II.—The Nature of Inference in Hindu Logic

Aim and scope of Hindu Logic.

The word Nyáya is often mistaken as equivalent to Logic. But in reality the word Nyáya may be roughly taken as equivalent to argument. The word however now stands for a system of Indian Philosophy. One of the six systems of Hindu Philosophy is called Nyáya, because it treats of arguments more thoroughly than any other. Nyáya then is not synonymous with Logic. (¶1)

According to British logicians generally, Logic is the doctrine of Inference, and the end of Logic is the attainment of truth by thought, i.e. by the comparison of one thing with another. Intuitive or immediate knowledge is according to them beyond the province of Logic, which is concerned only with inferential or mediate knowledge. In this sense Logic is equivalent to Anumánbád or the doctrine of Anumán, which means knowledge of one thing through another. But in European Philosophy Logic is also taken in a far wider sense, in which all truth, i.e. all knowledge intuitive and inferential, immediate and mediate, is the end of Logic. Ueberweg the great German logician is one of those who adopt this wider view of Logic. In this sense Logic is equivalent to the Indian Pramánbad or the doctrine of Proof or means of valid knowledge. Proof or Pramána is the means of arriving at Pramá or knowledge of things as they are, whether that knowledge be inferential or immediate. Pramánabád deals with the whole subject of knowledge and lays down the conditions of valid knowledge. Proof accordingly includes Intuition, in what I am inclined to call Hindu Logic, taking the word Logic in the same sense in which Ueberweg uses it. British Logic or the doctrine of Inference is thus only a part of Ueberweg’s or Hindu Logic. (¶2)

Hindu Logic is essentially material or objective, for the result of Proof is Pramá, which is thus defined by Bisvanáth, a commentator on Gotama: Pramá is the knowledge of things as they are; and truth which is the object of Hindu Logic means not merely formal but material truth. (¶3)

Parts of Hindu Logic.

Hindu Logic is divided into as many parts as there are kinds of Proof. Even an ordinary student of British Logic knows how much difference of opinion there is on logical subjects. Hindu Logic too is not less a field of contention. There are different opinions on every subject, and, as in British Logic, here too a student has the liberty of forming his own opinions and criticising others. (¶4)

Gotama, the founder of the Nyáya system, notices the difference of opinion as to the varieties of Proof in the second section of the second chapter of his Nyáya Aphorisms. Eight is the largest number of varieties of Proof maintained in Indian Logic. They are (1) Pratyaksham, (2) Anumánam, (3) Upamánam, (4) Sabdas, (5) Aitihyam, (6) Arthápattis, (7) Sambhabas, (8) Abhábas. I shall briefly explain these in their order. (¶5)

(1) Pratyaksham is defined as follows in the Bhásya, the oldest commentary on Gotama’s Aphorisms. Pratyaksham is knowledge gained through the direct relationship of the sense and the object. The senses include the five external senses and what is called in Nyáya Philosophy the manas. This word mana is mistranslated by the English word mind. Mana has no equivalent in the English language; but in respect of its function it may be translated by the Internal Sense. By the Internal Sense, according to some British writers, the Ego can know itself and its own states or phenomena. With them it means the power of Introspection, which is called the Internal Sense only metaphorically; for there is no Material Sense for that purpose. But according to some of our philosophers there is a Material Sense called mana specially fitted for the purpose, which can therefore be really called a Sense, exactly as the eye or the ear is called a sense. It is now easy to translate the word Pratyaksham, for it is the same as Intuition, which includes Internal and External Perception, i.e. Perception of the external objects as well as of the Ego and its phenomena. (¶6)

(2) Anumánam, as we have seen, is knowledge of one thing through another, which latter serves as the Lingam or sign or mark. It may be taken as equivalent to Mediate Inference. It excludes Immediate Inference. (¶7)

(3) Upamánam, according to the Bhásya, is such knowledge of similarity as as the cow so is the Gabaya. I know that Gabaya is the name of an animal like the cow; the animal however has never been seen by me. I now see an animal like cow. Hence I know that this is the animal whose name is Gabaya. The Upamánam is the process of discovering for one’s self the connection between a thing and its name, when the description of the thing is previously known. The Bhásya holds the object of Upamánam is the meaning of a name. First it is known that Gabaya is like a cow. An animal like cow is perceived by the senses; hence it is known that this animal’s name is Gabaya. Similarly having heard that mudgaparni is like mudga and mashparni is like mash, an individual recognises these objects by Upamánam and then gathers these herbs for medicinal purposes. The Britti, a later commentary on Gotama’s Aphorisms, adds Dissimilarity or distinction also enables us to discover the meanings of names. E.g. we learn that this animal is called camel, because it possesses the distinction of a very large neck, i.e. in this it is dissimilar to other beasts. We thus see that Upamánam is the application of names to things, through their similarity or dissimilarity to other things. It is difficult to find a word in English Logic that will correspond to Upamánam. It is often carelessly translated by Similarity, or Comparison, and sometimes, ridiculously enough, even by Analogy. I do not think it fair to translate it by any English word. (¶8)

