David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Stanford Encyclopedia of Philosophy (2008)
Ordinary English contains different forms of quantification over objects. In addition to the usual singular quantification, as in 'There is an apple on the table', there is plural quantification, as in 'There are some apples on the table'. Ever since Frege, formal logic has favored the two singular quantifiers ∀x and ∃x over their plural counterparts ∀xx and ∃xx (to be read as for any things xx and there are some things xx). But in recent decades it has been argued that we have good reason to admit among our primitive logical notions also the plural quantifiers ∀xx and ∃xx. More controversially, it has been argued that the resulting formal system with plural as well as singular quantification qualifies as ‘pure logic’; in particular, that it is universally applicable, ontologically innocent, and perfectly well understood. In addition to being interesting in its own right, this thesis will, if correct, make plural quantification available as an innocent but extremely powerful tool in metaphysics, philosophy of mathematics, and philosophical logic. For instance, George Boolos has used plural quantification to interpret monadic second-order logic and has argued on this basis that monadic second-order logic qualifies as “pure logic.” Plural quantification has also been used in attempts to defend logicist ideas, to account for set theory, and to eliminate ontological commitments to mathematical objects and complex objects.
|Keywords||plural logic plural quantification|
|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
No references found.
Citations of this work BETA
Keith Hossack (2014). Sets and Plural Comprehension. Journal of Philosophical Logic 43 (2-3):517-539.
Simon Hewitt (2012). Modalising Plurals. Journal of Philosophical Logic 41 (5):853-875.
Similar books and articles
Øystein Linnebo & David Nicolas (2008). Superplurals in English. Analysis 68 (299):186–197.
Gilad Ben-Avi & Yoad Winter (2003). Monotonicity and Collective Quantification. Journal of Logic, Language and Information 12 (2):127-151.
Francesca Boccuni (2010). Plural grundgesetze. Studia Logica 96 (2):315-330.
Berit Brogaard (2007). Sharvy's Theory of Definite Descriptions Revisited. Pacific Philosophical Quarterly 88 (2):160–180.
Alex Oliver & Timothy Smiley (2006). A Modest Logic of Plurals. Journal of Philosophical Logic 35 (3):317 - 348.
Helen Morris Cartwright (1993). On Plural Reference and Elementary Set Theory. Synthese 96 (2):201 - 254.
Gabriel Uzquiano (2003). Plural Quantification and Classes. Philosophia Mathematica 11 (1):67-81.
Enrico Martino & Massimiliano Carrara (2010). To Be is to Be the Object of a Possible Act of Choice. Studia Logica 96 (2):289-313.
Øystein Linnebo (2003). Plural Quantification Exposed. Noûs 37 (1):71–92.
Philippe De Rouilhan (2002). On What There Are. Proceedings of the Aristotelian Society 102:183 - 200.
Added to index2009-01-28
Total downloads92 ( #16,785 of 1,679,336 )
Recent downloads (6 months)14 ( #16,510 of 1,679,336 )
How can I increase my downloads?