Ancient Indian Logic

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Ancient Indian Logic Shobhit Shukla Department of Information & Communication Technology, MIT, Manipal

Abstract—Indian Logic has a rich history of development into various branches spanning over several thousand years. It is distinctive of the Western formal logic as it developed embedded in epistemology where it strives to formulate conditions of human reasoning in general. So, Indian Logic can be viewed as systems of nonmonotonic reasoning, which is being used in modern computer simulation of actual human reasoning processes. Indian Logic also challenges skepticism, the view that true knowledge is impossible to obtain. According to Indian Logic, even though humans are imperfect, they may assume that they are justified in their established beliefs. Any doubt of those beliefs has to be reasonable or has to have its own grounds for consideration. Much of the Western Logic assumes that any and all doubts can undermine established claims of knowledge. Index Terms—Nyaya Sastra, Navya Nyaya, Limb, Nyaya Sutras

I. I NTRODUCTION In India, logic was never developed as a seperate discipline but was imbibed in epistemology. Indian Logic (Nyaya Sastra), meaning the science of critical inquiry, has a long history spanning about three thousand years. Nyaya Sastra includes logic, the art of debate (Tarka Sastra) and the science of reasons or causes (Hetu Vidya). While Tarka Sastra lays the principles of argumentation to be used in debates, Hetu Vidya descibes inference as a source of sound knowledge of the world. There have been three phases of develpoment of logic in India. The ancient phase extends from 650 B.C. to 100 A.D. The earliest name given to this form of science was Anvikshiki (The Science of Inquiry). Akshapada Gautama’s work Nyaya Sutra is the key work of this period. The medieval phase extends from 100 A.D. to 1000 A.D. This period saw massive contributions from Buddhists and Jain logicians. An important text of this period is Pramana Samuchchaya of Dignaga. In this period, the science is called Pramana Sastra (The Science of Right Knowledge). The modern phase, called Navya Nyaya (New logic) includes the work done after 1000 A. D. continued to this day by traditional schools of Sanskrit learning.The most instrumental work of this period is Gangesa’s Tattva Chintamani (The Jewel of Reflection of Reality). II. I NDIAN L OGIC VERSUS W ESTERN L OGIC Since logic in India has been embedded in epistemology, it has developed some unique features not found in Western logic. First,over and above its truth-preserving aspect, an inference must possess a truth-giving aspect. That is, for inference as a way of knowing, it is not enough that the conclusion follows from the premises, the conclusion must also be true. It is anticipated of such a theory that it provides the conditions of

validity/consistency as well as completeness and soundness. In Western Logic, conditions of validity do not depend in any way on conditions of truth or soundness. So, an inference can give true conclusion without being valid, and an inference can be valid even without giving a true conclusion.In a formal system, syntax can be developed without any reference to semantics. Hence in Western Logic, semantic considerations are brought in after all syntactic rules are laid down and syntactic consequences are derived.The connection between the syntactic and the semantic sides of a logical system is made by two theorems of completeness and soundness. Ont the other hand, Indian logic is primarily a study of inference-patterns, and inference is clearly identified as a source of knowledge, a pramana. So it includes general questions regarding the nature of the derivation of knowledge from information supplied by evidence, where evidence may itself be another piece of knowledge. In Indian logic,the syntax always has a reference to semantics. For inference as an qualified source of knowing the world, validity is not enough; soundness and epistemic progress also need to be guaranteed.Also, in Indian Logic the idea of validity/invalidity of an inference usually presumes many various information. Two necessary corollaries of this idea are (a) no constituent of an inference can have zeroinformation content like a tautology, and (b) validity of an inference cannot be considered different from soundness, hence an inference is valid only if it yields a true conclusion. Second, to a casual observer, discussion of the logical theories in India would seem to be heavily burdened with psychologistic and intuitionistic terminology, a feature which logicians in the West have tried carefully to diacard from modern logical discussions. Yet the role of psychology i.e. how one mental event causes another mental event or events and how one is connected with the other, seems to be dominant in the Indian presentation. Third, all Indian logicians adopted a grammar-based model of logical analysis, while in Western logic the mathematical model is used. But interestingly, this grammar-based model has led the Naiyayika’s to the understanding of mathematical logicians. They understand general sentences as containing two predicates. Fourth, Western formal logic is extensional. On the other hand, Indian logic is basically logic of properties and hence intensional. But what Indian logicians mean by the term property is somewhat different from its meaning in English. The term property here signifies any locatee, be it an abstract property or a concrete object, which resides in a locus. So the basic combination in Indian logic is not a straightforward subject-predicate proposition but a Sanskrit sentence of the locus-locatee model, for example, a has X-ness. But as the sentences of the form a has X-ness can be easily correlated

