Continuity theory sits in an uneasy but productive relationship with doctrines of rebirth and resurrection across the traditions in this atlas, since most such doctrines want to say that the person who is reborn or resurrected is genuinely, strictly the same person as before, not merely someone psychologically continuous with them, a distinction continuity theory itself puts pressure on by asking exactly how strict that sameness needs to be if memory and psychological connection are interrupted, as they typically are held to be, by death itself.
Buddhist teaching handles this tension distinctively, since its doctrine of anatta already denies any persisting substantial self to begin with, making a continuity-style account, in which what carries forward is a causal-psychological stream rather than an unchanging substance, considerably more natural to Buddhist metaphysics of rebirth than to traditions committed to a substantial, unchanging soul. Substance theorists press the sharpest philosophical objection to continuity theory generally: they argue psychological continuity can, in principle, be replicated, duplicated, or interrupted and later resumed in ways that seem to leave the deeper question of strict numerical identity, whether this later person really is, and not merely resembles, that earlier one, entirely unanswered by continuity alone.