You’re being consistent, but I don’t think it’s enough to say “we have to accurately describe the process.” That doesn’t determine what we should say here. We can “accurately” describe the process using a language that counts people who share memories in the right way “the same person,” and we can also “accurately” describe the process using a language that does not count two entities as the same person if their timeline is not completely physically continuous in the normal biological way. These are two different languages one can use to describe the situation, the situation can be fully and accurately described either way, and normal English is ambiguous between these two languages.
How do we choose between languages, and does it matter?
It does matter because the semantic properties of a language can have psychological and political effects. Here’s what I mean. If the person post-duplication is to be called “the same person” as the person pre-duplication, then we will take ourselves to owe the post-duplication person all the same rights that were due to the pre-duplication person. The prior person’s house is now the later person’s house, and so on. But if we use the other language, we’ll treat the later person differently. He’s not the same person as the prior person, so he doesn’t get all the prior person’s stuff. The prior person is dead. We have an estate sale. Too bad for the later person.
It’s not a question of accuracy, then–again, both ways of describing the situation are completely adequate to the physical facts and vice versa. It’s instead a question of, basically, (in this case), political systems. Should we use a language that gives rights W X and Y to entity Z, or should we use a language that doesn’t?
How do you decide that? In this case, my own instinct is to think “Geez, what if I were that poor duplicate? I’d have all the memories of the past person, yet all these people would be treating me as though I weren’t him and had no right to his stuff and so on.” That’d suck pretty hard. If I think the right political system is one that minimizes things sucking pretty hard, then I think that the language that strips this entity of rights is not the right language to use.
Of course in more complicated duplication systems, more complicated problems might arise concerning the rights of the entities involved, and more complicated problems about language would develop concomitantly. I’m just looking at one kind of scenario here. My main point is that “adequacy to the facts” actually doesn’t determine which description to use here. Different languages, each plausibly in keeping with English usage, are all adequate to the facts. Yet different languages have different consequences in practice, for a matter like this anyway. Hence we have a choice to make, and can’t base the choice on the criterion of factual accuracy.