I often mind myself wanting to quick link a definition of my view of personal identity to link to, but the only one I know is embedded deep in David Chalmer's essay, 'The Singularity: A Philosophical Analysis'. So I'm going to cheekily extract the relevant section here and hope he doesn't mind:
More succinctly, Wikipedia (in the entry on Open Individualism) defines it thus:
David Chalmers wrote:A deflationary(sic) view of survival holds that our attempts to settle open questions about survival tacitly presuppose facts about survival that do not exist. One might say that we are inclined to believe in Edenic survival: the sort of primitive survival of a self that one might suppose we had in the Garden of Eden. Now, after the fall from Eden, and there is no Edenic survival, but we are still inclined to think as if there is.
If there were Edenic survival, then questions about survival would still be open questions even after one spells out all the physical and mental facts about persons at times. But on the deflationary view, once we accept that there is no Edenic survival, we should accept that there are no such further open questions. There are certain facts about biological, psychological, and causal continuity, and that is all there is to say.
A deflationary view is naturally combined with a sort of pluralism about survival. We stand in certain biological relations to our successors, certain causal relations, and certain psychological relations, but none of these is privileged as “the” relation of survival. All of these relations give us some reason to care about our successors, but none of them carries absolute weight.
One could put a pessimistic spin on the deflationary view by saying that we never survive from moment to moment, or from day to day. At least, we never survive in the way that we naturally think we do. But one could put an optimistic spin on the view by saying that this is our community’s form of life, and it is not so bad. One might have thought that one needed Edenic survival for life to be worth living, but life still has value without it. We still survive in various non-Edenic ways, and this is enough for the future to matter.
More succinctly, Wikipedia (in the entry on Open Individualism) defines it thus:
The view that personal identities correspond to a fixed pattern that instantaneously disappears with the passage of time