The reduplication problem
The main point
If a relationship between person A and person B does not logically exclude a third person C's having the same relationship to A or B, then the fact that the relationship holds between A and B is not sufficient to show that A and B are the same person.
Psychological continuity seems to be such a relationship. At least, it seems to be if psychological continuity is understood to permit so-called "body switching."
The root of the problem is that there is no distinction between qualitative and numerical identity for psychological states and character traits. (Quinton seems to agree: see the last paragraph under the heading "particularity" in the notes on Quinton's broader psychological theory.)
Appreciating this undermines both of Quinton's rationales for a psychological approach, according to Williams.
The particularity argument
Williams's point here is tricky, so I'll repeat it.
The point is that caring about a cluster of psychological features isn't necessarily the same thing as caring about a particular person. The logical possibility of series persons shows that caring about a cluster of psychological characteristics could involve caring about a group of series persons. As Williams notes, our concept of loving someone would break down if that were the case.
One reply is a dead end: if you say "those series persons will diverge, psychologically, so in caring about a cluster of psychological features, I really would just care about one particular series person." That's a dead end because it would imply far too strict a view about normal people: by hypothesis, we care about people only because of their psychological qualities (that's what the particularity argument asserts). But people change. If I only cared about a very sharply defined set of psychological qualities, I would quickly stop caring about my friends. The only way the particularity argument can be made to seem plausible is if it admits that I care about a wide enough range of psychological characteristics to allow my friends to change over time. But then the range will be wide enough to accommodate a fair number of series persons.
In the end, I think the both the particularity argument and Williams's reply are misleading.
For all Williams says, it may still be true that in fact I care only about a particular person for her psychological characteristics. There aren't any series persons, after all, and the logical possibility of their existence does not seem to be enough to show that in caring about the real Mary Smith's mind (and mind alone!) I actually care about the hypothetical gaggle of logically possible series-Mary Smiths.
Quinton's use of the particularity argument has its flaws too (again, see the notes on Quinton's broader psychological theory). Chief among them is the fact that even if we did care only about psychological characteristics, that wouldn't be caring about a particular thing, it would be caring about a set of qualities. These qualities, in turn, could be exhibited by a number of different persons.
Retaining the psychological criterion
There was a lot of sentiment in favor of retaining some sort of psychological account, perhaps melded with something about the body. Tanja wants to see a positive account of the bodily criterion. Kristie thinks that the two accounts correspond to first and third person ways of understanding personal identity (but take a look at §3 of "Personal Identity and Individuation").
Tanja will have to read something else, I'm afraid: most defenders of the bodily criterion seek to show that the psychological views are mistaken and suggest that the body is the only alternative. (One marvelous exception that I just read this summer is Eric Olson's The Human Animal (Oxford University Press, 1997). I have the library's copy, but would be happy to share. It's in paperback at the Co-op too.)
Kristie will not have to wait long: Williams creates all sorts of trouble for her view in "The Self and the Future."
Here are two other possible diagnoses of the desire to retain the psychological criterion.
(1) Only a psychological view could account for the importance of persons, why they're valuable.
(2) The reduplication problem shows that the psychological views have a problem with identity but they still seem to be on the right track concerning persons. Maybe if we're really concerned with persons, we'll discover that questions about identity are less important than they seem.
See if either of those points express something on your mind. They'll come up again with increasing frequency.
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