How do I refute the claim that the Buddha was actually preaching Vedanta?

This is a modified version of the answer that I posted on Hinduism.SE comparing the Buddhist Madhyamaka (by Nagarjuna) and the Hindu Advaita Vedanta (by Adi Shankara). Usually, the emptiness in Madhyamaka is equated to Nirguna Brahman (formless attributeless God) in Advaita by Hindu scholars like Prof. Chandradhar Sharma. Prof. Sharma also equated the Eternal Buddha concept (based on the Buddha's Dharma body) to God. I modified this answer for posting here.

First: What did Adi Shankaracharya teach?

We can see this from Adi Shankaracharya's own compositions:

Brahman is real, the universe is an illusion. The jiva is Brahman itself and not different. (Brahmajnanavalimala 20)

This Atman is a self-cognised entity because It is cognised by Itself. Hence the individual soul is itself and directly the Supreme Brahman, and nothing else. (Vivekachudamani 216)

There exists no other material cause of this phenomenal universe except Brahman. Hence this whole universe is but Brahman and nothing else. (Aparokshanubhuti 45)

The pot, wall, etc., are all nothing but clay. Likewise, the entire universe is nothing but Brahman. (Brahmajnanavalimala 19)

Brahman is Existence, Knowledge, Infinity, pure, supreme, self-existent, eternal and indivisible Bliss, not different (in reality) from the individual soul, and devoid of interior or exterior. It is (ever) triumphant. It is this Supreme Oneness which alone is real, since there is nothing else but the Self. Verily, there remains no other independent entity in the state of realisation of the highest Truth. All this universe which through ignorance appears as of diverse forms, is nothing else but Brahman which is absolutely free from all the limitations of human thought. A jar, though a modification of clay, is not different from it; everywhere the jar is essentially the same as the clay. Why then call it a jar ? It is fictitious, a fancied name merely. None can demonstrate that the essence of a jar is something other than the clay (of which it is made). Hence the jar is merely imagined (as separate) through delusion, and the component clay alone is the abiding reality in respect of it. Similarly, the whole universe, being the effect of the real Brahman, is in reality nothing but Brahman. Its essence is That, and it does not exist apart from It. He who says it does is still under delusion - he babbles like one asleep. This universe is verily Brahman - such is the august pronouncement of the Atharva Veda. Therefore this universe is nothing but Brahman, for that which is superimposed (on something) has no separate existence from its substratum. (Vivekachudamani 225-231)

Therefore the universe does not exist apart from the Supreme Self; and the perception of its separateness is false like the qualities (of blueness etc., in the sky). Has a superimposed attribute any meaning apart from its substratum? It is the substratum which appears like that through delusion. (Vivekachudamani 235)

Becoming thyself the self-effulgent Brahman, the substratum of all phenomena - as that Reality give up both the macrocosm and the microcosm, like two filthy receptacles. (Vivekachudamani 289)

The above quotes clearly show the teaching of eternalism.

Brahman is eternal, infinite, self-existent and transcendental absolute reality. Brahman is the substratum or foundation of the universe. Brahman is the material cause of the universe. Brahman is the only thing that is permanent and ultimately real, while the universe is ultimately an illusion.

The individual soul, which is a self-cognized entity, is ultimately the same as Brahman.

While Brahman is without qualities, it appears as the universe and individuals with qualities, through delusion.

This summarizes the nature of reality according to Advaita Vedanta.

Second: What did the Buddha teach?

We can see this in the Buddha's own words (Buddhavacana), from the Sutta Pitaka in Pali, which is included in the Mahayana Agamas and the Tibetan Kangyur.

It is widely speculated that some Buddhist schools teach annihilationism or nihilism, but this is not true. It is only non-Buddhists who have this wrong impression. The Buddha and 99.9% of Buddhist schools teach the middle way between eternalism and annihilationism. This "middle way" teaching is the unique feature of the Buddha's teachings.

