Am I the same "me" as I was when I was a small child, yesterday or five minutes ago? Is it fair to punish me for a crime that an earlier "me" committed? Theodore Sider's explores these ideas in an essay here (pdf file):
It's a well-written, entertaining and lucid survey to the philosophical questions that surround personal identity.
I think many philosophers start from an odd premise (it's intellectually odd, but understandable from an emotional point-of-view). The (generally) unstated assumption is "we WANT personal identity to exist, and we want it to exist free of illogic, so sets see how we can reason it to be so." The same assumption underlies most discussions of Free Will.
(For centuries, philosophers played this game with God. "God must exist," they said, "so lets try to work the logical kinks out of a universe with a god." Few were willing to say, "What if God doesn't exist? Does that elimantate the kinks?")
Few people are willing to say, "It FEELS like there's such a thing as a 'me', but maybe that's an illusion. Maybe THAT'S why I keep hitting walls of illogic -- because I believe in an illusion." Again, people feel the same way about Free Will (it's a linked topic to identity). We FEEL like we have free will, so we assume it exists. But does a feeling, no matter how strong, really point to a facet of the physical world?
I think it's fine to assume something exists and then try to show a logical framework for it. Often good science proceeds this way (testing a hypothesis). But one should be honest about one's methods. ("I know 'me' might be an illusion, but I'm going to assume it exists and see what happens.")
I suspect that there is no "me" -- or rather that "me" is an interpretation (i.e. a sort of metaphorical thinking) that we use to make sense of our world. The interpretation is imperfect, but that's okay. It's generally good enough. But if you act like it's a description of physical reality, you will eventually run into contradictions and absurdities. It's one of those concepts that help you get through the day, and as-long-as you don't think about it too deeply, you'll be fine.
Let's say I walk into a transporter. It's supposed to obliterate me and then make an exact copy of me somewhere else. But it malfunctions and creates a copy without destroying the original.
The copy will FEEL like it's me. And I will also feel like I'm me. There's no contradiction here, unless you insist on dubbing one of us "the REAL me." If you insist on this, then you run into all sorts of absurdities. The fact that we really FEEL like insisting on it (there MUST be a real me) doesn't mean that there is a real me. It just means we have a really strong feeling. Just because reality makes us uncomfortable, that doesn't stop it from being reality. In fact, reality is reality even if it's unbearable. Or inconceivable.
Let's say the copied me goes home (to what he FEELS is his home) and takes up where I left off -- living with my wife. She will feel as if she's still living with me. To her, the copy IS me. Her experience of me is from the outside -- via my actions, my appearance, my smell, etc. That is how she chooses (or is forced by her brain) to define me. And since the copy meets those requirements, to her it IS me.
I arrive home a few weeks later and am horrified. From my point of view, the guy kissing my wife is an imposter. I am the real me.
Who is right? Answer: both of us. We're both right, because though we seem to be answering the same question (Who is the real me?) we are actually answering two totally different questions. I am answering "Who is me from my point-of-view?" My wife is answering "Who is me from her point-of-view?"
She may have a hard time, now that there are two MEs. Her brain is going to push her really hard to point to the "real" me. Maybe she'll make some arbitrary choice, just to preserve her sanity. But there IS no real me. There are two versions of something me-like. There's no deep intellectual problem here (there IS a deep emotional problem) unless you insist that there MUST be a real me. (Of course, "real" is just a word, and "The Real Me" is just a title. We can bestow that word and title on anyone we want. We can arbitrarily choose some definition of "real," or we can choose a definition that makes people feel most comfortable, in which case we're admitting that "real" is a metaphor -- a human mental construct -- not a description of reality.)
Similarly, there's no deep problem when you see a dozen cans of Coke in the grocery store. We agree that they are all Coke cans. Since we're not emotionally invested in there being a primary Coke can, we're fine with doing this.
Fidelity plays a role here: think about video tapes of movies. My VHS of "The Godfather" is missing information that's in the original film. There are no scenes missing, but it doesn't look as good as the theatrical version. If I look really closely at the image on the screen, I'll see it's somewhat degraded -- lacking the resolution of the film version. But to me it's still "The Godfather." I've decided -- or my brains has made me decide -- that this level of coarseness is good enough. Someone else might differ. "Good Lord! That's not 'The Godfather'! It's a travesty of 'The Godfather!'" Who is right? Both of us! Neither of us! It's a low-res Godfather (which I simply call "The Godfather"). It is not a high-res Godfather (which my friend calls "The Godfather"). We run into trouble when we perversely insist that there must be ONE Godfather.
If the world was full of malfunctioning transporters, we'd have all sorts of problems -- which copy should be punished for a crime? Who should be allowed to spend money from a bank account? Etc. And, as the Sider essay suggests, we may already have these problems (Is it okay to punish someone for a crime they committed 5 years ago? Is the present person and the past person really the same person?). But these are practical problems, not philosophical problems. They all assume identity exists and then try to grapple with what POLICY we should pick when identity issues become complex.
I think we're trapped with the illusion of identity -- just as I think we're trapped with the illusion of Free Will. We can't NOT feel identity. We can't NOT feel free will. (Many people can't NOT feel God.) So it makes sense to come up with practical solutions to problems created by the feelings (feelings generated by illusions). That illusions are false. The feelings are real.