There has sometimes been a tendency, particularly in the Western world, to confuse Buddhism with Hinduism, a confusion that has not always been confined to the ill-informed and the ignorant. This stems in part from the historical accident that the Buddha was born and lived his whole life in India, a country which today has come to be identified almost exclusively with Hinduism. The habit of many students of religion in the West of lumping all "Eastern Religions" (by which term is often meant only Hinduism and Buddhism) into one category, for the purpose of comparison with Abrahamic religion (particularly the Judeo-Christianity of the West), has tended to perpetuate this confusion,. It forgets that unlike Hinduism, which in a sense has been an ethnic religion, Buddhism was a universal doctrine from its inception and cannot be confined to a particular nation or geographical locale. Then there is the tendency of some modern "enlightened" Hindus to look upon the Buddha's teaching as reducing ultimately to one or the other of the doctrines contained in the Vedas, the Upanishads, or the classic systems of Hindu philosophy (the dharshanas), not to mention the misguided attempt by their forebears to transform the Buddha into an "avatar" of Vishnu. In these circumstances it is useful to examine the fundamentals of Hinduism and Buddhism in order to demonstrate their basic incompatibility, despite the sharing of a common terminology (itself a source of confusion). A couple of preliminary issues will have to be considered first. One is a purely terminological question, viz. the appropriateness of the term "Hinduism" to cover all the changing phases of India's traditional religion; and the other a chronological one, viz. to relate the emergence of the main doctrines of Hinduism and Buddhism to each other in a purely historical way.
The word Hinduism was coined by the Muslim scholar Alberuni in the 11th century CE and while its appropriateness to describe the dominant system of religious belief in the India of his time (and of ours) is unquestionable, its use to describe the oldest religious beliefs in India (some scholars even applying the term to describe the pre-Aryan civilization represented by the Harappan culture), is clearly suspect. In this respect the practice of the earlier scholars to use the term "brahmanism" to designate the system which prevailed amongst the Aryan invaders before the Buddha's time, and to confine the word "Hinduism" to designate the system which was synthesised in the Bhagavadgîta, a work compiled centuries after the Buddha, which became the foundation of almost the whole of later Hinduism, could be commended. This terminology will be used here as far as possible, except that the word "Hinduism" will sometimes have to be used to designate the combined systems of Brahmanism and Hinduism proper, the actual context hopefully making clear what usage is meant.
The question of chronology has usually been considered a difficult one. Hany students of Hinduism after proclaiming the impossibility of ascribing dates to early Brahmanical works, then not only proceed to do so, but give them very ancient ones with little or no justification. This is true not only of Hindu traditionalists, but also of many Western orientalists, who in the words of Nirud C. Chauduri "have succumbed to Hindu chronological fantasies" [Hinduism (1979), p.33]. It may be mentioned that the antiquity claimed for the Hindu texts contrasts strongly with the lateness of all extant epigraphcial, iconographical and archelogical evidence. In contrast to this morass of uncertainty the dates of the Buddha (563 - 483 BCE) have been established with little or no error. In fact the Buddha is perhaps the first truly historical figure to emerge in India, just as the Buddhist remains are the earliest religious archeological evidence unearthed. And the earliest Buddhist literature contain abundant information on the rival systems of belief prevalent in the India of that time. These references cover both the main Brahmanical religion based on the Vedas, and the emerging dissentient views proclaimed by the new sramana philosopher-teachers of the time (the "gymnosophists" of the later Greek observers of the Indian scene).
The Brahmanical literature to which there is clear reference in the Buddhist literature are the "Three Vedas", and the Brahmanas based on these three sa.mhitas (the latter only insofar as the practices recommended by them are castigated). The three Vedas are, of course, the Rig, the Sâma, and the Yagur. The absence of any references to the fourth Veda (the Artharva) is an indication that this was not then known as an independent one. This is borne out by an inspection of this Veda which shows that it is quite different to the other three, being closer to the Upanishads in some parts, and to a more primitive magic and sorcery in others. It is therefore a polygot compilation of later times.
