Inference

Inference

The second kind of knowledge is anuma or inferential or relational and its means is called anumana or inference. It is defined as that cognition which presupposes some other cognition.

 

It is mediate and indirect and arises through a ‘mark’, the ‘middle term’ (linga or hetu) which is invariably connected with the ‘major term’ (sadhya). It is knowledge (mana) which arises after (anu) other knowledge. Invariable concomitance (vyapti or avinabhavaniyama) is the nerve of inference. The presence of the middle term in the minor term is called paksadharmata. The invariable association of the middle term with the major term is called vyapti. The knowledge of paksadharmata as qualified by vyapti is called paramarsha. And inference is defined as knowledge arising through paramarsha, i.e., the knowledge of the presence of the major in the minor through the middle which resides in the minor (paksa-dharmata) and is invariably associated with the major (vyapti). Like the Aristotelian syllogism, the Indian inference has three terms. The major, the minor and the middle are here called sadhya, paksa and linga or hetu respectively. We know that smoke is invariably associated with fire (vyapti) and if we see smoke in a hill we conclude that there must be fire in that hill. Hill is the minor term; fire is the major term; smoke is the middle term. From the presence of smoke in the hill as qualified by the knowledge that wherever there is smoke there is fire, we proceed to infer the presence of fire in the hill. This is inference. Indian logic does not separate Reduction from induction. Inference is a complex process involving both. Indian logic also rejects the verbalist view of logic. It studies thought as such and not the forms of thought alone. The formal and the material logic are blended here. Verbal form forms no integral part of the inference. This becomes clear from the division of inference into svartha (for oneself) and parartha (for others). In the former we do not require the formal statement of the different members of inference. It is a psychological process. The latter, the parartha which is a syllogism has to be presented in language and this has to be done only to convince others. There are five members in the Nyaya syllogism. The first is called Pratijna or proposition. It is the logical statement which is to be proved. The second is Hetu or ‘reason’ which states the reason for the establishment of the proposition. The third is called Udaharana which gives the universal concomitance together with an example. The fourth is Upanaya or the application of the universal concomitance to the present case. And the fifth is Nigamana or conclusion drawn from the preceding propositions. These five propositions of the Indian syllogism are called ‘members’ or avayavas.

 

 

The following is a typical Nyaya syllogism:

1. This hill has fire (Pratijna).
2. Because it has smoke (hetu).
3. Whatever has smoke has fire, e.g., an oven (Udaharana).
4. This hill has smoke which is invariably associated with fire (upanaya).
5. Therefore this hill has fire (nigamana).

                    If we compare it with the Aristotelian syllogism which has only three propositions, we will find that this Nyaya syllogism corresponds to the Barbara (AAA) mood of the First Figure which is the strongest mood of the strongest figure. Though the Nyaya syllogism has five and the Aristotelian has three propositions, the terms in both are only three— the sadhya or the major, the paksa or the minor and the hetu or the middle. Out of the five propositions, two appear redundant and we may easily leave out either the first two or the last two which are essentially the same. The first coincides with the fifth and the second with the fourth. If we omit the last two» the first three propositions correspond with the conclusion, the minor premise and the major premise respectively. Or, if we omit the first two, the last three propositions correspond to the major premise, the minor premise and the conclusion of the Aristotelian syllogism. Hence if we leave out the first two members of the Nyaya syllogism which are contained in the last two, we find that it resembles the Aristotelian syllogism in the First Figure:

1. All things which have smoke have fire (Major premise).
2. This hill has smoke (Minor premise).
3. Therefore this hill has fire (Conclusion).

                    And the typical Aristotelian syllogism may be stated in the Nyaya form thus:

1. Socrates is mortal (Pratijna).
2. Because he is a man (hetu).
3. Whoever is a man is a mortal, e.g., Pythagoras (Udaharana).
4. Socrates is a man who is invariably a mortal (Upanaya).
5. Therefore Socrates is mortal (nigamana).

