Synthese 96 (2):201 - 254 (1993)

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.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/BF01306897
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 63,247
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Naming and Necessity.Saul Kripke - 1980 - In Darragh Byrne & Max Kölbel (eds.), Philosophy. Routledge. pp. 431-433.
Parts: A Study in Ontology.Peter Simons - 1987 - Oxford University Press.
Philosophy of Logic.W. V. O. Quine - 1970 - Harvard University Press.

View all 40 references / Add more references

Citations of this work BETA

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.
A Note on Plural Pronouns.H. M. Cartwright - 2000 - Synthese 123 (2):227 - 246.

Add more citations

Similar books and articles

Superplurals in English.Øystein Linnebo & David Nicolas - 2008 - Analysis 68 (3):186–197.
Plural Quantification and Classes.Gabriel Uzquiano - 2003 - Philosophia Mathematica 11 (1):67-81.
E Pluribus Unum: Plural Logic and Set Theory.John P. Burgess - 2004 - Philosophia Mathematica 12 (3):193-221.
On What There Are.Philippe De Rouilhan - 2002 - Proceedings of the Aristotelian Society 102:183 - 200.
Sharvy's Theory of Definite Descriptions Revisited.Berit Brogaard - 2007 - Pacific Philosophical Quarterly 88 (2):160–180.
Logic, Logic, and Logic.George Boolos - 1998 - Harvard University Press.
Plural Quantification and the Iterative Concept of Set.Stephen Pollard - 1985 - Philosophy Research Archives 11:579-587.


Added to PP index

Total views
100 ( #107,458 of 2,448,581 )

Recent downloads (6 months)
2 ( #303,766 of 2,448,581 )

How can I increase my downloads?


My notes