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Indian Philosophy v2.c24.s5: VII Anumāna or Inference

Indian Philosophy v2.c24.s5

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VII Anumāna or Inference

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Anumāna means literally the measuring after something. It is knowledge which follows other knowledge. From the knowledge of the sign (liṅga) we get a knowledge of the object possessing it. Anumāna is usually translated by the word "inference," which, however, is to be taken in a comprehensive sense, as including both deduction and induction. Anumāna is sometimes defined as knowledge which is preceded by perception. Vātsyāyana holds that "no inference can follow in the absence of perception." Only when the observer has perceived fire and smoke to be related to each other is he able to infer the existence of the fire on the next occasion he perceives smoke.⁴ Uddyotakara mentions some points of distinction between perceptual and inferential knowledge: (1) All perception is of one kind, if we exclude yogic intuition, while there are varieties of inference; (2) Perception is confined to objects of the present time and within the reach of the senses, while inference relates to the past, the present and the future; (3) Inference requires the remembrance of a vyāpti, or a universal relation, which is not the case with perception.¹ Where perception is available, inference has no place.² We need not reflect much to know objects present to our perception.³ Inference operates " neither with regard to things unknown, nor with regard to those known definitely for certain; it functions only with regard to things that are doubtful."⁴ It is employed to know that part of the real which does not fall within the directly perceived. What is perceived points to something else, not perceived, with which it is connected. Bhāsarvajña in his *Nyāyasāra* defines inference as the means of knowing a thing beyond the range of the senses through its " inseparable connection with another thing " which lies within their range. Gaṅgeśa,⁵ following Śivāditya,⁶ defines inferential knowledge as knowledge produced by other knowledge.

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⁴ N.B., ii. 1. 31

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¹ N.V., ii. i. 31.

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² Pratyakṣatvād anumānāpravṛtteḥ (Śaṃkara : D.S.V., p. 88 n.).

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³ Ghaṭo 'yam iti vijñātuṃ niyamaḥ ko nv apekṣate.

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⁴ N.B., i. i. 1.

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⁵ *Tattvacintāmaṇi*, ii. p. 2. Cp. Māṇikyanandi's definition of inference as *sādhanāt sādhyavijñānam* (*Parīkṣāmukha Sūtra*).

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⁶ *Saptapadārthī*, p. 146.

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Gautama distinguishes inference into three kinds : *pūrvavat*, *śeṣavat* and *sāmānyato dṛṣṭam*⁷; and Vātsyāyana offers slightly different explanations of this division, which indicates that even before Vātsyāyana there were conflicting interpretations of the Nyāya aphorisms. In inference we pass from the perceived to the unperceived with which it is related; and this relation may be of three kinds, according as the element to be inferred is either the cause of the element perceived or its effect, or as the two are joint effects of something else. When we see the clouds and expect rain, we have a case of *pūrvavat* inference, where we perceive the antecedent and infer the consequent. It is, however, used to indicate not merely inference from a cause but also inference based on former experience. When we see a river in flood and infer that there was rain, we have a case of śeṣavat inference, where we perceive the consequent and infer the antecedent. It is also used to cover the inference of one member of a pair of correlatives from the other, or inference from a part or from elimination. The inference of the nature of sound as quality is given to illustrate the principle of exclusion or elimination. We prove that sound is not generality, particularity or inherence, not even substance or action, and so conclude that it must be a quality. When we see a horned animal and infer that it has a tail, we have a case of sāmānyatoḍṛṣṭa inference. It is based, not so much on causation, as on uniformity of experience. Uddyotakara agrees with this and gives as an illustration the inference of the existence of water in a particular place from the appearance of cranes. It is also used to indicate inference of supersensible truths (sāmānyato' dṛṣṭa).¹ We perceive the different places of the sun, and infer that the sun must be moving, though we do not see it. Perceiving aversion, affection, etc., we infer the existence of a soul which we do not perceive.²

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⁷ Cp. P.M., S. i. 2. 19, 22, 23, 29; iii. 1. 2-3; iii. 2-1, where the words *pūrva* and *śeṣa* occur as referring to the logically prior and posterior parts of a sentence or a paragraph, and are sometimes used to refer to *vidhi* and *arthavāda*. *Pūrva* is the principal or the primary, and *śeṣa* is the secondary. Evidently in the P.M. an argument from *śeṣa* would be one from the subsidiary to the principal. Perhaps the Nyāya interpreted the relation of principal and secondary as one of cause and effect. See Professor Dhruva's article on " *Trividham Anumānam* " in the *Proceedings of the Oriental Conference*, Poona, p. 265.

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¹ Keith thinks that this interpretation is an impossible one (I.L.A., p. 88 n.).

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² Uddyotakara criticises Vātsyāyana's illustration of the inference of the motion of the sun from its appearance at different places in different times on the ground that we see only different portions of the solar orb and not the movement of the sun. It may be noted that Uddyotakara regards the distinction into pūrvavat, śeṣavat and sāmānyatoḍṛṣṭa not as three kinds of inference, but as three conditions of a valid inference: (1) pūrvavat means that the middle term (hetu) should be invariably accompanied by its antecedent (pūrva) or the sādhya or the major term; (2) śeṣavat means that the middle term must have been observed as invariably accompanied by the major term in other (śeṣa) cases; (3) sāmānyatoḍṛṣṭa is analysed into sāmānyataḥ and adṛṣṭa, and taken to mean that the middle term should not be common to the predicate and the absence of the predicate (P and not P, sādhya and sādhyābhāva), i.e. it must not be too wide, which is the fallacy of sādhāraṇa. To these, two other conditions supposed to be implied by ca at the end of the sūtra are added, namely, that the inference should not be opposed to perceptual and scriptural evidence. All these five conditions are to be fulfilled in a valid anvayavyatireki inference and four in Kevalānvayi and Kevalavyatireki.

