The authors of Advaita Vedānta maintain that God, the impersonal brahman, is the only reality and that each hint of dualism or pluralism is due to māyā ‘illusion’. In other words, the absolute, the brahman, is the only reality and everything else (including the material world and the conscious beings within it) only seems to exist, due to māyā, but is not ultimately real. Due to the the Advaita Vedānta’s absolute monism, the brahman cannot have any quality, as any quality would introduce a duality in the singular nature of the brahman. Thus, given that the brahman is the only reality and that it is absolutely simple (since any complexity would entail plurality) it cannot contain any intentional knowledge*, since any such knowledge would be necessary articulated according to the distinction between a knowing subject and the objects it knows and exactly such distinction is considered illusory by Advaita Vedānta authors.

In contrast, these authors contend that the brahman, being the only reality, does not have knowledge as its quality. However, they would also not be content with a brahman conceived as just the material and unconscious cause of the world. Accordingly, the brahman is for them nothing but pure knowledge. Knowledge is therefore conceived as a substance and no longer as a quality. What is this consciousness about? Nothing. It cannot have any content, since any content would alter the pure monism mentioned above. Thus, it is nothing but pure consciousness, cit, without any content.

In summary, Advaita Vedānta authors uphold an absolute monism, where only a single and simple substance exists. Due to the absoluteness of this monism, it is even difficult to speak of ‘existence’ in the case of the brahman, which is in a possibly non-existential way, since it is the only reality, outside of time and space, being also illusory.
All that seems to exist to common beings, by contrast, strictly speaking does not exist at all. Its ontological status is compared by Advaita Vedānta authors to that of the reflection of the moon on the water, insofar as it is only superimposed on the real brahman. The whole world as common beings know it, therefore, has an ambiguous ontological status, insofar as it is neither a substance nor a quality or an action, but only pure illusion which happens to be superimposed on something real, the brahman, upon which it thus depends. The world as common beings know it, therefore, exists only as a superimposition relating to the brahman. This superimposition is, in turn, only illusory, since it cannot be considered to be a different reality, due to the absolute monism of Advaita Vedānta.

Can we speak of a substance ontology at all in the case of Advaita Vedānta?

* ”Intentional” is here used in Franz Brentano’s sense, according to which knowledge can only be knowledge of something.

(cross-posted on the Indian Philosophy blog, where you can read further interesting comments)