The Buddha rubbished the notion that there is no self of any kind:

“So, brahmin, when there is the element of endeavoring, endeavoring beings are clearly discerned; of such beings, this is the self-doer, this, the other-doer. I have not, brahmin, seen or heard such a doctrine, such a view as yours. How, indeed, could one — moving forward by himself, moving back by himself — say ‘There is no self-doer, there is no other-doer’?” - Attakari Sutta

However, the Buddha was very clear in the Ananda Sutta (SN44.10) that rejecting both eternalism and annihilationism, he teaches that "all phenomena is not self", which means that there is no permanent or eternal standalone entity of a self in all phenomena (sabbe dhamma anatta).

"Ananda, if I — being asked by Vacchagotta the wanderer if there is a self — were to answer that there is a self, that would be conforming with those brahmins & contemplatives who are exponents of eternalism [the view that there is an eternal, unchanging soul]. If I — being asked by Vacchagotta the wanderer if there is no self — were to answer that there is no self, that would be conforming with those brahmins & contemplatives who are exponents of annihilationism [the view that death is the annihilation of consciousness]. If I — being asked by Vacchagotta the wanderer if there is a self — were to answer that there is a self, would that be in keeping with the arising of knowledge that all phenomena are not-self?"

"No, lord."

"And if I — being asked by Vacchagotta the wanderer if there is no self — were to answer that there is no self, the bewildered Vacchagotta would become even more bewildered: 'Does the self I used to have now not exist?'"

The Buddha instead taught that the self is not eternal and not non-existent, but is dependently originated (Pratītyasamutpāda):

When the Buddha was asked by the naked ascetic Kassapa whether suffering was of one's own making or of another's or both or neither, the Buddha replied "Do not put it like that." When asked whether there was no suffering or whether the Buddha neither knew nor saw it, the Buddha replied that there was, and that he both knew and saw it. He then said "Kassapa, if one asserts that 'He who makes (it) feels (it): being one existent from the beginning, his suffering is of his own making,' then one arrives at eternalism. But if one asserts that one makes (it), another feels (it); being one existent crushed out by feeling, his suffering is of another's making,' then one arrives at annihilationism. Instead of resorting to either extreme a Tathaagata teaches the Dhamma by the middle way (by dependent origination)" - summarized here from Acela Sutta

A summary of dependent origination is that the self arises dependent on the inter-working of the five aggregates of form, feeling, perception, mental fabrications, and consciousness. Please see this answer for further elaboration, including the lute analogy.

He taught that both the views of "I have a self" and "I have no self" are inaccurate in the Sabbasava Sutta. He also taught that the views of one being Nirvana, one being in Nirvana, one being apart from Nirvana, calling Nirvana "mine", and delighting in Nirvana, are inaccurate in the Mulapariyaya Sutta.

The Buddha did teach emptiness, but it is restricted to the nature of the self i.e. all phenomena is empty of a self (see Shunya Sutta). The Buddha did not comment on the nature of all non-sentient things like the universe, besides noting them as being conditioned and impermanent.

The Buddha was not interested in commenting on the nature or origin of the universe, because he considered it to be unimportant to the path to liberation from suffering - see the Parable of the Poisoned Arrow (from MN63). The Buddha was not interested in metaphysical speculations. It was not because he taught the Upanishadic truths through silence, as implied by Prof. Chandradhar Sharma.

Third: What did Nagarjuna teach?

While the Buddha stopped at describing the "middle way" and emptiness with respect to the nature of the self, Nagarjuna expanded these concepts to cover the nature of the universe and all reality. He did this in his magnum opus, the Mūlamadhyamakakārikā, whose name itself means "Fundamental Verses on the Middle Way". Nagarjuna did not contradict the Buddha's teachings, but rather, expanded it.