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These illustrations are enough to bring out the necessity of a universal connection or vyāpti. Each vyāpti relates the two elements of a vyāpaka or the pervader and the vyāpya or the pervaded. Anumāna or inference derives a conclusion from the ascertained fact of the subject possessing a property which is pervaded or constantly attended by another property. We ascertain that the mountain is on fire from the fact that the mountain has smoke, and smoke is universally attended by fire. By the contemplation of the sign, middle term, smoke, we infer that the object which has smoke has also fire. Inference, according to Uddyotakara, is the argument from sign as aided by remembrance,¹ or the knowledge which is preceded by the perception of the hetu (middle term) and remembrance of its invariable concomitance with the sādhya or the major term. The different factors of inferential reasoning are brought out in the form of the syllogism.

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¹ Smṛtyanugṛhīto liṅgaparāmarśo 'numānam (N.V., i. 1. 5).

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THE SYLLOGISM

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The five members of the syllogism are : (1) pratijñā, or the proposition : the hill is on fire ; (2) hetu, or the reason : because it smokes ; (3) udāharaṇa, or the explanatory example : whatever shows fire shows smoke, e.g. a kitchen ; (4) upanaya, or the application : so is this hill ; (5) nigamana, or the statement of the conclusion : therefore the hill is on fire.²

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² N.S., i. 1. 32. Cp. the names given by Praśastapāda : pratijñā, apadeśa, nidarśana, anusamdhāna and pratyāmnāya. This difference in terminology suggests the independent growth of logical views in the Vaiśeṣika. Vātsyāyana points out that the syllogism contains elements contributed by the different pramāṇas. The first is verbal, the second inferential, the third perceptual, the fourth analogical, and the conclusion suggests that all these bear on the same problem (N.B., i. 1. 1).

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Pratijñā, or the proposition, sets forth at the very beginning the thesis to be established. It fixes the problem and limits the inquiry. The suggestion to be established controls the process from the very start, and the act of inference tries to strengthen and reinforce the suggestion. The proposition is only a " suggestion or mere probability."³ There can be no argument unless we are impelled to know more about (ākāṅkṣā) the suggestion or the hypothesis which is set forth in the pratijñā, or the proposition. The proposition has the two factors of subject or what is observed, which is generally an individual or a class capable of being regarded as a single object,¹ and the predicate which is to be proved. In "the hill is on fire," the hill is the subject, the minor term, the pakṣa or the dharmin, and "on fire" is the predicate or the major term, the sādhya, the dharma or the anumeya, or that which is to be inferred. The subject calls our attention to a part of the real, and the predicate particularises the subject by suggesting its possession of a property P or its inclusion in the class of objects denoted by P. The syllogism is intended to prove that the subject presented in perception possesses the feature indicated in the predicate. The copula is an accident of language and not an essential part of the proposition.² The proposition should not be opposed to direct perception or the testimony of the scriptures. According to Dignāga, unintelligible, self-contradictory and self-evident propositions cannot serve as theses.² They should not contain any unfamiliar terms, should not be opposed to well-established truths, or one's own convictions.³ To find out whether the proposition, S is P, is true, we attend to the minor term, analyse it into its elements and discover in it the presence of the middle term. In all reasoning, the analysis of the minor follows the statement of the thesis. The second member of the syllogism states the presence of the middle term called hetu, or ground, sādhana, or the means of proof, liṅga, or the sign, in the minor term. It gives the possession of the character which entitles its possessor to be the subject of the conclusion, or pakṣadharmatā. The hill is found to be smoky. Pakṣatā is a necessary condition of inference. Any hill is not the minor, or pakṣa, though it becomes one, the moment we perceive smoke in it and desire to infer that it has fire also. If we see the fire also, it is not a pakṣa. Pakṣa is defined by Annaṃ Bhaṭṭa as the subject in which the predicate or that which is to be proved is doubted.⁴ Pakṣa is more a proposition than a term. We now have the three terms necessary for a syllogistic inference, namely, the minor term or the pakṣa, that about which something is inferred, the major term or the sādhya, that which is inferred about the minor term, the middle term, by which the major is inferred to be true of the minor.

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³ N.B., i. 1. 39.

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¹ N.S., ii. 2. 66.

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² See *History of Indian Logic*, p. 290. See also P.P., p. 234, and V.S., iii. 1, 15.

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³ See also P.P., p. 234; V.S., iii. 1. 15.

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⁴ *Tarkasaṃgraha*, p. 51, Saṃdigdhasādhyavān.

