In inference, knowledge of vydpti (invariable concomitance) is necessary. It is a ground of inference. Vydpti is the necessary universal relation of inseparability {avinabhava-sambandha) or invariable concomitance (niyata sdhacarya). A thing is said to have the necessary universal relation of inseparability with another thing, if it does never exist without the other thing.1 As for instance, non-existence of smoke in the absence of fire— this type of relation which smoke is having with fire is its necessary universal relation of inseparability with fire. As this vydpti of the form of necessary universal relation of inseparability (i.e., invariable concomitance) subsists in smoke, smoke is called vydpya (vydpya of fire, i.e., pervaded by fire), because smoke is pervaded by fire. And as fire pervades smoke, it is called vydpaka (vydpaka of smoke, i.e., one that pervades smoke). Thus vydptiis the relation of vydpya with its vydpaka. In other words, the characteristic The term avindbhava contains three words: a + vina + bhava. Vina means without (i.e., in the absence of) probandum (sddhya); a and bhdva = abhava means absence of probans (sddhana). Thus complete sense of the term is: non-presence (abhava) of probans in the absence of (vind) probandum. This constitutes the one and only defining characteristic of being pervaded by the pervader (vydpaka), which characterises the vydpya (that which is pervaded) is called vyapti. Vyapti is a relation obtain­ing between two things or terms, of which one is pervaded (vydpya) and the other pervades (vydpaka). A thing is said to pervade another when it always accompanies the other. A thing is said to be pervaded by an­other, when it is always accompanied by the other. In this sense, smoke is pervaded by fire, since it is always accompanied by fire. But fire is not always accompanied by smoke, e.g., the red-hot iron ball. So fire is not pervaded by smoke. As the pervader is proved or established by the pervaded, the pervader is called sddhya (the thing to be proved, probandum, major term) and the pervaded is called sddhana (the thing that proves, probans, middle term) or hetu (logical reason). To know and ascertain vyapti the joint method of agreement in presence (anvaya) and in absence (vyatireka) is very useful. The method of agreement in pres­ence means the invariable presence of probandum in the presence of probans. The probandum is necessarily and invariably present where the probans is present. And the method of agreement in absence means the invariable absence of probans in the absence of probandum. The invari­able presence of fire in the presence of smoke is a case of the method of agreement in presence. And the invariable absence of smoke in the absence of fire is a case of the method of agreement in absence. Thus, as smoke is having both anvaya (relation of agreement in presence) and vyatireka (relation of agreement in absence) with fire, we know and as­certain, on their basis, the invariable concomitance (vyapti) of smoke with fire.

Smoke is pervaded by fire. But fire is not pervaded by smoke. In other words, wherever there is smoke there is fire; there is no exception to it. But it is not that wherever there is fire, there is smoke. That is, where there is fire, there may or may not be smoke. Therefore, we can infer fire from smoke, but can never infer smoke from fire. A vyapti between two things or terms of unequal extension, such as smoke and fire, is called asama-vydpti or visama-vydpti. It is a relation of non-equipollent concomi­tance between two things or terms, from one of which we may infer the other, but not vice versa. We may infer fire from smoke, but not smoke from fire. As distinguished from this, a vyapti between two things or terms of equal extension is called sama-vydpti or equipollent concomitance. Here the vyapti holds between two things or terms which are co-extensive, so that we may infer either of them from the other, e.g., flavour and colour. Wherever there is flavour, there is colour, and vice versa. In shori the vydpaka is generally greater in extent than the vydpya, though no necessarily so; for in some cases where both may be co-extensive, botl are vydpaka and vydpya of each other.

The vydpti (invariable concomitance) is grasped and ascertained b; hypothetical reasoning or cogitation (tarka). As for example, 'Smoke i never present in the absence of fire, wherever there is smoke there is fire there is not a single place where smoke is present but fire is not present'— this type of invariable concomitance of smoke with fire, which is called vydpti can be established or proved by hypothetical reasoning. On seeing two things together in many places or on observing their successive oc­currence in many places, we cannot establish or arrive at their invariable concomitance. But on exploring as to whether there is any logical or practical difficulty in separating the two or in not accepting their invari­able succession, if we certainly find some difficulties—that is, the invari­able concomitance is found without having any exception—, then the invariable concomitance between the two stands established or proved. This method of establishing or arriving at invariable concomitance (xjydpti) is hypothetical reasoning (tarka). The invariable concomitance of smoke with fire is grasped or established by the hypothetical reasoning as fol­lows: 'Wherever there is smoke, there is fire'—this is the statement of vydpti (invariable concomitance). If it is false, then its contradictory, viz., 'There are some places where smoke is present but fire is absent', must be true. This means that there may be smoke without fire. But this supposition is contradicted by the law of universal causation, for to say that there may be smoke without fire is just to say that there may be an effect without a cause. It is so because, fire is the only known cause of smoke. If any one has obstinacy to say that sometimes there may be effects without causes, he must be silenced by reference to the practical contra­dictions involved in his position. If there can be an effect without a cause, why do they who desire smoke seek fire?

