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

Grimau Roca, Berta (2018) From plurals to superplurals: in defence of higher-level plural logic. PhD thesis, University of Glasgow.

Abstract

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 (analogously for higher levels). 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.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Logic, philosophy, philosophy of logic, plural logic, higher-order logic, higher-level plural logic, logicism, plural reference, superplural reference, plural quantification, superplural quantification.
• Subjects: B Philosophy. Psychology. Religion > B Philosophy (General); B Philosophy. Psychology. Religion > BC Logic
• Colleges/Schools: College of Arts & Humanities > School of Humanities > Philosophy
• Funder's Name: Arts & Humanities Research Council (AHRC)
• Supervisor's Name: Rieger, Dr. Adam
• Date of Award: 2018
• Depositing User: Ms Berta Grimau
• Unique ID: glathesis:2018-30780
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 20 Sep 2018 10:50
• Last Modified: 11 Oct 2018 12:09
• URI: https://theses.gla.ac.uk/id/eprint/30780