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The presence of the middle in the minor (pakṣadharmatā) cannot lead to a valid inference unless it is combined with a universal relation between the middle and the major terms. The third member, udāharaṇa, or example, “whatever is smoky has fire, like the kitchen,” takes us to the basis of inference, the major premise. Gautama means by example a similar instance possessing the essential property of the major term. Vātsyāyana seems to be of the same opinion. There is little to suggest that these two thinkers regarded the example as an illustration of a general rule. It was perhaps their idea that all reasoning was from particulars to particulars. Certain individuals have a given attribute, an individual or individuals resemble the former in certain other attributes: therefore they resemble them also in the given attributes. It may be that the Nyāya syllogism is developed out of the argument by example which Aristotle recognises.¹ It was soon realised that, though it is the way in which we often do reason, it is not a logical inference, where the conclusion is warranted by the premises. The argument is invalid if the example is not indicative of a general rule. The similarity (sādharmya) suggests class nature (sāmānya). Praśastapāda is familiar with the conception of sāhacarya, or concomitance, and attributes it to Kaṇāda.² Later logic equates the third member with the statement of the general relation.³ No inference is possible unless there is an invariable concomitance (vyāpti) between the mark and the character inferred. The Vedāntaparibhāṣā says: “The instrument of inference is the knowledge of the universal relation.”⁴ The mention of the example indicates that inference is both inductive and deductive. The generalisation is based on instances, and it helps us in deducing new truths. The auxiliary and non-essential character of the example was emphasised by Dignāga. Dharmakīrti holds that the example is unnecessary and inserted only to help the person spoken to. The example illustrates but does not establish the universality of the rule. The third member, according to Dr. Seal, “ combines and harmonises Mill’s view of the major premise as a brief memorandum of like instances already observed, fortified by a recommendation to extend its application to unobserved cases, with the Aristotelian view of it as a universal proposition which is the formal ground of the inference.”¹ Examples may be of different kinds, homogeneous or affirmative (sādharmya) where the property to be proved (major) and the ground (middle) are present, as the kitchen, and heterogeneous or negative (vaidharmya), where the property to be proved and the ground are both absent, as the lake.² Dignāga adds to these two, analogical examples. He also mentions ten kinds of fallacies relating to examples, while Siddhasena Divākara gives six kinds of fallacies about homogeneous and six about heterogeneous examples.

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¹ Cp. the war of Athens against Thebes was mischievous, because it was a war against neighbours, just as the war of Thebes against Phokis was.

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² P.P., p. 205.

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³ Vyāptipratipādikaṁ vākyam (Tarkasaṁgraha), p. 46.

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⁴ Anumitikaraṇaṁ ca vyāptijñānam, ii.

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¹ The Positive Sciences of the Ancient Hindus, p. 252.

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² N.B., i. 1. 36-37.

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Regarding the distribution of the middle term, it is said: (1) that the middle should cover the whole of the extension of the minor, as in the illustration, “ sound is non-eternal because it is a product,” where the middle term product includes all cases of sound (All S is M); (2) that all things denoted by the middle must be homogeneous with the things denoted by the major, as in the example, “ all products are non-eternal ” (All M is P), and (3) that none of the things heterogeneous from the major term must be included in the middle, “ no non-eternal thing is a product ” (No non P is M). Dignāga insists that the middle term must be universally and invariably connected with the major term. Uddyotakara argues that there must be a universal relation between the middle and the major, such that, wherever the major is, there must be the middle, and wherever the major is not, the middle must not be. Praśastapāda affirms the same view when he says that the liṅga, or the middle term, is “ that which is related to the object to be inferred, and is known to exist in that which is connected with that object, and does not exist where it is not present.”³ Varadarāja mentions five characteristics of the middle term, which are: (1) pakṣadharmatā, or the presence of the middle in the minor, the smoke in the hill; (2) sapakṣasattva, or the presence of the middle in positive instances homogeneous with the proven, as smoke in the kitchen; (3) vipakṣasattva, or non-presence of the middle in negative instances heterogeneous from the proven, as no smoke in the lake; (4) abādhitaviṣayatva, or non-incompatibility with the minor; and (5) asatpratipakṣatva, or the absence of counteracting forces.¹ In the case of an exclusively affirmative or exclusively negative inference, the valid middle term fulfils only four requirements, since it cannot abide in negative or positive instances. Annam Bhaṭṭa holds that the middle term is of three kinds corresponding to the three kinds of inference: (1) positive and negative (anvayavyatirekin), where the middle is invariably concomitant with the major, as smoke with fire, wherever there is smoke there is fire, as in the kitchen: where there is no fire, there is no smoke, as in a lake²; (2) merely positive (kevalānvayin), where we have only affirmative invariable concomitance, as in "what is knowable is nameable," where we cannot have a negative instance to illustrate the position "what cannot be named cannot be known"; and, (3) merely negative (kevalavyatirekin), where a positive instance is not possible. All beings that possess animal functions have souls, where we can prove only that chairs and tables have no animal functions, and therefore no souls, but cannot give positive instances, since souls and beings that possess animal functions are coextensive in their nature.³ According to the Vedāntaparibhāṣā, inference from an affirmative universal is regarded as anumāna, while that from a negative universal is treated as arthāpatti, on the ground that there is not in the latter an application of a general principle to a particular case.⁴ The Nyāya is, however, of the view that every

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³ P.P., p. 200. Yad anumeyena saṁbaddham prasiddhaṁ ca tadanvite Tadabhāve ca nāsty eva tal liṅgam anumāpakam.

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¹ The first three are mentioned by Dharmakīrti and Dharmottara. See Nyāyabinduṭīkā, p. 104, and also Laugākṣi Bhāskara's Tarkakaumudī, p. 12, Bombay ed.

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² It is to be noted that the negation of the pervaded becomes the pervader in the negative vyāpti and the negation of the pervader becomes the pervaded. See S.V., Anumāna, p. 121.

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³ Tarkasaṃgraha, p. 48. This distinction is accepted by Uddyotakara and Gaṅgeśa. Cp. with this the classification of inference in the Jaina canonical works into: (1) This is, because that is. There is fire because there is smoke. (2) This is not, because that is. It is not cold, because there is a fire. (3) This is, because that is not. It is cold here, because there is no fire. (4) This is not, because that is not. There is no mango-tree here, because there are no trees at all.

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⁴ ii.

