Philosophy of Mathematics Seminar

Andreas Ditter, Queen’s College, Oxford

Higher-order essences

This talk presents a logic of essence (HLE) in the framework of higher-order logic, providing a general framework for theorizing about the essences of objects, properties, propositions, and logical operations. Kit Fine’s counterexamples to the definability of essence in terms of metaphysical necessity have convinced many philosophers that the right approach to take in theorizing about essence is to work with a primitive notion of essence not explained in terms of metaphysical modality or anything else. This conceptually basic notion has since been used and discussed in a variety of different areas, from metaphysics to the philosophy of mathematics and metaethics. Yet the logic of this notion remains relatively little explored. In the first part of the talk, I will present some key features of HLE, show how metaphysical necessity can be reduced to essence in HLE, and highlight a revisionary consequence this reduction might have for the logic of metaphysical necessity. In the second part, I will present a semantics for HLE and explore some questions about the fineness of grain of propositions and the connection between essence and (higher-order) identity.