I would say it depends on ontology and definition. For instance, the Nyaya attempts to prove the existence of a self by:
(a)Identifying all possible substances.
(b)Identifying all possible qualities.
(c)Claiming qualities absolutely NEED a substance to exist. [Buddhists disagreed here.]
(d)Proving that there are certain qualities that cannot subsist in any substance other than the self.
The issue is, if you accept the ontology of Nyaya, their argument is correct and the self is proven as a substance.
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