A Note
on the Methodology
in the Study
of Indian
Logic
Hidenori
Kitagawa
Indian logic has been studied by many scholars and by now we are in possession of a fairly large amount of knowledge 'concerning this subject; however, it has been customary among scholars to interpret Indian logic using the terminology of Aristotelean logic and here lies a problem. If we want to learn something really new from a foreign system of thought, we must first try to understand it as it is. To interpret Indian logic using the terminology of Aristotelean logic, according to my opinion, is not to represent Indian logic as it is, but merely to review Aristotelean logic as applied to Indian logic.
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Since I am engaged in the study of Dignaga, let me explain my point with material from his works. One of his most favorite examples of valid sylogism is:
(paksa) Sound is non-eternal.
(hetu) Because of (its] nature of being a product.
(drstanta) a) Whatever is a product is non-eternal, like a pot. b) Whatever is eternal is not a product, like the ether. Now, according to the customary interpretation paksa is the equivalent of the conclusion of the Aristotelean syllogism, hetu the equivalent of the minor premiss and drstanta the equivalent of the major premiss; and so far there is no serious misinterpretation. But the customary interpretation that"sound,""nature of being a product" and"non-eternal" of the above example correspond to the Aristotelean minor term, middle term and major term respectively is by no means a scientific interpretation. For, if there
(1) A great Indian logician who belongs to the first half of the fifth century A. D.
be a middle term, it should be"product" and not"nature of being a pro-duct." This will be quite clear if we re-state the above Indian syllogism in the complete form of the Aristotelean syllogism.
(major premiss) All products are non-eternal. (minor premiss) All sounds are products.
(conclusion) Therefore, all sounds are non-eternal.
Perhaps to avoid this difficulty i. e. the difficulty of calling"nature of being a product" the middle term the second member (=hetu) of the above Indian syllogism is sometimes loosely translated by"Because [it is] a product." Indeed, by thus translating it, it seems to become possible to apply the Aristotelean techniques"minor term,""middle term" and"ma-jor term" to the syllogism of Indian logic, the first being applied to "sound," the second to"product" and the thi
rd to"non-eternal." But then another difficulty arises namely, the customarily accepted interpretation that the Aristotelean technique"middle term" is the equivalent of the Indian technique"linga" is not correct. For, "linga" literally means a mark and therefore refers to the nature of being a product, while"middle term" means the term common to the minor and major premisses and
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therefore should refer to the term"product." Another example will perhaps make my point clearer. Notice:
(paksa) There is a fire on the hill. (hetu) Because of [its] smoke.
(drstanta) a) Wherever there is smoke there is a fire, like a kitchen. b) Wherever there is no fire there is no smoke, like a lake. In this syllogism the smoke is the linga. For it is the mark of the existence of a fire on the hill. But if we re-state this Indian syllogism in
(2) Notice that the expression"product" is put in quotation marks here while the expression"the nature of being a product" is used without quotation marks. All through this paper the quotation marks are used with great care. The expression together with quotation marks is the name of the expression itself, while the expression without quotation marks is the name of the object of that expression.
the form of the Aristotelean syllogism, it will become as follows: (major premiss) All smoky things are firy.
(minor premiss) The hill is smoky. (conclusion) Therefore the hill is firy.
No doubt, "smoky (or, smoky thing)" is the middle term here. So, it is quite clear that linga and middle term are not the same, the former being the smoke towering from the hill while the latter is the term "smoky. "
Moreover, as the reader will see, the techniques that do not correspond to each other are not just "linga" and "middle term. " Strictly speaking, most of the techniques of Indian logic do not have their equivalents in the system of Aristotelean logic. And this means that if we stick to the
Ari-stotelean terminology in our interpretation of Indian logic, we cannot re-present Indian logic as it is, and consequently cannot understand the Indian approach to LOGIC.
Then, where has the discordance in terminology between these two systems of logic originated ? According to my opinion it has originated in the fact that Indian logic deals directly with entities while Aristotelean logic deals with terms. Look at the famous example of Aristotelean syl-logism.
(major premiss) All human beings are mortal. (minor premiss) Socrates is a human being. (conclusion) Therefore, Socrates is mortal.
