Vyapti (Invariable Relation)

Vyapti is the invariable concomitance (sahacharya-niyama) between hetu and sadhya: wherever the hetu is, the sadhya is. It is the ground of inference. Navya-Nyaya defines it, among other ways, as "absence of the hetu in the loci of the absence of the sadhya".

• Anvaya-vyapti (positive): wherever there is smoke there is fire.

• Vyatireka-vyapti (negative): where there is no fire there is no smoke.

• Samavyapti (equal extension): hetu and sadhya co-extensive (nameable and knowable).

• Vishamavyapti (unequal extension): hetu is less extensive than sadhya (smoke and fire); the relation is one-way only.

1. Bhuyodarshana: repeated observation of co-presence (anvaya-sahachara).

2. Vyabhichara-agraha: non-observation of any counter-instance (the hetu without the sadhya).

3. Tarka: hypothetical reasoning that removes doubts about possible exceptions ("if smoke were without fire it would be without a cause").

4. Absence of upadhi: no conditioning factor.

5. Samanyalakshana pratyaksha: explains how a universal relation is grasped from a few cases.

A single observation is not enough, and mere repeated observation alone cannot guarantee universality, because a future exception cannot be ruled out by observation alone. That is why tarka and the absence of upadhi are added.

Upadhi is a condition that is pervasive (co-extensive) of the sadhya but not pervasive of the hetu. Example: the inference "the hill has smoke because it has fire" fails because of the upadhi wet fuel (ardrendhana), present wherever smoke is, but not wherever fire is. "Violence is sinful because it is violence" has the upadhi prohibition by scripture (nishiddhatva). An upadhi shows that the vyapti is conditional, not unconditional.