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The Vedas, Sanskrit sacred writings (Veda, sacred knowledge), include the hymns of the Rigveda, the ritual Brahmanas and the philosophical Upanishads, and their dates may stretch back as far as 2500 BCE, certainly predating Buddha (d. 480 BCE).
Vedanta is one of the six orthodox systems of Indian philosophy, the ‘conclusion’ (anta) of the Vedas, and based mainly on the Upanishads, their interpretations in the Brahma-sutras, and the Bhagavad Gita (‘Song of the Lord’ from the Mahabharata). Vedanta forms the philosophical basis of most forms of Hinduism, and all schools of Vedanta hold certain doctrines, such as reincarnation, the desirability of release, the authority of the Vedas, that Brahman is the cause of the world, and that Atman is the agent of its own Karma, but also diverge, for instance on the relationship of Atman to Brahman, including non-dualist, theist and dualist interpretations.
Shankara, Sankara or Shankaracharya (the last form means ‘Shankara the Teacher’) founded non-dualist or advaita Vedanta; since ‘there can be no unity apart from variety, he does not describe his teaching as monism but only as ‘non-dualism’ (advaita)’.
Yoga (or its slightly hybrid variant Sankhya-Yoga) is one of the other six orthodox systems of Indian philosophy, its central text being the Yoga-sutra (Aphorisms) of Patañjali (2nd century BCE), whose teachings form the basis of specifically Raja Yoga. Yoga looks towards union (yoga) with a Godhead in samadhi. Despite some similarities with Advaita Vedanta, there is a fundamental difference in the notion of matter, which in Yoga is independent of spirit and is ultimately real, whereas in advaita matter is seen as maya or illusion.
See M. Hiriyanna, The Essentials of Indian Philosophy (1948; Delhi: Motilal Banarsidass Publishers, 1995) esp. 154 and 161.
The term Vedic is often used rather loosely to refer to those elements of Indian Philosophy that are regarded as contemporary with the Vedas or, even more loosely, just ancient: the three Gunas (qualities or attributes) of Sattva, equilibrium, Rajas, activity, and Tamas, inertia, are referred to by Alan Leo as Vedic and, more generally, Jyotish (jyoti, light & Isha, Lord or God) is sometimes called ‘Vedic astrology’.