According to the Aristotelean way of thinking the validity of this syllogism lies in the fact that the extension of the minor term ("Socrates") is subsumed by that of the middle term ("human being") and the extension of the latter again by that of the major term ("mortal"). And this is why the propositions of Aristotelean syllogism must always take the subject-copula- predicate form. Contrasted to this approach to LOGIC by Aristote-leans, Indian logicians tried to approach it from a different angle. Instead
of terms they tried to deal with entities i. e. the objects of terms; there-f ore, there-for them it was not necessary to have all the propositions of a
"dhar-ma" and"dharmin," which have been customarilly interpreted as the equi-valents of"predicate" and"subject" respectively, are not really their equi-valents."dharma" means a property, and"dharmin" means the possessor of the property, thus these two words refer to entities, while predicate and subject are not entities but terms of a proposition. For example, when Aristotelean logicians say"Socrates is mortal" the term"Socrates" is the subject and the term"mortal" is the predicate. But when Indian logicians say"Sound is non-eternal," the entity sound is the dharmin and its property
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non-eternality, which also is an entity, is the dharma. In other words, for Indian logicians to say"Sound is non-eternal" is the same as saying that the entity sound has the property of non-eternality, while for Aristotelean logicians to say"Socrates is mortal" is the same as saying that the exten-sion of the term"Socrates" is subsumed by that of the term"mortal."
But here an objection may arise: -i. e."It is not correct to say that Aristotelean logic deals with terms while Indian logic deals with entities. For, even when Aristotelean logicians say `Socrates is mortal, ' this does not assert the subsumptive relation between the two terms 'Socrates' and 'mortal,' but asserts the fact that the man Socrates (not the term `Socrates') is mortal."
My answer to this objection is as follows : I do not say that in Aristo-telean logic the proposition"Socrates is mortal" is an assertion about the term"Socrates" while in Indian logic the proposition"Sound is non-eternal" is an assertion about the entity sound. Certainly the proposition"Socrates is mortal" is just as much an assertion about the entity Socrates as the proposition"Sound is non-eteral" is an assertion about the entity sound. Thus, the difference which I am trying to establish between the two systems of logic is the difference in the theories of procedure for logical
(3) It has to be noted that dharma is not necessarily the quality. For, when Indian logicians say"There is a fire on the hill," the fire is the dharma of the hill, though it is not a quality as opposed to a substance. Generally
speaking, if A possesses B, B is the dharma of A, and A is the dharmin of B.
operation, not the difference in any fact that is asserted by a proposition. Let me explain my point in greater detail. For example, when Aristotelean logicians want to make a logical operation on such a proposition as"Socra-tes swims well," they must first re-phrase this expression into"Socrates is a good swimmer." What Indian logicians should do in this case is to understand the same expression as informing them of fact that Socrates has the abillity to swim well. The reason why Aristotelean logicians must re-phrase"Socrates swims well" into"Socrates is a good swimmer" is that their logical operation is possible only with propositions in the subject-copula- predicate form. The reason why Indian logicians must understand the same expression as informing them of the fact that Socrates has the ability to swim well is that their logical operation is possible only with a world which is analysed into dharmas and dharmins. Indeed Aristotelean logicians have the techniques "subject, "" copula" and" predicate" that refer to the terms "Socrates, "" is" and "good swimmer" respectively, but have no techniques that refers to the expression "swims well." On the other hand, Indian logicians have the techniques "dharma" and "dharmin" that refer to the ability to swim well and Socrates respectively, but have no tech-nique that refers to the term"good swimmer," nor even the technique that refers to the term"Socrates." The Indian technique"dharmin" refers
to the man Socrates but not to the term"Socrates."
Thus far I have made clear the following two points: 1) The tech-niques of Indian logic do not correspond to those of Aristotelean logic; 2) This discordance in terminology is due to the fact that the theories of procedure for logical operation of Indian logic deal with entities while
those of Aristotelean logic deal with terms. Now is the time to show how Indian logicians (particularly Dignaga) have built up a system of logic with such techniques as"dharma,""dharmin,""linga" etc. ; however before
we can take up this topic, a few more techniques of Indian logic must be defined.
Paksa This word has three meanings: 1) the first member of an Indian syllogism, such as the proposition"Sound is non-eternal";
2) the fact asserted in this proposition such as the fact that the (4)
dharmin sound, has the dharma non-eternality; 3) its subject ter, such as the dharmin sound. It is necessary to note that the paksa
in the last sense should not be identified with the Aristotelean nor term; the former being the subject matter sound while the
latter is the term"sound."
