David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 35 (3):317 - 348 (2006)
We present a plural logic that is as expressively strong as it can be without sacrificing axiomatisability, axiomatise it, and use it to chart the expressive limits set by axiomatisability. To the standard apparatus of quantification using singular variables our object-language adds plural variables, a predicate expressing inclusion (is/are/is one of/are among), and a plural definite description operator. Axiomatisability demands that plural variables only occur free, but they have a surprisingly important role. Plural description is not eliminable in favour of quantification; on the contrary, quantification is definable in terms of it. Predicates and functors (function signs) can take plural as well as singular terms as arguments, and both many-valued and single-valued functions are expressible. The system accommodates collective as well as distributive predicates, and the condition for a predicate to be distributive is definable within it; similarly for functors. An essential part of the project is to demonstrate the soundness and completeness of the calculus with respect to a semantics that does without set-theoretic domains and in which the use of settheoretic extensions of predicates and functors is replaced by the sui generis relations and functions for which the extensions were at best artificial surrogates. Our metalanguage is designed to solve the difficulties involved in talking plurally about individuals and about the semantic values of plural items
|Keywords||Alibi principle all-in-one principle axiomatisability collective completeness proof co-partial function distributive functor inclusion many-valued function plural description plural logic plural variable quasi-classical|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Enrico Martino & Massimiliano Carrara (2010). To Be is to Be the Object of a Possible Act of Choice. Studia Logica 96 (2):289-313.
Alex Oliver & Timothy Smiley (2004). Multigrade Predicates. Mind 113 (452):609-681.
Byeong-Uk Yi (2005). The Logic and Meaning of Plurals. Part I. Journal of Philosophical Logic 34 (5/6):459-506.
Thomas J. McKay (2006). Plural Predication. Oxford University Press.
Byeong-uk Yi (2006). The Logic and Meaning of Plurals. Part II. Journal of Philosophical Logic 35 (3):239-288.
Øystein Linnebo & David Nicolas (2008). Superplurals in English. Analysis 68 (299):186–197.
Alex Oliver & Timothy Smiley (2005). Plural Descriptions and Many-Valued Functions. Mind 114 (456):1039-1068.
Helen Morris Cartwright (1993). On Plural Reference and Elementary Set Theory. Synthese 96 (2):201 - 254.
Added to index2009-01-28
Total downloads48 ( #28,011 of 1,004,684 )
Recent downloads (6 months)1 ( #64,743 of 1,004,684 )
How can I increase my downloads?