Essay on a third classification gives us the three kinds of kevalanvayi

Kevalavyatireki and anvayavyatireki inferences this classification is more logical in as much as it is based on the nature of the induction by which we get the knowledge of vyapti, on which inferences depend.

An inference is called kevalanvayi when it is based on a middle term which is only positively related to the major terms.

Hence the knowledge of vyapti between the middle and the major term is arrived at only through the method of agreement in presence (anvaya), since there is no negative instance of their agreement in absence. This is illustrated by the following inference:

All knowable objects are nameable:

The pot is a knowable object;

Therefore the pot is nameable.

According to another interpretation, purvavat inference is that which is based on previous experience of the concomitance between two things sesavat is praises or inference by elimination, e.g. sound is a quality, because it cannot be a substance or an activity or anything else.

In this inference the major premise is a universal affirmative proposition in which the predicate ‘nameable’ is affirmed of all knowable objects.

It is not really possible for us to deny the predicate with regard to the subject and say that here is a knowable object which is not nameable, because we have at least to speak of it as an object.

The minor premise and the conclusion of this inference are also universal affirmative propositions and cannot be otherwise. Hence, in its logical form, this inference is a syllogism of the first mood of the first figure, technically called Barbara.

A kevalavyatireki inference is that in which the middle term is only negatively related to the major term. It depends on a vyapti between the absence of the major term and that of the middle term.

Accordingly, the knowledge of vyapti is here arrived at only through the method of agreement in absence (vyatireka), since there is no positive instance of agreement in presence between the middle and the major terms excepting the minor term. This is illustrated thus by the Naiyayikas:

What is not different from other elements has no smell.

The earth has smell.

Therefore the earth is different-from-other-elements.

In this inference, the major premise is a universal negative proposition in which the predicate of the middle term ‘smell’ is denied of the subject or the negative of the major term ‘different-from-other-elements’.

It is not possible for us to affirm the predicate ‘smell’ of any other subject excepting the earth which is the minor term of the inference.

Hence the only way in which we can relate the middle to the major is the negative way of saying that ‘what is not different from the other elements has no smell.’

Hence the major premise is a universal negative proposition arrived at only through the method of agreement in absence between the major and the middle terms.

The minor premise is an affirmative proposition, but although one of the premises is negative, the conclusion is affirmative, which is against the general canons of the syllogism in Formal Logic.

Hence we are to say that this inference is not any of the valid moods of syllogism recognized by Formal Logic, nor should we forcibly convert the conclusion into a negadve proposition.

But the validity of such an inference has been admitted by Bradley as a special case of negative reasoning.

An inference is called anvayavyatireki when its middle term is both positively and negatively related to the major term. In it there is a vyapti or universal relation between the middle and the major terms in respect of both their presence and absence.

So the knowledge of the vyapti or the universal proposition is based on the Joint Method of agreement in presence (anvaya) and in absence (vyatireka).

The universal proposition is affirmative when it is the result of the observation of positive instances of agreement in presence, and negative when based on the observation of negative instances of agreement in absence, between the middle and the major terms.

The difference between the universal affirmative and negative propositions (anvaya and vyatirekavydpti) is that the subject of the affirmative proposition becomes predicate and the condradictory of the predicate becomes subject in the corresponding negative proposition.

Hence inference may be based on both universal ^rmative and universal negative propositions. It is illustrated ^ln the following pair of inferences:

(2) No non-fiery object is smoky.

The hill is smoky.

Therefore the hill is fiery.

The Fallacies of Inference

The fallacies of inference (hetvabhasa) in Indian logic are all material fallacies. So far as the logical form of inference is concerned, it is the same for all inferences.

There is, strictly speaking, no fallacious form of inference in logic since all inferences must be put in one or other of the valid forms.

Hence if there is any fallacy of inference that must be due to the material conditions on which the truth of the constituent premises depends.

It may be observed here that in the Aristotelian classification of fallacies into those in dictione and those eitra dictionem there is no mention of the formal fallacies of inference like the undistributed middle, the illicit process of the major or minor term, and so forth.

The reason for this, as Faton rightly points out, is that ‘to one trained in the arts of syllogistic reasoning, they are not sufficiently persuasive to find a place even among sham arguments.’

As for Aristotle’s fallacies in dictione, i.e., those that occur through the ambiguous use of words, they are all included by the Naiyayika among the fallacies of chala, jati and nigrahasthana with their numerous subdivisions.

In Indian Logic, a material fallacy is technically called hetvabhasa, a word which literally means a hetu or reason which appears as, but really is not, a valid reason.