(4) Sabdas literally means word and is translated by Authority. It is thus defined by Gotama: Word is the teaching of the reliable. This definition is explained in the following lines of the Bhyasya:—Word (or word considered as proof) is the word of the veracious, i.e. those who have actually observed the things of which they are speaking, and who are at the same time impelled by the desire of relating things and events exactly as they saw; be they Rishis, Aryas, or Mlechchhas. (¶9)

(5) According to the Britti, Aitihya includes all those sayins which begin with It is said, and of which the first speaker is unknown, and which have been handed down from generation to generation. It may be translated by Tradition. (¶10)

(6) According to the Bhásya, Arthápattis is the inference of a meaning which is implied in the direct meaning of a sentence or proposition. As, for instance, when it is said If there is no cloud, there is no rain, it may be inferred that when there is rain, there is cloud. All such inference in which we make explicit the implicit meaning of a proposition is called Arthápattis. It may therefore be translated by Immediate Inference. The above definition seems to identify Immediate Inference with Arthápattis. In reality, however, Hindu Logic does not recognise Immediate Inference as proof. The only kind of Immediate Inference here spoken of, which some of the schools of Hindu Logicians recognise, is the so-called Hypothetical-Categorical Syllogism, which is in reality no proof at all but a form of Immediate Inference. J. S. Mill justly observes that in immediate inference there is not really any inference; there is in the conclusion no new truth, nothing but what was already asserted in the premisses, and obvious to whoever apprehends them. The so-called Hypothetical-Categorical Syllogism is an inference of this kind. (¶11)

(7) According to the Britti, Sambhava is knowledge derived from the knowledge of (mere) coexistence. It is the same as Probability. E.g. a Bráhman is probably learned; a hundred is probable in a thousand. (¶12)

(8) The Britti says Abhaba is the inference of the presence of a thing from the absence of what is contradictory in nature to it; as the inference of the existence of snake from the absence of Nakul (a species of weasel). (¶13)

The above eight are varieties of proof. What conditions each of them must satisfy in order that each kind of Proof may be valid is an altogether different question and cannot be dealt with here. As has been said above, all these are not admitted to be independent proofs by all the different schools of Indian Philosophy. The following is a summary of the difference of opinion on this subject. (¶14)

(1) The Chárbákas hold that there is no proof other than Perception. (2) The Vaisesikas hold that Perception and Inference are the only Proofs. They do not reject the others as proofs, but maintain that the others are reducible to inference, are only different applications of inference. This remark is also applicable, mutatis mutandis, to the following opinions. (3) In the seventh aphorism of the Samádhipáda of Pátaugala Philosophy it is held that Perception, Inference, and Authority are the only proofs. (4) Gotama admits the first four, Perception, Inference, Authority, and Upamán, as proofs. The following opinions are gathered from Pandit Jayanáráyan’s Commentary on the fifth Aphorism of the second section of the ninth chapter of Vaisesika Darsana. (5) The Mimánsakas add Immediate Inference or Arthápatti to the four of the Naiyáyikas, and thus maintain that there are five proofs. (6) The Pauránikas add Tradition and Probability to the five of the Mimánsakas and hold the seven as proofs. (7) According to the Bhattas and the Vedantikas, Abhába or inference through absence is also a proof. (¶15)

Of all the various kinds of Proof, Perception is the most certain. The Bhásya says Perception is the most certain knowledge. When we have a desire of knowing a thing, if we receive instruction about it from some authority, there is yet a desire to know it by Inference. Even when we infer the object, there is still a desire to perceive it. But as soon as we perceive the thing the desire is for ever quenched. We do not want to know a thing more certainly when we perceive it. (¶16)

Nature of Inference

I shall now try to give a rough idea, as best I can in a foreign tongue, of the nature of Inference (the subject matter of British Logic) as conceived in the most advanced school of Hindu Logic. It should be borne in mind that we cannot expect to find in Hindu Logic of Inference parts exactly corresponding to the several parts of British Logic. The process of Inference is called Anumán, and the product is called Anumiti. It is generally identified by English writers with Deduction. But as will appear hereafter this identification can be only a very rough one. In fact like J. S. Mill’s True type of reasoning it includes both Induction and Deduction. (¶17)

