This is the concern of cryonicists: what is the nature of identity?
If you don’t have any recollection of your own past, are you still you? If you forget who you are, but have maintained a record of your life, when you go back and read it and refamiliarize yourself, are you “you” again? If so, why wouldn’t anyone who read it become “you”? And if that is “you,” then why not just clone yourself and educate the clone with your memories? Intuitively, it feels like it might be someone else who thinks it’s you, but it’s not really you. Of course, Star-Trek-like teleportation has the same problem — is the person who stepped out of the transporter you, or a physical copy of you with the same memories? Is that continuity sufficient? How does it differ from the you that went to bed last night and woke up this morning (or in my case, the several mes that woke up repeatedly during the night)? Is that the same continuity, or one different in kind?
I’m sure that I’ve told this story before, but years ago, at the California Science Museum in Exposition Park, there was a display on health and medical ethics and it had various questions to poll the visitors. One of them was:
You have an inoperable brain tumor. If a donor became available because their body had failed, would you accept a brain transplant to save your life?
An astonishing number of people said “yes.” Which means they apparently had difficulty with the concept.