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Dharmakīrti thinks that unless the middle term is present in those things in which the thing to be inferred exists, and is absent in all things in which it is not found, the inference is of doubtful validity. Siddhasena Divākara defines the middle term as "that which cannot occur otherwise than in connection with the major term." Smoke cannot arise from any other thing than fire.

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negation has a positive opposed to it, and so affirmative conclusions can be derived from negative universals.¹ The chief characteristic of the middle term is that it should be free from all conditions. We cannot argue that A is dark simply because he is B’s son, like other children of B and unlike other men’s children. The conclusion may or may not be true as a matter of fact, but it is logically defective, since there is not an unconditional relationship (anupādhikasambandha) between B’s sonship and dark complexion.

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¹ Vyāpti, or universal, may be either affirmative (anvaya) or negative (vyatireka), and of the former there are two kinds : samavyāpti (equipollent concomitance), where M and P are coextensive, as in the case “ all produced things are non-eternal ”; and viṣamavyāpti (non-equipollent concomitance), where the two are not coextensive. All cases of smoke are cases of fire, but not vice versa.

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Application is the fourth member of the syllogism. It asserts the presence or absence of the ground suggested in the minor term. It is affirmative in the former case, as in the example, “ so is this hill,” *i.e.* smoky, and negative in the latter case, as in the example, “ not so is this hill,” *i.e.* not smoky.²

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² N.S., i. I. 38.

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Conclusion restates the proposition as grounded : “ therefore the hill is on fire.”³ What is tentatively put forth in the first member is established in the conclusion.

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³ N.S., i. I. 39.

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Vātsyāyana points out that some logicians regarded the syllogism as consisting of ten members. In addition to the five given above, the following are included: (1) jijñāsā, or the desire to know the exact truth of the proposition, whether the hill is on fire in all its parts or in only some; (2) saṁśaya, or doubt about the reason, whether after all that which we regard as smoke is only vapour; (3) śakyaprāpti, or the capacity of the example to warrant the conclusion whether smoke is always a concomitant of fire, since it is not present in a red-hot iron ball; (4) prayojana, or purpose of drawing the conclusion; and (5) saṁśaya-vyudāsa, or the removal of all doubts about the relation of the middle to the major and its presence in the minor.⁴ These five additional members of the syllogism are, according to Vātsyāyana, unnecessary for proof, though they help to make our cognitions clear. They have in view the psychological process. Jijñāsā, or the desire to know, is undoubtedly the starting-point of all knowledge; but, as Uddyotakara observes, it is not an integral factor of reasoning or proof.¹

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⁴ N.B., i. I.

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³² This is an indication that the form of the syllogism developed out of the practices and traditions of the art of debate. Bhadrabāhu, the Jaina logician gives a different list of the ten members of the syllogism, viz. : (1) pratijñā, or the proposition; (2) pratijñāvibhakti, or the limitation of the proposition; (3) hetu, or the reason; (4) hetuvibhakti, or the limitation of reason; (5) vipakṣa, or the counter-proposition; (6) vipakṣapratiṣedha, or the denial of the counter-proposition; (7) dṛṣṭānta, or example; (8) ākāṅkṣā, or doubt about the validity of the example; (9) ākāṅkṣāpratiṣedha, or the dispelling of the

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¹ N.V., i. I. 32.

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It was soon realised that the conclusion repeats the first proposition, while the fourth member is a restatement of the second. Strictly speaking, every syllogism has only three members. Nāgārjuna is said to have started the view of the three-membered syllogism in his Upāyakauśalya Sūtra, where he urges that a conclusion can be established through a reason and an example, affirmative or negative.² Sometimes Dignāga is given the credit for it.³ In his Nyāyapraveśa he mentions only three members of the syllogism, though the third states both an affirmative and a negative example; this hill is on fire, because it has smoke; all that has smoke has fire, like a kitchen, and whatever is not on fire has no smoke, like a lake. In Dignāga the third factor is a general law with suggestive illustrations. Dharmakīrti thinks that even the third member is unnecessary, since the general proposition is implied in the reason. It is enough to say the hill is on fire because it smokes. This form which corresponds to an enthymeme is found much in use in Hindu philosophical treatises as well. The Jaina logicians, Māṇikyanandi and Devasūri,⁴ are of this view. The Mīmāṃsakas and the Vedāntins admit only the three-membered syllogism. The Vedāntaparibhāṣa allows the use of the first three or the last three members.⁵

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² History of Indian Logic, p. 119.

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³ Suguira : Hindu Logic as preserved in China and Japan ; Ui : Vaiśeṣika Philosophy, p. 82, n. 2.

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⁴ Pramāṇanayatattvālokālaṃkāra, p. iii.

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⁵ ii. Varadarāja, in his Tārkikarakṣā, refers to the Mīmāṃsā view of the three-membered syllogism and the Buddhist view of the two-membered. Māṭharavṛtti is aware of the three-membered syllogism of pakṣa, hetu and dṛṣṭānta.

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Both Vātsyāyana and Uddyotakara argue against the attempt to dispense with the last two members of the syllogism.⁶ They admit that the first member of the syllogism is restated in the conclusion,

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⁶ N.B., i. I. 39 ; N.V., i. I. 39.

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doubt; (10) nigamana, or the conclusion (Daśavaikālikaniryukti, p. 74, Nirṇayasāgar edition). Bhadrabāhu here adopts the double method of proof. When a reasoning is put forward to prove the non-eternity of sound, the counter-proposition is asserted and denied by means of the statement. If sound were eternal, it would not be a product. This hypothetical reasoning lends support to the previous inference, though by itself it has not much value. Siddhasena Divākara reduces the syllogism to five members in his Nyāyāvatāra. Anantavīrya, commenting on the latter (13), says that the best of the syllogism has ten members, the mediocre of five, and the worst of two.

