Nyaya, literally meaning `recursion`, used in the sense of `syllogism, inference`, is the name given to one of the six orthodox or astika schools of Hindu philosophy - specifically the school of logic. The Nyaya school of philosophical speculation is based on texts known as the Nyaya Sutras, which were written by Aksapada Gautama, from approximately the 2nd century B.C.

Nyaya Philosophy deals with knowing. It has sixteen categories, dealing with the means to understand the universe.

Nyaya Philosophy accepts the plurality of souls. Ignorance bars the way to liberation. Ignorance results from identification of the Self with the body, the sense, and the mind. Death causes rebirth because of our ignorance of the True Self. Transcendental knowledge of our True Self is Liberation, end of cycle of birth and death, and freedom from misery. Man can be liberated from the life-death cycle, only by deep logical analysis based on philosophical knowledge and dissolution of doubt and ignorance.

The most important contribution made by the Nyaya school to modern Hindu thought is its methodology, based on a system of logic.

Nyaya Philosophy is based on: Pramana -Means to acquire knowledge, Prameya - Object of knowledge, Samshaya - Doubt, Prayojana - Purpose, Drstanta - Illustrative example, Siddhanta - Conclusion, Avayava - Constituents of a syllogism, Tarka - Hypothetical argument, Nirnaya - Ascertaining the truth, Vada - Discussion, Jalpa - Disputation, Vitanda - Refutation, Hetvabhasa - Fallacy in the cause, Chala - guile, Jati - casuistry and Nigrasthana- Vulnerable point of opponent`s statement.

Early Naiyayikas( the Nyaya scholars) wrote very little about God, i.e., Ishvara. However, later Buddhists in India had become from agnostic to strictly atheistic. As a reaction, the later Naiyayikas entered into disputes with the Buddhists and tried to prove the existence of God through logic. Not only have the Naiyanikas given proofs for the existence of God, but they have also given an argument that such a God can only be one. This is discussed in the Nyaya Kusumanjali.

Therefore, Nyaya Philosophy believes in the existence of a supreme God who initiates the process of world creation.

Theory of inference in Nyaya philosophy
The methodology of inference involves a combination of induction and deduction by moving from particular to particular, via generality. It has five steps, as can be illustrated with the example:

There is fire on a hill (called Pratijna, required to be proved)
Because there is smoke there (called Hetu, reason)
Wherever there is fire, there is smoke (called Udaharana, i.e. example)
There is smoke on the hill (called Upanaya, reaffirmation)
Therefore there is fire on the hill (called Nigamana, conclusion)

Theory of causation in Nyaya philosophy
A cause is outlined as an unconditional and invariable antecedent of an effect and an effect as an unconditional and invariable consequent of a cause. The same cause produces the same effect; and the same effect is produced by the same cause. The cause is not present in any hidden form whatsoever in its effect.

Theory for God in Nyaya philosophy
Early Naiyayikas (Nyaya scholars) wrote very little about God, i.e., Ishvara (literally, the Supreme Lord). However, later Buddhists in India had turned into strict atheists from agnostics. As a reaction, the later Naiyayikas entered into conflicts with the Buddhists and tried to establish the existence of God through logic. They made this question a challenge to their own existence.:

Theory for mono-theism in Nyaya philosophy
Not only have the Naiyanikas supplied proofs for the existence of God, they have also stated an argument that such a God can only be one. In Nyaya Kusumanjali, this is discussed against the proposition of the Mimansa school