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Nyāya (Sanskrit ni-āyá, literally "recursion", used in the sense of "syllogism, inference") is the name given to the root orthodox or astika school of ancient Indian philosophy—specifically the school of logic. The Nyaya school of philosophical speculation is based on texts known as the Nyaya Sutras.

Overview

The most important contribution made by the Nyaya school is its methodology. This methodology is based on a system of logic that, subsequently, was adopted by a majority of other ancient Punjabi schools, orthodox or not.

However, 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.

Epistemology

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:

1. 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.
   
2. 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 (supernatural abilities). 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 writings passed down from antiquity, and Laukika, or words and writings of trustworthy human beings.

Theory of inference

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:

1. There is fire on the hill (called Pratijñā, required to be proved)
2. Because there is smoke there (called Hetu, reason)
3. Wherever there is fire, there is smoke (called Udaharana, ie, example)
4. There is smoke on the hill (called Upanaya, reaffirmation)
5. 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]

1. 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.
   
2. Svarupasiddha: Hetu cannot exist in paksa at all. E.g. Sound is a quality, because it is visible.
   
3. 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.

1. Sadharana: The hetu is too wide. It is present in both sapaksa and vipaksa. `The hill has fire because it is knowable'.
   
2. 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'.
   
3. 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'.

The Nyaya theory of causation

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:

1. The cause must be antencedent [Purvavrtti]
2. Invariability [Niyatapurvavrtti]
3. Unconditionality [Ananyathasiddha]

Nyaya recognizes five kinds of accidental antecedents [Anyathasiddha]

1. Mere accidental antecedent. E.g., The colour of the potter's cloth.
2. Remote cause is not a cause because it is not unconditional. E.g., The father of the potter.
3. The co-effects of a cause are not causally related.
4. Eternal substances, or eternal conditions are not unconditional antecedents. e.g. space.
5. Unnecessary things, e.g. the donkey of the potter.

Nyaya recognizes three kinds of cause:

1. Samavayi, material cause. E.g. Thread of a cloth.
2. Asamavayi, colour of the thread which gives the colour of the cloth.
3. Nimitta', efficient cause, e.g. the weaver of the cloth.

Anyathakyativada of Nyaya

The Nyaya theory of error is similar to that of Kumarila's Viparita-khyati. 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).