The Wikipedia article on Madhyamaka (which contains its own citations) summarized Nagarjuna's teachings very well:

Central to Madhyamaka philosophy is śūnyatā, "emptiness." The term refers to the "emptiness" of inherent existence: all phenomena are empty of "substance" or "essence" (Sanskrit: svabhāva) or inherent existence, because they are dependently co-arisen. At a conventional level, "things" do exist, but ultimately they are "empty" of inherent existence. But this "emptiness" itself is also "empty": it does not have an existence on its own, nor does it refer to a transcendental reality beyond or above phenomenal reality.

Nagarjuna's critique of the notion of own-nature (svabhāva) argues that anything which arises according to conditions, as all phenomena do, can have no inherent nature, for what is depends on what conditions it. Moreover, if there is nothing with own-nature, there can be nothing with 'other-nature' (para-bhāva), i.e. something which is dependent for its existence and nature on something else which has own-nature. Furthermore, if there is neither own-nature nor other-nature, there cannot be anything with a true, substantial existent nature (bhāva). If there is no true existent, then there can be no non-existent (abhāva).

Rather than the annihilationism that nothing exists or the eternalism that something exists eternally, Nagarjuna taught the "middle way" that all phenomena is empty of its own "inherent existence" or "substance" or "essence" (what he called svabhāva).

If nothing has inherent substance, then nothing can depend on something else for substance, so there is no other inherent substance (para-bhāva).

Nagarjuna's unique philosophy however, is that even this emptiness is empty i.e. this emptiness does not have its own inherent substance. This means that there is no transcendental reality beyond phenomenal reality. This is what is implied by ultimate reality not being absolute reality.

A very nice and simplified explanation of the Madhyamaka emptiness can be found in Zen master Thich Nhat Hanh's writing, "The Fullness of Emptiness".

The only disagreement between Theravada and Madhyamaka is the need to expand the "middle way" and "emptiness" beyond what the Buddha taught. What is common between Theravada and Madhyamaka is that both reject eternalism and annihilationism.

Fourth: Comparing Advaita and Madhyamaka

Comparing what Adi Shankaracharya taught and what Nagarjuna taught, we come to see very clearly that both are not the same and in fact, completely incompatible:

• Shankara said Brahman is eternal and absolute. Meanwhile, Nagarjuna said nothing is eternal and absolute.
• Shankara's Brahman (clay analogy) implies that it is the only thing that has a true inherent substance (what Nagarjuna called svabhāva). Meanwhile, Nagarjuna says nothing has inherent substance.
• Shankara's Brahman is the material cause (again, clay analogy) of the universe. Meanwhile, Nagarjuna's emptiness is not a material cause for anything including itself.
• Shankara said that the universe depends on Brahman as its substratum (what Nagarjuna called para-bhāva). Meanwhile, Nagarjuna said there is no other inherent substance (para-bhāva) i.e. no substratum for anything else.
• Shankara's Brahman is the Ultimate Reality that is the Transcendental Absolute Reality. Meanwhile, Nagarjuna's Ultimate Reality is an "emptiness of emptiness" that is devoid of transcendental or absolute reality.

What is common between Advaita and Madhyamaka is that both proclaim the non-dualism between the Ultimate Reality and the phenomenal reality. However, Advaita's Ultimate Reality is a Transcendental Absolute Reality, while Madhyamaka's Ultimate Reality is the "emptiness of emptiness" that is devoid of any transcendental or absolute reality.

My conclusion is that Adi Shankaracharya's Nirguna Brahman and Madhyamaka's "emptiness of emptiness" are not the same and in fact, completely incompatible.

This is supported by Banaras Hindu University Professor T. R. V. Murti's statement (quoted below) in this book chapter: Murti T.R.V. (1973) Saṁvṛti and Paramārtha in Mādhyamika and Advaita Vedānta. In: Sprung M. (eds) The Problem of Two Truths in Buddhism and Vedānta. Springer, Dordrecht

It has been the fashion to consider that the differences between the Madhyamika śūnyatā and Brahman are rather superficial and even verbal, and that the two systems of philosophy are almost identical. At least Professor Radhakrishnan thinks so, and Stcherbatsky's and Dasgupta's views are not very different. I hold a contrary view altogether: that in spite of superficial similarities in form and terminology, the differences between them are deep and pervasive.

