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More technically, the concept of self could be basically divided in two ways:
1. When Hinayana schools (Vaibashika and Sautrantika tenets) speak about self, they refer to a self, which if it existed, would be unchanging (eternal, not changing from moment to moment), and would be in control of the five aggregates. They negate such a self and usually they call the fact that self does not exist in this way selflessness. They speak mostly about self of a person.
2. When Mahayana schools (Chittamatra and Madhyamika tenets) speak about self, they refer to a self, which if it existed, would be inherently or truly existent (this is actually extension of Hinayana view). So, they negate self which would be inherently or truly existent. They speak about self of a person and about self of phenomena. They usually call the fact that self or objects does not exist in this way emptiness.
These negations of Hinayana and Mahayana do not mean that self does not exist at all, rather it means that self is a mere imputation on a valid basis.