As we have seen before, inference is, in Indian logic, a combined deductive-inductive reasoning consisting of at least three categorical propositions.
All inferences are thus pure syllogisms of the categorical type which are at once formally valid and materially true.
Hence we have not here a classification of inferences into deductive and inductive, immediate and mediate, syllogistic and non-syllogistic, pure and mixed types.
The Naiyayikas give us three different classifications of inferences which we shall now consider.
According to the first classification, inference is of two kinds, namely, svartha and parartha. This is a psychological classification which has in view the use or purpose which an inference serves.
An inference may be intended either for the acquisition of some knowledge on our part or for the demonstration of a known truth to other persons. In the first case, we have svarthanumana inference for oneself.
In the second, we have pararthanumana0r inference meant for others. The first is illustrated by a man first perceives a mass of smoke in the hill, then remembers that there is a universal relation between smoke and fire, and finally infers that there is fire in the hill.
On the other hand, an inference is parartha when in making it a man aims at proving or demonstrating the truth of the conclusion to other men.
This is illustrated 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, and argues like this: ‘The hill must be fiery; because it smokes; and whatever is smoky is fiery e.g. the kitchen: so also the hill is smoky; therefore, it is fiery’.
According to another classification, we have three kinds of inference, namely, purvavat, sesavat and samanyatodrsra.”
This classification has reference to the nature of the vyapti or universal relation between the middle and the major terms. While purvavat and sesavat inferences are based on causal uniformity, the last is based on non-causal uniformity.
A cause is defined as the invariable and unconditional antecedent of an effect. Conversely, an effect is the invariable and unconditional consequent of a cause.
Accordingly, a purvavat inference is that in which we infer the unperceived effect from a perceived cause, e.g. the inference of future rain from the appearance of dark heavy clouds in the sky.
A sesavat inference is that in which we infer the unperceived cause from a perceived effect, e.g. the inference of past rain from the swift muddy current of the river.
In these two kinds of inference, the vyapti or universal relation between the middle and the major terms is a uniform relation of causality between them.
They are thus dependent on what is known ‘scientific induction’. In samanyatodrsta inference, however, the vyapti or universal relation between the middle and the majo terms does not depend on a causal uniformity.
The middle is related to the major neither as a cause nor as an effect. We infer the one from the other not because we know them to be causally connected, but because they are uniformly related in our experience.
This is illustrated when, on seeing the different positions of the moon at long intervals, we infer that it moves, although the motion might not have been perceived by us. In the case of other things, whenever we perceive change of position, we perceive motion also.
From this we infer motion in the moon, although the movement of the planet is not perceived. Similarly, we may infer the cloven hoof of an unknown animal simply by seeing its horns.
These inferences depend not on a causal connection, but on certain observed points of general similarity between different object of experience. Samanyatodrsta inference is thus similar to analogical argument.