Buddhism has not proved the truth of Nonduality. Buddha pointed out the unreality of the world but he told people they were foolish to cling to it. But he stopped there. He came nearest to Advaita in speech but not to Advaita fully.
Sage Sankara disagrees with Buddhists who say, there is nothing - a nonentity. Sage Sankara believes there is some reality, even though things are not what they appear to be. If one knows the truth, he will know what to do to find inspiration for action. The seeker of truth‘s subject is to know what is it that is Real.
Buddhism says: all things are illusory and nothing exists. However, Advaita avers that it is not so. It says that the universe, of course, is illusory, but there is Brahman (consciousness), that exists forming the very substratum of all things (illusion or universe).
Only when we independently search for the truth without religion and its doctrine then we will be able to realize the truth beyond form, time, and space.
There is no need to study neither Advaita nor Vedas nor Buddhism to realize the ultimate truth or Brahman or God in truth. It is no use going roundabout way; trace the Brahman.
Sage Sankara said: ~ Neither by the practice of yoga nor philosophy, nor by good works nor by learning, does liberation come, but only through the realization that Atman and Brahman are one in no other way. (1) Vivekachoodamani v 56, pg 25
Advaita is the next step higher than Buddhism because it gives the missing reason, viz. unity, non-difference from others, and because it explains that it used the concept of removing the sufferings of others, of lifting them up to happiness, only as we use one thorn to pick out another, afterwards throw both away. Similarly, Advaita discards both concepts of misery and happiness in the ultimate standpoint of non-duality, which is indescribable.
Buddhists say that a thing exists only for a moment, and if that thing has still got some of the substance from which it was produced, how then can they deny that its cause is continuing in the effect; hence its existence is more than a moment. Vedanta is concerned with whether it is one and the same thing which has come into being or has it come out of nothing.
Even in Buddhism: - Buddhist teaching has itself become a kind of interactive and Self-evolving process, much like its idea of pratityasamutpada. However, the end goal is still Nirvana, which is an experience ultimately beyond all concepts and language, even beyond the Buddhist teachings. In the end, even the attachment to the Dharma, the Buddhist teaching, must be dropped like all other attachments. The tradition compares the teaching to a raft upon which one crosses a swift river to get to the other side; once one is on the far shore; there is no longer any need to carry the raft. The far shore is Nirvana, and it is also said that when one arrives, one can see quite clearly that there was never any river at all.
Dalai Lama said:~ Buddhism need not be the best religion though it is most scientific and religion and inquisitive. But Buddhism has no answer to certain questions like the existence of Atama [Soul] and rebirth. Dali Lama said that as an individual he believes in rebirth as he had come across a few cases of rebirth. Modern science, Dalai Lama hoped would unearth the mystery behind the rebirth. (In DH –dec-212009-Gulbarga).
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Critics say Sage Sankara and Sage Goudpada borrowed their ideas from Buddhism. But in Manduka (page 281) these two declare they are not Buddhists, only a number of their ideas agree with those of Buddhism, whilst they point out their difference of view from Sunyavada Buddhists and Vijnanavadins. Thus, Sage Sankara, and Sage Goudpada both agree and disagree with Buddhists.
Sunyavadins say there is nothing, neither matter nor mind: they are nihilists. How do they know the mind ceases to exist? Where is the proof? When you know everything is mind, both the changing forms and the underlying substances how can you posit its real change into nothingness? Mind, Brahman always remains really itself because of its nature. We see change every minute but by an inquiry into the nature of change and cause, we see that it is only when we imagine that there is cause and change.
The distinction between Sage Sankara's Advaita, and Vijnanavadin Buddhism is that the former is mentalism i.e. mind is the real, whereas the latter is idealism, i.e. ideas are real. We follow the former.
Buddhism did not graduate its teaching to suit people of varying grades; hence its failure to affect society in Asia.
Bhagavan Buddha's teachings that all life is misery belongs to the relative standpoint only. For you cannot form any idea of misery without contrasting it with its opposite, happiness. The two will always go together. Buddha taught the goal of cessation of misery, i.e. peace, but took care not to discuss the ultimate standpoint for then he would have had to go above the heads of the people and tell them that misery itself was only an idea, that peace even was an idea (for it contrasted with peacelessness). That the doctrine he gave out was a limited one, is evident because he inculcated compassion. Why should a Buddhist sage practice pity? There is no reason for it. Advaita is the next step higher than Buddhism because it gives the missing reason, viz. unity, non-difference from others, and because it explains that it used the concept of removing the sufferings of others, of lifting them up to happiness, only as we use one thorn to pick out another, afterwards throw both away. Similarly, Advaita discards both concepts of misery and happiness in the ultimate standpoint of non-duality, which is indescribable.
Buddhists say that a thing exists only for a moment, and if that thing has still got some of the substance from which it was produced how then can they deny that its cause is continuing in the effect; hence its existence is more than a moment. Vedanta is concerned with whether it is one and the same thing which has come into being or has it come out of nothing.
Even the Sunyavada ultimate of the "void" is really a breath, and therefore an imagination and not truth.
Bhagavan Buddha as a constructive worker committed an error in failing to give the masses a religion, something tangible they could grasp something materialistic, if symbolic that their limited intellect could take hold of, in addition to his ethics and philosophy.
Sage Sankara gave religion; such as rituals, worship, etc.--to the ignorant masses, as well as Advaitic wisdom to serious and sincere seekers who were receptive.
Bhagavan Buddha gave as the central feature of his doctrine the great law of Karma in order to reiterate its ethical meaning. He did more good in this to uplift the people than the ritualists.
Zen has failed to influence the Japanese in practicing Zen, whether it is because Zen Buddhism has degenerated into religion instead of philosophy.
Tibetan and Chinese Buddhists who say that there are many Buddhas living in spirit bodies and helping our earth from the spiritual world are still in the sphere of religious illusion, not the ultimate truth. Their statements are wrong. Every sage realizes that the only way to help mankind is to come down amongst them, for which he must necessarily take on flesh-body. When people are suffering how can he relieve their suffering unless he appears amongst them? When people are suffering how can he feed them from an unseen world whether their struggle is for material bread or for spiritual truth? No! He must be here actually in the flesh. It is impossible to help them in any other way and all talk of Shiva living on Mount Kailas in spiritual body or Buddha in Nirmanakaya, invisible body belongs to the realm of delusion or Self-deception.:~Santthosh Kumaar