A Metaphysics for Indiscernible Objects

My research aims at studying the characteristics of ensembles of strongly indiscernible objects (i.e. objects agreeing with respect to all definable predicates in a given logical language), with the intent to develop an axiomatic formal metaphysics to model the behaviour of indiscernibles and clarify the laws governing their existence and their interactions with discernible individuals. A metaphysics so intended represents a necessary condition to settle the numerous questions regarding indiscernibles in the contemporary philosophical debate. My research aims at understanding the nature of indiscernible objects, in so getting closer to a definitive assessment of the logical and ontological validity of Leibniz's Principle of the Identity of Indiscernibles (also referred to as: PII). It is often thought that we can maintain our common intuitions about collections when we consider ensembles containing indiscernible objects. However, this assumption is not uncontroversial. Nizzardo (2018) has shown that a correct metaphysical account of indiscernible objects demands numerous restrictions on the first and second order definable predicates that are often thought to be applicable to indiscernibles, and it has argued to the extent that indiscernible objects cannot be elements of collections hereditarily respecting ZFC's axioms (Zermelo-Fraenkel's Set Theory's axioms). As a consequence, being a fragment of ZFC the usual metatheory for first and second order formal languages, the use of standard logical tools to study collections of indiscernibles and to assess the logical validity of PII is deemed to fail from the start. The advantage that a complete formal metaphysics for indiscernible objects will provide to the contemporary philosophical debate is twofold: on the one hand, it will deliver a complete understanding of indiscernibles; on the other hand, it will broaden the current understanding of the relation between qualitative and quantitative identity. Finally, such system will be valuable within those quartiers of philosophy that are interest in the challenges arising from Quantum Mechanics: it has been argued, in fact, that some systems of physically identical particles in the same state of motion may provide good examples of strong indiscernibility (cfr. French 1989, and Krause & Coelho 2005). The project will be set at the intersection of Philosophy and Logic. The canonical philosophical literature will constitute the scientific background of the research, and it will be discussed with the intent of clarifying and evaluating the intuitions that are usually applied to indiscernible objects. Formal techniques will be used in providing a suitable language for a correct formalisation of situations involving indiscernibles, while Mereology and Topology will be employed to understand how indiscernibles can be assigned physical properties, and how they can be consistently thought of in a space-time framework that also includes discernible objects.