While Buddhists famously deny the existence of a self, they distinguish between selves and persons, and allow for the existence of persons as entities having a sort of derived reality. By “self” they understand whatever counts as the essence of the psychophysical complex, while by “person” they understand the psychophysical complex as a whole. This essay explores the arguments whereby Buddhists sought to establish their claim that strictly speaking neither self nor person exists, but that persons are nonetheless useful posits of a scheme that is meant to accommodate our everyday interests and cognitive limitations. This yields a way of understanding the connection between reductionism about persons and consequentialism in ethics, as well as why it might be that puzzle cases have loomed so large in recent discussions of diachronic personal identity.