Plural quantification

Stanford Encyclopedia of Philosophy (2008)
  Copy   BIBTEX

Abstract

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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,219

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Superplurals in English.Øystein Linnebo & David Nicolas - 2008 - Analysis 68 (3):186–197.
Plural quantification exposed.Øystein Linnebo - 2003 - Noûs 37 (1):71–92.
Plural quantification and classes.Gabriel Uzquiano - 2003 - Philosophia Mathematica 11 (1):67-81.
Sharvy's theory of definite descriptions revisited.Berit Brogaard - 2007 - Pacific Philosophical Quarterly 88 (2):160–180.
Monotonicity and collective quantification.Gilad Ben-avi & Yoad Winter - 2003 - Journal of Logic, Language and Information 12 (2):127-151.
On What There Are.Philippe De Rouilhan - 2002 - Proceedings of the Aristotelian Society 102:183 - 200.

Analytics

Added to PP
2009-01-28

Downloads
236 (#81,878)

6 months
10 (#226,679)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Øystein Linnebo
University of Oslo

Citations of this work

Closed Structure.Peter Fritz, Harvey Lederman & Gabriel Uzquiano - 2021 - Journal of Philosophical Logic 50 (6):1249-1291.
Superplurals in English.Øystein Linnebo & David Nicolas - 2008 - Analysis 68 (3):186–197.
Ontological commitment.Agustín Rayo - 2007 - Philosophy Compass 2 (3):428–444.

View all 72 citations / Add more citations

References found in this work

Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.
Universals and scientific realism.David Malet Armstrong - 1978 - New York: Cambridge University Press.
Material Beings.Peter Van Inwagen - 1990 - Philosophy 67 (259):126-127.

View all 88 references / Add more references