An Exact Truthmaker Semantics for Permission and Obligation

Abstract

We develop an exact truthmaker semantics for permission and obligation. The idea is that with every singular act, we associate a sphere of permissions and a sphere of requirements: the acts that are rendered permissible and the acts that are rendered required by the act. We propose the following clauses for permissions and obligations: a singular act is an exact truthmaker of Pφ iff every exact truthmaker of φ is in the sphere of permissibility of the act, and a singular act is an exact truthmaker of Oφ iff some exact truthmaker of φ is in the sphere of requirements of the act. We show that this semantics is hyperintensional, and that it can deal with some of the so-called paradoxes of deontic logic in a natural way. Finally, we give a sound and complete axiomatization of the semantics.