(For a more detailed presentation see the highly authoritative web page called 'Creation Theories in Advaita'.)
Advaita does NOT teach a single theory but rather several theories, depending on the student's level of insight and spiritual progress. At the lower (vyAvahArika) level are the more dualistic sRRiShTi-dRRiShTi-vAda (what has been created is perceived) and dRRiShTi-sRRiShTi-vAda (perception is simultaneous with creation). The higher (pAramArthika) level teaches ajAti vAda (creation is not an absolute and real event). Shankara drew on all these views, whereas later Advaitins tended to emphasize one or the other. (Therefore it is misleading to over-emphasize a few selected quotations from Shankara. Like Ramana and the Upanishads, he sometimes seems to 'contradict' himself, because he addresses a wide variety of students.)
Basically, sRRiShTi-dRRiShTi-vAda is for beginning students, who naturally see the world as distinct from themselves, since this is the normal human reaction. This illusory view is intimately connected with the equally illusory view of oneself as an individual jIva (soul): they are two sides of the same coin. This jIva is the 'I am' of small-self affirmation, not the pure 'I' of Self affirmation. If we divide ourselves from the 'world' by drawing a conceptual boundary around what we are pleased to call our (small) self, then that same boundary 'causes' a distinct and seemingly real world to spring into being. ('Real' here means that the world appears as a distinct 'existing' entity, as do we.) Such a world needs a 'creator', and this is supplied by Brahman in its lower illusory conceptual representation as ISwara. This is also the view of Judaism, Christianity, Islam and other philosophically-challenged religions. (Ooops! There I go being prejudiced again!) Finally, there is not just one jIva but a multiplicity of them (as in the JCI religions).
From a purely logical point of view, this accordance of a measure of independent reality to mAyA (i.e. the 'world') clearly contradicts the mighty mahAvAkya which says Brahman is One without a second, which is the very essence of advaita. Nevertheless, in this lower 'dualistic' teaching, there is still a subtle distinction with the truly dualistic sAMkhya philosophy. It is understood that mAyA does not have an ultimate existence distinct from brahman. In sAMkhya the closely related concept of prakRRiti does indeed have an absolute existence of its own. The lower teaching of Advaita understands that mAyA is reabsorbed into brahman as illusion is dispelled.
The other 'dualistic' view is dRRiShTi-sRRiShTi-vAda (perception is simultaneous with creation). This view says that the various jIvas 'create' the world in the act of cognition. The webpage author finds similarities to subjective idealism and the Buddhist vij~nAnavAda. Whether this is true depends on just what is meant by 'create' here. In my view, subjective idealism and vij~nAnavAda do NOT create a distinct world but rather absorb the seemingly distinct world into perception, which is in turn an aspect of consciousness. Then one must ask if there is some subtle distinction between perception and the consciousness which is conscious of the perception. I believe that ultimately there is not, but there is a long tradition in Advaita which distinguishes between the Consciousness and the mind (including perceptions). Again, I believe that this distinction is only at the vyAvahArika level. Indeed, all distinctions of any kind must be at the vyAvahArika level, since at the pAramArthika level brahman is One without a second. QED.
Anyhow, let us move on to the last and highest (i.e. non-dual) advaitin view. This is ajAti-vAda (creation is not an absolute, real event), or, stated differently, creation never occurred. THIS is what I call subjective idealism and vij~nAnavAda. This is the view that mAyA (i.e. the apparent world) has no reality in itself, as brahman is the only reality (One without a second). (Advaitin math is very simple!) The seeming reality of the 'external' world is only an illusion projected or superposed (adhyAsa) by the mind upon the sole reality of Consciousness, like the snake on the rope, and this is called mAyA. This disappearance of mAyA naturally occurs as the jIva is understood to be an equally illusory creation of the mind. Conversely, ajAti-vAda is incomprehensible as long as one clings to any notion of oneself as a discrete self-existing entity (i.e. jIva). As mentioned above, these are two sides of the same coin.
The ajAti-vAda was taught by gauDapAda, Shankara's paramaguru, who may perhaps be considered the 'purest' advaitin since he was so unequivocally non-dual. (I imagine gauDapAda as being a true forest dweller.) Shankara dealt with a much vaster audience and had to teach a variety of views in order to accommodate the levels of the different students. An infant cannot learn to run until it first learns to walk. We embark on the spiritual path with a firm belief in the reality of what is revealed by our senses.
The article states that ajAti-vAda is also the realization that the true brahman is nirguNa, i.e. without attributes. When brahman is thus understood, mAyA dissolves, which establishes an interesting correspondence between the apparent reality of the world and the view of God with attributes. As brahman is realized in its essential nature as nirguNa, the world simultaneously 'disappears'. (By the way, the notions of nirguNa brahman and the disappearance of the world bear a striking resemblance to the 'emptiness' of mahAyAna Buddhism, but I won't belabor that point here.) I would only caution that the 'disappearance' of the world is not like a television screen going black when switched off. Rather, it means that there is no longer the dualism of perceiver and perceived, of jIva and jagat (world). It is in this sense that one says that this state is adRRiShTam (unseeable), agrAhyam (ungraspable), alakShaNam (without any attributes), acintyam (unthinkable), avyapadeshyam (cannot be indicated as an object), advaitam (nondual), and so forth.
Although this state is realized in its purest form in the 'fourth' stare of turIya [the other three states being jAgrat or waking state, svapna or dream state, and suShupti or deep sleep state], we must not forget that turIya encompasses these other three states and is in fact the essence of consciousness, the substratum itself. That is why the realized man can operate in the world as jIvanmukti. The turIya or realized state is one of complete peace and bliss, as all disturbance and suffering arise with the activity of the mind, as does the illusion of the world.
As the bRRihadAraNyaka says (Part 2 Chapter 4):
"For when there is duality, as it were, then one smells another, one sees another, one hears another, one speaks to another, one thinks of another, one knows another. But when everything has become the Self, then what should one smell and through what, what should one see and through what, what should one hear and through what, what should one speak and through what, what should one think and through what, what should one know and through what? Through what should One know That owing to which all this is known - through what, my dear, should one know the Knower?"
At this highest level the reality of the world is indeed denied, in the sense explained above. In my opinion, this is close to if not identical to subjective idealism and I could quote countless unambiguous passages from Shankara, Ramana and Nisargadatta in support of this view. Those who suggest that a few passages of Shankara seem to postulate a 'real' world simply do not understand that different views of 'creation' are taught in Advaita, depending of the level of the student.
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