                    But there are certain real differences between the Nyaya and the Aristotelian syllogism apart from the nominal difference between the numbers of the propositions in each. The Aristotelian syllogism is only deductive and formal, while the Nyaya syllogism is deductive-inductive and formal-material. The Nyaya rightly regards deduction and induction as inseparably related, as two aspects of the same process— the truth now realized in western logic. Inference, according to Nyaya, is neither from the universal to the particular nor from the particular to the universal, but from the particular to the particular through the universal. The example is a special feature of the Nyaya syllogism and illustrates the truth that the universal major premise is the result of a real induction based on the law of causation and that induction and deduction cannot be really separated. Again, while in the Aristotelian syllogism the major and the minor terms stand apart in the premises though they are connected by the middle term with each other, in the Nyaya syllogism all the three terms stand synthesized in the Upanaya. Again, while the Aristotelian syllogism is verbalistic, the Nyaya recognizes the fact that verbal form is not the essence of inference and is required only to convince others. Some people like Dr. Vidyabhusana and Prof. Keith have suggested that the Nyaya syllogism is influenced by Greek thought. But it is absolutely false. We find the development of the Nyaya inference before Aristotle. There are also certain fundamental differences between the two views and the view of Nyaya is accepted as better by the modern western logicians also. The view that vyapti, the nerve of inference, was introduced by the Buddhist logician Dinnaga who was influenced by Greek thought is also wrong. Vyapti was recognized much before Dinnaga, nor did he ‘borrow’ his doctrine from Greece. It is more reasonable to explain the similarities between the two as due to a parallel development of thought. Indian logic has been a natural growth.

 

There are five characteristics of the middle term:

1. It must be present in the minor term (paksadharmata); e.g., smoke must be present in the hill.
2. It must be present in all positive instances in which the major term is present; e.g., smoke must be present in the kitchen where fire exists (sapaksasattva).
3. It must be absent in all negative instances in which the major term is absent; e.g., smoke must be absent in the lake in which fire does not exist (vipaksasattva).
4. It must be non-incompatible with the minor term; e.g., it must not prove the coolness of fire (abadhita).
5. It must be qualified by the absence of counteracting reasons which lead to a contradictory conclusion; e.g., ‘the fact of being caused’ should not be used to prove the ‘eternality’ of sound (aviruddha).

                       Inference is generally regarded as of two kinds— Svartha and Parartha which we have already discussed. Gotama speaks of three kinds of inference— purvavat, shesavat and samanyatodrsta. The first two are based on causation and the last one on mere coexistence. A cause is the and unconditional antecedent of an effect and an effect is the invariable and unconditional consequent of a cause. When we infer the unperceived effect from a perceived cause we have purvavat inference, e.g., when we infer future rain from dark clouds in the sky. When we infer the unperceived cause from a perceived effect we have shesavat inference, e.g., when we infer past rain from the swift muddy flooded water of a river. When inference is based not on causation but on uniformity of co-existence, it is called samanyatodrsta, e.g., when we infer cloven hoofs of an animal by its horns. According to another interpretation, a purvavat inference is based on previous experience of universal concomitance between two things, a shesavat inference is parishesa or inference by elimination, and a samanyatodrsta is inference by analogy.

                       Another classification of inference gives us the kevalanvayi, kevalavyatireki and anvayavyatireki inferences. It is based on the nature of vyapti and on the different methods of establishing it. The methods of induction by which universal casual relationship is established may be anvaya, vyatireka or both. The first corresponds to Mill’s Method of Agreement, the second to his Method of Difference, and the third to his Joint Method of Agreement and Difference or the Method of Double Agreement.   We have kevalanvayi inference when the middle term is always positively related to the major term. The terms agree only in presence, there being no negative instance of their agreement in absence, e.g.,

All knowable objects are nameable;

The pot is a knowable object;

The pot is nameable.

