A lot of my recent work has been on personhood and continuity of identity (that is, how do I know that a person at some given time is the same person as a person at some prior time.) Some of my papers are linked on my academia.edu page.
One of the things I’m interested in is the multiple possible senses of continuity of identity.
Locke, who kicked off a lot of the modern discourse on the topic, thought that the question of continuity of identity was a forensic question; that is, that it mattered only for legal (or maybe some quasi-legal) matters. Is John the person who is responsible for the actions committed yesterday or last week? Is this John’s property? Etc.
Clearly, it’s extremely important in this area to know if someone is the same person as some prior person. But I doubt this is the only are where this matters.
After Locke, the question became more problematic because the pragmatic concern was removed. It seems like Parfit and Williams and Wiggins and Lewis* are sometimes asking the question in general, as though there were only one kind of identity relation between a future and past person.
But I think there needs to be a purpose to the question or it doesn’t make sense.
For example: suppose Sue loses her memory (I’m referencing the case of Sue Meck here, so this isn’t one of those wonderfully creative but purely imaginary philosophical cases). Complete memory wipe. She has a husband and two children. Over time she learns to speak and read and write and be an adult person again (again total memory wipe). Suppose that she stays married and manages to be a mother to her children through this.
Is Sue the same person she was before the memory loss? She doesn’t regain the old memories, though she does hear about her previous life, so she has a kind of memory access to it, but it’s like the memory access you have to anyone’s life you’ve heard about.
I don’t think there’s a simple, universal answer to this question. Even forensically, we have to split the question. I would guess she still owns the same property, but I would also guess that she would not be found responsible for criminal acts committed before the memory loss.
What about first and third person? The actual Sue talks about her prior self (if that even makes sense) as a different person, calling her “Sue 1.” But she maintained a marriage, friends in a community, a relation with her children. Do these people think that Sue 2 is a completely different person?
Imagine another case: Joe and his meth-dealer friends like hanging out by the river, getting high, spray-painting walls, etc. One day Joe discovers Jesus and becomes a born-again Christian and leaves his meth-world behind. He is instantly transformed into someone who’s concerned with virtuous behavior and who constantly asks himself, and abides by the answer to the question, “what is the Christian thing to do?” (This sounds odd but there are cases, so I don’t think it’s entirely imaginary case.)
We can imagine Joe’s old friends saying “ He’s not the guy I used to know,” or even “That’s not Joe anymore.” They wouldn’t be entirely wrong; he’s undergone a radical change of personality, and personality is a big part of what individuates a person. Forensically, he’s the same man; he’s still responsible for his crimes (though interestingly his change of personality can come up at sentencing, so while he’s still guilty of his crimes the penalty given could be lessened, as though to say, “he’s not quite the man who committed those crimes,” i.e. there’s been a partial change of personhood) but from the standpoint of being “my friend Joe,” he can rightly be seen as a different person.
I proposed the following thought experiment for cases like this
Which of these two cases is there greater continuity of identity:
1. You are transported to another world; there is no hope of return to earth. On this planet you must constantly fight other sentient beings for survival. Cannibalism is common, and often the only means of subsistence. Human relations are purely instrumental. Others can be trusted only to act in their own self-interest, and that interest is survival. You remain there for twenty years, adapting to this new environment, and doing what’s necessary to stay alive, then return home.
2. You suffer total personal memory loss. However, you are married, part of a large and intimate community who knows much about you. You retain most of your personal characteristics, and the community fills you in on your background: this is your spouse, these your children, your friends, those you had trouble getting along with, etc. They help you acclimate to your old life, and it’s generally agreed that your personality has remained consistent; you have many of the same interests (though you’re surprised you have them), show the same level of compassion, etc
(DiGiovanna, “You are not the person I knew: eclecticism and context in continuity of identity,” Appraisal, Vol. 9 No. 1, March 2012)
My guess is that people will answer that 1 involves greater continuity of identity, but if you switch “you” to “your friend,” they’ll answer 2.
Jesse Prinz has recently done a similar experiment (not yet published) in which he found that people did indeed think that continuity of identity was greater in cases of continuity of personality rather than in cases of continuity of memory.
So: there are a lot of ways to ask this question. Is Joe at time Tx the same person as Joe at time Tx+n? needs to be contextualized. Yes, for forensic purposes he is. Well, yes for ownership but no for responsibility. Yes for being the guy who’s my friend, but no for being the guy who’s your friend. Maybe Joe’s behavior towards Lisa has changed so drastically that for Lisa, Joe is not the same person, but Joe’s behavior towards Tom has not changed.
What about sex-change? Loss of abilities that one strongly identified with, like, say, an athlete who focused her identity heavily on her athletic prowess and activities is paralyzed from the neck down? Loss of religion? I’ve informally polled students on cases like this and gotten interesting results: while many will say that a person remains the same person through almost any change, they differ on which changes constitute a change of personhood. It was indeed a young athlete who told me that a loss of bodily function would be enough for her to lose her personhood. A young man told me he would not be the same person if he surgically changed his race and gender. Etc.
Listening to these differences is, I think, important. Philosophy is not (or at least not always) the act of telling people that their intuitions about the applications of “good” and “person” and “beautiful” and such are right or wrong. If the linguistic turn was of value, it was because it told philosophers that they sometimes had overly idiosyncratic uses of some terms. Listening to what’s important to non-philosophers when they ask about continuity of identity tells us what’s important about that topic (and other topics) in general.
*This is a little unfair…Williams at least hints at the possibility that the question is too complicated to be reduced to a single answer, though he’s not as explicit about this as I think he could be. See “The Self and the Future” Philosophical Review,. LXXIX, 1970, and collected in Problems of the Self, Cambridge. 1973, pp. 46-63
Popular Metaphysics 
Shouldn’t we just be eliminativists about personal identity? It seems we have competing criterions of synchronic and diachronic identity, competing logical notions of how the law of identity should be formulated, competing conceptions of whose intuitions concerning continuity matter among the diverse opinions of folk and experts, and contradictory answers to hypothetical examples among the folk which seem to not give rise to a systematic account (see Williams on identity). These findings seem to undercut the traditional model of balancing intuitions (which vary) against principles and arguments (read cultural artifacts) and seeking universal conclusions.
My problem with eliminatiism here (though I think it’s a viable option philosophically) is that we then give up an area of human importance. Asking around and finding out why people think future selves are important, and looking at existing criteria for determining sameness, seems at least a first step in better understanding why we have the problem of continuity of identity and what eliminativism would do, culturally, psychologically and socially. It’s clearly impossible to completely give up continuity of identity and still have a legal system, for example; some form of identity has to apply if we’re going to punish criminals. So maybe in the end we reduce it to Lockean identity. But I think we also work with a sense of sameness for things like romance: I can’t just say, “O, that’s someone new, who cares,” each time I see a romantic partner. I’m excited to see that person because of a continuity of certain traits. My point is partly eliminativist, in that I want to eliminate the universal, totalizing sense of continuity of identity, and then I want to look at all the little continuities (romantic, interpersonal, familial, forensic, etc.) and see how they are important to people and why we care about them.