We have seen above that Anumán is the knowledge of one thing through another. In every inference three things are necessary, viz. (1) the Paksha or that about which something is inferred, (2) the Sádhya or that which is inferred about the Paksha, and (3) the Hetu, reason, or Linga, lit. mark (the same word as used by Mill), by means of which the Sádhya is inferred in the Paksha. But it is evident that anything is not inferred of anything. Every Anumiti or inference must satisfy the two following psychological conditions:—we must be sure (1) that the relation between the Hetu and the Sádhya is such that we are warranted to infer the latter through the former; (2) that the Hetu or mark is in the Paksha. In other words, the Hetu or Linga must be Vyáptibisishta, i.e. have Vyápti, the Inference-Relation, and have Pakshadharmatá, i.e. existence in the Paksha. Anumiti is defined by Ganges Upádhyáya, the founder of the modern system of Nyáya, as Knowledge derived from the knowledge of the Hetu having Vyápti and being in the Paksha. Vyápti means such a relation between the Hetu and the Sádhya as warrants us to infer the latter from the former, to regard the former as the unmistakeable sign or mark of the latter. Dr Roer truly remarks It is difficult to find an adequate word for this term in English. I therefore translate it by Inference-Relation. (¶18)

It is exceedingly interesting to observe that this type of reasoning exactly corresponds with J. S. Mill’s True type of reasoning. Mill was justly dissatisfied with what he called the popular division of reasoning into Induction and Deduction, and to him belongs the merit of discovering, in the European world, the True type of reasoning, which falls under neither of these descriptions, and which, nevertheless, is not only valid, but is the foundation of both the others. His description of this type of reasoning exactly corresponds to what I have given above as the definition of Anumiti. Having discovered the universal type of the reasoning process, he divides the operation into two steps answering to what Upádhyáya lays down as the two conditions of Inference and by which he defines Reasoning. Mill’s two steps, stated in a general form, are:—first, that of ascertaining what attributes are marks of what others; and, secondly, whether any given individuals possess those marks. He identifies the first with Induction and the second with Deduction. In Hindu Logic Reasoning is not divided into two steps, but in every reasoning that which is used as the Hetu or mark (1) must have a definite specific relation with what is inferred of any individual or individuals; and (2) it must be in the Paksha or the individual or individuals of which something is inferred. (¶19)

I shall try to illustrate the nature of Anumiti by an example. Suppose that I see smoke issuing out of a mountain. From that I conclude that the mountain has fire. The conclusion is stated in Sanskrit as Parbato bahnimán, the mountain with-fire. Thus the conclusion has only two parts mountain and with-fire. The former is a noun and the later is a predicative adjective. In the opinion of English logicians in general this cannot be the form of the conclusion, which, inasmuch as it is a judgment, must always be stated in the form of a proposition consisting of the Subject, the Predicate, and the Copula expressing the relation between the Subject and the Predicate. In a Sanskrit logical proposition we have no copula at all. At first in the sight of a European reader this may seem to be a grave defect; but it is not so. The introduction of the copula into the logical analysis of a proposition is merely an accident of the language. The copula is not an essential part in the analysis of knowledge or of a judgment. In Hindu Logic all knowledge and therefore all inference can have this simple form:—this substance with this attribute. The copula depends upon the spirit of a language, and as far as I can see if the logic of a language can and does dispense with the copula so much the better. As W. E. Johnson truly observes in Mind N.S. No. 1 (p. 23), The usual logical analysis of the predicative-term into copula and predicate-term is not fundamental and is in some respects particularly misleading. This analysis is generally, in fact, a merely verbal device, having no logical significance. He would have a proposition analysed into two parts, the subject-term and the predicative-term, exactly as we have got in our Sanskrit Logic. In the above example of Inference (¶20)

Mountain is the Paksha, and
Fire is the Sádhya. (¶21)

The Sádhya, fire, is inferred of the Paksha, mountain. The Hetu or mark of the Sádhya is always stated by a single word, the name of the thing which serves as the mark, with a certain inflection. The Hetu in the above instance is given as (¶22)

Dhumát, because of smoke. (¶23)

In English Logic the Hetu or reason of inference should be stated in the form of the proposition the mountain has smoke. (¶24)

