Buddha: - There are only two mistakes one can make along the road to truth: not going all the way... and not starting
The word Brahman means ultimate truth or reality which cannot be indicated by any word. The Brahman can be expressed through silence because it is beyond the experience form, time, and space. Therefore, the word Brahma in the clearly stands for the essence of the three states, which is consciousness only. The final use of the pursuit of the truth is to know that the 'Self ' is the Soul, which is present in the form of the consciousness.
Sage Sri, Sankara opposed the Buddhists only, who misunderstood Buddha and became atheists. According to Sage Sri, Sankara meditation always means the critical analysis about the self to get salvation from the worldly tensions. Due to the eccentric ego of the then atheists, Sage Sri, Sankara did not go beyond this since the atheists will not accept God beyond themselves. This limitation is not due to limited knowledge of Sage Sri, Sankara, but is due to the then existing situation of the psychology of the surrounding society. Even Buddha kept silent about God because the society dealt by Him consisted of Purvamimamsakas, who were strong atheists. Buddha told that everything, including the self is only relatively real (Sunya). This is correct because the self is a part of the universe, which is relatively real with respect to the absolute unimaginable God. The Buddha stopped at this point because the atheists cannot realize the existence of unimaginable God indicated through His silence.
The point of Buddha is that if God is non-existent, the entire creation, including self is non-existent. Sage Sri, Sankara wanted to establish the existence of the Brahman. For this purpose, He made the Atman as the Brahman. He brought out the identity of self with the consciousness and made the Atman the Brahman. Since one will not negate the existence of his self, he will accept the existence of the Brahman, which is the Atman or soul, the innermost self. BothBuddha and Sage Sri, Sankara kept silent about the absolute unimaginable God. The same philosophy was dealt by them in different angles in different situations.
Buddha was a Gnani, but his interpreters are not. Buddha did not enter into scriptural interpretation. So the Hindus threw him out of their religion Sage Sri, Sankara however although he agreed in nearly all points with Buddha, was a tactician and wanted to teach these truths within the Hindu fold. Hence, he did in Rome as Rome does! He made himself outwardly appear as an orthodox Hindu, and thus secured his aim.
Buddhism has failed through misunderstanding Gotama and believing that nothing is left to exist after Nirvana. What is it that sees the illusory nature of the finite ego? This is what the Buddhists need to answer and cannot on their theories.
Only Advaita can reply: it is the witness. The Buddhists are in error in regarding the finite ego as illusory, and as having nothing more behind it: but they would have been perfectly correct in such outlook had they added the notion of the witness.
How is it that Skandas come together and compose the ego? Who sees them come and go? It is the witness, the Atman, and this lack Advaita supplies in the witness and witnessed Analysis. When they say that mind comes and goes they are forgetting that there must be another part of the mind as the consciousness which notices it and which tells them of this disappearance and appearance. All their misunderstandings arise from the fact that Buddha refused to discuss ultimate questions.
When Buddhism degenerates into Nihilism we refute it (See Manduka P.281).
The truth of a single reality within or underlying the illusory ego is all-important and without it Buddhism becomes fallacious.
Vedanta admits the transitoriness and evanescence of thoughts just like Buddhism, but not of the Atman which observes this transitoriness and knows it.
Buddhists borrowed from Upanishads because they were Indians. The Vedantins did not need to borrow from Buddhism therefore (see P.396 v.99 of Manduka Up)