Derek Parfit, answered from the texts and cited to the page.
Personal identity over time is reducible to physical and psychological continuity-and-connectedness; there is no further deep fact of personal identity over and above these continuities.1234 The Cartesian Ego is illusory: there is no separately-existing entity called the self that owns the experiences and persists through change. Personal identity admits of degrees (the Combined Spectrum case shows this), contrary to common intuitions about the all-or-nothing character of survival.
What matters in survival is psychological continuity-and-connectedness, not strict identity; identity is not what matters. The Teletransporter case (RP §75) makes the structural point: when a machine destroys my body and transmits the information to Mars where a perfect copy is built, the question whether the person who wakes up on Mars is me has no answer of the deep-further-fact kind that Cartesian intuitions demand.
The case is not undecidable; it is a case where the question, properly understood, has no further fact to settle it. The late paper 'We Are Not Human Beings' (2012) modifies the metaphysics — we are not human beings (animals) but the conscious thinking parts of human beings, perhaps the cerebrum — while preserving the central Reductionist thesis that what matters is psychological continuity-and-connectedness.5
On the Psychological Criterion, personal identity over time just involves the various kinds of psychological continuity, with the right kind of cause. These views are both Reductionist. They are Reductionist because they claim (1) that the fact of a person's identity over time just consists in the holding of certain more particular facts.Reasons and Persons, p. 227
And there would be similar changes in this person's body. Near the far end, most of my cells would be replaced with dissimilar cells. The person who wakes up would have only a few of the cells in my original brain and body, and between her and me there would be only a few psychological connections. She would have a few apparent memories that fit my past, and a few of my habits and desires.Reasons and Persons, p. 254
The other, 'con tinuity', is the holding of a chain of such relations. If, say, I can not now remember some earlier day, there are no 'connections of memory' between me now and myself on that day. But there may be 'continuity of memory'. This there is if, on every day between, I remembered the previous day. Of these two general relations, I define 'continuous with' so that, in its logic, it has no degrees.Later Selves and Moral Principles, p. 4
Our identity over time consists in physical and/or psychological continuity. (E) imagine cases which questions about identity would indeterminate: having no answers. These questions would also be in the following sense empty: they would about different possibilities, but only about different descriptions of the same course of events. Even without answering such questions, we could know what would happen.Experiences Subjects and Conceptual Schemes, p. 218
That is the question lecture taken material written support Foundational Research Grant Ammonius Foundation, whose generosity I am very grateful. I hope to publish other parts of this material elsewhere. I have been much helped by comments from Eric Olson, Sydney Shoemaker, and Ingmar Persson. involved, for example, in an identity crisis. But I shall be discussing our numerical identity.We Are Not Human Beings, p. 6
The Reductionist account in Reasons and Persons Part III is one of the most influential and most contested positions in late-twentieth-century philosophy of mind. The Dancy volume (Reading Parfit 1997) contains four major engagements: Shoemaker, Johnston, Thomson, McDowell. Williams's earlier 'The Self and the Future' (1970) presses a different challenge through the asymmetry of the imagined-from-the- inside vs imagined-from-the-outside cases. Lewis's 'Survival and Identity' (1976) and Perry's 'Importance of Being Identical' (1976) attempt to preserve identity-talk within a continuity framework. Olson's animalism (The Human Animal 1997) argues we are essentially organisms; the late Parfit response in 'We Are Not Human Beings' (2012) is the considered late position. The debate continues; the Reductionist framework remains the dominant starting point.