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with the sentence of the form a is X, it is possible to read such logic of properties extensionally. Finally, Indian Logic cannot be neatly categorized as deductive or inductive in the standard sense. Ancient Indian logicians were trying to formulate conditions of human reasoning in general. They were trying to determine under what conditions an inferential leap from the known to the unknown would be warranted. As T.K. Sarkar[1] points out The problem that Indian logicians were concerned with was neither the development of a formal theory of deductive or syllogistic reasoning, nor was it the problem of induction as we understand itnow, nor even the problem of how to make a palatable cocktail of the two. Their real concern centered around the problem of selecting the right sort of projectionbase and of framing appropriate rules for distinguishing between projectable and non-projectable properties.

Step 5. Therefore it is so, i.e., there is fire on the hill. Thus, the structure of Five-Limbed Syllogism can be stated as:1. Hypothesis (Pratijna) (To assert: The hill has fire.) (Parvato vahnimaniti Pratijna) 2. Reason or cause (Hetu) (Because it has smoke) ( Dhumavatvat iti hetuh) 3. Example or analogy (Udaharana) (Wherever there is smoke, there is fire, e.g. as in a kitchen.) (Yo yo dhumavansa vahniman yatha mahanasa ityudaharanam) 4. Application (Upanaya) (The example applies to the present situation.) (Tatha cha ayamiti upanayah)

III. N YAYA (O LD ) L OGIC Aksapada defined a method of philosophical argumentation, called the nyaya method or the nyaya model. Nyaya philosophy is based on the aphorisms called Nyaya Sutra of Gautama who is believed to have compiled them in the second century after Christ. In his first aphorism he mentions 16 kinds of things beginning with pramana. By pramana Gautama describes the means or instrument for prama. Prama is knowledge and is obtainable through either perception or inference or comparison or testimony. Prameya or knowable is that thing whose ignorance or misconception leads to suffering and whose knowledge yields freedom from suffering. The most important of these knowable entities is atman or self. The other knowables are related to inference.One of them is limb (avayava) or constituent of an argument (nyaya). A. The Five-Limbed Syllogism The limbs were the most important part of design of the structure of a logical reasoning.To validate the knowledge obtained by inference, the Indian logicians introduced a five-limbed syllogism(panchavayava)[2] as a standard format for inferential information. The first step is the statement of the thesis, the second is the statement of reason or evidence, the third is citation of an example (a particular example, well-recognized and acceptable to both sides) that illustrates the general principle and thereby supports the reason or evidence. The fourth is the showing of the present thesis as a case that belongs to the general case, for reason or evidence is essentially similar to the example given above. The fifth is the assertion of the thesis again as proven or established. Here is an illustration:Step 1. There is fire on the hill.

5. Conclusion (Nigamana) (Therefore, hill has fire.) (Tasmattatheti nigamanam)

conclude:

The

In symbolic logic, this may also be stated as, A →B, (A implies B or If A is true, then B is true), ensuring deductive certainty. The hetu is called a rule (with syntax IF hpremisei, THEN hactioni) in a modern rule-based Expert System. Such systems have been in use since 1980s in diverse applications. But this proof is not the main issue or objective of Indian logic. According to a Nyaya Sutra : Pratyakshanumanopamana sabdah pramanani There are four means of acquiring valid knowledge: pratyaksha, anumana, upamana and sabdah. Sources of valid knowledge are sensory perception, inference, analogy and verbal testimony (of an expert or quotation from a source recognized as standard). Even about the means of sensory perception (pratyaksha) there are concerns as the Nyaya Sutra says: Indriyartha sannikarshotpannam-jnanam-avyapadesyamavyabhichari-vyaavasayatmakam. Even though the perceptual knowledge is obtained by contact of the sensory organ with the object, there are problems. Because of environment (bad light) a rope may be confused as a snake. This is a mistaken perception. Water may be perceived when it is not there, as in a mirage, which is only a visual illusion. With respect to anumana, the following rule is stated: Atha tatpurvakam trividhanumanam samanyato drstancha

purvavat

seshavat

Step 2. For there is smoke. Step 3. (Wherever there is smoke, there is fire), as in the kitchen. Step 4. This is such a case (smoke on the hill).

i. Purvavat: The effect is inferred from the cause. A causes B.If A is TRUE Then infer B. From the cloud cover, infer (predict) it will rain shortly. This provides a reasonable prediction as in weather forecasting. The relation between cloud and rain is previously held knowledge of the

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observer. The effect follows the cause in a causal system. The knowledge is that of a causal relation. ii. Seshavat: The cause is inferred from the effect. A causes b. Observe b and infer A. In modern logic this reasoning is called abduction. It is similar to the process used by doctors to see signs and symptoms of a patient and identify causes such as what the patient consumed yesterday. (This does not preserve truth, but provides plausible explanation). iii. Samanya drsta: This means ”commonly seen”. From ”birds fly” and ”X is a bird”, conclude that ”X flies”. This is called ”default reasoning”, a case of ”common sense reasoning”. This can fail in an exceptional case, e.g. if X is a penguin. Two rules from Nyaya Sutra regarding the pramana (validity) of sabda (verbal testimony) are the following: Aptopadesa sabdah and Sa dvividhoh drsta adrstarthatvat In modern knowledge-based systems, this method of using Apta-vakya corresponds to ”knowledge acquisition” from domain experts. This is an example of ”Learning by being told” an important part of the educational process. There is, of course, no guarantee, that any teacher or expert’s knowledge is correct, complete and valid. Another Sutra characterizes a real entity. Vyaktyakrtijatayastu padarthah The primary components of a term denoting a real entity (or a padartha) are of three kinds: the generic character (Jati), the form or shape of the object (Akrti) and the individual object (Vyakti). IV. N YAYA S UTRAS Table 1 lists all of the Gautama’s Nyaya Sutras[3], each with thier meaning English. TABLE I G AUTAMA’ S N YAYA S UTRAS Pramana Prameya Samsaya Prayojana Dristanta Siddhanta Avayava Hetvabhasa Nigrahasthana Jati Tarka Nirnaya Vada Jalpa Chala Vitanda Tattvajnanat Nihsreyassadhigama

Proof, means of knowledge Provable, Knowable, Objects of knowledge Doubt Aim, Purpose, Relevance Example, Instance Conclusion, Thesis Members of syllogism Fallacy (false middle terms) Occasion for rebuke, Defeat situation Futility, refutations Debate, judgment Conclusion, decision Discussion, debate Dispute using sophistry Quibbling, equivocation Cavil, wrangling From knowledge of true nature Attainment of supreme good

