The memory theory and its critics share an assumption: that personal identity is a factual matter, there either is or is not a fact of the matter about whether today's person is identical to yesterday's. Two important alternatives challenge this assumption.
Narrative identity, developed by philosophers including Paul Ricoeur and Charles Taylor, holds that personal identity is not a psychological fact but an ongoing interpretive achievement. You are not identical to your past self in virtue of some chain of memory-links; you are the same person in the sense that you tell a story in which all these experiences belong to a single meaningful life. Identity is not found but constructed through the narrative you give your life.
The analogy: a novel has unity not because all its sentences are made of the same ink but because they are woven into a single narrative arc with recurring characters, themes, and tensions. Your life has personal identity in the same way, not because there is a metaphysical thread running through all your experiences but because you organize them into a story that makes sense. This means personal identity is both retrospective (it requires telling a coherent story of the past) and forward-looking (the story is incomplete and continues to be written).
This view has important ethical dimensions. Alasdair MacIntyre argued that you can only understand what someone should do if you understand the narrative context of their life, virtues are not abstract properties but qualities that make sense relative to the kind of narrative a life is. Moral philosophy that ignores narrative identity (as Kantian universalism tends to) misses the way that actual moral lives are shaped by particular stories, commitments, and characters.
The Buddhist no-self doctrine (anātman) takes the most radical position of all: there is no personal identity, because there is no self. What we call a person is a bundle of five aggregates (skandhas), form, sensation, perception, mental formations, and consciousness, in constant flux, with no underlying substance or entity that persists through them. The sense of a continuous self is a cognitive construction, a useful fiction that conceals the true nature of experience, which is impermanent, interdependent, and without a fixed center.
The Buddhist view is not nihilism about persons, it does not deny that there are conventionally identifiable people with names, histories, and moral responsibilities. It denies that behind the conventional story there is a metaphysically real, persisting self. And it argues that clinging to the illusion of a permanent self is the root cause of suffering (dukkha), because anything built on a false foundation will eventually collapse.
The convergence of Parfit's analytic conclusion (personal identity is not what matters. The deep question is really about psychological continuity) and the Buddhist doctrine of no-self (the self is a construction. What matters is the quality of each moment's experience and the cultivation of compassion) is remarkable, and Parfit himself noticed it. Both traditions arrive, by very different routes, at the conclusion that the strong, persistent, bounded self we take ourselves to be is less solid and less fundamental than we ordinarily suppose.