On Plural Arbitrary Reference

This chapter introduces a new approach to plural quantification through the concept of plural arbitrary reference. It highlights the implicit presupposition in mathematical reasoning that any individual in the universe of discourse can be referred to. By introducing a team of ideal agents capable of direct access to any individual, plural arbitrary reference is achieved through simultaneous acts of choice by each agent. This idealized notion of reference provides a basis for understanding plural quantification without second-order entities, maintaining the ontological innocence of second-order logic by distinguishing between acts and entities.