Arbitrary Reference in Logic and Mathematics

This insightful exploration in Arbitrary Reference in Logic and Mathematics offers a fresh take on plural arbitrary reference and mereology, appealing to those in analytic philosophy and logic.

This book presents a novel perspective on plural arbitrary reference and delves into the complexities of mereology. It critically analyzes four theses regarding the purported innocence of mereology, offering a fresh lens through which to view these concepts. The authors introduce the idea of plural arbitrary reference as it relates to idealized plural acts of choice, carried out by a suitable group of agents, setting the stage for a deeper exploration of logical frameworks.

In the first section, readers will encounter a re-evaluation of Boolos' interpretation of second-order logic, framed through the lens of plural quantification. The book sketches a structuralist reconstruction of second-order arithmetic, leveraging the axiom of infinity, reminiscent of Dedekind's approach as the sole non-logical axiom. The authors engage with various critiques, including Linnebo's objections regarding the legitimacy of second-order logic, while also proposing a comprehensive theory of logical concepts.

The second part shifts focus to grounding mereology in plural arbitrary reference, arguing against the conclusiveness of claims regarding the ontological innocence of mereology. The authors suggest that, under specific applications, a thesis of innocence akin to that of plural arbitrary reference can be defended. They propose a virtual theory of mereology, where the role of individuals is represented by plural choices of atoms. This insightful work is particularly suited for scholars in analytic philosophy, logic, and the philosophy of mathematics.