nyAya basics - an aide memoire

pancha avayava vAkya
anumAna, or inference, is of two kinds - svArthAnumAna and parArthAnumAna. The former is a situation where a person makes an inference themselves, and the latter is a situation where a person conveys information that allows another person to draw an inference. The naiyyAyika (logician) believes there are five components that are required for parArthAnumAna.  Let us consider the classic inference example: The mountain is on fire, as smoke is seen. Like the smoky kitchen fire. parvato vahnimAn, dhUmatvAt; mahAnasavat. 

1) pratijnA - a hypothesis that needs to be proved.  In our example, parvato vahnimAn - the mountain is on fire. This is the statement that needs to be proved. The pratijnA consists of two elements - the  sAdhya (the idea to be proved) and the paksha (the locus where it should be proved).
2) hetu - reason. dhUmatvAt - on account of the smoke.
3) driShTAnta - example. yo ya: dhUmavAn sa: vahnimAn. mahAnasavat. Wherever there is smoke, there is fire - like the invariable concomitance observed in instances like the kitchen fire (we are talking of old-school wood-fired kitchens.)
4) upanaya: - application. ayam dhUmavAn - there is smoke on this mountain.
5) nigamanam - conclusion. tasmAt vahnimAn - therefore this mountain must be on fire.

The term vyApti, or invariable concomitance, refers to the conclusion drawn by the seer that wherever the hetu is present, the sAdhya will also be present. This vyApti jnAna is made by the seer when he observes the fire being present along with the smoke in the kitchen. When the same person sees the smoke in the mountain later, he recalls the vyApti and infers the presence of fire, based on his prior knowledge.

According to the naiyyAyika, if a parArthAnumAna consists of these five parts (pancha avayava), it is certain to generate anumiti, inferential understanding, in the hearer.

The mImAmsaka, on the other hand, says that it is sufficient if any three are present (1-3 or 3-5), for anumiti to be generated.

Types of hetvAbhAsa (fallacious reasons)
The naiyyAyika outlines the basis errors in reasoning that are possible in the inferential process. He categorises them into five groups. Whether the defect is present in the hetu, sAdhya, paksha or drishTAnta, the naiyyAyika chooses to call it a hetvAbhAsa, an error in the hetu.

1) vyabhichAra - where the hetu, the reason, is present in the paksha, but the sAdhya, the thing to be proved is absent from the paksha. For example, wherever there is smoke, there is fire. However, the reverse is not true. Where there is fire, there is no necessity for smoke. So if someone wanted to argue that there is smoke in the mountain, because of perceived fire - in this reverse of the classic anumAna, fire is the hetu and smoke is sAdhya. There are several instances where fire (the hetu) is present, but smoke (the sAdhya) is absent. This would be a case of vyabhichAra.
2) asiddhi - the hetu is not present in the paksha. in the parvato vahnimAn dhUmatvAt, if there is no dhUma (smoke), no inference can be drawn. This is an instance of svarUpAsiddhi. There are two other kinds of asiddhis outlined. AshrayAsiddhi, where the paksha itself is absent (the sky lotus is fragrant, like a lotus, is an oft-cited example). vyApyatvAsiddhi, where the hetu is dependent on some extraneous factors. In the inference, the mountain is smoky, because of fire - the hetu, fire, is dependent on wet fuel for smoke to be present. This factor, upon which the hetu is dependent to indicate the sAdhya, is termed (quite confusingly from an advaitin's perspective) as upAdhi. That conditionality is an instance of vyApyatvAsiddhi. If the paksha is not well-known (aprasiddha paksha), that is another instance of vyApyatvAsiddhi.
3) bAdham - if the sAdhya is not present in paksha. For example, if someone tries to argue that fire is cold, that is an instance where coldness (sAdhya) can never be present in the paksha (fire). This is usually established by some other contradicting means of knowledge, like perception etc.
4) viruddham - if the sAdhya and hetu are in contradiction. If the hetu proves the opposite of the sAdhya it is a case of viruddham. For example, if the anumAna is parvato vahnimAn, jalatvAt (the mountain is on fire, because of water being present there), that would be an instance of viruddha.
5) satpratipaksha - if the opponents in a debate give two hetus - one to prove a sAdhya and the other to prove its opposite. If both the hetus are equally strong, then it is an instance of satpratipaksha doSha. One of the two hetus could even be correct, but unless the hearer knows which, no anumiti is generated.

(Originally posted on 27th August, 2017.)