# Anvaya – Vyatireka In Hindu Logic

In Hindu logic, the invariable vyapti (concomitance) is of three varieties –

1. The anvaya (positive)
2. The vyatireka (negative)
3. Anvaya – Vyatireka (positive – negative or the absence)

The presence or the absence of hetu (the sign) and the Sadhya (signal) denies this vyapti and accordingly, the syllogism also. Invariable presence of smoke indicates the invariable presence of fire. This is an anvaya (positive) vyapti. Invariable absence of fire also denotes the invariable absence of smoke. This is a negative vyapti. It can be expressed as follows:

This mountain has fire. This can be said because there is smoke here; wherever there is smoke, there is fire as for example in the kitchen; therefore the mountain has fire because there is smoke.

This is positive vyapti and also a positive inference.

The negative vyapti in the same example would be – This place is without fire because it is without smoke; wherever there is no fire, there is no smoke, as in a water-body; therefore as this place has no smoke, it has no fire.

So anvaya-vyapti (positive) and vyatireka – vyapti (negative) can be derived from this statement. Negative vyapti is not mere negation of sign or the signal or mere negation of the signal or the sign. The negation of both of them must invariably be connected. In case of smoke and fire, it can be proved with illustration. Therefore, this is a positive-cum-negative invariable concomitance and hence is an example of both types of anumana (inference).

Anvaya means invariable presence and vyatireka means invariable absence. In the present illustration, invariable presence of smoke (sign) with invariable presence of fire (signal) can be proved and so also the absence of both. Therefore, this is called anvaya-vyatireka.