Inference (_anumana_) is the second means of proof (prama@na) and the most valuable contribution that Nyaya has made has been on this subject. It consists in making an assertion about a thing on the strength of the mark or linga which is associated with it, as when finding smoke rising from a hill we remember that since smoke cannot be without fire, there must also be fire in yonder hill. In an example like this smoke is technically called linga, or hetu. That about which the assertion has been made (the hill in this example) is called pak@sa, and the term "fire" is called sadhya. To make a correct inference it is necessary that the hetu or linga must be present in the pak@sa,and in all other known objects similar to the pak@sa in having the sadhya in it (sapak@sa-satta), i.e., which are known to possess the sadhya (possessing fire in the present example). The linga must not be present in any such object as does not possess the sadhya (_vipak@sa-vyav@rtti_ absent from vipak@sa or that which does not possess the sadhya). The inferred assertion should not be such that it is invalidated by direct perception {_pratyak@sa_) or the testimony of the s'astra (_abadhita-vi@sayatva_). The linga should not be such that by it an inference in the opposite way could also be possible (_asat-pratipak@sa_). The violation of any one of these conditions would spoil the certitude of the hetu as determining the inference, and thus would only make the hetu fallacious, or what is technically called hetvabhasa or seeming hetu by which no correct inference could be made. Thus the inference that sound is eternal because it is visible is fallacious, for visibility is a quality which sound (here the pak@sa) does not possess [Footnote ref 512]. This hetvabhasa is technically called _asiddha-hetu_. Again, hetvabhasa of the second type, technically called _viruddha-hetu_, may be exemplified in the case that sound is eternal, since it is created; the hetu "being created" is present in the opposite of sadhya {_vipak@sa_), namely non-eternality, for we know that non-eternality is a quality which belongs to all created things. A fallacy of the third type, technically called _anaikantika-hetu_, is found in the case that sound is eternal, since it is an object of knowledge. Now "being an object of knowledge" (_prameyatva_) is here the hetu, but it is present in things eternal (i.e. things possessing sadhya), as well as in things that are not eternal (i.e. which do not possess the sadhya), and therefore the concomitance of the hetu with the sadhya is not absolute (_anaikantika_). A fallacy of the fourth type, technically called _kalatyayapadi@s@ta_, may be found in the example--fire is not hot, since it is created like a jug, etc. Here pratyak@sa shows that fire is hot, and hence the hetu is fallacious. The fifth fallacy, called _prakara@nasama_, is to be found in cases where opposite hetus are available at the same time for opposite conclusions, e.g. sound like a jug is non-eternal,since no eternal qualities are found in it, and sound like akas'a is eternal, since no non-eternal qualities are found in it.
The Buddhists held in answer to the objections raised against inference by the Carvakas, that inferential arguments are valid, because they are arguments on the principle of the uniformity of nature in two relations, viz. _tadatmya_ (essential identity) and _tadutpatti_ (succession in a relation of cause and effect). Tadatmya is a relation of genus and species and not of causation; thus we know that all pines are trees, and infer that this is a tree since it is a pine; tree and pine are related to each other as genus and species, and the co-inherence of the generic qualities of a tree with the specific characters of a pine tree may be viewed as a relation of essential identity (_tadatmya_). The relation of tadutpatti is that of uniformity of succession of cause and effect, e.g. of smoke to fire.
Nyaya holds that inference is made because of the invariable association (_niyama_) of the li@nga or hetu (the concomitance of which with the sadhya has been safeguarded by the five conditions noted above) with the sadhya, and not because of such specific relations as tadatmya or tadutpatti. If it is held that the inference that it is a tree because it is a pine is due to the essential identity of tree and pine, then the opposite argument that it is a pine because it is a tree ought to be valid as well; for if it were a case of identity it ought to be the same both ways. If in answer to this it is said that the characteristics of a pine are associated with those of a tree and not those of a tree with those of a pine, then certainly the argument is not due to essential identity, but to the invariable association of the li@nga (mark) with the li@ngin (the possessor of li@nga), otherwise called niyama. The argument from tadutpatti (association as cause and effect) is also really due to invariable association, for it explains the case of the inference of the type of cause and effect as well as of other types of inference, where the association as cause and effect is not available (e.g. from sunset the rise of stars is inferred). Thus it is that the invariable concomitance of the li@nga with the li@ngin, as safeguarded by the conditions noted above, is what leads us to make a valid inference [Footnote ref 513].
