The contemporary Buddhist view of the doctrine of eternalism (sassatavada) is the belief that the individual has an unchanging self or soul. In Buddhism, the doctrine of eternalism is generally found in this form: “the self and the world are eternal" (sassato attâ ca loka ca) (Ud VI, v). So what does this really mean? The commentary to the Udana, the Udanatthakatha, translated by Peter Masefield, describes the phrase this way:
“[T]hey [eternalists] take some particular item amidst (the [five] khandhas of) material form and on to be "the self" and "the world", and then describe this as "eternal, permanent", also understanding that others likewise, in accordance with which there is said: "They [eternalists] declare material form to be the self and the world, stating such to be not only the self and the world but also eternal; they declare sensation ... perception ... the formations ... consciousness to be the self and the world, stating such to be not only the self and the world but also eternal (344, p. 882)." (Brackets are mine.)
What first stands out is eternalism rests on the Five Aggregates, namely, material form, sensation, perception, the formations, and consciousness. Thus, an aggregate by an eternalist is held to be fundamentally eternal besides being the self and the world. But according to the Buddha, the aggregates are impermanent and suffering; they are certainly not the self, either. The common refrain by the Buddha is always, with respect to each aggregate: "This is not mine, this I am not, this is not my self."
Given the position of the eternalist with respect to the Five Aggregates, that they are the self and the world and, moreover, eternal, the Buddha’s self transcends the aggregates.
For modern Buddhists to insist that eternalism pertains to an unchanging or transcendent self is wrong. This has the force of denying a self which transcends the Five Aggregates which the Buddha, in the discourses, does not deny. How, for example, in this passage is the Buddha denying a self which transcends the aggregates?
"Now, Aggivessana, a disciple of mine in regard to whatever is material shape, past, future, present, subjective or objective, gross of subtle, low or excellent, distant or near, sees all material shape as it really is by means of perfect intuitive wisdom as [ditto with the rest of the aggregates]: This is not mine, this I am not, this is not my self” (M. i. 234).
The position that the Buddha takes in this passage is that the self is never an aggregate, or the same, it is never to be identified with the Five Aggregates. The self is thus transcendent because it lies beyond the pale of the Five Aggregates. This is not eternalism. That the bulk modern Buddhists don’t get this is astonishing, to say the least.