(Continued from post below)
II Two Approaches to the Cases
There are then at least two different approaches, the linguistic and the affective:
The linguistic approach asks how are we (whoever “we” is) using words like “same person” now, and based on that, how will we use those words in odd cases.
The affective approach asks what sort of feelings of identity do we (again) have towards future and past persons who might be ourselves. Parfit’s Russian nobleman case is a great example of this where “identification” is used in the psychological sense.
In short, there is a young Russian socialist who later inherits land and becomes a wealthy aristocrat. The young socialist would not identify himself with his later form, and would count it as a form of non-continuity of identity, if that aristocrat betrayed the socialist values the young man holds. Recent (unpublished) research by Jesse Prinz and Joshua Knobe found that most people surveyed had a similar intuition: they would consider themselves non-continuous with a future self that betrayed most or all of their deeply held moral beliefs. Obviously (or perhaps obviously to someone raised in a Western legal tradition) the Russian nobleman would still be responsible for crimes committed and debts incurred when he was the young socialist. But the fact that there is an internal lack of identification is important, in that a person is not just what the law says, but also how we identify our friends, family and selves. If we think someone has changed so drastically as to not be the same person, it’s not helpful to be told that some law or some philosopher has said that this person is the same person. He’s only the same person for some particular purpose, and while the criterion employed may work for identifying one’s creditor, they are clearly not the same as the criteria employed for the purpose of identifying one’s friends, or even oneself (understanding “self” here as that being we identify as.)
Similar points have been raised about emotional connectedness by Marilyn Friedman in Autonomy and the Split Level Self, Marya Schechtman in “Self Expression and Self Control,” as well as Tim Henning in “Why Be Yourself” where he argues that we have a particular obligation to desires that our “our own,” and that some desires that we nonetheless feel and experience are not “our own,” nor should be identified as properly our own. Of course the seminal work on self-identification with emotions and desires is Harry Frankfurt’s in The Importance of What We Care About, notably in the essays “Freedom of the Will and the Concept of the Person” and “The Importance of What We Care About.”
I think both the linguistic and affective approaches have value, but it’s important to distinguish them, because they’re asking slightly different questions. Most who do the linguistic analysis approach seem to think they’ll get at the truth about whether a person is two people prior to fission, or one person who ceases to exist in fusion, or etc. Again, I’m not convinced there’s an interesting answer here.
When Plutarch raised the case of Theseus boat, which, over the course of its voyages, had, bit by bit, all of its parts replaced, he seemed to be suggesting that we should be puzzled about whether this was the same boat or not (or at least note that the “philosophers” were puzzled, and since I assume my audience is philosophers, then “we.”) But we all know all the details, we all know when each part was replaced, and that at the end no parts are held in common between the initial and final boat. So what’s the question?
It’s whether we want to apply the term “same boat.” But this is, as Parfit would say, an empty question. We all agree on the particulars, so it’s a matter of convention, or perhaps some practical importance (for purpose of resale, or compliance with law in advertising, etc.) whether we say it’s the same boat or not.
If it’s merely a convention whether it’s the same boat, that convention is nonetheless subject to the forces that create conventions. Perhaps I cannot sell it as the same boat if it has no common parts. Perhaps I can sell it as a “brand new boat,” if all the parts were replaced within the last two months. Etc.
Now, with the thought experiment cases, when we do the linguistic approach, we reach the impasse that we are asking how we are to apply words in cases that are beyond the normal scope of the application of the words and thus, instead of being able to present the “right” use of the terms, sometimes we have to make proposals for ways to use the words. Obviously, words are usable beyond the limited set of ways they’ve been used in the past, but they’re not always going to be infinitely flexible in future circumstances. Heisenberg famously noted that the words “really” and “happens” reach their limits in attempting to talk about what’s “really happening” on the quantum level when no observation is being made.
So, how should we make our proposals? That is, given that we reach a linguistic limit, what basis should we use for proposing that we say “same person” or “not same person?” I’d hold that we can look at the thought experiment cases, and naturalize them, to get some idea of what’s important in each case, and then ask about why we would want to say “same person” and why we might not want to say “same person” and see if there are practical reasons for these.
 Friedman, Marilyn, “Autonomy and the Split Level Self,” Southern Journal of Philosophy, 24, pp 31, Spring (1986)
 Schechtman, Marya, “Self Expression and Self Control” in The Self, ed by Galen Strawson, Blackwell, , pp 26-44 (2005)
 Henning, T, “Why Be Yourself: Kantian Respect and Frankfurtian Identification” Philosophical Quarterly, Vol 61 no 245, October 2011