We perceived in many cases that a li@nga (e.g. smoke) was associated with a li@ngin (fire), and had thence formed the notionthat wherever there was smoke there was fire. Now when we perceived that there was smoke in yonder hill, we remembered the concomitance (_vyapti_) of smoke and fire which we had observed before, and then since there was smoke in the hill, which was known to us to be inseparably connected with fire, we concluded that there was fire in the hill. The discovery of the li@nga (smoke) in the hill as associated with the memory of its concomitance with fire (_t@rtiya-li@nga-paramars'a) is thus the cause (_anumitikara@na_ or _anumana_) of the inference (_anumiti_). The concomitance of smoke with fire is technically called _vyapti._ When this refers to the concomitance of cases containing smoke with those having fire, it is called _bahirvyapti_; and when it refers to the conviction of the concomitance of smoke with fire, without any relation to the circumstances under which the concomitance was observed, it is called _antarvyapti._ The Buddhists since they did not admit the notions of generality, etc. preferred antarvyapti view of concomitance to bahirvyapti as a means of inference [Footnote ref 514].
Now the question arises that since the validity of an inference will depend mainly on the validity of the concomitance of sign (_hetu_) with the signate (_sadhya_), how are we to assure ourselves in each case that the process of ascertaining the concomitance (_vyaptigraha_) had been correct, and the observation of concomitance had been valid. The Mima@msa school held, as we shall see in the next chapter, that if we had no knowledge of any such case in which there was smoke but no fire, and if in all the cases I knew I had perceived that wherever there was smoke there was fire, I could enunciate the concomitance of smoke with fire. But Nyaya holds that it is not enough that in all cases where there is smoke there should be fire, but it is necessary that in all those cases where there is no fire there should not be any smoke, i.e. not only every case of the existence of smoke should be a case of the existence of fire, but every case of absence of fire should be a case of absence of smoke. The former is technically called _anvayavyapti_ and the latter _vyatirekavyapti._ But even this is not enough. Thus there may have been an ass sitting, in a hundred cases where I had seen smoke, and there might have been a hundred cases where there was neither ass nor smoke, but it cannot be asserted from it that there is any relation of concomitance,or of cause and effect between the ass and the smoke. It may be that one might never have observed smoke without an antecedent ass, or an ass without the smoke following it, but even that is not enough. If it were such that we had so experienced in a very large number of cases that the introduction of the ass produced the smoke, and that even when all the antecedents remained the same, the disappearance of the ass was immediately followed by the disappearance of smoke (_yasmin sati bhavanam yato vina na bhavanam iti bhuyodars'ana@m, Nyayamanjari,_ p. 122), then only could we say that there was any relation of concomitance (_vyapti_} between the ass and the smoke [Footnote ref 515]. But of course it might be that what we concluded to be the hetu by the above observations of anvaya-vyatireka might not be a real hetu, and there might be some other condition (_upadhi_) associated with the hetu which was the real hetu. Thus we know that fire in green wood (_ardrendhana_) produced smoke, but one might doubt that it was not the fire in the green wood that produced smoke, but there was some hidden demon who did it. But there would be no end of such doubts, and if we indulged in them, all our work endeavour and practical activities would have to be dispensed with (_vyaghata_). Thus such doubts as lead us to the suspension of all work should not disturb or unsettle the notion of vyapti or concomitance at which we had arrived by careful observation and consideration [Footnote ref 516]. The Buddhists and the naiyayikas generally agreed as to the method of forming the notion of concomitance or vyapti (_vyaptigraha_), but the former tried to assert that the validity of such a concomitance always depended on a relation of cause and effect or of identity of essence, whereas Nyaya held that neither the relations of cause and effect, nor that of essential identity of genus and species, exhausted the field of inference, and there was quite a number of other types of inference which could not be brought under either of them (e.g. the rise of the moon and the tide of the ocean). A natural fixed order that certain things happening other things would happen could certainly exist, even without the supposition of an identity of essence.
