What exactly are we conscious beings? Do we have immaterial souls, souls that are substances and can survive the destruction of our physical bodies? Richard Swinburne has recently given an affirmative answer to the latter question on the basis of a strikingly simple Cartesian argument. This paper shows why Swinburne’s argument ultimately fails, owing to an instructive dilemma concerning the logical possibility of conscious beings’ surviving bodily destruction. Perhaps we do have substantial immaterial souls, but Swinburne’s Cartesian argument, we shall see, does not cogently deliver the conclusion that we do.