Abstract

Leibniz's conceptual containment theory says that singular propositions of the form a is F are true when the complete concept of being a contains the concept of being F. In this paper, I provide a new semantics for first-order logic built around this idea. The semantics resolves longstanding problems for Leibniz's theory and can represent, without possible worlds, both hyperintensional distinctions among properties and a certain kind of presumably impossible situation that standard approaches cannot represent. The semantics also captures the strong soundness and completeness of classical first-order logic.