Locke-memory-criterion suggests personal identity memory i.e. you’re the same person if and only if you remember being that past self. Professor compares this to a flashlight: memory only illuminates certain moments of the past, leaving much of it in the darkness.
This raises the problem that there is plenty from our past we can’t recall but still consider a part of who we are. This is shown in Reid-on-personal-identity and his objection based on the transitivity of identity.
To fix this, Professor X suggests a chain-link model: each stage of the self is connected through overlapping memories, forming a continuous chain even if the ends don’t directly touch. Identity is preserved through indirect memory connections; there is always a version of myself that remembers the earlier version.
This preserves Locke’s idea that memory grounds identity but avoids Reid’s problem by allowing indirect memory connections to maintain continuity of the self.
Baier-on-the-relational-view-of-self shifts the focus away from the metaphysical question of what a person is to how we value and relate to persons. She highlights Susan Wolf’s point that reasons for caring about people have little to do with their metaphysical composition. Even if a person could be reduced to a series of conscious experiences or actions (and I believe she is referring to Locke-on-personal-identity here), that reduction doesn’t change the way we understand them morally or relationally. This gives and alternative model where personhood is not connected to memory, but is grounded in relationships. (Baier, p. 323)