(1) Attribution of personhood should be an objective ground for respect, and this ground cannot be lost "through illness, poverty, villainy, inanity, or senility."
(2) Persons as legal entities (liability, legally defined responsibility, guarantee of specifically defined rights and duties).
(3) Persons as autonomous agents, capable of self-defining choices.
(4) Persons as identified "by their mutual interactions, by the roles they enact in the dynamic dramas of their shared lives" (p. 37).
(5) Persons as beings with a characteristic life story.
(6) Persons as units of genetic individuation with conatus.
(7) A person experiences himself or herself as an I.
Now, in one sense I see why Rorty doesn't think all these functions hang together; but part of my problem is that I don't see why all of these are supposed to be plausible functions for the notion of personhood. (6) very clearly is completely worthless; that's not a plausible requirement for personhood, nor does the concept of person do a particularly good job in such a role. And as for (2), the law never defines things in themselves but only insofar as they are relevant for the practical purposes of the law; the law does not decide what a person is, but what is sufficiently person-like given the particular issues on which the law focuses. So (6) and (2) should be set aside complete. (4) clearly only gives us a mark or note of personhood; it is obviously and on the surface an identifying characteristic, not a defining one. This leaves (1), (3), (4), (5), and (7). And, in fact, these are the only ones that show up in Rorty's attempted synthesis:
A person is a unit of agency, a unit that is (a) capable of being directed by its conception of its own identity and by what is important to that identity, and (b) capable of acting with others, in a common world. A person is an interactive member of a community, reflexively sensitive to the contexts of her activity, a critically reflective inventor of the story line of her life. (p. 43)
As she rightly notes, as she presents her synthesis it isn't clear whether the elements are conjunctive or nested; but, naturally, that's simply an issue with her synthesis. It's clear, for instance, that 'unit of agency' must be presupposed by all the others. (a) and (b) simply identify potentialities of this unit of agency. The second sentence is the really unclear part of her synthesis, since (1) it doesn't identify a capability but an actuality (what the person actually does), and it isn't actually clear why; and (2) it isn't clear how the three parts of it are related to each other; and (3) all three parts nonetheless presuppose everything in the first sentence, so it isn't clear why they need to be considered as more than corollaries in the first place. She then makes an argument against taking the metaphysical notion of a person as primary, an argument I don't understand at all because I have no clue what she means by 'the metaphysical notion of a person' in this context. Rorty really hasn't done anything to show what she claimed she would show.
There are several other indications throughout the article that suggest that she is poorly equipped for the sort of argument she is making. She says of the concept that for Christians the contrast class for 'person' is that of unsouled beings (p. 32), and she later talks about "the Christian idea of the immortal soul" (p. 33) and again of "a divinely assured immortal soul" (p. 36) as if this somehow encapsulated the Christian view. Now, this is manifestly false. The Christian notion of personhood derives from Trinitarian and Christological discussions; the issue of immortal souls never arises at all in the first sort of discussion, and while it arises in the latter sort, it does not do so in the relevant way. The Persons of the Trinity are not persons in virtue of having immortal souls; the Incarnate Word has an immortal soul, but it is not what makes him a person -- and indeed, insistence on exactly this was the whole point of Chalcedon [And Ephesus before it, and III Constantinople after it --ed.]! Given that the Christian conception of person was important enough to be mentioned several times as part of her argument, such an absurd slip is not heartening. I suspect, however, that it's a slip that would be commonly made. (If she had really wished to bring in the Christian conception of personhood, the Boethian definition, and the Victorine modifications of it in favor of a more social conception of person, would have been relevant.)