Now let us ask a student of British Logic the following question:—Given this mountain has fire as conclusion, and this mountain has smoke as premise; what is the suppressed constituent of the inference? He will readily answer that it is All that has smoke has fire. This universal proposition is taken as the ground of inference. If you ask the same question of a student of Hindu Logic he will say that the ground of inference is the relation Vyápti of smoke with fire. It is this difference between the European and the Hindu Systems of Logic that I mean to emphasize. The peculiarity of Inference in Hindu Logic consists in the Vyápti. The word does not seem to be as old as Hindu Logic itself. Gotama the founder of the Nyáya System, and his earliest commentator Pakshila Svamin, also called Vátsáyana, the author of the Bhásya, do not use the word Vyápti in their definitions of Antumiti. Nor does it occur in the definition given by Kanáda, the founder of the Vaisesika system. The Bhásya very concisely yet clearly explains the process of inference as follows:—Inference must always be preceded by Perception, viz. perception of the sign and the significate as related. We first perceive the related two; and afterwards by either perceiving or remembering the sign in a particular thing we infer the significate which we do not perceive. What is here called by the simple and general name of relation is afterwards changed by later logicians for the specific Inference-Relation or Vyápti. Knowledge of Vyápti is now regarded as an essential and indispensable condition of inference. Vyápti is itself a relative term, implying two correlatives. The Sádhya is called the Vyápaka and the Hetu is called the Vyápya; and the relation between them, without the knowledge (valid or invalid) of which inference never takes place, is called Vyápti. Vyápti-báda or the theory of Vyápti comprises a discussion of two very important questions:—(1) Ká Vyáptis, i.e. what is the nature of this Inference-Relation? and (2) Katham Vyápti-graha, i.e. how is this Relation known? (¶25)

An ordinary student of British Logic may be inclined to ask, Why this elaborate attempt to define Vyápti? The Indian philosophers, like the European logicians, ought to have taken the universal proposition as the ground of inference. To this the British logicians themselves, like J. S. Mill, have given an unanswerable reply. If the universal proposition be taken as the ground of inferring a particular included in it, reasoning must always move in a Chakraka (lit. a circle). Besides, the Indian logician asks, What is the psychological necessity of inferring the particular when the universal is already in the mind? Thus the supposition, that the universal proposition is taken as the ground of inferring a particular included under it, involves a psychological fiction and a logical chakraka (circle). How do you know the universal all Hetu is Sádhya? Such a knowledge is impossible. All H is S ordinarily means a collocation of all such instances as this H is S, that H is S &c. &c. But it is impossible that all H should form the object of one piece of knowledge. There must always be many H’s which will be absent from your mind both in time and in place. How can these form the object of your knowledge? It must be maintained therefore that all H is present to your thought only through its connotation. Thus instead of taking H and S in their denotation, you are compelled to take them in their connotation. Connotation is unitary, and therefore the connotation of all H can form the object of a single piece of knowledge. Now, the knowledge of the connotation of H (Hetu), and the knowledge of the connotation of S (Sádhya), so long as they remain two disconnected pieces of knowledge, or even one knowledge, if possible, of two distinct disconnected connotations, cannot be the ground of inference. To produce inference the two connotations must be known as related as Vyápya and Vyápaka. To know them thus related is to know their relation Vyápti. Viewing the question through the light of European Logic we may say that Vyápti is that relation between H and S, on the knowledge of which we can assert the universal proposition All H is S. Vyápti itself is the relation which forms the ground of the universal affirmation. We thus see that Hindu Logic lays special stress upon the knowledge of a relation as the indispensable psychological source of inference. Mill resolves the universal type of the reasoning process…into the following elements: 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 attribute. from this analysis we try to find the nature of Vyápti or the relation between the other attribute (the Hetu) and the given attribute (the Sádhya), it seems to be mere coexistence. From the knowledge of the mere coexistence of two attributes we infer the one from the other. British logicians have made no attempt to define this relation. It is because Hindu Logic makes the knowledge of this relation an indispensable condition of inference, that the discussion of the nature of Vyápti has formed an important chapter of Hindu Logic. British Logic has nothing corresponding to it. We thus see the importance of the question asked by Ganges Upádhyáya immediately after the definition of inference, viz. What is Vyápti the knowledge of which is a condition of inference? (¶26)

