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, subsequently, has been adopted by the majority of the other Indian schools, orthodox or not. This is comparable to how Western science and philosophy can be said to be largely based on Aristotelian logic.
However, Nyaya differs from Aristotelian logic in that it is more than logic in its own right. Its followers 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. Nyaya is thus a form of epistemology in addition to logic.
According to the Nyaya school, there are exactly four sources of knowledge (pramanas): perception, inference, comparison, and testimony. 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, in the process creating a number of explanatory schemes. In this sense, Nyaya is probably the closest Indian equivalent to contemporary analytic philosophy.
The Naiyayikas (the Nyaya scholars) accepted four means("pramana") of obtaining correct knowledge (prama), viz., Perception, Inference, Comparison and Word.
Perception, called PratyakŞha, occupies the foremost position in the Nyaya epistemology. Perception is defined by sense-object contact and is unerring. Perception can be of two types:
Ordinary (Laukika or Sadharana), of six types, viz., visual-by eyes, olfactory-by nose, auditory-by ears, tactile-by skin, gustatory-by tongue and mental-by mind.
Extra-ordinary (Alaukika or Asadharana), of three types, viz., Samanyalakshana (perceiving generality from a particular object), Jñanalakshana (when one sense organ can also perceive qualities not attributable to it, as when seeing a chili, one knows that it would be bitter or hot), and Yogaja (when certain human beings, from the power of Yoga, can perceive past, present and future and have supernatural abilities, either complete or some). Also, there are two modes or steps in perception, viz., Nirvikalpa, when one just perceives an object without being able to know its features, and Savikalpa, when one is able to clearly know an object. All laukika and alaukika pratyakshas are savikalpa. There is yet another stage called Pratyabhijñā, when one is able to re-recognise something on the basis of memory.
Inference, called Anumana, is one of the most important contributions of Nyaya. It can be of two types: inference for oneself (Svarthanumana, where one does not need any formal procedure, and at the most the last three of their 5 steps), and inference for others (Parathanumana, which requires a systematic methodology of 5 steps). Inference can also be classified into 3 types: Purvavat (inferring an unperceived effect from a perceived cause), Sheshavat (inferring an unperceived cause from a perceived effect) and Samanyatodrishta (when inference is not based on causation but on uniformity of co-existence). A detailed anaysis of error is also given, explaining when anumana could be false.
Comparison, which is the rough translation of Upamana. It is the knowledge of the relationship between a word and the object denoted by the word. It is produced by the knowledge of resemblance or similarity, given some pre-description of the new object beforehand.
Word, or Shabda are 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, having been composed by God, and Laukika, or words and writings of trustworthy human beings.
The methodology of inference involves a combination of induction and deduction by moving from particular to particular via generality. It has five steps, as in the example shown:
There is fire on the hill (called Pratijñā, required to be proved)
Because there is smoke there (called Hetu, reason)
Wherever there is fire, there is smoke (called Udaharana, ie, example)
There is smoke on the hill (called Upanaya, reaffirmation)
Therefore there is fire on the hill (called Nigamana, conclusion)
In Nyaya terminology for this example, the hill would be called as paksha (minor term), the fire is called as sadhya (major term), the smoke is called as hetu, and the relationship between the smoke and the fire is called as vyapti(middle term). Hetu further has five characteristics: (1) It must be present in the Paksha, (2) It must be present in all positive instances, (3) It must be absent in all negative instances, (4) It must not incompatible with the minor term or Paksha and (5) All other contradictions by other means of knowledge should be absent. The fallacies in Anumana (hetvābhasa) may occur due to the following:
Asiddha: It is the unproved hetu that results in this fallacy. [Paksadharmata]
Ashrayasiddha: If Paksha [minor term] itself is unreal, then there cannot be locus of the hetu. e.g. The sky-lotus is fragrant, because it is a lotus like any other lotus.
Svarupasiddha: Hetu cannot exist in paksa at all. E.g. Sound is a quality, because it is visible.
Vyapyatvasiddha: Conditional hetu. `Wherever there is fire, there is smoke'. The presence of smoke is due to wet fuel.
Savyabhichara: This is the fallacy of irregular hetu.
Sadharana: The hetu is too wide. It is present in both sapaksa and vipaksa. `The hill has fire because it is knowable'.
Asadharana: The hetu is too narrow. It is only present in the Paksha, it is not present in the Sapaksa and in the Vipaksha. `Sound is eternal because it is audible'.