                    We have kevalavyatireki inference when the middle term is the differentium of the minor term and is always negatively related to the major term. The terms agree only in absence, there being no positive instance of their agreement in presence, e.g.,

What is not different-from-other-elements has no smell;

The earth has smell;

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

                    We have anvayavyatireki inference when the middle term is both positively and negatively related to the major term. The vyapti between the middle and the major is in respect of both presence and absence. There is Double Agreement between the terms— they agree in presence in the positive instances and they also agree in absence in the negative instances; e.g.,

All things which have smoke have fire;

This hill has smoke;

Therefore, this hill has fire; and

No non-fiery things have smoke;

This hill has smoke;

Therefore, This hill is not non-fiery;

i.e., this hill has fire.

                    In Indian logic a fallacy is called hetvabhasa. It means that the middle term appears to be a reason but is not a valid reason. AH fallacies are material fallacies. We have mentioned the five characteristics of a valid middle term. When these are violated, we have fallacies. Five kinds of fallacies are recognized:

1. Asiddha or Sadhyasama: This is the fallacy of the unproved middle. The middle term must be present in the minor term (paksadharmata). If it is not, it is unproved. It is of three kinds—
2. Ashrayasiddha: The minor term is the locus of the middle term. If the minor term is unreal, the middle term cannot be present in it; e.g., ‘the sky-lotus is fragrant, because it is a lotus, like the lotus of a lake’.
3. Svarupasiddha: Here the minor term is not unreal. But the middle term cannot by its very nature be present in the minor term; e.g., ‘sound is a quality, because it is visible’. Here visibility cannot belong to sound which is audible.
4. Vyapyatvasiddha: Here vyapti is conditional (sopadhika). We cannot say, e.g., ‘wherever there is fire there is smoke’. Fire smokes only when it is associated with wet fuel. A red-hot iron ball or clear fire does not smoke. Hence ‘association with wet fuel’ is a condition necessary to the aforesaid vyapti. Being conditioned, the middle term becomes fallacious if we say: ‘The hill has smoke because it has fire’.

(2)   Savyabhichara or Anaikantika: This is the fallacy of the irregular         middle. It is of three kinds:

1. Sadharana: Here the middle term is too wide. It is present in both the sapaksa (positive) and the vipaksa (negative) instances and violates the rule that the middle should not be present in the negative instances (vipaksasattva); e.g., ‘the hill has fire because it is knowable’. Here ‘knowable’ is present in fiery as well as non-fiery objects.
2. Asadharana: Here the middle term is too narrow. It is present only in the paksa and neither in the sapaksa nor in the vipaksa. It violates the rule that the middle term should be present in the sapaksa (sapaksasattva); e.g., ‘sound is eternal, because it is audible’. Here audibility belongs to sound only and is present nowhere else.
3. Anupasarhhari: Here the middle term is non-exclusive. The minor term is all-inclusive and leaves nothing by way of sapaksa or vipaksa; e.g., ‘all things are non-eternal, because they are knowable’.

(3)     Satpratipakça: Here the middle term is contradicted by another middle term. The reason is counter-balanced by another reason. And both are of equal force; e.g., ‘sound is eternal, because it is audible’ and ‘sound is non-eternal, because it is produced’. Here ‘audible’ is counter-balanced by ‘produced’ and both are of equal force.

(4)     Badhita: It is the non-inferentially contradicted middle. Here the middle term is contradicted by some other pramana and not by inference. It cannot prove the major term which is disproved by another stronger source of valid knowledge; e.g., ‘fire is cold, because it is a substance’. Here the middle term ‘substance’ becomes contradicted because its major term ‘coldness’ is directly contradicted by perception.

(5)    Viruddha: It is the contradictory middle. The middle term, instead of being pervaded by the presence of the major term, is pervaded by the absence of the major term. Instead of proving the existence of the major term in the minor term, it proves its non-existence therein; e.g., ‘sound is eternal, because it is produced’. Here ‘produced’, instead of proving the eternality of sound, proves its non-eternality. Here the middle term itself disproves the original proposition and proves its contradictory, while in the Savyabhichara the middle term only fails to prove the conclusion, and in the Satpratipakca the middle term is inferentially contradicted by another middle term both of which are of equal force, and in the badhita the middle term is non-inferentially contradicted and the major is disproved by a stronger pramana other than inference.

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