But sometimes it happens that different kinds of causes often have the same kind of effect, and in such cases it is difficult toinfer the particular cause from the effect. Nyaya holds however that though different causes are often found to produce the same effect, yet there must be some difference between one effect and another. If each effect is taken by itself with its other attendant circumstances and peculiarities, it will be found that it may then be possible to distinguish it from similar other effects. Thus a flood in the street may be due either to a heavy downpour of rain immediately before, or to the rise in the water of the river close by, but if observed carefully the flooding of the street due to rain will be found to have such special traits that it could be distinguished from a similar flooding due to the rise of water in the river. Thus from the flooding of the street of a special type, as demonstrated by its other attendant circumstances, the special manner in which the water flows by small rivulets or in sheets, will enable us to infer that the flood was due to rains and not to the rise of water in the river. Thus we see that Nyaya relied on empirical induction based on uniform and uninterrupted agreement in nature, whereas the Buddhists assumed _a priori_ principles of causality or identity of essence. It may not be out of place here to mention that in later Nyaya works great emphasis is laid on the necessity of getting ourselves assured that there was no such upadhi (condition) associated with the hetu on account of which the concomitance happened, but that the hetu was unconditionally associated with the sadhya in a relation of inseparable concomitance. Thus all fire does not produce smoke; fire must be associated with green wood in order to produce smoke. Green wood is thus the necessary condition (_upadhi_) without which, no smoke could be produced. It is on account of this condition that fire is associated with smoke; and so we cannot say that there is smoke because there is fire. But in the concomitance of smoke with fire there is no condition, and so in every case of smoke there is fire. In order to be assured of the validity of vyapti, it is necessary that we must be assured that there should be nothing associated with the hetu which conditioned the concomitance, and this must be settled by wide experience (_bhuyodars'ana_).
Pras'astapada in defining inference as the "knowledge of that (e.g. fire) associated with the reason (e.g. smoke) by the sight of the reason" described a valid reason (_li@nga_) as that which is connected with the object of inference (_anumeya_) and which exists wherever the object of inference exists and is absent in all cases where it does not exist. This is indeed the same as the Nyaya qualifications of _pak@sasattva, sapak@sasattva and _vipak@sasattva_ of a valid reason (hetu). Pras'astapada further quotes a verse to say that this is the same as what Kas'yapa (believed to be the family name of Ka@nada) said. Ka@nada says that we can infer a cause from the effect, the effect from the cause, or we can infer one thing by another when they are mutually connected, or in opposition or in a relation of inherence (IX. ii. 1 and III. i. 9). We can infer by a reason because it is duly associated (_prasiddhipurvakatva_) with the object of inference. What this association was according to Ka@nada can also be understood for he tells us (III. i. 15) that where there is no proper association, the reason (hetu) is either non-existent in the object to be inferred or it has no concomitance with it (_aprasiddha_) or it has a doubtful existence _sandigdha_). Thus if I say this ass is a horse because it has horns it is fallacious, for neither the horse nor the ass has horns. Again if I say it is a cow because it has horns, it is fallacious, for there is no concomitance between horns and a cow, and though a cow may have a horn, all that have horns are not cows. The first fallacy is a combination of pak@sasattva and sapak@sasattva, for not only the present pak@sa (the ass) had no horns, but no horses had any horns, and the second is a case of vipak@sasattva, for those which are not cows (e.g. buffaloes) have also horns. Thus, it seems that when Pras'astapada says that he is giving us the view of Ka@nada he is faithful to it. Pras'astapada says that wherever there is smoke there is fire, if there is no fire there is no smoke. When one knows this concomitance and unerringly perceives the smoke, he remembers the concomitance and feels certain that there is fire. But with regard to Ka@nada's enumeration of types of inference such as "a cause is inferred from its effect, or an effect from the cause," etc., Pras'astapada holds that these are not the only types of inference, but are only some examples for showing the general nature of inference. Inference merely shows a connection such that from this that can be inferred. He then divides inference into two classes, d@r@s@ta (from the experienced characteristics of one member of a class to another member of the same class), and samanyato d@r@s@ta. D@r@s@ta (perceived resemblance) is that where the previously known case and the inferred case is exactly of the same class. Thus as an example of it we can point out that by perceiving that only a cow has a hanging mass of flesh on its neck (_sasna_), I can whenever