S'abara says that when a certain fixed or permanent relation has been known to exist between two things, we can have the idea of one thing when the other one is perceived, and this kind of knowledge is called inference. Kumarila on the basis of this tries to show that inference is only possible when we notice that in a large number of cases two things (e.g. smoke and fire) subsist together in a third thing (e.g. kitchen, etc.) in some independent relation, i.e. when their coexistence does not depend upon any other eliminable condition or factor. It is also necessary that the two things (smoke and fire) coexisting in a third thing should be so experienced that all cases of the existence of one thing should also be cases involving the existence of the other, but the cases of the existence of one thing (e.g. fire), though including all the cases of the existence of the other (smoke), may have yet a more extensive sphere where the latter (smoke) may not exist. When once a permanent relation, whether it be a case of coexistence (as in the case of the contiguity of the constellation of K@rttika with Rohi@ni, where, by the rise of the former the early rise of the latter may be inferred), or a case of identity (as in the relation between a genus and its species), or a case of cause and effect or otherwise between two things and a third thing which had been apprehended in a large number of cases, is perceived, they fuse together in the mind as forming one whole, and as a result of that when the existence of the one (e.g. smoke) in a thing (hill) is noticed, we can infer the existence of the thing (hill) with its counterpart (fire). In all such cases the thing (e.g. fire) which has a sphere extending beyond that in which the other (e.g. smoke) can exist is called _gamya_ or _vyapaka_ and the other (e.g. smoke) _vyapya_ or _gamaka_ and it is only by the presence of gamaka in a thing (e.g. hill, the pak@sa) that the other counterpart the gamya (fire) may be inferred. The general proposition, universal coexistence of the gamaka with the gamya (e.g. wherever there is smoke there is fire) cannot be the cause of inference, for it is itself a case of inference. Inference involves the memory of a permanent relation subsisting between two things (e.g. smoke and fire) in a third thing (e g. kitchen); but the third thing is remembered only in a general way that the coexisting things must have a place where they are found associated. It is by virtue of such a memory that the direct perception of a basis (e.g. hill) with the gamaka thing (e.g. smoke) in it would naturally bring to my mind that the same basis (hill) must contain the gamya (i.e. fire) also. Every case of inference thus proceeds directly from a perception and not from any universal general proposition. Kumarila holds that the inference gives us the minor as associated with the major and not of the major alone, i.e. of the fiery mountain and not of fire. Thus inference gives us a new knowledge, for though it was known in a general way that the possessor of smoke is the possessor of fire, yet the case of the mountain was not anticipated and the inference of the fiery mountain is thus a distinctly new knowledge (_des'akaladhikyadyuktamag@rhitagrahitvam anumanasya, Nyayaratnakara_, p. 363) [Footnote ref 543]. It should also be noted that in forming the notion of the permanent relation between two things, a third thing in which these two subsist is always remembered and for the conception of this permanent relation it is enough that in the large number of cases where the concomitance was noted there was no knowledge of any case where the concomitance failed, and it is not indispensable that the negative instances in which the absence of the gamya or vyapaka was marked by anabsence of the gamaka or vyapya, should also be noted, for a knowledge of such a negative relation is not indispensable for the forming of the notion of the permanent relation [Footnote ref 544]. The experience of a large number of particular cases in which any two things were found to coexist together in another thing in some relation associated with the non-perception of any case of failure creates an expectancy in us of inferring the presence of the gamya in that thing in which the gamaka is perceived to exist in exactly the same relation [Footnote ref 545]. In those cases where the circle of the existence of the gamya coincides with the circle of the existence of the gamaka, each of them becomes a gamaka for the other. It is clear that this form of inference not only includes all cases of cause and effect, of genus and species but also all cases of coexistence as well.
The question arises that if no inference is possible without a memory of the permanent relation, is not the self-validity of inference destroyed on that account, for memory is not regarded as self-valid. To this Kumarila's answer is that memory is not invalid, but it has not the status of pramana, as it does not bring to us a new knowledge. But inference involves the acquirement of a new knowledge in this, that though the coexistence of two things in another was known in a number of cases, yet in the present case a new case of the existence of the gamya in a thing is known from the perception of the existence of the gamaka and this knowledge is gained by a means which is not perception, for it is only the gamaka that is seen and not the gamya. If the gamya is also seen it is no inference at all.
As regards the number of propositions necessary for the explicit statement of the process of inference for convincing others (_pararthanumana_) both Kumarila and Prabhakara hold that three premisses are quite sufficient for inference. Thus the first three premisses pratijna, hetu and d@rstanta may quite serve the purpose of an anumana.
There are two kinds of anumana according to Kumarila viz. pratyak@satod@rstasambandha and samanyatod@r@s@tasambandha. The former is that kind of inference where the permanentrelation between two concrete things, as in the case of smoke and fire, has been noticed. The latter is that kind of inference where the permanent relation is observed not between two concrete things but between two general notions, as in the case of movement and change of place, e.g. the perceived cases where there is change of place there is also motion involved with it; so from the change of place of the sun its motion is inferred and it is held that this general notion is directly perceived like all universals [Footnote ref 546].
Prabhakara recognizes the need of forming the notion of the permanent relation, but he does not lay any stress on the fact that this permanent relation between two things (fire and smoke) is taken in connection with a third thing in which they both subsist. He says that the notion of the permanent relation between two things is the main point, whereas in all other associations of time and place the things in which these two subsist together are taken only as adjuncts to qualify the two things (e.g. fire and smoke). It is also necessary to recognize the fact that though the concomitance of smoke in fire is only conditional, the concomitance of the fire in smoke is unconditional and absolute [Footnote ref 547]. When such a conviction is firmly rooted in the mind that the concept of the presence of smoke involves the concept of the presence of fire, the inference of fire is made as soon as any smoke is seen. Prabhakara counts separately the fallacies of the minor (_pak@sabhasa_), of the enunciation (_pratijnabhasa_) and of the example (_d@r@s@tantabhasa_) along with the fallacies of the middle and this seems to indicate that the Mima@msa logic was not altogether free from Buddhist influence. The cognition of smoke includes within itself the cognition of fire also, and thus there would be nothing left unknown to be cognized by the inferential cognition. But this objection has little force with Prabhakara, for he does not admit that a prama@na should necessarily bring us any new knowledge, for prama@na is simply defined as "apprehension." So though the inferential cognition always pertains to things already known it is yet regarded by him as a prama@na, since it is in any case no doubt an apprehension.