From the definition of inference it will appear that an inference must have as its constituent’s three terms and at least three propositions.
In inference we arrive at the knowledge of some character of a thing through the knowledge of some mark and that of its universal relation to the inferred character.
Thus in the above inference of fire we know the unperceived fire in the hill through the perception of smoke in it and the knowledge of an invariable relation between smoke and fire.
There is, first, the knowledge or apprehension of smoke as a mark in the hill. Secondly, there is a recollection of the relation of invariable concomitance between smoke and fire, as we have observed it in the past. Thirdly, we have the resulting knowledge of the existence of the unperceived fire in the hill.
Now in this inference the hill is the paksa (minor term), since it is the subject under consideration in the course of the inferential reasoning.
Fire is the sadhya (major term), as that is something which we want to prove or establish in relation to the hill by means of this inference.
Smoke is the liiiga (middle term), as it is the mark or sign which indicates the presence of fire. It is also called the hetu or sadhana, i.e. the reason or ground of inference.
Thus corresponding to the minor, major and middle terms of the syllogism, inference, in Indian logic, contains three terms, namely, paksa, sadhya, and hetu. The paksa is the subject with which we are concerned in any inference.
The sadhya is the object which we want to know in relation to the paksa or the inferable character of the paksa. The hetu is the reason for our relating the sadhya to the paksa. It is the ground of our knowledge of the sadhya as related to the paksa.
In order of the events which take place when a certain thinker is inferring; the first step in inference is the apprehension of the hetu (smoke) in the paksa (hill), the second, recollection of the universal relation between hetu and sadhya (smoke and fire), and the last is the cognition of the sadhya (fire) as related to the paksa (hill).
But as a matter of a formal statement or verbal expression, the first step in inference is the predication of the sadhya with regard to the paksa, e.g., ‘The hill is fiery.’ The second is the affirmation of the hetu as related to the paksa, e.g., ‘Because the hill is smoky.’
The third is the affirmation of the hetu as invariably related to the sadhya, e.g., ‘Wherever there is smoke, there is fire, as in the kitchen.’ Thus in inference we must have at least three propositions, all of which are categorical and one must be affirmative and the others may be affirmative or negative.
The first proposition corresponds to the conclusion of the syllogism, the second to the minor premise, and the third to the major premise. Thus inference, in Indian logic, may be said to be a syllogism consisting of three categorical propositions.
But the order of the propositions is reversed in Indian logic, insofar as it puts the conclusion of the syllogism first, and its usual major premise last, in the formal statement of an inference.
Indian logicians are agreed that so far as inference is swarthy or for oneself, it requires no formal statement by way of a number of propositions. It is only in the case of inference which is Parartha, i.e., meant to prove or demonstrate some truths, that require stating an inference in the form of a rigorous chain of argument without any gap.
This is the logical form of an inference. We may say that in Indian logic inference corresponds roughly, in respect of its form, to the categorical syllogism of Western logic.
But there are certain important differences between the Indian and Western forms of the syllogism.
In Western logic, the syllogism is generally stated in the form of three propositions, of which the first is the major premise, the second is the minor premise, and the last is the conclusion.
According to the Naiyayikas, however, inference, as a conclusive proof, must be stated in the form of five propositions, called its avayavas or members. These are pratijna, hetu, udaharana, upanaya, and nigamana. The five-membered syllogism may be thus illustrated:
1. Ram is mortal (pratijna);
2. Because he is a man (hetu);
3. All men are mortal, e.g., Socrates, Kant, Hegel (udaharana);
4. Ram also is a man (upanaya);
5. Therefore he is mortal (nigamana).
The pratijna is the first proposition, which asserts something. The hetu is the second proposition, which states the reason for this assertion.
The udaharana is the universal proposition, showing the connection between the reason and the asserted fact, as supported by known instances.
Upanaya is the application of the universal proposition to the present case. Nigamana is the conclusion which follows from the preceding propositions.