The term Vyápti is surely older than Ganges Upádhyáya, the founder of modern Nyáya, who is supposed to have lived in the latter end of the 14th century. He criticises the definition of Vyápti as given by an ancient author. Philosophical authors in Sanskrit do not as a rule give the names of those whose opinions they notice or criticise. Their annotators generally supply the names of those authors or schools. The origin of the old definition that Ganges criticises at the beginning was evidently unknown to his commentators, for they do not supply it. The definition is Avyabhicharitatvam Vyápti. Ganges first gives five possible meanings to this definition, probably those in which it was actually taken by the ancient school, and then rejects them all by a single objection. This part of the text with the annotations on it is called the Vyápti-panchaka, the Five Vyáptis. I shall not give the five meanings, but only two of them which are considered important. The two meanings are Sádhyábhábabadabrittitvam and Sádhyabadanyábrittitvam; first, that the Hetu does not exist in that which has the absence of the Sádhya, and secondly, that the Hetu does not exist in what is other than that which has the Sádhya. These two meanings are embodied in No H is not-S, or No not-S is H, which is called in English Logic the obverse and the contrapositive respectively of All H is S. In English Logic it is thus assumed that No H is not-S is equivalent to All H is S. In ordinary text-books of Deductive Logic these are given as equivalents without any qualifying observation. No doubt whatever is entertained about their equivalence. It is however a relief to find that Dr P. K. Ráy in the fifth edition of his Text-book of Deductive Logic (Macmillan and Co. 1891) states in Appendix G that this equivalence is not always true. There is a class of cases in which this is not true, viz. those in which there is no contradictory of S, in which not-S does not exist. He says If the term B in the proposition all A is B has no contradictory, i.e. if it covers the whole sphere of thought and existence, then the proposition can be neither obverted nor contraposed. You will seek in vain for such a qualifying remark in ordinary text-books of English Logic. But what does not strike even the authors of text-books of British Logic is, strange to say, the very first thing that every student of Hindu Logic has to learn. The very first thing he has got to learn when he is said to begin the study of inference is that all H is S is not always equivalent to No H is not-S. The latter proposition is an absurdity when S is Kebalánvayi, i.e. covers the whole sphere of thought and existence. The two-fold definition of Vyápti given above is thus too narrow, because it is inapplicable where the Sádhya is found in every object of thought and existence. There not-S is an absurdity and an inconceivability. Knowable and Nameable are among examples of Kebalánvayi terms. If you say there is a thing not-knowable, how do you know it? If you say there is a thing not-nameable, you must point that out, i.e. somehow name it. Thus you contradict yourself. This thing is knowable because nameable. This inference is valid because whatever is nameable is knowable, and vice versa. Each of the two terms covers the whole sphere of thought and existence. Not-S, i.e. not-knowable, is an absurdity and has therefore to be rejected out of account by Indian Logic. (¶27)

Ganges Upádhyáya himself gives four alternative definitions of Vyápti, one of which as improved and altered by his commentators is now accepted as the Sidhántalakshana, i.e. final definition. I shall first briefly explain the technical terms used in the definition, and then give the definition itself, without entering into the discussions contained in the celebrated treatise by Yagadisha, called the Sidhántalakshana. (¶28)

(1) In English Logic propositions are divided according to their quantity, and by the position of a term in a logically stated proposition we can at once tell whether it is distributed or not. The distribution of a term means that the whole of its denotation has been taken into consideration, i.e. every individual possessing the connotation of the term has been taken into consideration. In Sanskrit Logic the same idea is expressed in a different manner. The abstract noun from Sádhya is Sádhyatá. Now, there cannot be such a thing as pure indeterminate Sádhyatá. It must be avachchhinna, i.e. determined by something; and the attribute or attributes connotated by the term used as Sádhya is said to be the determinant of the Sádhyatá. Thus in the example this mountain has fire, because of smoke, fire is the Sádhya and fireness is the determinant of the Sádhyatá; and things denoted by the term used as Sádhya is expressed by the phrase individuals possessing the attribute which is the determinant of Sádhyatá. (¶29)

(2) Similarly, smokeness is the determinant of Hetutá, which is the abstract noun from Hetu; and things denoted by the term used as the Hetu is expressed by the phrase individuals possessing the attribute which is the determinant of Hetutá. (¶30)

(3) Again, there cannot be such a thing as pure absolute negation. Negation is always correlated to a position or affirmation. The negative must always have a positive or affirmative correlated to it. The positive in relation to the negative is called the Pratiyogi. Thus in the phrase Patábháva, i.e. negation of cloth. Pata or cloth is the Pratiyogi. The abstract noun from Pratiyogitá. Pratiyogitá cannot be pure undetermined. The attribute determining Pratiyogitá is called the determinant. In the instance given above Petatva or cloth-ness is the determinant of Pratiyogitá. (¶31)

Now, Vyápti as most briefly expressed implies that the determinant of Sádhyatá is the non-determinant of the Pratiyogitá of every negation that exists in the object where the Hetu is; that the connotation of the term used as Sádhya is the non-determinant of every position correlated to the negation in that which has the Hetu. For the sake of shortness, instead of using the clumsy phrase non-determinant of the Pratiyogitá or position correlated to the negation, I shall use non-determinant of the negation, taking the two to mean the same thing for our present purpose. (¶32)

