Self and no self, a big problem
When the wanderer Vacchagotta, in the Ananda Sutta (S. iv. 400) asks the Buddha whether the self exists (atthatt'ti) or does the self not exist (natthatt'ti) we learn Vacchagottas questions were based on the current popular theories of self. These theories had no connection with how the Buddha regarded the self. The Buddha had a different take on the self or in Pali, att.
For Vacchagotta, the question of self can only be understood in one of two ways. Either there is the self of the Eternalists whose position held the self to be one or more of the Five Aggregates which are believed to be eternal (cp. Udana Atthakatha, 344); or there is no self at all which was the position of the Annihilationists. Both of these positions, however, were put aside by the silence of the Buddha.
The self of the Buddha is certainly real but it was not one of the Five Aggregates. The Buddha never fails to make it clear to us that his self is not an aggregate (M. i. 136). When the Buddha says that all things, including the Five Aggregates, are anatt he is actually saying, All things are not-the-self not that there is no self or nattha att. This is like saying, "All things are not the Tathagata."
The two particular views Vacchagotta clung to concerned an eternal material, aggregate self and no self. He couldnt understand the idea of self as transcendent to all determination which is the Buddhas self; which is elaborated on in the Mahayana Mahaparinirvana Sutra.