The use of brain technology that contributes to psychological changes has spurred a debate about personal identity. Some argue that neurotechnology does not undermine personal continuity (Levy, 2011) while others argue that it does (Kreitmair, 2019; Schechtman, 2010). To make these assessments, commentators fail to identify psychological changes that cause personal discontinuity. In this paper, I present a view that identifies personal continuity with the maintenance of a self-concept. I argue that a concept of self requires the ability to self-ascribe physical and psychological features and that the diachronic self emerges with self-ascriptions of features that require endurance over time. I maintain that an adequate concept of self does not depend on the maintenance of any particular combination of self-ascriptions and that it can be maintained despite even significant changes in psychological or physical traits. Finally, I apply the self-concept view to identify changes that can result in discontinuity of self.