Take the old example again, This mountain has fire, because of smoke. Here smoke is the Hetu; and the culinary hearth, e.g. is a thing which has the Hetu, smoke. From the culinary hearth many things are absent; e.g. cloth is not in the culinary hearth. Therefore cloth-ness, the attribute connoted by cloth, is a determinant of a negation in culinary hearth. Cloth is negated in (or denied of) culinary hearth; therefore cloth-ness can be said to determine the negation in culinary hearth. But fire-ness which is the determinant of the Sádhyatá is a non-determinant of the negation in culinary hearth, for it cannot be said that fire is not in the culinary hearth while smoke is there. The principal part of Ganges’ definition as modified by Rahunáth Siromani may not now be unintelligible. As, however, a literal trnanslation will still be wholly unintelligible to those who have not studied the subject in the original, I shall try to give only a very rough idea, which is the utmost that I can do, the subject being extremely abstruse and the language a foreign one. The main part of the definition runs thus: (¶33)

The coexistence of anything of the Hetu and that which has for its connotation an attribute which is non-determinant of the negations in that thing, is the Vyápti of things having the connotation of the Hetu with things having that non-determinant attribute for their connotation. (¶34)

The merit of the above definition consists in this, that Vyápti is conceived to be a relation between two connotations. Thus Vyápti between two connotations is the coexistence of two things having the two connotations respectively, in one (or more than one) thing, under the condition that the connotation of the Sádyha is non-determinant of the negations in that thing (or things). The objection to the ancient definitions is thus avoided because Ganges’ definition does not make use of the negation of Sádhya, or things other than those having the Sádhya. From the knowledge of mere coexistence of the two things in one or more things we do not infer the existence of the one from the existence of the other, unless we have the knowledge that the former does not and cannot exist without the latter, that the connotation of the former is the non-determinant of the negations in things having the latter. When it seems to us that a man draws an inference from mere coexistence he really bases the inference on mistaken Vyápti. When from the existence of A, we infer the existence of B, it is not from the knowledge that all A is B, but from the knowledge that A cannot exist without B. This the Hindu logician does not express by saying No not-B is A, or No A is not-B, for there are cases in which not-B is an absurdity; but by saying that the attribute connoted by B is non-determinant of the negations in that which has the connotation of A for its connotation. Thus the emphasis is everywhere laid on the attributes and connotations. (¶35)

There was still a class of cases which presented a further difficulty to the Hindu logicians, viz. those cases in which A coexists with, as well as without B, when B and not-B exist in the same thing in different parts. E.g. the tree contains monkey (on its branches), and the want or absence of monkey (on its trunk). To include these cases within the definition, negation in the above definition is qualified by the phrase not coexisting with its correlated position. The connotation of the Sádhya must be the non-determinant of such a negation as does not coexist with its correlative position; otherwise in such cases although the Sádhya coexists with the Hetu, its connotation becomes the determinant of the negation, for the Sádhya is also absent there. (¶36)

Improvement of the definition by Siromani

There were many definitions of Vyápti accepted by the various logical sects of India, before and during the time of Ganges Upádhyáya. He was a native of Mithila (north-east Behár). He founded the modern school of Nyáya. His great work, the Tattvachintámani, of which the subject is Proof, is the text which has always been regarded as the great authority on Proof, and on which it was the great ambition of later logicians to write commentaries. And gradually the study of Logic came to mean the study of a few selected portions of Ganges’ work with commentaries on them, till at last the study of Logic has been confined to that portion of Ganges’ work which treats of Inference. Didhiti, the commentary on Ganges’ Inference, which is most universally read, is by Raghunáth Sirmomani. There are two important elucidations of this commentary, one by Yagodish Tarkálankár, and the other by Gadádhar Bhattácháryya. Different portions of these are read in connection with the Didhiti of Raghunáth. The celebrated work Didhiti, though calling itself a commentary on the portion on Inference in Ganges’ Tattvachintámani, is in many respects an original work. The author, Raghhunáth Siromani, is supposed to have lived at a time which seemed particularly favourable to the growth of learning and independence of thought in Bengal, especially in Nuddea; for, according to tradition, he was a contemporary of Chaitanya, the great religious reformer of modern India. In fact, he was such a powerful thinker in an age of scholastic infertility that he distinctly declared that he cared not if his conclusions and theories were contradictory to the six systems of philosophy prevalent in India, provided they were in accordance with reason. This was not an insignificant thing in a writer of that period. His life, too, would be a very interesting and instructive study, if the materials for a biography could be at all procurable in India. He was not satisfied with Ganges’ definition of Vyápti, and even after giving it the most favourable interpretation (which I have given above) could not help substituting a better one. His claim to original thinking however is not based mainly on his treatment of Vyápti. (¶37)

