In this paper I discuss a paradox, due to David Kaplan, that in his view threatens the use of possible worlds semantics as a model-theoretic framework for intensional logic.¹ Kaplan's paradox starts out from an intuitively reasonable principle that I refer to as the Principle of Plenitude. From this principle he derives a contradiction in what he calls Naive Possible World Theory. Kaplan's metatheoretic argument can be restated in the modal object language as an intensional version of the Liar paradox.