The doctrines of the Vedānta are laid down in the Brahma-sūtras of Bādarāyaṇa. This text-book, the meaning of which is not intelligible without the aid of a commentary, was expounded in his bhāshya by the famous Vedāntist philosopher Çankara, whose name is intimately connected with the revival of Brahmanism. He was born in 788 A.D., became an ascetic in 820, and probably lived to an advanced age. There is every likelihood that his expositions agree in all essentials with the meaning of the Brahma-sūtras, The full elaboration of the doctrine of Māyā, or cosmic illusion, is, however, due to him. An excellent epitome of the teachings of the Vedānta, as set forth by Çankara, is the Vedānta-sāra of Sadānanda Yogīndra. Its author departs from Çankara’s views only in a few particulars, which show an admixture of Sānkhya doctrine.

Among the many commentaries on the Brahma-sūtras subsequent to Çankara, the most important is that of Rāmānuja, who lived in the earlier half of the twelfth century. This writer gives expression to the views of the Pāncharātras or Bhāgavatas, an old Vishnuite sect, whose doctrine, closely allied to Christian ideas, is expounded in the Bhagavadgītā and the Bhāgavata-purāṇa, as well as in the special text-books of the sect. The tenets of the Bhāgavatas, as set forth by Rāmānuja, diverge considerably from those of the Brahma-sūtras on which he is commenting. For, according to him, individual souls are not identical with God; they suffer from innate unbelief, not ignorance, while belief or the love of God (bhakti), not knowledge, is the means of salvation or union with God.

The last two orthodox systems of philosophy, the Vaiçeshika and the Nyāya, form a closely-connected pair, since a strict classification of ideas, as well as the explanation of the origin of the world from atoms, is common to both. Much the older of the two is the Vaiçeshika, which is already assailed in the Brahma-sūtras. It is there described as undeserving of attention, because it had no adherents. This was certainly not the case in later times, when this system became very popular. It received its name from the category of “particularity” (viçesha) on which great stress is laid in its theory of atoms. The memory of its founder is only preserved in his nickname Kaṇāda (also Kaṇabhuj or Kaṇa-bhaksha), which means “atom-eater.”

The main importance of the system lies in the logical categories which it set up and under which it classed all phenomena. The six which it originally set up are substance, quality, motion, generality, particularity, and inherence. They are rigorously defined and further subdivided. The most interesting is that of inherence or inseparable connection (samavāya), which, being clearly distinguished from that of accident or separable connection (saṃyoga), is described as the relation between a thing and its properties, the whole and its parts, genus and species, motion and the object in motion. Later was added a seventh, that of non-existence (abhāva), which, by affording special facilities for the display of subtlety, has had a momentous influence on Indian logic. This category was further subdivided into prior and posterior non-existence (which we should respectively call future and past existence), mutual non-existence (as between a jar and cloth), and absolute non-existence (as fire in water).

Though largely concerned with these categories, the Vaiçeshika system aimed at attaining a comprehensive philosophic view in connection with them. Thus while dealing with the category of “substance,” it develops its theory of the origin of the world from atoms. The consideration of the category of “quality” similarly leads to its treatment of psychology, which is remarkable and has analogies with that of the Sānkhya. Soul is here regarded as without beginning or end, and all-pervading, subject to the limitations of neither time nor space. Intimately connected with soul is “mind” (manas), the internal organ of thought, which alone enables the soul to know not only external objects but its own qualities. As this organ is, in contrast with soul, an atom, it can only comprehend a single object at any given moment. This is the explanation why the soul cannot be conscious of all objects simultaneously.

The Nyāya system is only a development and complement of that of Kaṇāda, its metaphysics and psychology being the same. Its specific character consists in its being a very detailed and acute exposition of formal logic. As such it has remained the foundation of philosophical studies in India down to the present day. Besides dealing fully with the means of knowledge, which it states to be perception, inference, analogy, and trustworthy evidence, it treats exhaustively of syllogisms and fallacies. It is interesting to note that the Indian mind here independently arrived at an exposition of the syllogism as the form of deductive reasoning. The text-book of this system is the Nyāya-sūtra of Gotama. The importance here attached to logic appears from the very first aphorism, which enumerates sixteen logical notions with the remark that salvation depends on a correct knowledge of their nature.

Neither the Vaiçeshika nor the Nyāya-sūtras originally accepted the existence of God; and though both schools later became theistic, they never went so far as to assume a creator of matter. Their theology is first found developed in Udayanāchārya’s Kusumānjali, which was written about 1200 A.D., and in works which deal with the two systems conjointly. Here God is regarded as a “special” soul, which differs from all other individual eternal souls by exemption from all qualities connected with transmigration, and by the possession of the power and knowledge qualifying him to be a regulator of the universe.

Of the eclectic movement combining Sānkhya, Yoga, and Vedānta doctrines, the oldest literary representative is the Çvetāçvatara Upanishad. More famous is the Bhagavadgītā in which the Supreme Being incarnate as Kṛishṇa expounds to Arjuna his doctrines in this sense. The burden of his teaching is that the zealous performance of his duty is a man’s most important task, to whatever caste he may belong. The beauty and the power of the language in which this doctrine is inculcated, is unsurpassed in any other work of Indian literature.

By the side of the orthodox systems and the two non-Brahmanical religions, flourished the lokāyata (“directed to the world of sense”), or materialistic school, usually called that of the Chārvākas from the name of the founder of the doctrine. It was regarded as peculiarly heretical, for it not only rejected the authority of the Vedas and Brahmanic ceremonial, but denied the doctrines of transmigration and salvation accepted by all other systems. Materialistic teachings may be traced even before the time of Buddha, and they have had many secret followers in India down to the present day. The system, however, seems never to have had more than one text-book, the lost Sūtras of Bṛihaspati, its mythical founder. Our knowledge of it is derived partly from the polemics of other schools, but especially from the Sarvadarçana-saṃgraha, or “Compendium of all the Philosophical Systems,” composed in the fourteenth century by the well-known Vedāntist Mādhavāchārya, brother of Sāyaṇa. The strong scepticism of the Chārvākas showed itself in the rejection of all the means of knowledge accepted by other schools, excepting perception. To them matter was the only reality. Soul they regarded as nothing but the body with the attribute of intelligence. They held it to be created when the body is formed by the combination of elements, just as the power of intoxication arises from the mixture of certain ingredients. Hence with the annihilation of the body the soul also is annihilated. Not transmigration, they affirm, but the true nature of things, is the cause from which phenomena proceed. The existence of all that transcends the senses they deny, sometimes with an admixture of irony. Thus the highest being, they say, is the king of the land, whose existence is proved by the perception of the whole world; hell is earthly pain produced by earthly causes; and salvation is the dissolution of the body. Even in the attribution of their text-book to Bṛihaspati, the name of the preceptor of the gods, a touch of irony is to be detected. The religion of the Brahmans receives a severe handling. The Vedas, say the Chārvākas, are only the incoherent rhapsodies of knaves, and are tainted with the three blemishes of falsehood, self-contradiction, and tautology; Vedic teachers are impostors, whose doctrines are mutually destructive; and the ritual of the Brahmans is useful only as a means of livelihood. “If,” they ask, “an animal sacrificed reaches heaven, why does the sacrificer not rather offer his own father?”

On the moral side the system is pure hedonism. For the only end of man is here stated to be sensual pleasure, which is to be enjoyed by neglecting as far as possible the pains connected with it, just as a man who desires fish takes the scales and bones into the bargain. “While life remains, let a man live happily, let him feed on ghee even though he run into debt; when once the body becomes ashes, how can it ever return again?”