He pointed out that in all inferences at least three relations are involved; e.g. in the inference this mountain has fire, because of smoke, (1) we know that the Hetu, smoke, is in the mountain, i.e. has a certain relation with the mountain, viz. contact. This relation between the Paksha and the Hetu may not be the same in all instances. The relation which the Hetu is conceived to have with the Paksha is called the relation which determines the Hetutá. (2) The relation between the Hetu and the Sádhya is, as we have seen, the Vyápti. (3) By reason of the Vyápti, the Sádhya is inferred in the Paksha, i.e. we infer that a certain relation exists between the Sádhya and the Paksha. The relation in which the Sádhya is conceived to be in the Paksha is called the relation which determines the Sádhyatá. (¶38)

Similarly Pratiyogitá (i.e. position or affirmation correlated to a negation) is also determined by a relation. In other words, in every affirmation or negation we have in view a certain relation. For instance, when we say that the cloth is absent from the hearth, we mean that it is absent there in the relation of contact. One thing may be absent from one place in one relation, and present in that place in another relation. E.g. fire is present in this mountain in the relation of contact, i.e. fire is in contact with this mountain; but fire is absent from this mountain in the relation of inherence (the relation in which an attribute, e.g. exists in a substance, or the whole exists in its parts), i.e. fire is neither an attribute nor an integral part of this mountain. When therefore one thing is denied of another thing a certain relation is had in view. (¶39)

The following definition should therefore be substituted for the definition given by Ganges: (¶40)

The simultaneous existence, in one and the same thing, of the Hetu, in a definite relation; and of a thing having a certain attribute for its connotation, in a definite relation, which latter (attribute and relation) are joint non-determinants of negations which have the Hetu;—such simultaneous existence is Vyápti of things having the connotation of Hetu for their connotation, with things having that non-determinant attribute for their connotation, under those definite relations. (¶41)

An example or two will make the definition clear. This mountain has fire, because of smoke. Now, culinary hearth is that which has the Hetu, smoke, in the definite relation of contact. The relation in which fire exists there is contact. Positions correlated to negations in culinary hearth cannot be determined by fire-ness plus contact; i.e. contact of fire cannot be wanting in culinary hearth when there is smoke; therefore fire-ness and contact are the joint non-determinants of negations in culinary hearth. Fire may be absent from it in any other relation, or something else may be absent from it in the relation of contact; fire-ness in the relation of contact is non-determinant of negations in the culinary hearth. Hence smoke has Vyápti with fire, i.e. fire exists in the relation of contact in that in which smoke exists in the relation of contact. (¶42)

The two relations in this example happen to be the same, but there are instances in which they are different; e.g. in the inference, Chaitra has happiness, because of wealth or money, the Sádhya happiness exists in the individual Chaitra in the relation of inherence, i.e. the state or property of happiness inheres in Chaitra; but the Hetu, wealth or money, exists in him in the relation of possession, is related to him as a possession, i.e. is possessed by him. When we know that wealth exists in the latter relation, we can infer the existence of happiness in the former relation; otherwise not. We know, e.g. that money exists in the chest in the relation of contact; from this we cannot infer that happiness exists in the chest in the relation of inherence. Vyápti thus always supposes two relations which determine the coexistence of the Hetu and the Sádhya. (¶43)

The qualification of negation as not coexisting with its correlated position applies to the definition given by Siromani as well as to that given by Ganges. (¶44)

With regard to these definitions the reader must not ask about the origin or ground of knowledge of Vyápti. It would be irrelevant to ask here as to how the knowledge of the coexistence of two things under a certain condition, on one or two or any limited number of occasions, can give rise to inference. I am giving here the bare substance of that chapter of Hindu Logic which deals only with the definition of Vyápti, and hope to be allowed to take up those questions on some future opportunity. Unless we have the knowledge of Vyápti in the Hetu we cannot infer anything from it. The question with which we have been concerned in this paper was, what does the knowledge of Vyápti in the Hetu mean? We now see that the knowledge of Vyápti means the knowledge of the coexistence of the Hetu and the Sádhya in a limited number of cases under a certain condition, viz. that negations in those cases are non-determined by the Sádhyatá-determining attribute and relation. (¶45)

Thus we see very clearly that the Hindu theory of inference is essentially the same as Mill’s theory. For he also contends that inference really passes from particulars to particulars. It should, however, be noted that knowledge of mere coexistence* is not the basis of Inference. Inference is in reality based upon the knowledge of coexistence under a condition. (¶46)

The present plan of teaching Hindu Logic in India.

