Higher-Level Plural Logic
Orestis Dimou Belegratis

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.