MoL-2025-35: Higher-Level Plural Logic

MoL-2025-35: Dimou Belegratis, Orestis (2025) Higher-Level Plural Logic. [Report]

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Abstract

In the current thesis, I aim to explore numerous logical and philosophical questions regarding higher-level plurals. I begin by proposing my own conception of higher-level plural reference, dubbed Combinatorial Reference, in a way that: (a) supports the intelligibility of higher-level plurals, (b) enjoys several conceptual advantages over the alternatives in the literature, and (c) naturally motivates a specific logical framework. I then compare the formal aspects of that framework to what I consider to be the best alternative to higher-level plural logic, namely the generalized cover approach to plurals. I axiomatize both logics as many-sorted first-order theories and then prove that they are both Morita Equivalent and Bi-interpretable. Subsequently, I turn to an important question regarding the height of the hierarchy of higher-level plurals and how this hierarchy can motivate another one consisting of more and more expressive higher-level plural languages. I compare my strategy to others from the literature, most notably that of Linnebo and Rayo (2012), and I find that I can both avoid the criticisms voiced against them and reach a similar conclusion. Finally, I consider the arguments of Button and Trueman (2022) regarding the formalization of higher-level plural logic. While they purport to establish that the formalization should be carried out in a one-sorted framework, I argue for my preferred, typed formalization due to its intimate conceptual connection to Combinatorial Reference.

Item Type:	Report
Report Nr:	MoL-2025-35
Series Name:	Master of Logic Thesis (MoL) Series
Year:	2025
Subjects:	Language Logic
Depositing User:	Dr Marco Vervoort
Date Deposited:	23 Jun 2026 13:51
Last Modified:	23 Jun 2026 13:51
URI:	https://eprints.illc.uva.nl/id/eprint/2426

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