Nyaya, traditionally founded by Akshapada Gautama (6th cent. B.C.), is a school of logic and epistemology that defined the rules of debate and canons of proof. Its views were accepted with modification by most of the other schools. The atomist school, Vaisheshika, founded by Kanada (3d cent. B.C.), analyzed reality into six categories: substance, quality, activity, generality, particularity, and inherence. The universe is made up of nine kinds of substance: earth, water, light, air, ether, time, space, soul (or self), and mind.
The Samkhya school, founded by Kapila (6th cent. B.C.), admits two basic metaphysical principles, purusha (soul) and prakriti (materiality). Prakriti consists of three gunas or qualities: sattva (light or goodness), rajas (activity or passion), and tamas (darkness or inertia). When these constituents are in equilibrium, prakriti is static. However, disturbance of the equilibrium initiates a process of evolution that ultimately produces both the material world and individual faculties of action, thought, and sense. The purusha appears to be bound to prakriti and its modifications and may become free only through the realization that it is distinct from prakriti. Early versions of Samkhya, now lost, may have been theistic, but the classical system does not include God. The yoga school expounded by Patanjali (2d cent. B.C.) accepts Samkhya metaphysics to explain the validity of yogic processes described in the Yoga Sutras and also accepts the concept of an Ishvara, God or supreme soul. Yoga is defined as "cessation of the modifications of consciousness" and is achieved by an eight-stage discipline of self-control and meditation.
The Purva Mimamsa school, founded by Jaimini (2d cent. B.C.), set forth sophisticated principles for interpreting the Veda, which was regarded as entirely composed of injunctions to ritual action. Its epistemology and theory of meaning were constructed to show that the words of the Veda had eternal and intrinsic validity. The different schools of Uttara Mimamsa or Vedanta are all based on the Upanishads and the Brahma-Sutras of Badarayana (c.200 B.C.–A.D. 200), but differ in their concepts of God, world, soul, and the relation between them.