Abstract
English distinguishes between singular quantifiers like "a donkey" and plural quantifiers like "some donkeys". Pluralists hold that plural quantifiers range in an unusual, irreducibly plural, way over common objects, namely individuals from first-order domains and not over set-like objects. The favoured framework of pluralism is plural first-order logic, PFO, an interpreted first-order language that is capable of expressing plural quantification. Pluralists argue for their position by claiming that the standard formal theory based on PFO is both ontologically neutral and really logic. These properties are supposed to yield many important applications concerning second-order logic and set theory that alternative theories supposedly cannot deliver. I will show that there are serious reasons for rejecting at least the claim of ontological innocence. Doubt about innocence arises on account of the fact that, when properly spelled out, the PFO-semantics for plural quantifiers is committed to set-like objects. The correctness of my worries presupposes the principle that for every plurality there is a coextensive set. Pluralists might reply that this principle leads straight to paradox. However, as I will argue, the true culprit of the paradox is the assumption that every definite condition determines a plurality.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
DOI 10.5007/1808-1711.2021.e70853
Options
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: 65,593
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

Plural Logic.Alex Oliver & Timothy Smiley - 2013 - Oxford, England: Oxford University Press UK.
Nominalist Platonism.George Boolos - 1985 - Philosophical Review 94 (3):327-344.
A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (2):56-68.
Pluralities and Sets.Øystein Linnebo - 2010 - Journal of Philosophy 107 (3):144-164.

View all 12 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Generalized Quantifiers, and Beyond.Hanoch Ben-Yami - 2009 - Logique Et Analyse (208):309-326.
Plural Quantification.Ø Linnebo - 2008 - Stanford Encyclopedia of Philosophy.
Life on the Range.G. Aldo Antonelli - forthcoming - In A. Torza (ed.), Quantifiers, Quantifiers, and Quantifiers. Synthese LIbrary.
Plural Predication.Agustin Rayo - 2000 - Dissertation, Massachusetts Institute of Technology
Self-Commuting Quantifiers.Dag Westerståhl - 1996 - Journal of Symbolic Logic 61 (1):212-224.
A Note on the Monotonicity of Reducible Quantifiers.R. Zuber - 2010 - Journal of Logic, Language and Information 19 (1):123-128.
Superplurals in English.Øystein Linnebo & David Nicolas - 2008 - Analysis 68 (3):186–197.
Henkin Quantifiers.M. Krynicki & M. Mostowski - 1995 - In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. pp. 193--263.
Quantifiers Definable by Second Order Means.M. Mostowski - 1995 - In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. pp. 181--214.
Quantifiers, Some Problems and Ideas.M. Krynicki & M. Mostowski - 1995 - In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. pp. 1--21.
Symmetric and Contrapositional Quantifiers.R. Zuber - 2006 - Journal of Logic, Language and Information 16 (1):1-13.

Analytics

Added to PP index
2021-07-11

Total views
1 ( #1,515,676 of 2,462,098 )

Recent downloads (6 months)
1 ( #448,940 of 2,462,098 )

How can I increase my downloads?

Downloads

Sorry, there are not enough data points to plot this chart.

My notes