I wrote up about a page-long reply, then realized it probably deserves its own posting. I'll see if I can get to that in the next day or so. There's a wide spectrum of possible solutions to the personal identity problem, from physical continuity (falsified) to pattern continuity and causal continuity (described by Eliezer in the OP), to computational continuity (my own view, I think). It's not a minor point though, whichever view turns out to be correct has immense ramifications for morality and timeless decision theory, among other things...