The Naiyayikas solve this problem by having recourse to a special type of perception. They hold that whenever we perceive a particular we also perceive the universal which characterize it, e.g. when we perceive a smoke we perceive smokeness too. For, to perceive a smoke means to perceive something as smoke, which again means to perceive it as characterized by smokeness. They hold also that when a universal e.g., smokeness, is being perceived in any particular, the universal or its cognition functions as an operative relation (sannikarsa) between the relevant sense-organ and all the particulars which exemplify the universal smokeness. This is a non-physical operative relation (alaukika sannikarsa) known as samanyalaksana sannikarsa.14 Thus when our sense-organ is in contact with only one instance of smokeness, we can perceive, in a special way, all the instances of smokeness, albeit not in their particularity, but only as the exemplifiers of the universal smokeness. Therefore, the Naiyayikas argue, when only one instance of smoke is actually present before us, we can have a special type of perception of all smokes and can have the belief that all smokes are pervaded by fire, that is, every instance of smoke is accompanied by fire. The Naiyayikas have also conceded that just as we can form a belief about all smokes being pervaded by fire, when we have that special type of perception of all smokes, one can also have a doubt as to whether or not all smokes are accompanied by fire. This doubt stands in the way of ascertainment of the invariable relation of vyapti (pervasion). So unless this doubt is removed, the belief to the effect that there is a relation of pervasion between smoke and fire, cannot be justified.

The inferer himself may have such doubt or some one else may raise it. In any case, if one’s belief regarding the relation of vyapti in a particular case of inference is shaken or challenged, one has to dispel the doubt that the relation of vyapti may not hold in that case. This can be done with the help of a tarka or an indirect argument. In an indirect argument the denial of the belief under consideration is taken as a supposal and it is shown that the supposal leads to a consequence which is unacceptable. If, for example, one doubts that smoke is pervaded by fire then the indirect argument may be like this: if smoke were not pervaded by fire (that means, if smoke could be found in places where fire was absent) then smoke would not have been caused by fire. This shows that the denial of the accepted causal relation between the fire and the smoke. This is not welcome, so the belief about the relation of pervasion is reinstated.

In some cases, however, a doubt as to whether or not the relation of pervasion holds between a particular hetu and a particular sadhya, may not be entertained at all. In such cases the absence of the doubt is said to be self-evident (svatah siddha), for to entertain such a doubt is to make a practical life impossible. So no one can really entertain such a doubt. For example, no one can doubt whether eating satisfies hunger or can hold the contradictory belief that eating does not satisfy hunger because that would lead to a belief-behaviour contradiction.

Thus either by removing the doubt or a contradictory belief concerning the relation of pervasion, or by showing that no such belief or doubt can be entertained at all, the belief in the relation of pervasion can be justified.15

We may now come back to the question of epistemic progress. From what we have discussed about the relation of pervasion and its ascertainment, it should be clear that the cognition of the relation of pervasion includes the cognition of the relata which, in our example, comprises all the members of the class of smoke and members of the class of fire. So when the inferer has the cognition of the relation of vyapti he already knows the sadhya, viz. fire and hence there seems to be no scope for epistemic progress. As we have seen, the particular instance of fire which is to be inferred is also admitted to be perceived in a special way along with all the members of the class of fire, when we see a particular smoke to be accompanied by a particular fire in a kitchen.

In spite of this, the Naiyayikas would argue, their theory of inference permits epistemic progress. In the inferential cognition or in the conclusion of the inference the inferable property figures as the qualifier of the paksa (the subject of inference). For example, we infer fire in a hill; that means, fire is inferred as existing in a particular hill or as qualifying that particular hill. But while ascertaining the relation of pervasion between smoke and fire, the fire is known only as the pervader (vyapaka) of smoke. So what is inferred in the conclusion was not known before, that is, at the time of ascertaining the relation of vyapti (pervasion), and there is definitely a progress in knowledge for the inferer.

