The second type of inference known as parârthânumâna agrees with svârthânumâna in all essential characteristics; the main difference between the two is this, that in the case of parârthânumâna, the inferential process has to be put verbally in premisses.
Pandit Ratnâkarasânti, probably of the ninth or the tenth century
A.D., wrote a paper named Antarvyâptisamarthana in which
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[Footnote 1: na hi yo yatra svabhâvena na pratibaddha@h sa tam apratibaddhavi@sayamavs'yameva na vyabhicaratîti nâsti tayoravyabhicâraniyama. Nyâyabindu@tîkâ, p. 29.]
[Footnote 2: The inseparable connection determining inference is only possible when the li@nga satisfies the three following conditions, viz. (1) pak@sasattva (existence of the li@nga in the pak@sa—the thing about which something is inferred); (2) sapak@sasattva (existence of the li@nga in those cases where the sâdhya oc probandum existed), and (3) vipak@sâsattva (its non-existence in all those places where the sâdhya did not exist). The Buddhists admitted three propositions in a syllogism, e.g. The hill has fire, because it has smoke, like a kitchen but unlike a lake.]
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he tried to show that the concomitance is not between those cases which possess the li@nga or reason with the cases which possess the sâdhya (probandum) but between that which has the characteristics of the li@nga with that which has the characteristics of the sâdhya (probandum); or in other words the concomitance is not between the places containing the smoke such as kitchen, etc., and the places containing fire but between that which has the characteristic of the li@nga, viz. the smoke, and that which has the characteristic of the sâdhya, viz. the fire. This view of the nature of concomitance is known as inner concomitance (antarvyâpti), whereas the former, viz. the concomitance between the thing possessing li@nga and that possessing sâdhya, is known as outer concomitance (bahirvyâpti) and generally accepted by the Nyâya school of thought. This antarvyâpti doctrine of concomitance is indeed a later Buddhist doctrine.
It may not be out of place here to remark that evidences of some form of Buddhist logic probably go back at least as early as the Kathâvatthu (200 B.C.). Thus Aung on the evidence of the Yamaka points out that Buddhist logic at the time of As'oka "was conversant with the distribution of terms" and the process of conversion. He further points out that the logical premisses such as the udâhara@na (Yo yo aggimâ so so dhûmavâ—whatever is fiery is smoky), the upanayana (ayam pabbato dhûmavâ—this hill is smoky) and the niggama (tasmâdayam aggimâ—therefore that is fiery) were also known. (Aung further sums up the method of the arguments which are found in the Kathâvatthu as follows:
"Adherent. Is A B? (@thâpanâ).
Opponent. Yes.
Adherent. Is C D? (pâpanâ).
Opponent. No.