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while the fourth is a combination of the second and the third. Though they are unnecessary from the standpoint of logic, they are useful for purposes of debate, since they confirm the reason and reassert decisively the proposition tentatively set forth in the first member. A distinction was drawn between the five-membered syllogism, useful for convincing others (parārthānumāna), and the three-membered one, sufficient for convincing oneself (svārthānumāna). The latter deals with inference as a process of movement of thought, and so belongs to the science of discovery, while the former deals with proof. Gautama and Kaṇāda do not explicitly mention it, though later logicians admit it.¹ Praśastapāda distinguishes inference for oneself (svaniścitārtha) from inference for others (parārtha).² Inference for the sake of others (parārthānumāna) is rather a formal exposition. We see a hill, and are in doubt whether it has fire or not. Noticing smoke, we remember the connection between fire and smoke, and conclude that there must be fire on the hill. When we attempt to convey this information to others we use the five-membered form.³

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¹ Dignāga, Praśastapāda, Dharmakīrti, Siddhasena Divākara, Māṇikyanandi, Devasūri, Bhāsarvajña, and Gaṅgeśa, among others, adopt this distinction.

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² P.P., p. 231. Cp. with this Dharmottara's distinction between jñānātmaka and śabdātmaka (Nyāyabinduṭīkā, p. 21) and Śivāditya's artharūpatva and śabdarūpatva (Saptapadārthī, p. 154).

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³ Tarkasaṃgraha, p. 45.

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In spite of differences in regard to the number of the parts of the syllogism, all logicians are agreed that the two essentials of a valid inference are vyāpti (universal relation), or the major premise, and pakṣadharmatā, or the minor premise. The former gives the universal connection of attributes, and the latter states that the subject possesses one member of the universal relation.⁴ These answer to the two steps of J. S. Mill, ascertaining (1) what attributes are marks of what others, and (2) whether any given individuals possess these marks.

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⁴ Tattvacintāmaṇi, ii. p. 2; Bhāṣāpariccheda and Siddhāntamuktāvalī, pp. 66 and 68.

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Neither the major by itself nor the minor by itself can warrant the conclusion. A synthesis of the two is necessary. Liṅgaparāmarśa or consideration of the sign, is the essential element of the inferential process. According to Gaṅgeśa, vyāpti by itself is the indirect cause of inferential knowledge, while liṅgaparāmarśa, or consideration of the sign, is the last cause (caramakāraṇa) or the chief cause (karaṇa).⁵ It is the synoptic view of the fact that the middle related to the major abides in the minor,¹ that leads to the conclusion. Inferential act is, however, an integral one.

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⁵ Tattvacintāmaṇi, ii. p. 2.

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¹ Vyāptiviśiṣṭapakṣadharmatājñānam (Tarkasaṃgraha, p. 44). See Bhāṣāpariccheda, p. 66; Tattvacintāmaṇi, ii. 2; Jānakīnātha’s Nyāyasiddhāntamañjari, pp. 86–87, Paṇḍit ed.

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The Advaita argues that there is no such thing as the reflection on the middle term. Knowledge of a universal relation is the instrumental cause; we remember it and derive the conclusion.² The objection seems to be directed against the view that we first have an act of perception, next an act of recollection, and lastly the act of inference. The Advaita tries to make out that the inferential act is not a putting together of two judgments, but one single process (vyāpāra), where the perceived element (the minor) operates along with the revived general principle, the major. These two elements are not substantive mental states, and are not operative as definite stages in the inferential process. The Naiyāyika, who is more of a logician than a psychologist, urges that the act of synthesis is necessary for inference.

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² Vedāntaparibhāṣā.

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Dignāga raises the interesting question about the nature of the thing that is inferred. We do not infer fire from smoke, since it is not a piece of new knowledge. We know already that smoke is connected with fire. We cannot be said to infer the relation between the fire and the hill, since relation implies two things, while in inference we have only one thing, the hill, as the fire is not perceived. What is inferred is neither the fire nor the hill, but the fiery hill.³ The conclusion is a judgment.

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³ Dignāga, quoted in N.V.T.T., N.S., i. 1. 5. Vedāntaparibhāṣā (ii), says that the hill is perceived and the fire is inferred.

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The Naiyāyika did not attach much importance to the different positions in which the middle term might occur. He regarded Barbara as typical of all syllogistic reasoning. The use of positive and negative instances inclined him to view the affirmative and the negative general propositions as mutually involved. All inference, strictly speaking, is supported from both the sides.⁴ Hindu logic has practically only one figure and one mood. From the knowledge that the subject of the proposition possesses a characteristic, which is invariably accompanied by the property, the presence of which we wish to establish, we infer that the subject has the said property. The principle is expressed in terms of connotation. If it is translated into terms of classes, we get the dictum de omni et nullo. Whatever may be asserted of every individual in a class may be asserted of any individual belonging to the class. The detailed distinctions of figures and moods are not so necessary for purposes of correct thinking, though they afford a training-ground for subtle thinking.¹ Aristotle admitted that the last three figures could be reduced to the first. The Nyāya recognises even in the first figure only Barbara. Darii and Ferio are not used in the Nyāya, since the conclusion refers always to a limited object, and the distinction between the universal and the particular does not arise. This distinction is only relative, as what is universal with regard to a limited class is particular in a wider reference. The minor term in the Nyāya syllogism is always an individual object or a class, and so a universal and not a particular. A conclusion about "some" cases gives us no definite information about the individual case in question. Celarent is easily derived from Barbara. Aristotle admitted that all his moods could be reduced to the first two moods of Figure 1, and these two are interchangeable if we know that all judgments are double-edged.