Fifth: Comparing Vedanta and Buddhism

All Vedanta schools accept that Atman (soul) is eternal (according to Bhagavad Gita 2.20), and Brahman is absolute and eternal. This is based on the teachings of the Upanishads.

Meanwhile, the anatman teaching subscribed by all schools of Buddhism, states that there is no eternal self (i.e. no permanent standalone eternal entity) in all phenomena.

A very apt conclusion for this comes from eminent German indologist Professor Helmuth von Glasenapp's essay "Vedanta and Buddhism: A Comparative Study":

In the light of these researches, all attempts to give to the Atman a place in the Buddhist doctrine, appear to be quite antiquated. We know now that all Hinayana (sic) and Mahayana schools are based on the anatma-dharma theory. ... Nirvana being a dharma, is likewise anatta, just as the transitory, conditioned dharmas ... Nirvana is no individual entity which could act independently. For it is the basic idea of the entire system that all dharmas are devoid of Atman, and without cogent reasons we cannot assume that the Buddha himself has thought something different from that which since more than 2000 years, his followers have considered to be the quintessence of their doctrine.

and

Nothing shows better the great distance that separates the Vedanta and the teachings of the Buddha, than the fact that the two principal concepts of Upanishadic wisdom, Atman and Brahman, do not appear anywhere in the Buddhist texts, with the clear and distinct meaning of a "primordial ground of the world, core of existence, ens realissimum (true substance)," or similarly.

by making baseless, historically inaccurate and factually incorrect claims.

This is what you need to focus on. You have to show them why the claims are baseless, inaccurate and incorrect, both factually and historically. If you mention their arguments in detail, we can discuss them.

Then you have to compare the core teachings of Vedanta with Buddhism and show them that they are not compatible. Ex: Hinduism talks about Atman and Brahma being the creator of the universe. Buddhism talks about Anatta and refutes creationism.

But make sure to stick to Theravada Buddhism, the school of elders when you are doing this comparison. That's generally accepted as the school closest to the original teachings of the Buddha.

VEDĀNTA vs BUDDHISM: REFUTATIONS IN RESPECTIVE LITERATURE

[Many Hindu Gurus/Swamis/Pundits/Scholars opine that the Buddha taught something that is already found in Vedic/Upaniṣadic literature. However, in the following excerpted article, the author shows how Buddhist masters such as Sāntarakṣīta and Hindu Vedāntic gurus such as Ādi Samkharācārya have refuted each other’s view in their respective literature. Since Vedānta is based on Upaniṣadic literature, this shows that Buddhism in definitely not a branch of Vedic/Brāmanical Hinduism. Buddhism considers Vedāntic view as a wrong view (mithyā-dṛṣṭi)(because it is an eternalist view or sāsvatavāda), which doesn’t not bring realization/enlightenment.].

“Vedānta is based on the Upaniṣads…. Shankarācārya (also known as Sankara), who was from the 8th century, is the most famous commentator of the Upanishads, and today, the majority of the Hindus follow his commentaries. In the Bodhāyana commentary, according to him, the hermeneutic of the Upanishads existed even before his time. Although he was from around the 8th century, he became popular among the Hindus only after the 10th century when one of his lineage holders, Vācaspati Misra, wrote a sub-commentary on his commentary. Today, Shankarācārya is considered among the greatest Hindu philosophers and even educated Hindus in India subscribe to him. However, since he became well known only after the 10th century, no Buddhist scholars like Sāntideva, Śāntarakṣita, Ratnākarasānti, Jñānagarbha, etc., seem to mention him or refute him in their work.

Śāntarakṣita has however refuted the Upanishadic non-dualism in the Tattva Sangraha’ chapter 7, section 5. In his refutation of the Upanishadic view he has referred to the followers of the Upanishad as those who postulate that the ātmā is eternal, one and of the nature of knowledge/conciousness/ Jñānasvarūpa. Kamalaśīla has also commented on this view describing it as,

“That is the ātmā is of the nature of one eternal consciousness / knowledge.”

