1. Nyaya  Darshana
Almost  all the branches of Indian philosophy deal with two subjects viz. pramanas or valid sources of knowledge  and prameyas or things to be known  from them. Since Nyaya Darshana gives priority to the first subject, thereby  laying the foundation for Indian logic, it is also called Nyaya Vidya or Tarka  Sastra.  The system derives its name from  the word Nyaya that meant ‘argumentation’ and indirectly indicates an analytical  and logical methodology adopted by it for drawing its conclusions.

The Nyaya school of philosophical speculation is based  on texts known as the Nyaya Sutras, which were written by Sage Gautama . The most important contribution  made by the Nyaya school to modern Hindu thought is its methodology. This  methodology is based on a system of logic that has  subsequently been adopted by most of the other Indian schools.

The followers of Nyaya believed that obtaining valid  knowledge was the only way to obtain release from suffering. They therefore  took great pains to identify valid sources of knowledge and to distinguish  these from mere false opinions.

According to the Nyaya school, there are four sources  of knowledge (pramanas): 1.  perception (pratyaksha),  2. inference (anumana), 3.comparison (upamana) and 4.verbal testimony (shabda). Knowledge obtained through  each of these can, of course, still be either valid or invalid. As a result,  Nyaya scholars again went to great pains to identify, in each case, what it  took to make knowledge valid, creating in the process a number of explanatory  schemes based on pure logic.

The Nyaya philosophy's another important achievement was  to prove the existence of God (one Supreme God, called Ishwara), mostly by  logic, in answer to repeated attempts by Buddhists to disprove the existence of  God.

Direct Perception, called Pratyaksha,  occupies the foremost position in the Nyaya epistemology. When a sense organ comes  into contact with a sense object it produces a true, clear and an unerring  knowledge of the object perceived which is termed as direct perception. Inference, called Anumana, is knowledge of an object based on the knowledge of  another object. Comparison, which is Upamana,  is the knowledge produced by a given description of an object which is already  known. Verbal Testimony or Word, or Shabda  is also accepted as a pramana.  It can be of two types, Vaidika  (Vedic), which are the words of the four  sacred Vedas, and are described as the Word of God, and Laukika, or words and writings of trustworthy human beings.

Nyaya Proof for God
Early Naiyanikas wrote very little about God, i.e., Ishvara (the Supreme Lord). However, when Buddhists  became atheistic from agnostic the later Naiyanikas entered into disputes with  the Buddhists and tried to prove the existence of God through logic. They made  this question a challenge to their own existence and gave the following nine  proofs for the existence of God.

Karyat (from effect): An effect is produced by a cause, and  similarly, the universe must also have a cause. Causes (according to  Naiyanikas) are of three kinds - Samavayi (in case of the universe, the atoms),  Asamavayi (the association of atoms) and Nimitta (efficient cause which is  Ishvara). The efficient cause of the world must have an absolute knowledge of  all the materials of creation, and hence it must be God. Hence from the  creation, the existence of the Creator is proved.

Aayojanaat (from combination): Atoms are  inactive and properties are unphysical. So it must be God who creates the world  with his will by causing the atoms to join. Self-combination of inanimate and lifeless  things is not possible as otherwise atoms would only combine at random,  creating chaos. Hence there is an invisible hand of a wise organiser behind the  systematic grouping of the ultimate atoms into molecules. Such a final  organiser is God.

Dhrite (from support): Just as  a material thing falls off without a support, similarly, God is the supporter  and bearer of this world, without which the world would not have remained,  integrated. This universe is hence superintended within God, which proves his  existence.

Padat (from word): Every word  has the capability to represent a certain object. It is the will of God that a  thing should be represented by a certain word. Similarly, we can not have any knowledge  of the different things of the world, unless there is a source of knowledge.  The origin of all knowledge should therefore be from an omniscient, omnipotent  and omnipresent entity. Such a being is not to be seen in this universe, and so  it must be outside it. This being is God.

Pratyatah (from faith): The Vedas,  are regarded as the source of eternal knowledge. Their knowledge is free from  fallacies and are widely believed as a source of proof. Their authors cannot be  human beings because human knowledge is limited. They cannot obtain knowledge  of past, present and future and in-depth knowledge of mind. Hence only God can  be the creator of the Vedas. Hence his existence is proved from his being the  author of the Vedas, which he revealed to various sages over a period of time.

Shruteh (from scriptures): The  Shrutis, i.e., the Vedas extol God and talk about his existence. "He is  the lord of all subjects, omniscient and knower of one's internal feelings; He  is the creator, cause and destroyer of the world", say the Shrutis. Since  the Shrutis are regarded as a source of proof    by Naiyanikas, the existence of God is proved.

Vakyat (from precepts): Again,  the Veda must have been produced by a person because it has the nature of  "sentences,", in other words, the sentences of the Veda were produced  by a person just as the sentences of human beings. That person must have been  God.

Samkhyaavisheshaat (from the specialty  of numbers): The size of a molecule depends on the number of the atoms that go  to constitute it. This requisite number of the atoms that go to form a  particular compound could not have been originally the object of the perception  of any human being; so its contemplator must be God.

Adrishtaat (from the unforseen): It is seen that some people in this world are happy, some  are in misery. Some are rich and some poor. The Naiyanikas explain this by the  concept of Karma and reincarnation. The fruit of an individual's  actions does not always lie within the reach of the individual who is the  agent. There ought to be, therefore, a dispenser of the fruits of actions, and  this supreme dispenser is God.

Nyaya  Darshana is the basis of all Sanskrit philosophical studies. A study of Nyaya  develops the power of reasoning and logic. It renders the intellect sharp and  subtle. One cannot understand the nuances of Brahma Sutras of Sage Veda Vyasa  without the knowledge of the Nyaya darshana.