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⁴ If A is, then B is. If B is not, then A is not. Dharmakīrti, while agreeing that all arguments can be expressed in the affirmative or negative form, when based on likeness (sādharmya) and unlikeness (vaidharmya), thinks that some arguments fall naturally into the latter form. All objects existent here and now are perceived. The jar is not perceived. Therefore the jar is not existent here and now. This is Camestres.

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¹ Gomperz says: "At an enormous expense of original thought, Aristotle investigated the forms of inference, distinguished them, and analysed their ramifications. And, lo and behold! in all his numerous works, covering the whole domain of knowledge which was then accessible, he makes practically no use of the 'kinds' (moods) and 'figures' of the syllogism. He does not even shrink from the admission that all this great wealth of forms might be reduced to a few fundamental ones without loss in practice. We may add that subsequent research, greatly as it has developed and refined its instruments, confirms him in this: that the figures and the moods have remained a collection of curiosities, preserved by the history of science, but never put to practical use by science itself" (Greek Thinkers, vol. iv, pp. 44-45). See also H. N. Randle: "A Note on the Indian Syllogism," October, Mind, 1924.

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The analysis of the reasoning process resembles pretty closely the syllogistic analysis of Aristotle. Even the five-membered form has only three terms, and the three-membered syllogism has three propositions, which correspond to Aristotle's conclusion, the minor premise and the major premise. The attempt has been made to account for the striking similarity by theories of mutual influence. Dr. Vidyābhūṣaṇ says: "It is not inconceivable that the knowledge of Aristotle's logic found its way through Alexandria, Syria and other countries into Taxila. I am inclined to think that the syllogism did not actually evolve in Indian logic out of inference, and that the Hindu logician owed the idea of the syllogism to the influence of Aristotle."¹ The learned professor believes that the art of the syllogism is "borrowed," while the doctrine of inference is an indigenous growth. Professor Keith writes: "Of logical doctrine in its early stages there is no reason whatever to suspect a Greek origin: the syllogism of Gautama and Kaṇāda alike is obviously of natural growth, but of stunted development. It is with Dignāga only that the full doctrine of invariable concomitance as the basis of inference in lieu of reasoning by analogy appears; and it is not unreasonable to hazard the suggestion that in this case Greek influence may have been at work."² He supports this suggestion by referring to the knowledge of Greek astrology possessed by Āryadeva, a predecessor of Dignāga by nearly two centuries. This, coupled with the alleged influence of Aristotle on the Hindu theory of drama as found in the Bharata Śāstra, makes probable some sort of cultural intercourse between India and Greece. It is sometimes made out that Aristotle was much influenced by the Hindu theory, which was conveyed to him by Alexander, who is reported to have had conversations with the logicians of India. Little positive evidence of direct influence is available, and when we remember that syllogistic types of reasoning are to be met with even in pre-Aristotelian works of the Hindu and the Buddhist thinkers,³ it is difficult to accept the theory of "borrowing" from Greece. The words of Max Müller can bear repetition, "that we must here also admit the existence of undesigned coincidences to a much larger extent than our predecessors were inclined to do. We must never forget that what has been possible in one country is possible in another also."'¹ This view is strengthened when we realise that there are fundamental differences between the Greek and the Indian syllogisms. There is little in the analysis of reasoning in Greek logic answering to the example which the Hindu thinkers regarded as indispensable for the statement of the universal relation. It does not require much thought to grasp that the basis of the inference is the universal relation, for the example is just the suitable embodiment of that relation.

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¹ History of Indian Logic, p. xv.

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² I.L.A., p. 18.

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³ History of Indian Logic, p. 500, n. 1, and Appendix B.

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¹ S.S., pp. 385-386.

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INDUCTION

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Inference claims to be true of reality, and the claim cannot be sustained unless the two premises are true. The minor premise is the result of perception, and the major takes us to the problem of induction.

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How are universal propositions arrived at? The Naiyāyika gives us different answers. He speaks of enumeration, intuition and indirect proof. The syllogism mentions an example along with the rule. While an example may be sufficient to illustrate a rule, it cannot by itself establish a universal relation. There may be invariable concomitance of the smoke in the kitchen with the fire in it, or of the smoke in the sacrificial ground with the fire in it, but from these we cannot infer fire in a hill, simply because we perceive smoke in it, unless we establish the invariable concomitance of all cases of smoke with cases of fire. If we observe smoke and fire in a number of instances, we are perhaps on better ground. Bhūyo darśana, or frequency of experience, without a single exception (avyabhicarita sāhacarya), helps us in framing a general rule. It is not enough if we observe smoke wherever there is fire; we should also notice that there is no smoke where there is no fire. Agreement in presence and agreement in absence are both necessary.² If uninterrupted agreement (niyata-sāhacarya) is reinforced by absence of exceptions (avinābhāvarūpasaṃbandha), we have unconditional concomitances, which exclude upādhis, or adventitious conditions.¹ We do not have smoke wherever we have fire. A red-hot iron ball has no smoke in it. Only fire fed by wet fuel is concomitant with smoke. The relation of fire and smoke is a conditional one, while that between smoke and fire is an unconditional one. The principle " all cases of fire are cases of smoke " is inadmissible, while the other, " all cases of fire fed by wet fuel are cases of smoke," is admissible. A condition is not necessarily a defect, since it misleads only when it is not recognised. Whenever conditions are suspected, it is necessary for us to examine the accompanying circumstances and show that the concomitance holds even when the suspected condition is absent. The positive instances disprove the case for conditions, since they show that the middle and the major are present, while nothing else is constantly present : the negative instances support the case by showing that the middle and the major are absent even when no other material circumstance is constantly absent. Later logic laid the greatest stress on the negative instances and even defined vyāpti so as to bring out the exclusive adequacy of the sign to the thing signified.² The Naiyāyika demanded that the disciplined mind should control its fancies and bow beneath the hard yoke of facts. An accurate account of the experimental methods is possible only with the development of the experimental sciences ; and, in the absence of the latter, the Indian logician's views about scientific method are not of great interest. The Naiyāyika was aware of the general problem of induction and the method of careful observation of the facts of nature by which universal propositions are arrived at.