Knowledge of invariable concomitance is the ground of inference. For any inference, the minimum condition is the knowledge of vydpti between the middle (sddhana, vydpya, hetu) and the major (sddhya, vydpaka) term. We can infer fire from smoke only when we know that smoke is invariably connected with fire. Without the knowledge of invariable concomitance of smoke with fire, inference of fire from smoke is impossible. So long as one does not have the knowledge of invariable concomitance of smoke with fire, one cannot infer fire from smoke. This is quite obvious. This shows that for inference the knowledge of invariable concomitance is necessary and this knowledge of invariable concomitance one can have through hypothetical reasoning (tarka).

Inference is the knowledge of sddhya (probandum) through the instru­mentality of sddhana (probans). This means that on knowing or perceiv­ing probans and consequently remembering the invariable concomitance of probans with probandum, the cogniser infers probandum. As for instance, when one who has known the universal relation that obtains between smoke and fire, that is, one who has comprehended the invari­able concomitance of smoke with fire, perceives smoke arising from some place, then at once he remembers the invariable concomitance of smoke with fire and consequently infers fire on that place. The emergence of inferential knowledge takes place subject to the fulfilment of two condi­tions, viz., perception or knowledge of probans and memory of the in­variable concomitance of probans with probandum.

Let us study some cases of inference: (1) A particular place has fire on it because it possesses smoke. (2) Word is destructible because it is pro­duced. (3) This is a tree because it is Nimba. (4) The constellation named Rohini will rise because the constellation named Krttika has already risen. (5) The constellation Bharani rose before, because the constellation Krttika is rising. (6) A particular fruit must have a particular colour because it has a particular flavour. Or, it must have a particular flavour because it has a particular colour.

In these cases of inference, the first probans is of the form of effect (kdrya), because smoke is an effect of fire. The second and the third ones are of the form of essential identity of nature {svabhava). The fourth one is the predecessor (purvacara) because Krttika is the predecessor of Rohini. The fifth one is the successor (uttaracara) because Krttika is the successor of Bharani. And the sixth one is co-occurrent or co-extensive (sahacara) because flavour and colour are co-occurrent or co-extensive.

From this we can have the idea of different types of probans. Again, we can see that it is not necessary that probans should be present when probandum is present. Krttika that is rising enables us to infer Rohini that is to rise as also Bharani that rose before. This means that probans and probandum belonging to the same time or different times and to the same place or different places should have invariable relation between them. It is not necessary for the probans to be present at that very time and place at which the probandum is present. The only thing required of it is that it should have invariable concomitance with probandum. The present rise of Krttika works as an instrument of inferring the posterior rise of Rohini and the prior rise of Bharani, because Krttika is having a relation of sequence with Rohini and Bharanl, which is an invariable necessary relation.

That which is contradictory of a particular thing acts as probans causing inferential knowledge of the absence of that thing. From certain facial changes we can infer the absence of the subsidence-of-anger. Here the probans of the form of certain facial changes is contradictory of the subsidence-of-anger or is the result of anger which is contradictory to the subsidence-of-anger. Therefore it acts as probans causing inferential knowledge of the absence of the subsidence-of-anger. From non-cogni­tion of the bodily movements characterising health, we infer the presence of some disease in the body. The fact of our not seeing the bodily move­ments characterising health leads us to infer the lack of health, that is, the presence of some disease in the body. For our present purpose this is enough. We close this topic.

There are two types of inference, viz. svdrthdnumdna (inference in­tended for oneself) and pardrthanumdna (inference intended for others). Without being instructed or taught by others, when one infers probandum from probans independently with his own reasoning, then that inference is called svdrthdnumdna. On the other hand, the inference employed by one to explain to others the truth of the conclusion one has arrived at is called pardrthanumdna. To n.ustrate, when a man, having inferred or known the existence of fire in a hill, tries to convince another man, who doubts or questions the truth of his knowledge, he argues like this: 'The hill must be fiery; because it smokes; and whatever is smoky is necessarily and invariably fiery, e.g. the kitchen; so also the hill is smoky; therefore it is fiery.' The statement generally contains five members. They are: proposition (pratijhd), reason (hetu), example (uddharana), application (upanaya) and conclusion (nigamana). In the above example, they are as follows:

(1) This place is fiery. (This is the statement of proposition or thesis orprobandum).
(2) Because it is seen smoky. (This is the statement of reason or probans).
(3) All smoky things are fiery, e.g. the kitchen. (This is the statement of invariable concomitance, showing the necessary universal connection between probans and probandum, as supported by a known instance).
(4) So also this place is smoky. (This is the statement of application).
(5) Therefore this place is fiery. (This is the statement of conclusion).

In pardrthdnumdna, one is required to follow this procedure.
Probans which does not have the relation of invariable concomitance with probandum is called pseudo-probans (hetvdbhasa). Pseudo-probans can never lead to valid inference.