I see the same hanging mass of flesh at the neck of an animal infer that it is a cow. But when on the strength of a common quality the inference is extended to a different class of objects, it is called samanyato d@r@s@ta. Thus on perceiving that the work of the peasants is rewarded with a good harvest I may infer that the work of the priests, namely the performance of sacrifices, will also be rewarded with the objects for which they are performed (i.e. the attainment of heaven). When the conclusion, to which one has arrived (_svanis'citartha_) is expressed in five premisses for convincing others who are either in doubt, or in error or are simply ignorant, then the inference is called pararthanumana. We know that the distinction of svarthanumana (inference for oneself) and pararthanumana (inference for others) was made by the Jains and Buddhists. Pras'astapada does not make a sharp distinction of two classes of inference, but he seems to mean that what one infers, it can be conveyed to others by means of five premisses in which case it is called pararthanumana. But this need not be considered as an entirely new innovation of Pras'astapada, for in IX. 2, Ka@nada himself definitely alludes to this distinction (_asyeda@m karyyakara@nasambandhas'cavayavadbhavati_). The five premisses which are called in Nyaya _pratijna, hetu d@r@s@tanta, upanaya,_ and _nigamana_ are called in Vais'e@sika _pratijna, apades'a, nidars'ana, anusandhana_, and _pratyamnaya_. Ka@nada however does not mention the name of any of these premisses excepting the second "apades'a." Pratijna is of course the same as we have in Nyaya, and the term nidars'ana is very similar to Nyaya d@r@s@tanta, but the last two are entirely different. Nidars'ana may be of two kinds, (1) agreement in presence (e.g. that which has motion is a substance as is seen in the case of an arrow), (2) agreement in absence (e.g. what is not a substance has no motion as is seen in the case of the universal being [Footnote ref 517]). He also points out cases of the fallacy of the example (_nidars'anabhasa_). Pras'astapada's contribution thus seems to consist of the enumeration of the five premisses and the fallacy of the nidars'ana, but the names of the last two premisses are so different from what are current in other systems that it is reasonable to suppose that he collected them from some other traditional Vais'e@sika work which is now lost to us. It however definitely indicates that the study of the problem of inference was being pursued in Vais'e@sika circles independently of Nyaya. There is no reason however to suppose that Pras'astapada borrowed anything from Di@nnaga as Professor Stcherbatsky or Keith supposes, for, as I have shown above, most of Pras'astapada's apparent innovations are all definitely alluded to by Ka@nada himself, and Professor Keith has not discussed this alternative. On the question of the fallacies of nidars'ana, unless it is definitely proved that Di@nnaga preceded Pras'astapada, there is no reason whatever to suppose that the latter borrowed it from the former [Footnote ref 518].
The nature and ascertainment of concomitance is the most important part of inference. Vatsyayana says that an inference can be made by the sight of the li@nga (reason or middle) through the memory of the connection between the middle and the major previously perceived. Udyotakara raises the question whether it is the present perception of the middle or the memory of the connection of the middle with the major that should be regarded as leading to inference. His answer is that both these lead to inference, but that which immediately leads to inference is _li@ngaparamars'a_, i.e. the present perception of the middle in the minor associated with the memory of its connection with the major, for inference does not immediately follow the memory of the connection, but the present perception of the middle associated with the memory of the connection (_sm@rtyanug@rhito li@ngaparamars'o_). But he is silent with regard to the nature of concomitance. Udyotakara's criticisms of Di@nnaga as shown by Vacaspati have no reference to this point The doctrine of _tadatmya_ and _tadutpatti_ was therefore in all probability a new contribution to Buddhist logic by Dharmakirtti. Dharmakirtti's contention was that the root principle of the connection between the middle and the major was that the former was either identical in essence with the latter or its effect and that unless this was grasped a mere collection of positive or negative instances will not give usthe desired connection [Footnote ref 519]. Vacaspati in his refutation of this view says that the cause-effect relation cannot be determined as a separate relation. If causality means invariable immediate antecedence such that there being fire there is smoke and there being no fire there is no smoke, then it cannot be ascertained with perfect satisfaction, for there is no proof that in each case the smoke was caused by fire and not by an invisible demon. Unless it can be ascertained that there was no invisible element associated, it cannot be said that the smoke was immediately preceded by fire and fire alone. Again accepting for the sake of argument that causality can be determined, then also cause is known to precede the effect and therefore the perception of smoke can only lead us to infer the presence of