V. B UDDHIST L OGIC Buddhist logic developed over a period of 1500 years. The Buddhists divided knowable objects into two groupsparticular and general; and accordingly admitted two different ways of knowing- perception and inference. Unlike the Naiyayikas, they thought that objects of perception cannot be known through inference, nor is it possible to perceive objects of inference. Perception is the means of directly understanding particulars in their pure form, undistorted by the play of fanciful imagination. Inference, on the other hand, is the means of indirectly apprehending objects in general after the mind imposes names, forms and the so called universals on them. Both perception and inference are supposed to yield certain and correct knowledge of objects. But of these two, perception is considered the means of correct awareness , because it is free from all possible errors. Inference, however, yields certainty when based on adequate evidence. Hence the Buddhist theory of inference is primarily a theory of adequate evidence. Dignaga’s Pramana Samucchaya is counted among the most important works of the medieval phase of Indian Logic. It has six chapters entitled Perception (Pratyaksha), Inference for oneself (Svarthanumana), Inference for others (Pararthanumana), Reason and example (Hetu, Drstanta), Negation of the opposite (Apoha) and Analogue (jati). Suppose a person in twilight mistakes a rope for a snake, his information and belief about the snake is a presumption. Dignaga also notes that a person can perceive a thing without knowing its name or genus. When a person sees a tiger, he only sees a particular tiger with all its peculiarities while he can indicate to others only an idea of a certain class of tigers. The knowledge gathered through inference is different, which is general knowledge regarding tigers. According to him inference for one’s self has one of three features. From cause, an effect is inferred. For example, from smoke, presence of fire is inferred. From identity (svabhava), a class label is inferred. From non-perception (anupalabdhi) of the mark, the non-existence of a thing is inferred. The Buddhists also divide inference into two typesinference for oneself (svarthanumana) and inference for others (pararthanumana).All inferences, according to the Buddhists too, must possess three terms: (a) a logical sign (hetu), (b) the signified (sadhyadharma) and (c) the subject-locus (paksa). When, for example, one infers fire on a hill, seeing smoke coming out of the hilltop, smoke is generally taken to be the logical sign, the hill the subject-locus and fire the signified. A. Inference for others (Pararthanumana) This occurs when a person demonstrates to others the conclusion drawn by him through self-understanding. The predicate or major term(Anumeya or Sadhya) is the object, which is to be established by means of a minor term, which does not contradict the information obtained by perception, inference or verbal testimony.e.g. The hill has fire. The law of extension (Paksha dharma) of the middle term (smoke) refers to the ”intersection” of minor (hill) and major terms (fire) and is stated as follows:a. The middle term must cover the minor term (paksha).

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nonexistence. Abhava is divided into four kinds: b. The middle term must be present in the homologue of the major term (sapaksha). c. The middle term must be absent from the heterologue of the major term (vipaksha). Dignaga thinks that these three conditions taken together constitute the necessary condition of a proposed sign VI. JAINA L OGIC The Jaina logicians define inferential knowledge as ”getting at the knowledge about the probandum (sadhya) on the basis of ones knowledge about the probans (sadhana)”. This very definition of inference is repeated verbatim by Hemacandra[4] and also by Yasovijaya[5]. Yasovijaya adds that inference is of two kinds, namely, svartha(for personal conviction of the inferer) and parartha(for the conviction of others, that is, the public in general). The Jainas bring the whole universe under one or other of two everlasting categories: the conscious (Jiva) and the nonconscious (Ajiva). The latter category includes matter, time and space. This shows the realistic and relativistic standpoint of the Jaina philosophy. Syadvada, the Jaina doctrine of relativism of judgments states that all assertions in regard to an object are relative and therefore conditionally true or false. Siddhasena Divakara alias Kshapanaka (480-550 A. D.), the first and one of the most eminent writer of Jain systematic logic in his work Nyayavatara gives an elucidation on the principles of Pramana(Sources of valid knowledge) and Naya which is a method of realizing things from particular perspectives. Pramanaor a complete judgment describes an object in terms of seven possibilities (Saptabhangi Naya) as follows: i. May be, it is (Syad-asti) ii. May be, it is not (Syad-nasti) iii. May be, it is and it is not different times(Syad-astinasti) iv. May be, it is and it is not at the same time which means it is indescribable(Syad-avaktavya) v. May be, it is and yet indescribable(Syad-asti-avaktavya) vi. May be, it is not and also indescribable(Syad-nastiavaktavya) vii. May be, it is and it is not and also indescribable(Syadasti-nasti-avaktavya)

Samantabhadra’s Aptamimamsa uses the concepts of Syad-asti and Syad-nasti and discusses the relation between asti, that is, bhava or existence and nasti, that is, abhava or

