David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
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)|
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
W. V. Quine (1960). Word and Object. The MIT Press.
David Lewis (1991). Parts of Classes. Blackwell.
Saul Kripke (2010). Naming and Necessity. In Darragh Byrne & Max Kölbel (eds.), Philosophy. Routledge 431-433.
W. V. Quine (1986). Philosophy of Logic. Harvard University Press.
Peter M. Simons (1987). Parts: A Study in Ontology. Oxford University Press.
Citations of this work BETA
Stephen Pollard (2007). Mathematical Determinacy and the Transferability of Aboutness. Synthese 159 (1):83-98.
Similar books and articles
Øystein Linnebo & David Nicolas (2008). Superplurals in English. Analysis 68 (299):186–197.
Alex Oliver & Timothy Smiley (2006). A Modest Logic of Plurals. Journal of Philosophical Logic 35 (3):317 - 348.
Stephen Pollard (1985). Plural Quantification and the Iterative Concept of Set. Philosophy Research Archives 11:579-587.
George Boolos (1998). Logic, Logic, and Logic. Harvard University Press.
Berit Brogaard (2007). Sharvy's Theory of Definite Descriptions Revisited. Pacific Philosophical Quarterly 88 (2):160–180.
Philippe De Rouilhan (2002). On What There Are. Proceedings of the Aristotelian Society 102:183 - 200.
John P. Burgess (2004). E Pluribus Unum: Plural Logic and Set Theory. Philosophia Mathematica 12 (3):193-221.
Enrico Martino & Massimiliano Carrara (2010). To Be is to Be the Object of a Possible Act of Choice. Studia Logica 96 (2):289-313.
Gabriel Uzquiano (2003). Plural Quantification and Classes. Philosophia Mathematica 11 (1):67-81.
Alex Oliver & Timothy Smiley (2005). Plural Descriptions and Many-Valued Functions. Mind 114 (456):1039-1068.
Added to index2009-01-28
Total downloads50 ( #86,921 of 1,911,306 )
Recent downloads (6 months)4 ( #178,269 of 1,911,306 )
How can I increase my downloads?