Translating atta as “soul”, it seems to me, runs the risk of reducing the Buddha’s teachings about anattā simply to the denial of some particular capital “S” SELF associated with some particular metaphysical doctrine, such as some specific Upanishadic doctrine about the Atman. The teachings’ connection with the cessation of suffering then becomes obscure, because it is perfectly possible for a person with corrected metaphysical views to still suffer. This approach also, it seems to me, artificially carves the anattā teachings away from the teachings about the cessation of I-making and my-making, and introduces an overly sharp split between the teachings about the grand metaphysical SELF of theory, and the everyday self, attā or “I” that is invoked whenever one speaks or think reflexively of oneself in the ordinary sense. The Buddha was talking about the latter just as much as the former.
If the Buddha wanted to restrict his teachings to the simple metaphysical denial of some Upanishadic metaphysics, he would have said so. It’s not that hard to do, and these denials are not that hard to express. But the Buddha said the heart of his teaching was very difficult to grasp and express.
Think deeper about the apple and tree examples:
People might not make the mistake of thinking “I am the apple”, but they still often conceive the apples they regard as belonging to themselves, as something they call “mine”. They conceptualize the apples they see in relation to themselves, to the I and me whose existence they instinctively presuppose.
They might not confuse themselves with a tree, but when they look at a tree, they likely at the same time think “I am looking at a tree.” Again, they conceptualize the tree they see in relation to themselves, to some I and me whose existence they instinctively presuppose. So rather than the content of their thought being filled entirely with the rising and passing forms that make up the “tree”, there is a projection onto that stream of thought of a completely invisible “I” that is supposedly thinking the thoughts or cognizing the forms. This is a much more fundamental and deeply rooted phenomenon than just having mistaken views about whether this I is an atman or some other piece of metaphysical furniture.
Also, people engage in all sorts of other subtle projections concerning the tree and themselves. If the tree is swaying gently in the breeze on a rainy day, and sadness arises in their hearts, thy might think, “that tree looks sad.” And if the tree is standing stiffly and motionlessly they might think or feel,“I am strong.” There is also a kind of pervasive narcissism going on with our experience, where, despite all logic, we have the feeling that what we see exists for us or is “held” in our minds.
I think the Buddha was aiming us toward a much more radically transformed state than the one we might achieve if we see what’s wrong with the doctrine of the Chandogya Upanishad. Since all suffering is rooted in self-regarding states, and pertains to anxieties about the perpetuation of ourselves, or our status in relation to the world and other people, or our fears about the future and regrets about the past, or our possessiveness toward our stuff and our territory, then this suffering is only blown out when the I-making process is suspended altogether.
People don’t just have false beliefs about the permanence, autonomy and eternity of what they are. The whole sense of a oneself that is anything at all is an illusion. There is a constant architectural process going on that builds an “I”, “me” and “mine” out of the raw stream of conditioned experience as it is. And that self that is being constructed is at bottom an illusion. One doesn’t cut through the mass of suffering until the architect is seen. Through very, very advanced spiritual practice - not metaphysical and philological debate - a state can occur where the architect stops building and “in the seen there is only the seen”, etc. not accompanied by the “I” that is usually being fictitiously constructed along with this stream of phenomena.
