Garrett's view combines the psychological and physical criteria. He believes that psychological continuity is the key ingredient but it must be supported by a structurally similar continuing physical entity - the brain or a suitable artificial replacement
Thus, A is the same person as B iff A and B are psychologically continuous and this psychological continuity is caused by the continuity of the brain or a physical entity that is continuous with the brain.
The main thought experiment that drives him to this view is the Branch-line case: Garrett accepts the intuitive response that the original person remains identical with the person on the branch-line, that is, the one on Earth (see Parfit, pp. 199-201). That's why Garrett insists on some kind of physical continuity and does not rest content with saying that mere psychological continuity is sufficient for survival (if not identity) as Parfit does.
It's also worth noting that Garrett has a specific view about the nature of identity: the Best Candidate view. According to this view, A is the same person as B if A best meets the criteria. So, no one could survive division on this view since no one best meets the criteria if there are ties.
Garrett regards this view of identity as the correct one because it best accounts for the Ship of Theseus. It thus strikes him as a good view of identity in general.
Further fact intuitions
I accused Garrett of trying to have our further fact intuitions while also rejecting them.
Specifically, I said that the intuitive response to the Branch-line case is driven by the thought that there is a further fact of identity in addition to facts about psychological and/or physical continuity: that's why we are uneasy about saying that the original person could survive on both Mars and Earth. But if that's what's behind our reactions to the Branch-line case, then we can't accept a Best-candidate theory of identity in the case of persons. After all, according to that view, whether A lives or dies depends not only on his relationship with a future person B, but also on whether he is related to some future person C in the same way. That runs against my further fact intuitions: if there's a deep fact about whether I survive as B, what happens to a different person, C, shouldn't be relevant. Why would the lights go out when the other half of my brain is transplanted into C's head?
That objection feels right to me. But what if Garrett replied like this? "You've got the further fact intuition wrong. We're intuitively inclined to respond as I say in both the Branch-line and fission cases: we think the original remains on Earth and that there's no such thing as surviving fission and enjoying a "double success." My theory accounts for both of these reactions, and thus it is consistent with our further fact intuitions."
I think there are two problems with that imagined reply. First, I think the intuitive response to fission goes the other way: most people agree that it's a double success. In my own case, I have to reason my way to the conclusion that this is problematic. Second, I very much doubt that we're intuitively inclined to accept a Best-candidate view of personal identity: most people reject the thought that whether A survives as B depends on what happens to some third party C.
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