According to a traditional principle of classification, more likely adopted by orthodox Hindu thinkers, the schools or systems of Indian philosophy are divided into two broad classes, namely, orthodox (astika) and heterodox (nastika).
To the first group belong the six chief philosopical systems (popularly known as sad-darsana), namely, MImamsa, Vedanta, Sarikhya, Yoga, Nyaya and Vaisesika. These are regarded as orthodox (astika), not because they believe in God, but because they accept the authority of the Vedas the Mimarhsa and the Sarikhya do not believe in.
God as the creator of the world, yet they are called orthodox (astika), because they believe in the authoritativeness of the Vedas.
The six systems mentioned here are not the only orthodox systems; they are the chief ones, and there are some other less important orthodox schools, such as the Grammarian school, the medical school, etc., also noticed by Madhavacarya.
Under the other class of heterodox systems, the chief three are the schools of the Materialists like the Carvakas, the Bauddhas and the Jainas. They are called heterodox (nastika) because they do not believe in the authority of the Vedas.
To understand this more clearly, we should know something regarding the place of the Vedas in the evolution of Indian thought.
The Vedas are the earliest available records of Indian literature, and subsequent Indian thought, especially philosophical speculation, is greatly influenced by the Vedas, either positively or negatively. Some of the philosophical systems accepted Vedic authority, while others opposed it.
The Mimamsa and the Vedanta may be regarded as the direct continuation of the Vedic culture. The Vedic tradition had two sides, ritualistic and speculative (karma and Jnanaa). The Mimamsa emphasised the ritualistic aspect and evolved a philosophy to justify and help the continuation of the Vedic rites and rituals.
The Vedanta emphasised the speculative aspect of the Vedas and developed an elaborate philosophy out of Vedic speculations.
As both these schools were direct continuations of Vedic culture, both are sometimes called by the common name, Mimamsa; and for the sake of distinction, the first is called Purva-Mimamsa (or Karma- Mimamsa) and the second, Uttara-Mlmamsa (or Jhana-Mlmamsa).
But the more usual names of these two are Mimamsa and Vedanta respectively, and we shall follow this common usage here.
Though the Sahkhya, Yoga, Nyaya and Vaisesika based their theories on ordinary human experience and reasoning, they did not challenge the authority of the Vedas, but tried to show that the testimony of the Vedas was quite in harmony with their rationally established theories.
The Carvaka, Bauddha and Jaina schools arose mainly by opposition to the Vedic culture and, therefore, they rejected the authority of the Vedas.