The indexical notion of actuality suggests that a world is only actual in a relativized sense.  This does not sit well with the notion of actuality employed by anti-possibilist metaphysicians.  I argue that we can appease the actualist while preserving many of the attractive features of the indexical notion by introducing a triply-indexed semantics: in addition to a circumstance of evaluation and a context of utterance, we should add a third index tracking the metaphysically privileged world.  By differentiating between the privileged world and the world of utterance, we make room for a world that is actual in an unrelativized sense, while still leaving us with a parameter whose value can shift when we want to consider some other world as actual (as we may in evaluating statements concerning conceptual possibility).

Kripke’s modal argument suggests that names are not semantically equivalent to non-rigid descriptions, but it does not imperil a rigidified descriptivist theory of names.  A revised version of the modal argument attacks even rigidified descriptivism by arguing that names exhibit a different kind of rigidity than do rigidified descriptions – names are obstinately rigid while rigidified descriptions are persistently rigid.  The revised modal argument thus purports to show that names are not semantically equivalent to rigidified descriptions.  Descriptivists and anti-descriptivists typically agree that rigidified descriptions are persistently rigid, but I argue here that it should also be common ground that names are persistently rigid.  As a result, names and rigidified descriptions have the same modal status after all, and so the revised modal argument will fail to establish the semantic inequivalence of names and rigidified descriptions.