The material fallacies being ultimately due to such fallacious reasons, the consider all these as being cases of hetvabhasa. According to the Naiyayikas, there are five kinds of material fallacies. These &

Ml Savyabhicara (2) Viruddha, (3) Satpratipaksa, (4) Asiddha, (5) Badhita.

The first kind of fallacy is called savyabhicara or the irregular middle. To illustrate:

All bipeds are rational.

Swans are bipeds.

Therefore swans are rational.

The conclusion of this inference is false. But why? Because the middle term ‘biped’ is not uniformly related to the major ‘rational.’ It is related to both rational and non-rational creatures. Such a middle term is called savyabhicara or the irregular middle.

The savyabhicara hetu or the irregular middle is found to lead to no one single conclusion, but to different opposite conclusions.

This fallacy occurs when the ostensible middle term violates the general rule of inference, namely, that it must be universally related to the major term, or that the major term must be present in all cases in which the middle is present.

The middle, however, is not uniformly concomitant with the major term. It is related to both the existence and the non-existence of the major term, and is, therefore, also called anaikantika or an inconstant concomitant of the major term.

Hence from such a middle term we can infer both the existence and the non-existence of the major term. To take another illustration:

All knowable objects are fiery.

The hill is knowable.

Therefore the hill is fiery.

Here the middle ‘knowable’ is indifferently related to both fiery objects like the kitchen, and fireless objects like the lake All knowables being thus not fiery, we cannot argue that a hill is fiery because it is knowable. Rather, it is as much true to say that, for the same reason, the hill is fireless.

The second kind of fallacy is called viruddha or the contradictory middle. Take this inference: ‘Air is heavy, because it is empty.’ In this inference the middle term ’empty’ is contradictory because it disproves the heaviness of air.

Thus the viruddha or the contradictory middle is one which disproves the very proposition which it is meant to prove.

This happens when the ostensible middle term, instead of proving the existence of the major, in the minor, which is intended by it, proves its non­existence therein.

Thus to take the Naiyayikas’ illustration, if one argues, ‘Sound is eternal, because it is caused,’ we have a fallacy of the viruddha or contradictory middle.

The middle term, ’caused’ does not prove the eternality of sound, but its non eternality, because whatever is caused is non-eternal.

The distinction between the savyabhicara and the viruddha is that while the former only fails to prove the conclusion, the latter disproves it or proves the contradictory proposition.

The third kind of fallacy is called satpratipaksa or the inferentially contradicted middle. This fallacy arises when the ostensible middle term of an inference is validly contradicted by other middle term which proves the non-existence of the major term of the first inference.

Thus the inference ‘sound is eternal, because it is audible’ is validly contradicted by another inference like this: ‘sound is non-eternal, because it is produced like a pot.

‘Here the non-existence of eternality (which is the major term of the first inference) is proved by the second inference with its middle term ‘produced’ as against the first inference with its middle ‘audible.’

The distinction between the viruddha and the satpratipaksa is that, while in the former the middle itself prove the contradictory of its conclusion, in the latter the contradictor; of the conclusion is proved by another inference based on another middle term.

The fourth kind of fallacy is.called asiddha or sadhyasama, i.e. ^e unproved middle. The sadhyasama middle is one which is not yet proved, but requires to be proved, like the sadhya or the major term.

This means that the sadhyasama middle is not a proved or an established fact, but an asiddha or unproved assumption.

The fallacy of the asiddha occurs when the middle term is wrongly assumed in any of the premises, and so cannot be taken to prove the truth of the conclusion.

Thus when one argues, ‘the sky-lotus is fragrant because it has lotusness in it like a natural lotus,’ the middle has no locus standi, since the sky-lotus is non-existent, and is, therefore, asiddha or a merely assumed but not proved fact.

The last kind of fallacy is called badhita or the non-inferentially contradicted middle. It is the ostensible middle term of an inference, the non-existence of whose major is ascertained by means of some other pramana or source of knowledge.

This is illustrated by the argument: ‘Fire is cold, because it is a substance.’ Here ‘coldness’ is the sadhya or major term, and ‘substance’ is the middle term. Now the non-existence of coldness may mean that the existence of hotness is perceived in fire by our sense of touch.

So we are to reject the middle ‘substance’ as a contradicted middle. The fallacy of satpratipaksa, as explained before, is different from this fallacy of badhita, because in the former one inference is contradicted by another inference.

While in the latter an inference is contradicted by perception or some other non- inferential source of knowledge. Another example of: sugar is sour, because it produces acidity.