Modal Definability in Kripke’s Theory of Truth

Abstract In Outline of a Theory of Truth , Kripke introduces many of the central concepts of the logical study of truth and paradox. He informally defines some of these—such as groundedness and paradoxicality—using modal locutions. We introduce a modal language for regimenting these informal definitions. Though groundedness and paradoxicality are expressible in the modal language, we prove that intrinsicality—which Kripke emphasizes but does not define modally—is not. This follows from a characterization of the modally definable sets and relations and an attendant axiomatization of the modal semantics.