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² Sāhacaryajñāna and Vyabhicārajñānaviraha (Tarkasaṃgraha, p. 45).

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¹ Udayana defines a condition or upādhi as a thing which imparts its own property to another object placed in its vicinity (upa samīpavartini, ādadhāti saṁkrāmayati, svīyaṁ dharmam ity upādhiḥ). The red flower which makes the crystal placed over it look like a ruby by imparting to it its own redness is an upādhi. Cp. Varadarāja's definition, sādhanavyāpakāḥ, sādhyasamavyāptā upādhayaḥ (Tārkikarakṣā). A valid universal must be free from all conditions (nirupādhikaḥ) which are suspected by oneself (śaṁkita) or with which one is charged by one's opponent (samāropita). See also Vācaspati's N.V.T.T., i. 1. 1. In logic, according to Udayana, an upādhi is (1) that which constantly accompanies the middle term, and (2) is accompanied by it, and (3) which does not constantly accompany the major term. Four kinds of upādhis are recognised in Tarkadīpikā. See Athalye : Tarkasaṁgraha, p. 317.

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² After reviewing several definitions of vyāpti, Gaṅgeśa concludes that " invariable concomitance is the co-presence of the middle term with the major term, which is not qualified by the nature of the counterpart of that absolute non-existence, which abides in the same locus with the middle term, but abides in a different locus in respect of that counterpart " (Tattvacintāmaṇi, ii). See History of Indian Logic, p. 424.

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Nature does not always supply us with positive and negative instances of the right kind to help us to establish or reject theories. The Naiyāyika says that we may employ the method of tarka or indirect proof to obtain the negative evidence. If the general proposition, where there is smoke there is fire, is not valid, then its contradictory that " sometimes smoke is not accompanied by fire " must be true. In other words, fire is not the invariable antecedent of smoke. But we cannot deny that fire is the cause of smoke. Thus tarka is employed to strengthen a universal proposition based on positive instances of uninterrupted agreement. It is also a way of establishing a hypothesis.¹ By pointing out the absurdities in which we are landed, if we deny a suggested hypothesis, indirect proof tends to confirm the hypothesis. It shows that no other hypothesis is able to account for the facts.²

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¹ N.S., i. 1. 31.

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² " A legitimate hypothesis must satisfy the following conditions: (1) The hypothesis must explain the facts. (2) Must not be in conflict with any observed facts or established generalisations. (3) No unobserved agent must be assumed where it is possible to explain the facts satisfactorily by observed agencies. (4) When two rival hypotheses are in the field, a crucial fact or test is necessary; the absence of such a test is fatal to the establishment of either. (5) Of two rival hypotheses, the simpler, *i.e.* that which assumes less, is to be preferred, *caeteris paribus*. (6) Of two rival hypotheses, that which is immediate or relevant to the subject-matter is to be preferred to that which is alien or remote. (7) A hypothesis that satisfies the above conditions must be capable of verification before it can be established as a theory" (Seal: *The Positive Sciences of the Ancient Hindus*, p. 288)

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Tarka is only an aid to the empirical method of induction, which cannot give us universal propositions. Even when we observe all possible cases and strengthen our conclusion by the method of indirect proof, still we do not reach absolute certainty about universal propositions. So long as they are based on limited observation, they do not possess any necessity. Enumerative universals are only probable, but not certain. While it is true that the experience of sensible particulars gives rise to the knowledge of the universals, it cannot be said that the apprehension of the universals is fully accounted for by the sensible particulars, since the universal goes beyond any or all of the particulars.

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Even collective judgments presuppose a knowledge of the universal. We do not count up all instances, but only those which possess a generic quality which entitles them to a place in the group. So even the method of enumeration cannot operate without an apprehension of the universal. The ancient Nyāya asserts that we can discern universals by means of perception. Gaṅgeśa recognises the non-sensuous activity involved in the apprehension of the universals (sāmānyalakṣaṇa), when he makes it a variety of alaukika pratyakṣa, or non-sensuous intuition.¹ On either view it is not necessary for us to make an exhaustive survey of instances. Through the perception of the universal smokiness, we apprehend all cases of smoke. We apprehend the universals of fire and smoke by sāmānyalakṣaṇapratyāsatti, and realise their invariable relation through that variety of perception called jñānalakṣaṇa. So by analysis of one instance we can discern the universal relation; and what is true of that instance can be rightly extended to all members of the class, since there is such a thing as identical nature. What is once true is always true. When we say "smoke," we do not have in our mind all cases of smoke; but the connotation of smoke is what is in our thought. The connotations of smoke and fire are related in the vyāpti as the vyāpya, the pervaded, and the vyāpaka, the pervader. A multiplicity of instances is necessary, not because we abstract the universal relation from these particulars, but because the relation is not clearly differentiated in a single case. Those with exceptional powers of discrimination can differentiate relations even from a few instances. The universal relation is a discovery and not a creation. Through an act of thought exercised on a single instance we can obtain a universal connection. If the universal relation is not presented to us in the judgment itself, a repetition of similar events cannot help us to it. It is given to the subject and not constructed by the understanding. What transcends sense-perception does not transcend experience. Methodical observation and experiment but confirm what is intuited sometimes from a single case. Every event of nature contains within itself the relation or law in accordance with which it has been brought about. It is intuition alone that helps us to distinguish the essential features of a given event from its accidental accompaniments. Universal propositions are connections of content. If all little-biled animals are long-lived, it is not because man, horse and mule, which are little-biled, are long-lived, but because there is a necessary connection between the contents of little-biled and long life. The significance of the Nyāya syllogism is best brought out if it is put in the hypothetico-categorical form. If A, then B. A, therefore B.

