This essay gives a new interpretation of Hume's second thoughts about minds in the Appendix, based on a new interpretation of his view of composition. In Book 1 of the Treatise, Hume argued that, as far as we can conceive it, a mind is a whole composed by all its perceptions. But—this essay argues—he also held that several perceptions form a whole only if the mind to which they belong supplies a “connexion” among them. In order to do so, it must contain a further perception or perceptions. But when the perceptions in question are all of those belonging to a given mind—as in the section “Of personal identity” and the Appendix—there cannot be a further perception in that mind, and so those perceptions do not form a whole. Hence, Hume's views were inconsistent. This essay argues that, unlike most others, this interpretation explains his retreat to skepticism in the Appendix.