Source: wikipedia
In Indian philosophy, the concept of a self is called ātman (that is, "soul" or metaphysical self), which refers to an unchanging, permanent essence conceived by virtue of existence. This concept and the related concept of Brahman, the Vedantic monistic ideal, which was regarded as an ultimate ātman for all beings, were indispensable for mainstream Indian metaphysics, logic, and science; for all apparent things there had to be an underlying and persistent reality, akin to a Platonic form. The Buddha rejected all concepts of ātman, emphasizing not permanence, but changeability. He taught that all concepts of a substantial personal self were incorrect, and formed in the realm of ignorance. The Buddha criticized conceiving theories even of a unitary soul or identity immanent in all things as unskillful in the Great Discourse on Causation. In fact, according to the Buddha's statement in Khandha Samyutta 47, all thoughts about self are necessarily, whether the thinker is aware of it or not, thoughts about the five aggregates or one of them.
In a number of major Mahayana sutras (e.g. the Mahaparinirvana Sutra, the Tathagatagarbha Sutra, the Srimala Sutra, among others), the Buddha is presented as clarifying this teaching by saying that, while the skandhas (constituents of the ordinary body and mind) are not the self, there does truly exist an eternal, unchanging, blissful Buddha-essence in all sentient beings, which is the uncreated and deathless Buddha-nature ("Buddha-dhatu") or "True Self" of the Buddha himself. The "tathagatagarbha"/Buddha nature does not represent a substantial self; rather, it is a positive language expression of "sunyata" (emptiness) and represents the potentiality to realize Buddhahood through Buddhist practices; the intention of the teaching of tathagatagarbha (Buddha nature) is soteriological rather than theoretical.[4]
This immaculate Buddhic Self (atman) is in no way to be construed as a mundane, impermanent, suffering "ego", of which it is the diametrical opposite. On the other hand, this Buddha-essence or Buddha-nature is also often explained as the potential for achieving Buddhahood, rather than an existing phenomenon one can grasp onto as being me or self.
Anatta is discussed in the Questions of King Milinda, composed during the period of the Hellenistic Indo-Greek kingdom of the 2nd and 1st centuries BCE. In this text, the monk Nagasena demonstrates the concept of absolute "non-Self" by likening human beings to a chariot and challenges the Greek king "Milinda" (Menander) to find the essence of the chariot. Nagasena states that just as a chariot is made up of a number of things, none of which are the essence of the chariot in isolation, without the other pieces, similarly no one part of a person is a permanent entity; we can be broken up into five constituents – body, sensations, ideation, mental formations and consciousness – the consciousness being closest to the permanent idea of "Self", but is ever-changing with each new thought according to this viewpoint.
According to some thinkers both in the East and the West, the doctrine of "non-Self", may imply that Buddhism is a form of nihilism or something similar. However, as thinkers like Nagarjuna have clearly pointed out, Buddhism is not simply a rejection of the concept of existence or meaning, but of the hard and fast distinction between existence and non-existence, or rather between being and no-thingness. Phenomena are not independent from causes and conditions and do not exist as isolated things as we perceive them to be. The lack of a permanent, unchanging, substantial Self in beings and things does not mean that they do not experience growth and decay on the relative level. But on the ultimate level of analysis, one cannot distinguish an object from its causes and conditions or even distinguish between object and subject (an idea appearing relatively recently in Western science). Buddhism thus has much more in common with Western empiricism, pragmatism, anti-foundationalism, and even poststructuralism than with nihilism.
In the Nikāyas, the Buddha and his disciples commonly question or declare "Is that which is impermanent, subject to change, subject to suffering fit to be considered thus: 'This I am, this is mine, this is my self'?" The question which the Buddha poses to his audience is whether compounded phenomena are fit to be considered as self, to which the audience agrees that it is unworthy to be considered so. And in relinquishing such an attachment to compounded phenomena, such a person gives up delight, desire and craving for compounded phenomena and is unbounded by its change. When completely free from attachments, craving or desire to the five aggregates, such a person experiences then transcends the very causes of suffering.
In this way, the insight wisdom or prajñā of non-Self gives rise to cessation of suffering, and not an intellectual debate over whether a self exists or not.
It is by realizing (not merely understanding intellectually, but making real in one's experience) the three marks of conditioned existence that one develops prajñā, which is the antidote to the ignorance that lies at the root of all suffering.