The question of the existence of a persistent self is a difficult one. In classical context, it gives rise to the paradox known as The Ship Of Theseus. And then there's the Buddhist doctrine of Anatta, that there is "no self." The Buddhist point is argued well, and I would gather is worth studying, even if ultimately fruitless. (I am just starting my studies now; I have a good book on the subject, but it's $50+, so probably not for the merely curious.) I've been introduced to Heidegger's existentialism in the past year, and while he doesn't directly answer this complaint, his analysis of the ontology of beings is very powerful.
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