The main point
The main point was to lay out Parfit's broad strategy. He wants to show that personal identity is less important than we think it is and that we should generally replace "is the same person as" with "is R-related to". The latter expression would be close to the former, but it would not be the same: this would have interesting implications for what we believe about self-interest and morality.
In laying out this broad strategy, we defined important terms. His position is reductionism, it is opposed by those who believe that persons are separately existing entities and those who believe in a further fact of personal identity. Relation-R is composed of psychological connectedness and psychological continuity.
Parfit's strategy goes like this:
(1) there are no separately existing entities
(2) If persons are not separately existing entities, questions about personal identity may have indeterminate answers. This can be seen by looking at ways of trying to ensure the determinacy of personal identity. They either (a) fail or (b) succeed by defining personal identity in a way that renders it unimportant.
(3) What we're left with (Relation-R) is less important than personal identity is. We see this by accepting the consequences of conceding that questions of personal identity need not have determinate answers.
Parfit wants to say that what is important about persons is Relation-R and that Relation-R should replace personal identity. Consequently, the constituents of Relation-R had better not presuppose personal identity: that would short-circuit the whole replacement idea.
Many of our psychological elements seem to presuppose personal identity, especially memory (see the Circularity objection).
A way around this is to define a broader kind of psychological element that includes all of the problematic psychological states but does not presuppose personal identity. In this case, quasi-memory: in order to be a quasi-memory, a psychological state must pass all the requirements of a normal memory except one: the requirement that the person who had the target experience be the same as the person who has the memory experience. All memories are quasi-memories therefore, all memories can be described (as quasi-memories) without presupposing personal identity.
Whether that would capture everything important about memory is another question. We'll have to check on that later.
What about indexicals involving me?
David asked whether Parfit thinks it's possible to give an impersonal description of a thought like "I really like myself." How can we say what this thought is a thought about unless we say who is thinking it?
Here's the way I would try to answer this question: could Parfit say the impersonal description is "The person who has this thought really likes himself or herself?" That would be true and it wouldn't presuppose anything about the identity of the person who has the thought.
Fortunately we have some evidence of how Parfit himself would answer. I have an old (circa 1994) draft of some of the material that will make up a book that Parfit is in the process of writing. Having skimmed through this, I can quote a bit that seems to answer David's question. WARNING: this is not published material, it was presented at the time as a rough draft, and it is five years old. You should not quote it in academic writing. It is nonetheless the copyrighted property of Prof. Parfit.
Where was I? Oh yes, indexicals. Here's the relevant passage, quoted in full for your reading pleasure.
"It can be argued that, even in my intended sense, IRC [the Impersonal Redescription Claim from Reasons and Persons -- mjg] is false. According to me, we could fully describe our thoughts without explicitly claiming that we exist. Cassam objects that the content of demonstrative thoughts -- ones that we express with words like 'this' or 'I' -- depends in part on what they are about. Since we have such thoughts about ourselves, we cannot fully describe these thoughts without claiming that we exist, in the way that IRC denies to be necessary.
This objection may refute IRC. But, if that is why this thesis fails, Reductionists can be unconcerned. As before, these remarks could be transferred to what are manifestly composite entities. Consider the thought 'That is my audio system'. Perhaps, to describe the content of this thought, we must say which audio system I have in mind. But that would case no doubt on the reductionist view that such a system just consists in certain components. The same applies to demonstrative thoughts about persons.
If IRC is false, Reductionists might turn instead to CIB [the claim that there Could be Impersonal Beings, explained in the next sentence -- mjg]. They might claim that there could be thinkers who were in other ways like us, and who knew at least as much as us, though they did not even have the concept of a person, or subject of experiences. If that claim is true, it could both illustrate and defend a Reductionist view. it would show the concept of a person to be, in one straightforward sense, theoretically optional or unnecessary. And Cassam's objection would not arise. Since these imagined beings would have no thoughts about persons, it could not be argued that, in a full description of their thoughts, it would have to be claimed that persons exist."
I don't have the citation for the paper Parfit is referring to, but I'd be willing to bet that this is the one he had in mind: Quassim Cassam, "Kant and reductionism" Review of Metaphysics vol. 43 (1989).
I'm still not sure that I see what's wrong with my answer, but I haven't read Cassam's paper. Note that Parfit does not concede the point: he only says that even if it were true it would only undermine a point that is not essential to Reductionism and can easily be replaced.
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