It is now generally recognized that the religion of the Vedas with its deification of the forces of nature, its constantly professed awe at the basic human functions of breath and speech, its blending of sacrifice, ritual and magic, its confounding of states of intoxication (produced by imbibing the Soma libation) with states of mysticism, and so on, relate to a very primitive stage in the development of the religious consciousness (and scientific knowledge) of the Indians. The so-called "Vedic wisdom" exhibited is of a very rudimentary kind, and explicable more in anthropological terms rather than in metaphysical or philosophical ones. Likewise its "eternal truths" are no more than the simple hypotheses inspired by the general ignorance of the times. It is also well-known that the characteristic doctrines of later Hinduism (like the soul-theory, re-incarnation, karman, moksha, devotion to some concrete manifestation of an omnipotent Godhead, etc) are either totally absent or present in a very rudimentary form. While the beginnings of the caste system are traceable it had not yet assumed the rigid religious form of the later Dharmashastras. Yet the Vedas contained the potential for all these developments.
By the Buddha's time this potential had already manifested itself, e.g. in the growth of a greedy priestly caste, and the extravagance of the sacrificial ceremonies (particularly the ashvamedha with its cruelty and sexual connotations, and even human sacrifice). It was the Buddha who showed that these were not accidental outgrowths, but were a consequence of the basic Vedic outlook itself. The Vedic seers thought that they could answer questions relating to the nature of the human condition, and proceeded to do so in terms of the conventional ignorance of the times, on which was established a whole system of religious practice and social conduct.
It is however not to the Vedas and the Brahmanas that the modern exponents of Hinduism turn to as repositories of "Vedic" knowledge, but to the Upanishads. It was on the basis of these treatises that elaborate systems of "Vedantist" philosophy came to be constructed later by philosophers like Samkara, Ramanuja and Madhva; but this was after the 9th Century CE, long after Buddhism had vanished from Indian soil.
It is therefore the doctrines in the original Upanishads and their relationship to the Dhamma that must concern us. Once again the chronological problem assumes some importance. The Indian philosopher Sarvapalli Radhakrishnan 
There are over. a hundred Upanishads in existence. and of these about a dozen could be traced to pre-Christian times. Some of these contain references to the Buddha's doctrines and to the Sangha (e.g. Maithri Upanishad 7.7 - 7.10); others are attached to the later Artharva Veda (e.g. the Mundaka and the Pra.sna); so all these are post-Buddhist. In fact only a very few, if any, can claim to be pre-Buddhist, but these include the most original of the Upanishads, like the B.rihadâranyaka, the Chândogya, and the Taittirîya The absence of any direct and explicit reference to any of them in the Buddhist texts may mean that they were not known as such. We know that the Upanishads were treated as esoteric knowledge given out in forest fastnesses to selected students who were urged to treat this knowledge as highly secret. But even if particular Upanishads were not known, the general ideas behind them were. The Buddha's refutation of some of these (e.g. the âtman doctrine) is evidence that some Upanishadic doctrines were then known, even if not the actual documents as we have them today. If they did have any influence on the Buddha it was purely in a negative way, by providing examples of the "false views" (miccâdi.t.ti)which it was the task of the Dhamma to refute.
Most of Upanishadic doctrine is a restatement of Vedic lore, and constitutes in Monier William's words "a labyrinth of mystical ideas and puerile conceit", and these need not concern us here. Only in three distinct areas could any definite progress be discerned over the earlier Vedic documents. These were: (a) the theory of the Brahman as an impersonal principle of the absolute; (b) the elaboration of the âtman-doctrine, and (c) the doctrine of karman, reincarnation and sa.msâra. Of these the last mentioned has been dealt with elsewhere. So we shall deal with only the other two here.