1. Antecedent non-existence(pragabhava), e.g. a lump of clay becomes no-existent as soon as a pot is made out of it, 2. Subsequent non-existence(pradhvamsabhava), e.g. when the pot is broken it ceases to exist 3. Mutual non-existence(anyonyabhava) e.g. relation between the pot and the clay with reference to each other and 4. Absolute non-existence(atyantabhava) e.g. the absence of life in a dead body. It has been examined that on the hypothesis of existence and the entire prohibition of non-existence a thing becomes all permeating, creation-less, everlasting, homogeneous and unimaginable. Here, we can easily discover the formal logical basis for the concepts of Brahman and Atman in Indian Philosophy explained in ancient literature such as Vedas including Vedanta(Upanishads). VII. Navya Nyaya(N EW L OGIC ) Navya Nyaya is considered one of the most important branches of Sanskrit studies after 1000 A. D. Its precise vocabulary enhanced Sanskrit language and influenced learning in diverse fields. It flourished after the works of Udayanacharya(1000 A.D.) and Gangesopadhyaya(1200 A. D.). Some special features of Navya Nyaya[6] are :1. The intricate structure of Navya Nyaya rests on the concept Sambandha(or relation). In a way Navya Nyaya may be called ”relational logic”. In a qualified knowledge(Visistadhi), three things become primarily the content of knowledge: the qualificand (Viseshya), the qualifier (Viseshana) and the relation(Sambandha) between the two. For e.g. Dandi purusha (a man with a stick) the qualifier is stick (danda), the qualificand is man (purusha) and the relation is the contact (Samayoga) between them. 2. An entity called pratiyogitva or pratiyogita is another concept of Navya Nyaya. From the derivation of the word Pratiyogi, it is to be understood as a contradictory relation. This deals with the knowledge characterized by the absence(abhava) of an entity. 3. The word Prakarata in the Navya Nyaya means an adjective of a qualifier(Viseshana). So the property which resides in the qualifier, by virtue of which it becomes a qualifier is its qualifierness(Prakarata). Prakarata is a particular kind of Vishayata, whose other name is Viseshanata. 4. In Navya Nyaya, negation or absence(Abhava) plays a very important role. Both negation and double negation are used to put forward and clarify a number of ideas. In the Vyaptipanchaka Gangesa defines Vyapti(pervasion) as Sadhyabhavavadavrittitvam, which means the non-existence of the hetu in the locus of absence of sadhya or the object of

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inference. If, on the other hand, sadhya is dhuma(smoke) and hetu is vahni(fire) and if Vyapti is defined without negation as Sadhyavadavrittitvam this is not correct. It may be seen that the middle term(hetu) exists in the locus of absence of sadhya(smoke) leading to a wrong conclusion of Dhumavan Vahneh(Fire always exist with smoke) as can be seen from the confirming example(sapaksha drstanta) of a red hot iron ball(taptayo-golakah) in which iron ball is on fire but no smoke is produced.

VIII. C ONCLUSION In this paper, a summary of how the science of Logic has evolved for over three thousand years in India has been given. It has been shown that how various branches of Indian Logic, on one hand are different from each other and on the other hand, seem to be deriving from a same common source of ancient Vedas and Upnishads. In recent years various disciplines of Indian Logic have received greater attention from equally from India and also the western world. Althogh, much work is to be done in studying the vast field of Indian Logic and carrying forward on the works of ancient and modern Indian Logicians, the modern world is slowly begining to realize the real power of Indian Logic as it is evident with many applications of the various aspects of Indian Logic in Computer Science and Information technology with Sanskrit gramma receiving much attention in the context of Natural Language processing (NLP) and Information Technology in Indian Languages with one of the main application area of Machine Translation (MT). R EFERENCES [1] T. Sarkar, “Jaina logic in perspective. in essays in indian philosophy,” 1997. [2] B. K. Matilal in The Character of Logic in India, 1998. [3] P. V. V. S. Sarma, “Indian logic and its relevance to computer science and information technology,” 2001. [4] Hemacandra in Pramanamimamasa, 1939. [5] Yasovijaya in Jaina Tarkabhasa, 1973. [6] L. Haaparanta in The Development of Modern Logic, 2009.