Indeed, both Śāntarakṣita and Kamalaśīla are refuting almost the same view that Sankarācārya postulates although neither Śāntarakṣita nor Kamalaśīla mentions his name or his work. It is important to understand that according to Śāntarakṣita and Kamalaśīla, the Upanishadic view is that there is a non-dual consciousness or a non-dual knowledge which is eternal and this is the ātmā or this is called the ātmā. It is important to understand that Śāntarakṣita himself has refuted 6 different interpretations of the ātmā as accepted in Hinduism in his time. This non-dual cognition / consciousness / knowledge which is eternal (nitya) is one of the ātmā-s refuted by Śāntarakṣita in his ‘Tattva Sangraha’. This ātmā is not dualistic; therefore it is not vijñāna (Tib. rnam-shes). It is non-dual and it is eternal. It is called jñāna (ye-shes/knowledge) by Śāntarakṣita, who used the very word the Upanishad and Sankarācārya uses.

This is how Śāntarakṣita refuted this view:

“The error in the view of these philosophies is a slight one – due only to the assertion of eternality of cognition.”

There is, however, a slight difference between this Upanishadic view refuted here by Śāntarakṣita and Sankarācārya’s Upanishadic view. Sankara’s view is called Maya-Vivartavād – i.e. the illusionist. The view refuted by Śāntarakṣita is called parināmavāda – modificationist. The difference is that this view considers the 5 elements, etc., and the world as illusory modifications of this non-dual eternal cognition / consciousness, while Sankara interprets the world and its 5 elements, etc., as illusory and therefore non-existent and this non-dual eternal cognition as separate from the illusion.

Sankarācārya even mentions the exact opposite view of what Śāntarakṣita mentioned above and refutes him. In exact opposite of what Śāntarakṣita says,

“The error in the view of these philosophers is a slight one – due only to the assertion of eternality of cognition.”

Sankara says about the Cittamātra

“The error in the view of these philosophies is only slight – they believe the non-dual mind as changing moment to moment; we believe it as unchanging eternal.”

The Hindu ātmā is not only non-dual cognition but is also unchanging, eternal, and truly existing. Sankarācārya defines existence (sat) in his Tattvaboda as that which remains the same in all the 3 times (past, present, future). In the commentary by Gaudapāda (who was Sankarācārya’s Guru’s Guru), of the Māndukya Upanishada, in verse number 96, he calls the eternally really existing non-dual cognition is non-relational, i.e., free from reference points. In the 37th verse of the same work it is said that this non-dual, eternal, really existing cognition is free from all sense organs, i.e., free from the dualistic mind (namshe). So, the Upanishadic view is that the really existing, eternal / permanent, non-dual, non-referential cognition is the ātmā, and this is not dualistic mind. This Upanishadic view existed even before the Buddha, and this was what Sankarācārya expounded very clearly and most powerfully around the 6th century. This view, similar to this Sankara view, was refuted by Śāntarakṣita as a wrong view."

~ Excerpted from "Vedanta vs Shengtong" by Acarya Mahayogi Sridhar Rana Rinpoche.

More on hindooism and buddhism differences can be found here.

The Buddha avatar was contextual, aimed at ridding the attachment to the karmas prescribed in the Mimamsa portions of the Vedas, to the utter neglect of the need totranscrndthem and realise oneself. Karma presupposes a doer and a God dispensing rewards in return. To enjoy the benefits of reward, another birth is needed, this cycle goes on endlessly. Sankara advised karmas as a kind of scaffolding for a search within. This helps the mind to concentrate, through detachment from the results of karma. The scaffolding must be discarded, if the building has to be occupied. Therefore, Buddha helped to put karmas in better light, Sankara sculpted the idea into the homogenous concept of Advaita. For this, He was called a ‘prachhanna Buddha’ by some contemporaries.