Anupasamhari: Here the hetu is non-exclusive. The hetu is all-inclusive and leaves nothing by way of sapaksha or vipaksha. e.g. 'All things are non-ternal, because they are knowable'.
Satpratipaksa: Here the hetu is contradicted by another hetu. If both have equal force, then nothing follows. 'Sound is eternal, because it is audible', and 'Sound is non-eternal, because it is produced'. Here 'audible' is counter-balanced by 'produced' and both are of equal force.
Badhita: When another proof (as by perception) definitely contradicts and disproves the middle term (hetu). 'Fire is cold because it is a substance'.
Viruddha: Instead of proving something it is proving the opposite. 'Sound is eternal because it is produced'.
A cause is defined 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.
The following conditions should be met:
The cause must be antencedent [Purvavrtti]
Nyaya recognizes five kinds of accidental antecedents [Anyathasiddha]
Mere accidental antecedent. E.g., The colour of the potter's cloth.
Remote cause is not a cause because it is not unconditional. E.g., The father of the potter.
The co-effects of a cause are not causally related.
Eternal substances, or eternal conditions are not unconditional antecedents. e.g. space.
Unnecessary things, e.g. the donkey of the potter.
Nyaya recognizes three kinds of cause:
Samavayi, material cause. E.g. Thread of a cloth.
Asamavayi, colour of the thread which gives the colour of the cloth.
Nimitta', efficient cause, e.g. the weaver of the cloth.
The Nyaya theory of error is similar to that of Kumarila's Viparita-khyati (see Mimamsa). The Naiyayikas also believe like Kumarila that error is due to a wrong synthesis of the presented and the represented objects. The represented object is confused with the presented one. The word 'anyatha' means 'elsewise' and 'elsewhere' and both these meanings are brought out in error. The presented object is perceived elsewise and the represented object exists elsewhere. They further maintain that knowledge is not intrinsically valid but becomes so on account of extraneous conditions (paratah pramana during both validity and invalidity).t
Early Naiyayikas wrote very little about God, i.e., Ishvara (literally, the Supreme Lord). 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. They made this question a challenge to their own existence. They gave the following nine proofs for the existence of God, enlisted in Udayana's Nyaya Kusumanjali:
Kāryāt (lit. "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 (which is Ishvara). The active cause of the world must have an absolute knowledge of all the material of creation, and hence it must be God. Hence from the creation, the existence of the Creator is proved.
Āyojanāt (lit., 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, otherwise atoms would only combine at random, creating chaos. There is to be seen the hand of a wise organiser behind the systematic grouping of the ultimate atoms into dyads and molecules. That final organiser is God.
Dhŗité(lit., 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.
Padāt (lit., 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, no knowledge can come to us of the different things here unless there is a source of this knowledge. The origin of all knowledge should be omniscient and, consequently, omnipotent. Such a being is not to be seen in this universe, and so it must be outside it. This being is God.
Pratyatah (lit, from faith): the Hindu holy scriptures, 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 indepth 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.
Shrutéh (lit., from scriptures): The Shrutis, e.g., 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. The Shrutis are regarded as a source of proofs by Naiyanikas. Hence, the eistence of God is proved.
Vākyāt (lit., from precepts): Again, the Veda must have been produced by a person because it has the nature of "sentences," i.e., the sentences of the Veda were produced by a person because they have the nature of sentences, just as the sentences of beings like ourselves. That person must have been God.
Samkhyāvişheshāt (lit., from the speciality of numbers): The size of a dyad or a molecule depends on the number of the atoms that constitute it. This requisite number of the atoms that form a particular compound could not have been originally the object of the perception of any human being; so its contemplator must be God.
Adŗişhţāt (lit., from the unforseen): It is seen that some people in this world are happy, some are in misery. Some are rich, and some are 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.
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. In the Nyaya Kusumanjali, this is discussed against the proposition of the Mimamsa school—that let us assume there were many demigods (Devas) and sages (rishis) in the beginning, who wrote the Vedas and created the world. Nyaya says that:
[if they assume such] omniscient beings, those endowed with the various superhuman faculties of assuming infinitesimal size, and so on, and capable of creating everything, then we reply that the law of parsimony bids us assume only one such, namely Him, the adorable Lord. There can be no confidence in a non-eternal and non omniscient being, and hence it follows that according to the system which rejects God, the tradition of the Veda is simultaneously overthrown; there is no other way open.
In other words, Nyaya says that the polytheist would have to give elaborate proofs for the existence and origin of his several celestial spirits, none of which would be logical. So it is much more logical to assume only One, eternal and omniscient God.