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Selfhood: the idea that there is something in each person that is unique to the point that even if two people had the exact same history, they wouldn't be the same person, or, in more radical forms, even if two people had the same genetics, and the same prenatal conditions, and the exact same life history, they wouldn't be the same person. Another way of saying this is to say that while there is a similarity between Bob-who-has-lived-Bob's-life and Suzy-who-has-lived-Bob's-life (i.e., has had all of Bob's experiences, parents, cultural circumstance, genetics, etc.), there is also a similarity between Bob-who-has-lived-Bob's-life and Bob-who-has-lived-Suzy's-life.
I definitely support this viewpoint, and don't think it's either compatible or incompatible with determinism, as it is based around a notion of something independent of external factors (one could postulate a kind of determinism as, in part at least, stemming from an intrinsic existence of self).