According to Nyaya philosophy, the second source of valid knowledge is inference. Inference is the means to 'anuma' knowledge. It is that knowledge preceding which there is some other knowledge. It is past or indirect and takes place through the medium of some mark which is called the 'hetu' and bears the relation of invariable concomitance with the observe feature. Inference literally means that knowledge which follows some other knowledge. The basis of inference is the relation of invariable concomitance. The invariable relation between the hetu and the 'Sadhya' is called 'Vyapti'. The knowledge of the qualities of the 'paksa' through the hetu is called paramarsa. Hence inference or anumana is said to be knowledge of the presence of the Sadhya in the paksa through the linga, which is in the quality of paksa and is invariably related by vyapti. For example, there is fire on the hill because there is smoke on the hill and where there is smoke there is fire. Hence there is the relation of vyapti or invariable concomitances between smoke and fire. For this reason the presence of fire on the hill is inferred from the presence of smoke on the hill because of vyapti, fire is invariably present where there is smoke.
Constituents of Inference:
In an inference there are three terms and at least three sentences. These three constituents of inference are respectively called paksa, hetu and linga. These are similar to the three items. Minor, Major and middle of the syllogism of Western Logic. paksa is that part of the inference about which there is inference. Sadhya denotes that which is proved of the paksa. Hetu establishes that there is relation between the Sadhya and the paksa. For this reason hetu is also known as the means. To illustrate by means of example, in the above inference of fire on the hill, smoke is the means of inference. It is the linga or hetu or sign the observation of which leads to the inference of the fire. This inference is based upon the invariable relation between fire and smoke. In this way the inference of fire from smoke has three parts- (1) There is smoke on the hill. (2) There is Vyapti or invariable concomitance between smoke and fire (of which we are already aware) and (3) There is fire on the hill. here the hill is the paksa because it is in relation to it that the inference is being made, fire is the sadhya because it is fire which is being proved of the paksa (Hill), and smoke is the linga. In this way, from the stand point of thought process, first of all in this inference is knowledge of paksa and sadhya and finally the decision about the relation of the sadhya with the paksa. But this same inference will be stated in the following manner-
There is fire on the hillside.
Because there is smoke on the hill side.
Where there is smoke there is fire as in the stove.
Comparison with the Western Syllogism:
In this, the first step is to establish a relation between the minor paksa and the major sadhya, the second is to describe the middle hetu and the final step is to give example to show the invariable relation of the sadhya with the hetu. This order of inference in Indian logic differs from the western syllogism only in respect of the order of Judgments, which are the same in both cases. All three Judgments of the foregoing example are similar to the conclusion. Minor premise and Major premise of the syllogism respectively. In the syllogism the order is the following -Major premise, minor premise and the conclusion. In this way, the order of the syllogism is the opposite o f the order of the anumana. In the syllogism, the major premise is stated first but in anumana it is stated last. All three sentences of anumana are categorical and can be either affirmative or negative.
Inference for self and other:
Inference has been divided into two kinds according to the purpose for which it is meant (1) Svarth or for self, and (2) parartha or for others. In the former distinction, the inference is intended for oneself while in the latter it is for conveying knowledge to others. In the former there is no necessity of presenting the statements in an orderly fashion but when it is a case of making another person understand it is necessary that the correct order of the sentences be adhered to. According to the Nyaya philosophers, inference for other consists of five constituents. An example of the five constituents of inference follows:
Pratijna - There is fire on the hill.
Hetu - Because (on the hill) there is smoke.
Drstanta - Where there is smoke there is fire, as in the stove.
Upanaya - There is smoke on this hill.
Nigamana - Hence, there is fire on this hill.
Hetu shows the reason for the pratijna. Drstanta is a complete comprehensive sentence which, along with an example, shows the invariable relation between sadhya and hetu. Upanaya shows that the drstanta sentence applies to this particular instance. Nigamana is that which results from its preceding sentences. In this inference the linga is observed thrice. the first time smoke is observed in the stove, second time in the hill and a third time when it is seen in relation to fire. This inference which has five constituents has been called 'paramanyaya' by Gautama because it includes four pramanas. In Gautama's ancient logic inference has been divided into three kinds on the basis of the distinctions of vyapti into its kinds -Purvavat, sesavat and Samanyatodrsta. Of these the first two are based upon the causal relationship while the last is not on this basis.
'Purva' mans first or preceding of the cause while 'vat' means like. In this way purvavat inference is that which is like the previous, or in other words, one in which the effect is inferred from the cause. In this manner, in purvavat inference, the future effect is anticipated on the basis of the present cause. It is purvavat inference on perceiving the clouds in the sky when it is said that it will rain. In purvavat inference there is a cause-effect relationship between the sadhana and sadhya.
Sesa' means effect. In this way, inference of the cause from its effect is sesavat inference. Contrary to purvavat inference, here the causal relationship is between sadhya and sadhana in the vyapti. In this, the previous or past cause is inferred from the present effect. To infer that it must have rained somewhere by observing an increase in the water in the river, its speed or its muddiness is to employee the sesavat form of inference. It is also sesavat inference, when on examining one part of the whole it is deduced that the remaining must also possess the same qualities. Thus it is sesavat inference when form tasting a beaker full of sea water it is inferred that the water in the rest of the sea must also be saline Commentators upon the classics have interpreted seavat inference in a different way also. When the possible are nullified and there is no possible material form left, then water remains is called 'sesa'. Any inference through the medium of this 'sesa' is called sesavat inference. For example, being a Characteristic quality, sound is not in time, space or mind. It cannot be the special quality of earth, water, fire, air or soul; because it is heard by the ears. That which is left is the sky. There is no nineth form of matter or 'padarth'. Hence according to sesavat inference it is proved that sound is the quality of the sky.
That inference which provides knowledge of any imperceptible or unperceived object is called samanyatodrsta, such as the reference of motion in the sun by observing it in the East in the morning and in the west in the evening. This inference is not based upon the relation of causality but is based on the fact that there is motion in the sun. It is inferred from the change of position because when other objects change their position, motion is always apparent. Hence samanyatodrsta resembles comparison to some extent.
Inference has been further divided into three by the neo Nyaya school, on the basis of the method of establishin vyapti or the relation of invariable concomitance- Kevalanvayi, Kevalavyatireki and anvayavyatireki.
This applies to the case where the means and objects are always found going together, meaning thereby that case in which the vyapti is established by an agreement in presence between the middle term and the major term, and in which there is no exception. For example:
All knowledge objects are nameable
The pot is a knowable object.
therefore, the pot is nameable.
Or that which can be known must also have a name. the pot can be known, hence it must also have a name.
In the first sentence of this reference there is the relation of vyapti between the subject and the object.
Where the inference proceeds not from the agreement in presence of the middle and the major term but from the vyapti between the absence of the major term and the absence of the middle term, it is called Kevala-vyatrireki inference. An example of the type of inference would be-
That which is not different from other elements. In this inference the first sentence establishes a relation between the absence of the major term and the middle term and the relation established is one of invariable concomitance. It is not possible to discover the characteristic 'smell' in any place other than 'earth'. For this reason it is not possible to establish a relation of agreement in presence between the major and the middle term. in this way, inference has here been made on the basis of absence through the medium of invariable concomitance.
When the relation between the major and middle term is based on both agreement in presence and absence, the reference is anyaya vyatireki. The following is an example of -
where there is smoke there is fire.
There is smoke on the hill.
Hence there is fire on the hill.
Where there is no fire there is no smoke.
Therefore there is fire on the hill.