Derek Parfit, answered from the texts and cited to the page.
The central claim is this: personal identity is not what matters in survival. What matters is relation R — psychological connectedness and/or psychological continuity, with the right kind of cause.1 To see why, consider what personal identity actually consists in. In nearly all ordinary cases, relation R takes a one-one form: it holds between one present person and exactly one future person.
When R holds in this non-branching way, we can use the language of identity — we can say that the future person will be me. But personal identity is just R holding uniquely; it is R plus the further fact of uniqueness, which I call U.2 The question is whether U adds anything of real value. It does not add much. If I will be R-related to some future person, the presence or absence of U makes no difference to the intrinsic nature of my relation to that person.3
And what matters most must be the intrinsic nature of the relation. So R without U would still have at least most of its value. Personal identity matters, when it does, mostly because R is present — not because the uniqueness condition is satisfied on top of it. The case of division makes this vivid. Suppose my brain is divided and each hemisphere transplanted into a different body.
R then takes a branching form. But personal identity cannot branch: I cannot be identical with two distinct people. So neither resulting person will be me.4 Yet each stands in exactly the relation to me that, in ordinary cases, would constitute my survival. To say that this non-identity matters — that something important is missing — is to treat identity as a further fact over and above the holding of R.5
That assumption is what I deny. The underlying metaphysics is what I call Constitutive Reductionism: our existence consists in the existence of a body and the occurrence of various interrelated mental processes and events, and our identity over time consists in physical and/or psychological continuity.6 There is no separately existing entity called the self that persists through change.
Personal identity does not have, as has been widely assumed, a special rational and moral importance over and above what is carried by psychological continuity and connectedness.7 Once division is properly understood, the conclusion that neither resulting person is me ceases to seem like a loss. Dying is one way of losing one's identity; dividing is another.
To treat them as equivalent is to confuse two with zero.8 Double survival is not ordinary survival, but it is even less like death.
Relation R is what matters. R is psychological connectedness and/or psychological continuity, with the right kind of cause.Reasons and Persons, p. 279
Personal identity consists in R holding uniquely—holding between one present person and only one future person. Since there is something more to personal identity than to relation R, we can rationally claim that, of the two, it is identity which is what matters.Reasons and Persons, p. 280
If I will be R-related to some future person, the presence or absence of U makes no difference to the intrinsic nature of my relation to this person. And what matters most must be the intrinsic nature of this relation.Reasons and Persons, p. 280
In the imagined case where I divide, R takes a branching form. But personal identity cannot take a branching form. I and the two resulting people cannot be one and the same person. Since I cannot be identical with two different people, and it would be arbitrary to call one of these people me, we can best describe the case by saying that neither will be me.Reasons and Persons, p. 279
If we do insist on this, we seem to be assuming that identity would be a further fact—that, in the relation between me and each resulting person, something is missing.Lewis Perry and What Matters, pp. 11–17
Our existence consists in existence of a body, occurrence of various interrelated mental processes and events. Our identity over time consists in physical and/or psychological continuity.Experiences Subjects and Conceptual Schemes, p. 218
Personal identity does not have, as widely assumed, rational and moral importance. That importance is carried by psychological continuity and connectedness, with any cause.Experiences Subjects and Conceptual Schemes, p. 218
You will lose your identity. But there are different ways of doing this. Dying is one, dividing is another. To regard these as the same is to confuse two with zero.Reasons and Persons, p. 279