Leibniz's Principle and the Problem of Nonindividuality
Matteo Nizzardo
Abstract:
With the emergence of contemporary formal logic, it has become customary to formalise Leibniz’s Principle of the Identity of Indiscernibles (pii) by means of the following second order formula: ‘∀x∀y(∀p(p(x) ↔ p(y)) → x = y)’. Under the assumption that this formula captures the ontological meaning of Leibniz’s Principle, the relation between a second order formalisation of the scenario presented in Black (1952) as a counterexample to pii and Leibniz’s Principle becomes interesting to explore. Furthermore, once shown that the objects described in Black’s scenario are nonindividuals, the question arises if and how it is possible to build a theory of collections that does not restrict (as zfc does) the possibility of being a member of a collection only to individuals. We will present a first attempt to formulate such theory of collections, and some interesting facts will be proved as theorems about collections containing nonindividuals as elements.