Vedantic view on the Buddhist 'Self'

There is a very fundamental difference between Hinduism of Upanishads and Buddhism regarding the nature of the Self. Gita refutes the Buddhist position: "....न्नायं भूत्वा भविता वा न भूयः।" (....nor once having been, can It cease to be.) ~ Gita (2/20). No matter which school of Buddhism there is, the Self (Aatma) is always time-dependent. "The Self is the product of the momentary knowledge. Flowing in the time it is born and dying. The consistency that is there is sacramental." For example, when one wave hits another wave, and then another wave hits the third wave, and the third wave hits the fourth wave, then in the wave as the rites of its predecessor wave follow its rite, the Self also follows the rites and it keeps on being born and dying in every moment. Consciousness is time-dependent, therefore it is not fundamental, consciousness is therefore void and momentary. When It is exiled, it will be completely abolished which will be the attainment of Nirvana. But as long as there is no cessation of desires, there will be no dissolution of the Self. In this way, due to the cessation of desires, the 'saṅtānatva" in vijñāna has become Nirvana and the cycle of birth and death stops. Due to It being born again and again in time, the Self of Buddhist philosophy became inert matter according to Vedānta and thus Buddhism is considered Nāstika (heterodox or heretic). In Vedānta, the Self is not considered to be born from matter or present in it (materialism), originating from the Space or present in the Space (Jainism), or originating from time or present in time (Buddhism); instead, it considers these three to be born from knowledge/consciousness. The Mādhyamaka Buddhists are of the opinion that the Self is Śūnya (zero or a vacuum). They state that the knowledge of the ahaṁ-idaṁ (I-this) is not present during the state of deep sleep. Then, what is present during the deep sleep state? Nothing, because nothing is clearly known as 'I' or 'this' (the body). Or, you can say that only Śúnya remains. The Ahaṁ-idaṁ emerges when the person awakens, and so Śúnya is the Atma supported by knowledge – the Jñānālaṁbanātmā. On the question of ‘What is the form or the essence of Śúnya?’ they have a popular saying, "It is a desert without a grain of sand. It is a forest without a single tree. It is a fire without flames. It is water without any drops. It is the space with nothing in it." and thus Buddhists believe this Śúnya to be indescribable, and free of the Catuṣkoṭi logical argument of the form of: asti (existence), nāsti (non-existence), asti-nāsti (existence and non-existence), nāsti-na-nāsti (no existence at all). The shoonya Atma is vinirmukta (free) of this chatushkoti. Thus making the Self free of these four 'corners' in logic. But Śaṅkara in his Aparokshānubhuti gives the counterargument that does the Buddhist Self, which is the form of Śúnya have an observer or not? If there is no observer, the Śúnya is imagined and nobody can have the experience of being a vacuum. The observer of the Vijñāna is ‘I exist’, and the absence of this Vijñāna during the deep sleep state cannot be Śúnya, and there has to be some form of consciousness. Therefore the Śúnya cannot be the Self.

Further Reading: Saraswati, Akhandananda: Vedanta Bodha