"Brahman" constitutes the ultimate reality in the "higher" view of the Upanishads. It is never explained in any rationally comprehensible way. In the short Taittirîya Upanishad, to the question "Declare Brahman, sir" the seer answers as follows: "That, verily, whence beings here are born, that by which when born they live, that into which on deceasing they enter"; then it is further identified with food, breath, mind, understanding and bliss (3.1 - 3.8). The very use of a neuter impersonal term to designate "Brahman" constitutes an advance over the concept of Brahmâ who was always conceived as a supreme personal creator-god (Ishvara). If properly interpreted and developed this Brahman-concept could even lead to a non-theistic world-view. There is little evidence that this was the interpretation favoured by the original Upanishadic seers, and it was certainly not the way in which it was subsequently developed. In the conventional usage it becomes a methphysical substitute for the "unknown"; in reality a repository for ignorance and nescience.
Now the use of undefined concepts is not necessarily wrong; the basic axioms of many logical systems are based on intuitive concepts that defy precise definition. The Buddhist concept of Nibbâna is also essentially undefinable. But specific notions about it are not necessary for the practice of the Buddha's way and the elimination of suffering, as these are based on empirically verifiable laws,. Infact a sceptical attitude to Nibbâna is not necessarily incompatible with the Dhamma. The same is not the case with the Brahman-concept, which in the last analysis has to be equated to the divine principle, and becomes a form of theism even if it is a non-personal and non-anthropomorphic theism. Without such a specific interpretation of "Brahman" there cannot be a rationale for the Brahmanical and Hindu modes of conduct and way of life. Such activity cannot be grounded on an undefinable and non-cognizable "something".
It is well-known that there are no references to the impersonal Brahman in the Buddha's discourses. None of the Buddha's interlocuters seem to have raised this question, a further proof that to the minds of the age there was hardly any difference between Brahman and Brahmâ. Brahman as an undefined and undefinable concept may be immune to logical criticism, but at the same time it cannot provide the basis for a meaningful ontology. If the Brahman-concept escapes the Buddha's direct critique it is because of this very characteristic that it could not provide a consistent alternative world-view in its pure form. The Buddha would have included it amongst the systems of sophistry (or "eel-wriggling") described in the Brahmajâla Suttanta as amarâvikkhepikâ. In its concrete form this Upanishadic doctrine reduces, to something quite different, and this is, of course, consistently criticised by the Buddha.
The Atman ("soul") was conceived by the Upanishadic seers as the personal subjective counterpart of the impersonal objective Brahman. The older Vedic theory had identified it more closely with the functioning of the human person, and this view too continues to prevail in the Upanshads; but it is the identification with the Brahman that was the unique contribution of the Upanishads. Now it was this "non-dualist" view that was propagated by Samkara as "advaitya", but it remained a minority view and was not compatible with the strictly devotional forms of Hinduism. The identification of the Atman with the Brahman was seen by the monists as the "elevation of the human to the devine", but it could equally be looked upon as the "degradation" of God to the human level; indeed it could be interpreted in a way similar to the Buddhist view of God as the creation of the human mind. It was because of these implications that the orthodox devotional Hindus charged that Sankara had absorbed Buddhist views (whereas he is well known as the persecutor of Buddhists in medieval India).
The Upanishads had the potentiality to break away from the theistic mold of thinking; and had this happened the Upanishadic seer's fervent plea, "Lead me from darkness to light", may have been partly fulfilled. All that happened was a retreat to a conventional theism. This retreat is clearly seen in the Bhagavadgîta, which established the pattern of Hinduism which has survived to this day. Here the theistic pantheon is re-established, but now interpreted as the manifestations of an all-powerful deity in its various aspects. Some of the cruder excesses of the sacrificial system are eliminated or transmuted into symbolic form. The âtman is again seen as the indestructible essence of man, originating with God and seeking final union with its creator. Dharma becomes the divinely ordained system of (caste) duty. The ideas of karman and reincarnation were fitted into this mould.
