The title of my paper may appear paradoxical, misplaced, or even worse, out of date. The possibility of a reasonable modal logic was denied by Quine on philosophical grounds, but his objections have been dead for a while, even though they have not yet been completely buried.¹ What has made a crucial difference is the development of what has generally been taken to be a viable semantics (model theory) for modal logic.² This semantics has provided a basis from which Quine's objections can apparently be answered satisfactorily and which yields a solid foundation for the different axiom systems for modal logic. Thus the question of the possibility of modal logic has apparently been disposed of for good, and my title question accordingly may seem pointless.