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Many Roads
When the destination is clear, a road is useful. Otherwise, its possible to go up and down the road over and over, without reaching anywhere. Though well-traveled roads are generally safe ways to go, cutting one's own path through unknown territory is another way. Within pan-Indian thought, there are at least eight different darshanas (points of view onto reality, or alternately, avenues to liberation). Six of these are considered orthodox because they hold the Vedas as authoritative; these are
Nyaya, Vaishesika, Samkhya, Yoga, Mimamsa and Vedanta. Buddhism and Tantra do not hold the Vedas as authoritative, but they still aim for the same goal; Liberation.
To be sure, there are contradictions between the views, but, and this must always be kept in mind, they all aim for the same goal. They offer different starting points, different orientations, and emphasize different ways of reaching Liberation. Even though they differ from each other in significant ways, it is still possible to see them as complementary because they all aim for the same goal. In surveying the 6 orthodox systems, Indologist Alain Danielou writes,
It cannot be said that any of these approaches is truer than any other, since each is realistic in its own field. The notion of multiple and eventually contradictory relative truths, coexisting on different levels and corresponding to the various human means of investigation, whether observation, thought, or intuition, has been a remarkable instrument in the formation of Hindu thought.
I would say that it is an error to critique these views as one might the academic, secular philosophies of the modern West, or to look upon them as stand-alone metaphysical systems. The following will perhaps make clear why such approaches would be off the mark:
Nyaya-Vaishesika

Vaishesika (literally, Particularity) is often termed an "atomic theory" because it posits that all objects are ultimately reducible to some fundamental, indivisible units (atoms, in the modern sense). Nyaya, translated as "that by which the mind is led to a conclusion" or "logic", is the way utilized to reach this position. Traditionally, Nyaya and Vaishesika are paired together because logic and analysis are two halves of the same circle. To appreciate Nyaya-Vaishesika, it is crucial to remember that its proponents are at pains to point out that understanding the world in this way is useful because it can lead to a non-attachment to the world of physical forms. The emphasis here is not on describing the world as a task in itself, but rather to see through it in some way, so that the mind may settle elsewhere. The point is not that the world is reducible to atoms, but that a deep analysis into the nature of the world can liberate a person from his naive impressions, and thus cut through his attachments at the root. The insight that everything, the desirable and the ugly, is composed of the same fundamental substance could be powerfully transformative, or it may make no difference to one's outlook at all; both results are possible. If this insight is transformative, then good, the roads known as Nyaya-Vaishesika ought to be traveled some more; otherwise, some other of the eight roads might be more salutary. If a person agrees with Vaishesika's claim that all physical forms are reducible to the same fundamental substance, but does not develop a non-attachment to objects, then the whole point of Vaishesika's analysis is lost. So in fact, it is not important whether Vaishesikas atomic claim can be substantiated in the realm of scientific fact, because the aim is liberation, and not the description of physical reality. Those criticizing Vaishesika as if it were a science in the modern Western sense are off the mark. Again, Vaishesika does not aim to describe the physical universe per se, but rather to see into it so deeply that its seeming "solidity" and seeming "independent existence" is seen through. Vaishesika has its sights squarely on the causal reality which lays hidden beyond the limits of the senses.
Nyaya-Vaishesika and Modern Science
However, because Nyaya-Vaishesika looks to analyze the physical universe, it resembles modern science more so than the other darshanas. In the modern era, Albert Einstein looked deeply into reality via the scientific method and came to formulate the famous "Theory of Relativity" as well as being one of the founders of "Quantum Mechanics". Here is a quote from Albert Einstein showing what scientific analysis did for his outlook:
"A human being is a part of a whole, called by us "universe", a part limited in time and space. He experiences himself, his thoughts and feelings as something separated from the rest... a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty."
Neils Bohr, one of the founders of Quantum Mechanics once said,
"In looking at Quantum Mechanics, if a person is not shocked by what he sees, he has not understood it." Einstein and Bohr were rare individuals, scientists or not; they had a hunger for understanding the deeper, underlying reality, what Einstein sometimes called "The Mind of God". Though he sometimes used this sort of language, it must also be remembered that Einstein clearly stated that he did not believe in a personal God, did not believe in a deity, did not believe in a Creator God. Its just that the language of science is limited in certain directions, and so one must sometimes speak a poetic tongue to get the point across.
For more on Yoga, "Relativity" and "Quantum Mechanics", see >>>
Yoga and Modern Thought
Buddha's attitude towards metaphysical formulations
Buddha said many times that he was not stating metaphysical truths about the world, but rather showing a way out of being in bondage to it. When asked metaphysical questions (e.g. Is the world finite or infinite?), he chose to remain silent. In a memorable discourse, Buddha compared the metaphysician with a man who had been pierced by an arrow, but refused to pull it out until he knew the name of the archer, the kind of wood which made up the shaft, whether the tip was stone or metal, etc. Here too, the aim is Liberation. Indian "philosophy" does not aim to describe the world in scientific terms. Its aim is instead to somehow orient the mind away from the temporal, the material, the impermanent, and towards the deeper, primary reality.
Samkhya and Yoga

Samkhya (literally, Discriminating Knowledge) and Yoga posit a fundamental dualism (separateness) between consciousness and matter. This could be taken as the pronouncement of a metaphysical truth, or as a suggested step along a road which leads to liberation. The praxis of Yoga is the complete identification with the ultra-subjective pole of the subject-object duality, so this dualistic orientation is applied in that most useful of activities called meditation, and this too eventually leads to Liberation. Samkhya is the theoretical portion, and Yoga the practical portion of the same road. On this road, Yoga is what you do, and Samkhya is how you think about what you're doing. A practitioner of Yoga will tell you that this way of seeing and doing things is very useful; never mind that when you conceive of the world as Samkhya does, you come up with Ayurveda as well (but that's another story). So there is a definite usefulness in seeing the world this way. In leading mind away from the phenomenal, the material, the temporal, the impermanent, there is engaged the opposite movement towards the Absolute. The world may be, and has been conceived in many, many ways, and there is some utility in every conception. It is not necessary to argue about which conception is "true". Instead, one may see them all as alternate views onto the same reality, take none as absolute truths, and keep those which suit one's purposes.
Nyaya, Vaishesika and Samkhya utilize analysis to arrive at the transformative realization that the material and the temporal rest upon a yet deeper reality, and Yoga is the practise of witnessing this within oneself. One can deduce or infer this deeper reality as Nyaya, Vaishesika and Samkhya do, or can directly sight it via the meditative methods of Yoga. Even though it may appear that we are speaking of four distinct roads, it must be remembered that practitioners actually utilize both analysis and gnosis (meditation). Phrases such as "The Six Views" might give the impression that we have here entirely distinct "philosophies", but in fact there are many overlapping elements, and of course they all share the same goal.
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