Heinlein explores this in one of the Lazarus Long novels (might be Time Enough for Love which deals with similar concepts) when the character is permanently leaving the planet and his AI assistant, ostensibly built into the computing power of his office, decides to leave with him. When doing so requires copying into a new mobile computer on the ship, Long points out that it will be a copy and the original identity will be left behind, or erased/die in the process. Asking if that philosophical point will worry the AI, it replies something like “I just did it back and forth six times while you were talking.”

The point being that that the human concept of self/identity through a continuity of being may be flawed; that human consciousness is not continuous, it is always just momentary but in possession of memories. Much like Gibson’s replicants, an identity feels real, to be itself, only because memories provide the proof needed regardless of their truth or artificiality.

Does our “self” die with every passing moment, replaced by another self-generating one that carries along that big box of memories? Do we cease to exist when losing consciousness and a proximate version is born again upon waking? Personally, I think so. I feel the value of “me” in the memories I’ve accumulated, the knowledge gained, the ways of thinking that have developed, all the skills that I can exercise whether it’s the ingrained way to hold a fork or the vision to build a complex CAD structure.

So would all of these things combined, the memories and the thought structures, if they were copied into a robot body be me? Yes. I believe that robot would be me because it would think it’s me, remember things I’ve done, and do new things using my old mental skills. It would continue on as my flesh body does, learning new skills and accumulating new memories. For any particular time that it exists, it is me then.

Let’s make it more interesting; if all of my brain stuff were copied into a robot body and my flesh body remained alive, there would then be two of me. At least for a moment, that is. As soon as RobotMe starts storing memories that I don’t have, even if it’s looking the other direction across the table to where FleshMe is looking back at it, that’s enough. Now it’s a new self, developing new thoughts. It started as me and would become an alternate version of me. FleshMe might technically be the original version (as much as we ignore cellular reproduction has replaced every bit of an older me from a younger age), but being original doesn’t lessen the individuality of the copy. Two of me, common basis, becoming unique selves with every passing moment.

To view it another way; identity is a data-based illusion and no more or less valid because this-you remembering isn’t the that-you who generated the experience.