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)
In Nyaya terminology for this example, the hill is called as paksha (minor term), the fire is called as sadhya (major term), the smoke is called as hetu, and the relationship between 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 be incompatible with the minor term or Paksha, and (5) All other contradictions by other means of knowledge should be absent. The fallacies in Anumana (hetv?bhasa) may occur due to the following:
Asiddha: It is the unproven 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-eternal, because they are knowable`.
Satpratipaksa: Here the hetu is contradicted by another hetu. If both have equal force, then nothing ensues. `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`.
