I've heard this view referred to as a time-slice view of personal identity before.
Personal identity is tied to ordinary questions about the identity and persistence of ordinary objects.
So, you should probably have the same set of persistence conditions (time-slice / constant replacement) for cups, computers, organisms, atoms etc.
If that's true, then "personality, relationships, and ongoing projects" are also only things that exist at a time-slices. Plausibly, they don't exist at all since each necessarily exists through time. Either way, there's no sense in which they can be shared with future selves.
I think this kind of issue is better solved by the "reductionist" understanding of Parfit's views than the "eliminativist" / "illusionist" version. There's no illusion of selfhood or constant replacement, just degrees of similarity that compose our idea of a self.
Thanks for this.
Even if this argument is successful, there are debates over decision theory (evidential, causal, functional). Does an ideally rational agent intervene at the level of states, actions, or decision procedures?
If it's decision procedures, or something similar, functional decision theory can you get views that look quite close to Kantianism.
This is a good post.
It would probably be better received if the substantive contents were detailed here and the link wasn't placed first.