The definition of Vyápti is an important and difficult part of the Hindu logical system. It has given rise to a long discussion embodied in a large number of big treatises full of intricate and abstruse matter. After the five definitions referred to above, Ganges criticises two others given by a logician of the name of SinhaVyaghhra (lit. Lion-tiger). The twofold definition is called after its author’s name. After these he criticises a dozen of others. The part of the text which contains this criticism is called the Purbapaksha. So that in all he criticises nearly a score of definitions before giving his own. The plan of teaching this part of Logic, followed in the place from which I write and which has for the last three or four centuries been regarded the centre of Nyáya learning in India, is as follows. The students begin with a very brief compendium of Vaisesika Philosophy written in verse in order to help the memory. The name of this text-book is Bhásháparichchheda. It is admirably fitted for the purpose of introduction. They do not at first read the notes on it, by its author, which contain an exhaustive treatment of the whole system. At first they get the whole or a considerable portion of the text by heart, having previously learnt its meaning. But they never read any portion of the text of Ganges without the elaborate notes on it by one or other of the annotators. (¶47)

After reading the Bhásháparichchheda they go on to the Vyáptipanchaka or five Vyáptis, referred to above, together with the notes on it by Mathuranáth, without learning the part of Ganges’ text before that, which, as being more difficult, they read after they have made some progress. The Five Vyáptis takes about two months’ regular study to finish. Then come the Lion-tiger definitions, which can be finished in a couple of days. The third treatise, which the regular logical students have to read cannot be finished in less than a year; it takes generally more than a year of regular study. This treatise is called Vyádhikarana, a treatise which has its origin in a perverse love of argument. An absurd argument of a logician of the name of Sandoda, which is refuted here, has given rise to this chapter of Hindu Logic. I consider the study of this chapter to be a cruel waste of time, a sacrifice to the perverse love of argument that prevailed in the period of Hindu Logic which we are just passing over and which I am inclined to call the scholastic period of Hindu Philosophy. (¶48)

Then comes the Purbapaksha, the criticism of a dozen definitions referred to above. This treatise is generally omitted. Even if read it would not take more than a month. Thus after having read criticisms of definitions and matters somehow or other connected with them for a period of nearly a year and a half, the student is allowed the privilege of studying the definition of Ganges himself, viz. the Sidhántalakshana given above. (¶49)

This plan seems to me to be mistaken. Beginners should be allowed to read the final definition at first without being taken into the intricacies of criticisms, replies and rejoinders, which more advanced students can read in less time if they are inclined to do so. The plan of teaching is mainly responsible for the neglect of philosophical study and scarcity of original philosophical thinking in modern India. No philosophical student can help being struck with the fact that as a rule the more ancient a philosophical work, the more interesting it is by reason of its variety of subjects, its candid unbiassed treatment, its freedom from the service of any particular religious doctrine, and the total absence from it of any indication of the spirit of scholastic disputation; whereas, as Pandit Mahámahopádhyáya Mahes Chandra Nyáyaratna truly remarks, a hair-splitting subtlety in the discussion of meanings of terms is the distinguishing characteristic of modern Nyáya. Yet however till recently, the works of Ganges Upádhyáya and his followers so completely superseded the ancient Nyáya works that very few Pandits of the present day even possess copies of these works. The pulsation of a reaction in favour of the ancient system and a just repugnance to the subtleties and technicalities of modern Nyáya is beginning to be felt. And it can be hoped that we shall soon pass over the scholastic period of Hindu philosophy. For the desire of returning to the old giants of ancient philosophy, one of the principal factors to which modern European philosophy owes its origin, is at work. But before the indiscriminate contempt characteristic of a reaction to the new system, which is not without its merits, may, I am afriad, be neeglected more than it deserves. To save it from being completely set aside, the plan of teaching should be thoroughly reformed, and the student should be taught only those portions of Ganges’ work (not merely of the part on inference) which contain his own opinions, and arguments in support of them. And only those portions of the commentaries should be read which bear directly on them and which give the most reasonable and on that account the most universally accepted interpretations of them. It would be to the greatest advantage of logical study in India, if a text-book could be published to serve this purpose, and introduced into the list of books required to be read for the examinations which are now held at various centres. As yet there are a few (but, alas! only a few who are fast disappearing) who can undertake such a heavy task, and are competent to teach the Hindu doctrine of proof on this plan. But they are hardly those who will look with any favour on such a reformation, such is the obstinate vitality of the perverse love of hair-splitting disputation. (¶50)