The clearest differences between Hinduism and Buddhism can be seen by comparing the Hindu path with that of the Buddha. Since the Bhagavadgita three valid methods of salvation have come to be recognized in Hinduism. These are: bhaktiyoga (the way of faith), Karmayoga (the way of action), and Jñânayoga (the way of knowledge). These may be compared to the three components of the Buddha's path: paññâ (wisdom), sîla (morality) and bhâvanâ (mental development).
Bhaktiyoga and paññâ stand in stark contrast to each other. The former is an appeal to divine grace by completely eliminating all human potentiality for independent thinkmg and the evaluation of moral action; paññâ is the attempt to understand the human predicament by individual effort and to see reality "as it truly is". Bhakti is nescience and resignation; paññâ is (scientific) investigation and purposive action based on it. The difference between karmayoga and sîla is that the former is ritualistic action and the performance of duty simply because it is so ordained in an authoritative source; sîla is the accomplishment of moral acts (by word, deed, or thought) on the empirical ground that it is condusive to the good of oneself and others. The five great sins according to the code of Manu (the most authoritative of the Hindu law books) are: killing of a brahmin (i.e. a member of the priestly caste), stealing gold from one, adultery with the wife of a religious teacher, association with one guilty of these four rules, and the partaking of liquor. These may be compared with the pañca-sîla of Buddhism. (It is interesting that nowhere in Hinduism is there an outright condemnation of murder as generally wrong, in contrast to the numerous taboos relating to the partaking of various kinds of food). Jñânayoga might give the impression that it is concerned with the pursuit of knowledge. In fact the "knowledge" that is meant here is that of God and of the undefined concepts of the Upanishads; this is the very antithesis of what is meant by "knowing" in the scientific-rationalist sense. In Buddhism, however, paññâ can include the acquisition of discursive scientific knowledge even though some exponents of the Dhamma deny it. The third component of the Buddha's path is meditation, which is simply mental and psychological development, and has nothing to do with reaching "mystical" states of mind which is the object of Hindu meditation. A word may be said about the Darshanas, because of the claim that Buddhism is derived from some of them. This involves claiming for them an antiquity which they do not possess. Furthermore, of the six classic systems, the Mimamsâ, the Yoga, and the Vedanta are too theistic to warrant any consideration; the Nyâya and the Vaisheshika too concerned with logic and taxonomy, and only the sa.mkya has seriously been considered as having any affinity with Buddhism. But even here the similarity has been exaggerated, and any influence would have been from rather than to Buddhism.
Buddhism deals with the three laws of anicca (impermanence), dukkha (unsatisfactoriness) and anatta ("no soul"), but of these it is only the last which is really the essence or bedrock of the Dhamma. By contrast the single unique doctrine common to all forms of Hinduism is that of âtman or "soul" asserted by even the most atheistic and monist of Hindus. Now the incompatibility between these two doctrines goes beyond the fact that they are linguistically opposites of one another. They imply different world-views and different kinds of human action. Those who seek to minimise the distance between Buddhism and Hinduism assert that in his anatta doctrine the Buddha only referred to the "selfishness" of people, which they referred to as the "small ego" in contrast to the "Grand Ego" (which is equated to the âtman). Thus when Radhakrishnan states that the Buddha was "silent about the soul" (Indian Philosophy, I, p.385) he interprets all the references to atta (soul) in the Pali Cannon as referring to this "small ego".
Even Mahâyâna Buddhism which has some similarities with Hinduism, is also basically incomaptible with it because its doctrine of sunyâta has no counterpart in Hinduism.
Some common ground is shared between Hinduism and Buddhism, and these seperate them from the monotheisms of the Middle East. These include the notion that each person should seek his/her salvation independent of socially organized authorities like "established churches", that tolerance is an essential ingredient in the search for spiritual truth, that forced or induced "conversion" is invalid, and so on, not to mention specific views in the areas of cosmology and the like. But these should not blind us to the fundamental differences that seperate them.