Early on in his Nicomachean Ethics, Aristotle argues that there must be a single end or good desired for its own sake, for the sake of which all of our other ends are desired. The argument includes the following conditional: “If we chose everything for the sake of something else so that the process went on forever, then our desire would be empty and futile.” This paper addresses that conditional. First, I explain why the conditional appears to be false. Second, I resolve some ambiguity in it. Third, I argue that the conditional enjoys a plausible and charitable reading when understood as a claim about ordinary human lives and psychology, and when read in the context of Aristotle’s conception of ethics.