Arbitrary Reference in Logic and Mathematics

This book develops a new approach to plural arbitrary reference and examines mereology, including considering four theses on the alleged innocence of mereology. The authors have advanced the notion of plural arbitrary reference in terms of idealized plural acts of choice, performed by a suitable team of agents. In the first part of the book, readers will discover a revision of Boolosʼ interpretation of second order logic in terms of plural quantification and a sketched structuralist reconstruction of second-order arithmetic based on the axiom of infinite, a la Dedekind, as the unique non-logical axiom. The work goes on to analyse the pros and cons of the new interpretation, also with respect to Linneboʼs objections to the thesis that second order logic is genuine logic. A theory of concepts that can be labelled as a theory of logical concepts is expounded.

In the second part of the book, the authors consider grounding megethology on plural arbitrary reference and argue that the arguments for the ontological innocence of mereology are not conclusive and that – for a certain use of mereology – a thesis of innocence, similar to that of plural arbitrary reference, is defensible. The work proposes a virtual theory of mereology in which the role of individuals is played by plural choices of atoms.

This considered work will appeal to scholars from branches of analytic philosophy, logic and the philosophy of mathematics in particular.

Massimiliano Carrara is a professor of Logic at the University of Padua, Italy, and serves as a visiting professor at the USI in Lugano, Switzerland. His scholarly focus encompasses logic and the philosophy of logic, alongside an active engagement in analytic metaphysics. He is one of the editors of “Individuals, Essence, and Identity: Themes of Analytic Metaphysics,” published by Springer (2002). Additionally, he contributed as an editor to “Unity and Plurality: Logic, Philosophy, and Linguistics,” (Oxford University Press, 2016).

Enrico Martino was Associate Professor of Logic at the University of Padua, Italy. His main interests are philosophy of logic and philosophy of mathematics. He has written papers for the Journal of Philosophical Logic, Topoi, Studia Logica, Review of Symbolic Logic, History and Philosophy of Logic and the Grazer of Philosohische Studien.