In Hindu logic, the invariable vyapti (concomitance) is of three varieties –
- The anvaya (positive)
- The vyatireka (negative)
- 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.