Chapters 5 and 6 of Ricoeur’s Oneself as Another are concerned with the concept of narrative identity, developed in his earlier three-volume work Narrative and Time. We get at least the beginning of an answer to the doubts that occurred to me about a concept of identity based on reflexivity rather than sameness, when he applied it to Aristotle. I have not yet consulted the earlier work, but the treatment of narrative identity here itself seems a bit literary and elliptical. On the other hand, reading this I had the thought that literary theory was finally giving something back to philosophy, after so much borrowing in the other direction.
Narrative identity is intended to be a sort of Aristotelian mean between an identity of character — which according to Ricoeur follows the pattern of sameness — and an opposite pole he introduces, associated with what he calls self-constancy, which is to follow the pattern of reflexivity. Self-constancy is associated especially with keeping promises, and more generally with being reliable. This provides a more concrete model of what identity based on reflexivity is supposed to look like. Self-constancy involves success in a constant, self-directed effort. The self-directedness of the effort makes it clearly reflexive, in a temporally extended sense that seems much less problematic than an instantaneous reflexivity.
This notion of self-constancy reminds me of what we would get if we separated out Brandom’s ethical use of a responsibility or imperative to aim for consistency in one’s commitments, and directly gave it a more explicit temporal dimension that for Brandom arises mainly in a larger context. Narrative identity itself seems like the kind of thing that for Brandom is constructed writ large by Hegelian genealogy.