The problems of the self (ātman) and personal identity over time were thoroughly analyzed in the classical Indian philosophy. The Buddhist philosophers rejected the Brahmanical commitment to a permanent unitary self which persists through changes of body and mind, and held that the self is a mere conceptual or thought construction (prajñāpti): there is no reality in the self; when we look more closely at what we call ‘I’, we will find only a stream of perceptions. Contrarily, the orthodox (āstika) philosophers argue that many common phenomena like memory or recognitive perception (pratyabhijñā) could not take place, if the rememberer and knower were different. One must endure through time as the same identical subject to be able to remember, have desire, commitments, responsibility etc. In favor of the classical Brahmanical position I argue that if a person is nothing more than a bundle of different fleeting psycho-physical states, none of them can be plausibly explained. The paper brings out also some connections between the Indian and the Western debates over the personal identity problem.