From plurals to superplurals: in defence of higher-level plural logic

Dissertation, University of Glasgow (2018)

Berta Grimau
Czech Academy of Sciences
Plural Logic is an extension of First-Order Logic with plural terms and quantifiers. When its plural terms are interpreted as denoting more than one object at once, Plural Logic is usually taken to be ontologically innocent: plural quantifiers do not require a domain of their own, but range plurally over the first-order domain of quantification. Given that Plural Logic is equi-interpretable with Monadic Second-Order Logic, it gives us its expressive power at the low ontological cost of a first-order language. This makes it a valuable tool in various areas of philosophy. Some authors believe that Plural Logic can be extended into an even more expressive logic, Higher-Level Plural Logic, by adding higher-level plural terms and quantifiers to it. The basic idea is that second-level plurals stand to plurals like plurals stand to singulars. Allegedly, Higher-Level Plural Logic enjoys the expressive power of type theory while, again, committing us only to the austere ontology of a first-order language. Were this really the case, Higher-Level Plural Logic would be a very useful tool, extending and strengthening some of the applications of Plural Logic. However, while the notions of plural reference and quantification enjoy widespread acceptance today, their higher-level counterparts have been received with scepticism. The main objection raised against them is that higher-level plural reference is unintelligible. This has been argued, among others, on the grounds that there are no higher-level plurals in natural language and that, if there were any, they could be eliminated. In this thesis, after introducing the debate on plurals in Chapters 1 and 2, I turn to defending the legitimacy of the notion of higher-level plural reference. To this end, in Chapter 3, I present and elucidate the notion. Next, in Chapter 4, I show that some natural languages clearly contain these expressions and that they do so in an ineliminable manner. Finally, in Chapters 5 and 6, I develop a semantics for higher-level plurals that employs only devices previously well-understood by English speakers. To finish, in Chapter 7, I describe an application of Higher-level Plural Logic: a strengthening of the neo-Fregean programme. After describing my proposal, I turn to the issue of the logical status of this formalism and defend an optimistic take on the matter.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 47,182
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

On Sense and Reference.Gottlob Frege - 2010 - In Darragh Byrne & Max Kölbel (eds.), Arguing About Language. Routledge. pp. 36--56.
Naming and Necessity.Saul Kripke - 1981 - Philosophy 56 (217):431-433.
Naming and Necessity.S. Kripke - 1972 - Tijdschrift Voor Filosofie 45 (4):665-666.
Plural Predication.Thomas McKay - 2006 - Oxford University Press.

View all 102 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Logic and Plurals.Salvatore Florio & Øystein Linnebo - 2018 - In Kirk Ludwig & Marija Jankovic (eds.), The Routledge Handbook of Collective Intentionality. Routledge. pp. 451-463.
The Logic and Meaning of Plurals. Part II.Byeong-uk Yi - 2006 - Journal of Philosophical Logic 35 (3):239-288.
The Logic and Meaning of Plurals. Part I.Byeong-Uk Yi - 2005 - Journal of Philosophical Logic 34 (5-6):459-506.
Plural Quantification.Ø Linnebo - 2008 - Stanford Encyclopedia of Philosophy.
Superplurals in English.Øystein Linnebo & David Nicolas - 2008 - Analysis 68 (3):186–197.
Modalising Plurals.Simon Thomas Hewitt - 2012 - Journal of Philosophical Logic 41 (5):853-875.
Plural Quantification Exposed.Øystein Linnebo - 2003 - Noûs 37 (1):71–92.
Plural Logic and Sensitivity to Order.Salvatore Florio & David Nicolas - 2015 - Australasian Journal of Philosophy 93 (3):444-464.
Plural Reference and Reference to a Plurality. Linguistic Facts and Semantic Analyses.Friederike Moltmann - 2016 - In Massimiliano Carrara, Alexandra Arapinis & Friederike Moltmann (eds.), Unity and Plurality. Logic, Philosophy, and Semantics. Oxford: Oxford University Press. pp. 93-120.
Plurals and Complexes.Keith Hossack - 2000 - British Journal for the Philosophy of Science 51 (3):411-443.


Added to PP index

Total views
17 ( #541,090 of 2,289,511 )

Recent downloads (6 months)
5 ( #236,562 of 2,289,511 )

How can I increase my downloads?


My notes

Sign in to use this feature