It may be questioned at this point, whether the conclusion was not known to the inferer when he had the cognition III, i.e., paramarsa which was the final causal condition to be followed immediately by the inferential conclusion or anumiti. Such an apprehension arises, because in the cognition called paramarsa, the three elements of inference, namely, the paksa, the sadhya and the hetu are revealed in their mutual relationship. If we take our stock example of the inference of fire from smoke, the paramarsa would reveal the hill (paksa) as characterised by such smoke (hetu) which is pervaded by (vyapya) fire (sadhya). In this cognition, therefore, the fire, which is the sadhya, having been known as the pervader of smoke which characterizes the hill, is implicitly known to characterize the hill. So in the conclusion nothing new is known. The apprehension is that in passage from paramarsa to anumati there is really no epistemic progress, for, when the inferer knows that the hill which he sees, possesses such smoke as is pervaded by fire, he also knows that the hill has fire. To this what can be said first is that since the former (paramarsa) implies the latter (anumiti), it is true that to know the former is to know in a way the latter, but still there is some difference between the two cognitions. In the anumiti (inferential conclusion) the inferable property or sadhya, i.e., the fire qualifies the subject of inference or paksa directly, whereas in the paramarsa, fire qualifies the paksa only indirectly, as the pervader of smoke which qualifies the paksa or the subject of inference directly. For, in the latter cognition the paksa is qualified by the hetu, i.e., smoke, which again is qualified by the relation of pervasion with the sadhya, i.e., fire, and so fire, which is the adjunct of the said relation, figures in this cognition as the qualifier of the qualifier of the paksa. Thus since the two cognitions are different in respect of their content, despite the sadhya forming a part of the content of both the cognitions, it can be claimed that in the passage from paramarsa to anumiti something new is known.

The second way of solving the problem may be this. It may be argued that paramarsa should not be regarded as a premise of the inference, but only as a step through which the conclusion is reached. To explain, for drawing an inference, viz. ‘The hill has fire because it has smoke’, two basic items if information are necessary,16 namely, (1)  that the hetu has the relation of pervasion with the sadhya and (2)  that the hetu is present in the paksa or the subject of inference. So these two may be treated as premises of an anumana or inference. But the actual inferential process includes a few more steps. The first item of information, viz., the information regarding the relation of pervasion is retained in the mind of the inferer in the form of a disposition (samskara). On having the second bit of information the disposition gets revived and gives rise to the recollection (smrti) of the relation. This recollective cognition forms a part of the actual inferential process, so the first item of information reproduced in this way is one of the premises of an anumana. As we have stated earlier, three cognitions, namely, paksadharmatajnana, that is, the cognition that the hetu or inferential mark is present in the paksa or the subject of inference, vyapti-jnana or the recollection of the relation of pervasion holding between the hetu (inferential mark) and the sadhya (the inferable property), and paramarsa, that is, the perception that the paksa is characterised by such a hetu (inferential mark) which is pervaded by the sadhya (inferable property), are the causal conditions which lead to the inferential cognition to the effect that the paksa (subject to inference) is characterised by the sadhya (inferable property). We have also seen that the first cognition leads to the second one, and the second cognition leads to the third, which finally leads to the conclusion. Now, on our proposed solution to the problem epistemic progress, the first two cognitions should be taken as premises but the third cognition which is in a sense a product of the two previous cognitions should be regarded as a step through which the conclusion is reached. Though according to the Nyaya theory, the third cognition, i.e., the paramarsa is not an inference from the other two cognitions, yet a perceptual cognition which connects or synthesizes two previous cognitions and hence, could not have occurred unless these cognitions had occurred. The content of this cognition includes the contents of both of its preceding cognitions. On the Nyaya view, paramarsa is considered as an intermediary operation (vyapara) through which the second cognition, i.e., vyapti-jnana produces the anumiti (conclusion). This shows that it would not be incompatible with the Nyaya position if paramarsa is regarded as a step17 in the inferential process rather than a premise. An acceptance of this interpretation would keep off the charge that the inferer knew the conclusion when he had known the premises and hence there is no epistemic progress. Actually it is through the paramarsa that the implication of the premises is finally drawn.

Therefore, epistemic progress through inference is not excluded by the Nyaya theory of inference.

To conclude, we can say that what has been discussed so far vindicates our claim that the Nyaya theory of inference is well suited to epistemology; the ideal which it recognizes is validity united with truth and it lays down the conditions for attaining this ideal.

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