fire at a preceding time and not contemporaneously with it. Moreover there are many cases where inference is possible, but there is no relation of cause and effect or of identity of essence (e.g. the sunrise of this morning by the sunrise of yesterday morning). In the case of identity of essence (_tadatmya_ as in the case of the pine and the tree) also there cannot be any inference, for one thing has to be inferred by another, but if they are identical there cannot be any inference. The nature of concomitance therefore cannot be described in either of these ways. Some things (e.g. smoke) are naturally connected with some other things (e.g. fire) and when such is the case, though we may not know any further about the nature of this connection, we may infer the latter from the former and not vice versa, for fire is connected with smoke only under certain conditions (e.g. green wood). It may be argued that there may always be certain unknown conditions which may vitiate the validity of inference. To this Vacaspati's answer is that if even after observing a large number of cases and careful search such conditions (_upadhi_) cannot be discovered, we have to take it for granted that they do not exist and that there is a natural connection between the middle and the major. The later Buddhists introduced the method of _Pancakara@ni_ in order to determine effectively the causal relation. These five conditions determining the causal relation are (1) neither the cause nor the effect is perceived, (2) the cause is perceived, (3) in immediate succession the effect is perceived, (4) the cause disappears, (5) inimmediate succession the effect disappears. But this method cannot guarantee the infallibility of the determination of cause and effect relation; and if by the assumption of a cause-effect relation no higher degree of certainty is available, it is better to accept a natural relation without limiting it to a cause-effect relation [Footnote ref 520].
In early Nyaya books three kinds of inference are described, namely purvavat, s'e@savat, and samanyato-d@r@s@ta. Purvavat is the inference of effects from causes, e.g. that of impending rain from heavy dark clouds; s'e@savat is the inference of causes from effects, e.g. that of rain from the rise of water in the river; samanyato-d@r@s@ta refers to the inference in all cases other than those of cause and effect, e.g. the inference of the sour taste of the tamarind from its form and colour. _Nyayamanjari_ mentions another form of anumana, namely paris'e@samana (_reductio ad absurdum_), which consists in asserting anything (e.g. consciousness) of any other thing (e.g. atman), because it was already definitely found out that consciousness was not produced in any other part of man. Since consciousness could not belong to anything else, it must belong to soul of necessity. In spite of these variant forms they are all however of one kind, namely that of the inference of the probandum (_sadhya_) by virtue of the unconditional and invariable concomitance of the hetu, called the vyapti-niyama. In the new school of Nyaya (Navya-Nyaya) a formal distinction of three kinds of inference occupies an important place, namely anvayavyatireki, kevalanvayi, and kevalavyatireki. Anvayavyatireki is that inference where the vyapti has been observed by a combination of a large number of instances of agreement in presence and agreement in absence, as in the case of the concomitance of smoke and fire (wherever there is smoke there is fire (_anvaya_), and where there is no fire, there is no smoke (_vyatireka_)). An inference could be for one's own self (_svarthanumana_) or for the sake of convincing others (_pararthanumana_). In the latter case, when it was necessary that an inference should be put explicitly in an unambiguous manner, live propositions (_avayavas_) were regarded as necessary, namely pratijna (e.g. the hill is fiery), hetu (since it has smoke), udahara@na (where there is smoke there is fire, as in the kitchen), upanaya (this hill has smoke), niga@mana (therefore it has gotfire). Kevalanvayi is that type of inference, the vyapti of which could not be based on any negative instance, as in the case "this object has a name, since it is an object of knowledge (_ida@m, vacyam prameyatvat_)." Now no such case is known which is not an object of knowledge; we cannot therefore know of any case where there was no object of knowledge (_prameyatva_) and no name (_vacyatva_); the vyapti here has therefore to be based necessarily on cases of agreement--wherever there is prameyatva or an object of knowledge, there is vacyatva or name. The third form of kevalavyatireki is that where positive instances in agreement cannot be found, such as in the case of the inference that earth differs from other elements in possessing the specific quality of smell, since all that does not differ from other elements is not earth, such as water; here it is evident that there cannot be any positive instance of agreement and the concomitance has to be taken from negative instances. There is only one instance, which is exactly the proposition of our inference--earth differs from other elements, since it has the special qualities of earth. This inference could be of use only in those cases where we had to infer anything by reason of such special traits of it as was possessed by it and it alone.