, in Boolos's treatment, reflect the behavior of plural quantifiers under negation and claim that any sentence that properly translates a second-order formula, in accordance with his treatment, has a first-order formulation. Support for this turns on the use of certain partitive constructions to assign values to variables in a way that makes Boolos's reading of second-order variables available for a first-order language and, with it, the possibility of interpreting quantification in an unrestricted domain.A first-order theory, T(D), is developed on the basis of Boolos's treatment of simple plural definite descriptions extended to Richard Sharvy's general theory of definite plural and mass descriptions. I introduce a primitive predicate, o, for the relation of the referent of a singular description to that of its plural. If o is simply added to T(D), is definable in T(D), and the result is inconsistent. If o is added to a theory with axioms for the fragment of T(D) I call D-mereology, the result is a natural basis for the development of a pluralized Zermelo set theory. This theory, however, is inconsistent in an unrestricted domain, unless it is recast as a second-order theory of sets interpreted in Boolos's way.



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Citations of this work

Plurals and complexes.Keith Hossack - 2000 - British Journal for the Philosophy of Science 51 (3):411-443.
Plural quantification and classes.Gabriel Uzquiano - 2003 - Philosophia Mathematica 11 (1):67-81.
Reciprocity and Cumulative Predication.Wolfgang Sternefeld - 1998 - Natural Language Semantics 6 (3):303-337.
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References found in this work

Word and Object.Willard Van Orman Quine - 1960 - Cambridge, MA, USA: MIT Press.
Philosophy of Logic.Willard Van Orman Quine - 1970 - Harvard University Press.
Parts: A Study in Ontology.Peter Simons - 1987 - Oxford, England: Oxford University Press.

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