I'd argue that it matters whether the replacement is gradual or immediate.
There is really no difference for other people if the copy is perfect, but there is a huge difference for me.
Let's say I am able to make a perfect digital copy of myself, and immediately after I die. Well, my identity as a person has not in the least bit been affected because I have a perfect digital copy of myself. But the copy of my identity that was destroyed will never experience anything ever again, and that to me is the same as death.
However if the process is gradual, and the original copy of my identity experiences the process, then I would not view that as death.
Compare my identity to a computer program that you want to be moved to another location. You can either make a copy, and then delete the original, or you could copy one small piece at a time and update the file locations so that the program can be running while file locations are being changed. The only difference for you is that the second is probably a lot more work. But I'd argue that no complete copy was deleted in the second case. And if the program is sentient, I see this as being drastically different for that program.
There is really no difference for other people if the copy is perfect, but there is a huge difference for me.
Let's say I am able to make a perfect digital copy of myself, and immediately after I die. Well, my identity as a person has not in the least bit been affected because I have a perfect digital copy of myself. But the copy of my identity that was destroyed will never experience anything ever again, and that to me is the same as death.
However if the process is gradual, and the original copy of my identity experiences the process, then I would not view that as death.
Compare my identity to a computer program that you want to be moved to another location. You can either make a copy, and then delete the original, or you could copy one small piece at a time and update the file locations so that the program can be running while file locations are being changed. The only difference for you is that the second is probably a lot more work. But I'd argue that no complete copy was deleted in the second case. And if the program is sentient, I see this as being drastically different for that program.