Personal identity is considered in philosophy to be metaphysics. The question is under which conditions a person at one time is the same person at another time, and what, in that case, is the bearer of this (numerical) identity.
The discussion naturally overlaps the problem of identity and the soul-body problem. The question has been dealt with very early and very extensively within the Eastern philosophical tradition. Within modern and classical philosophy there are three basic positions.
Reductionism
Denial
Non-reduktionismen