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¹ Cp. with this Aristotle’s apprehension of the universal by nous following upon the perception of the relevant particulars. An enumeration of instances, even when exhaustive, cannot give rise to absolute certainty unless we transcend the contingency of matter (Aristotle : An. Post., I. 5).

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On this view, the problem how deductive reasoning can give us more in its conclusion than was contained in its premises appears in a new light. General principles are not enumerative judgments, and the relations which govern the particulars are as real as the particulars themselves. When we derive a particular truth from a universal judgment, the conclusion goes beyond the premise in one sense, though it is contained in it in another.

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But if universal relations are real and require only to be intuited, how is it that lovers and lunatics miss the significance of those general principles which leap to the eye of scientists and philosophers? Nor is it easy to account for the fact that our generalisations sometimes fail to be true. The relations are not correctly apprehended in erroneous inductions. They are not properly differentiated from the unlimited fulness of the particulars. The complexity of reality makes discrimination of relations difficult. Under the influence of passion and prejudice, inertia and thoughtlessness, we accept propositions as true, though they are not so. In this sense, even particular perceptions may be wrong. The intuited inductive principles become more convincing when they are applied to fresh particulars, i.e. when we pass from the inductive to the deductive stage. As we shall see, the validity of the universal relations, like that of all other knowledge, is to be established by other forms of knowledge. The intuition unconfirmed by empirical verification is only a hypothesis. Mere intuition is not of much use. Exhaustion of empirical material is an unrealisable ideal. The two help each other. The general principle has some necessity about it, even though it is grasped by us only on the occasion of an empirical fact.

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The Nyāya view of vyāpti assumes that universals are factors of reality¹ and universal relations are real.² The Cārvākas, who are materialists, deny the possibility of universal relations, and so dispute the validity of inference. The Buddhists regard universal propositions as ideal constructions and not real relations. The universal is but a name and the identity a fiction. In the Buddhist work, Sāmānya-dūṣaṇadīprasāritā, the theory that we perceive the universals as real is criticised. We see the five fingers of the hand and not a sixth universal, which is as unreal as a horn on one’s head.³ Though a strict interpretation of this view makes all inference impossible, still the Buddhists assume its validity for all practical purposes and distinguish different kinds of universal relations. The middle term may be related to the major by way of identity (svabhāva, tādātmya), causality (tadutpatti), or negation (anupalabdhi). It comes to this, that our inferences are either affirmative or negative, and the former may be analytical or synthetical.⁴ We have an inference of the type of tādātmya, or analysis, identity, or co-existence, when we say that “ this is a tree because it is a kind of pine.” We have an inference of the type of tadutpatti, synthesis, causality or succession, when we say “ there is fire because there is smoke.” Inference by anupalabdhi, or non-perception, arises when we infer the non-existence of the jar from the non-perception of it. Universal relations are not derived from observation of facts, but are deduced from a priori notions of identity in essence and causal necessity. The Buddhists assume the universal validity of these principles of causality and identity, since it is impossible to live without accepting them. According to Dignāga, knowledge does not express real relations of objective existence. The relations of inherence and essence, quality and subject, from which we derive conclusions, are all imposed by thought.⁵ Relations are only logical.

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¹ Sāmānyasya vastubhūtatvāt (Tarkabhāṣā, p. 31, Poona ed.).

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² Svabhāvikas tu sambandho vyāptiḥ (p. 35).

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³ Keith: Buddhist Philosophy, p. 233. Cp. Berkeley’s view of abstract ideas in Principles of Human Knowledge, Introduction, p. 13.

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⁴ Nyāyabindu, p. 11.

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⁵ See Nyāyakandalī, p. 207. Vācaspati quotes from Dignāga to the effect, “ Sarvo ’yam anumānānumeyabhāvo buddhyārūḍhena, dharma dharmibhāvena na bahissatvam apekṣate ” (N.V.T.T., i. 1. 5).

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Vācaspati subjects the Buddhist view to a severe scrutiny. The law of causality, as the Buddhist conceives it, will be satisfied if we trace the smoke on the occasion of fire to the agency of an invisible demon (piśāca). Nor is there any necessity why the same effect should have the same cause. If the cause is what precedes the effect, it is not simultaneous with it. From the perception of smoke we can infer, not the present but the past existence of fire. If two things are identical, then the perception of one means the perception of the other, and there is no need for inference. Vācaspati and Jayanta urge that the relation between the pine and the tree is not one of identity, since all trees are not pines.¹ The Buddhist does not tell us how his principles of causality and identity of essence are themselves derived. There are many cases of concomitance which have little to do with causality or identity. The Naiyāyika includes all reciprocal relations under vyāpti, and not merely those of causal successions and genus and species, but such others as "all horned animals have cloven hoofs."²

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