Sadhya This word, which literally means that which is to be proved, also has three meanings: 1) the same meaning as the second meaning of" paksa"; 2) the same meaning as the third meaning of
" paksa"; 3) the dharma whose existence in the paksa (the paksa in the third sense, i. e. the dharmin sound in the above example) is to be proved. Here again it is necessary to note that the sadhya in the last sense should not be identified with the major term of Aristo, telean logic. The former is the property non-eternality, while the latter is the term"non-eternal."
From now on, in order to avoid confusion I shall use these two techniques in their third senses. So, unless otherwise mentioned, the dharmin sound, for example, shall be referred to by the word"paksa," and the dharma icon-eternality by the word"sadhya."
Sapaksa That which is similar to the paksa in that it possesses the sadhya. For example, when Indian logicians argue"Sound is eternal, because of [its] nature of being a product," every entity that possesses the dharma non-eternality is the sapaksa. It is sary to note that"sapaksa" is not the name of the class of all the entities that possess the sadhya, but is the name of each individual
(5) entity that possesses it.
(4) More exactly, the dharmin sound as qualitied by the dharma non-eternality
is the paksa in the second sense. See my article 因 を 以 て 宗 の 法 た る べ し と な す 陳 那 の 見 解P. 7. 附 記II
(5) This is quite clear from the fact that the second character of the three characters of linga requires that a valid linga must reside in sapaksas (See p. 7 ff.). For we can speak of a linga's residing or not residing in an individual entity, but we cannot speak of its residing or not residing in a class.
Vipaksa That which is dissimilar to the paksa in that it does not possess the sadhya. In the above example, every entity that does not possess the dharma non-eternality is the vipaksa. Here also it is necessary to note that "vipaksa" is not the name of the class of all the entities
that do not possess the sadhya, but is the name of each individual entity that does not possess it.
Now, let me show how Indian logicians (particularly Dignaga) have built a system of logic on such techniques as I have defined so far. For this purpose I shall choose the famous theory of the three characters of linga. Since this theory constitutes the most fundamental principles of Indian logic, its faithful representation will very possibly enable us to obtain a glimpse into the Indian approach to LOGIC.
In the example "Sound is non-eternal, because of (its] nature of being a product," the nature of being a product is the linga, i. e. the mark of the existence of non-eternality in sound. In the example "There is a fire on the hill, because of [its] smoke," the smoke is the linga, i. e. the mark of the existance of a fire on the hill. Now, according to the theory of the three characters of linga the nature of being a product and the smoke must be equipped with the following three characters in order to be valid lingas, namely, paksadharmatva, sapakse sattva and vipakse 'sattva. The first cha-racter paksadharmatva requires that a valid linga must be the dharma of the paksa -namely, the nature of being a produt must be the dharma of
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sound and the smoke must be the dharma of the hill. Now, if we stick to the terminology of Aristotelean logic, our interpretation of this condi-tion will be that the the extension of the middle term in Barbara syllo-gism must subsume the extension of the minor term; however, we must not forget that the linga in Indian logic is not really the middle term but a mark and therefore it has no extension. The formula "There is a fire
(6) In the preceding pages I supplemented the word "its" in brackets in lating "krtakatvat" and "dhumat, " which if translated literally would turn out to be "because of the nature of being a product" and "because of smoke" respectively. The character paksadharmatva justifies this supplement.
on the hill, because of [its) smoke, " for example, is of the form of po-inting out the existence of the dharma B in the dharmin A in order to convince the opponent in the existence of the dharma C in the dharmin A. The second character sepakse sattva requires that a valid linga must reside in sapaksas, and the third character vipakse 'sattva requires that a valid linga must not reside in vipaksas. Here again if we stick to the terminology of Aristotelean logic, our interpretation of these two characters, when combined, will be that the extension of the middle term should be subsumed by that of the major term; however, we must not forget that our linga is not the term but a mark, and therefore it has no extension. Thus, the most simple and natural interpretation of these two characters is that a valid linga must always reside in all or at least in some sapaksas
(7) b ut it must never reside in any vipaksas.
Dignaga called the lingas that lacked the first character asiddha, i. e. non-lingas; and he classified the other lingas into nine groups according to whether or not they lacked the second and the third characters. The following is the table of the so called nine groups of lingas:
Group I comprises those lingas that reside in all sapaksas and in all vipaksas, like the linga when we argue "Sound is eternal, because
(8) of (its) nature of being the object of cognition. "
Group II comprises those lingas that reside in all sapaksas and in no vipaksas, like the linga when we argue "Sound is non-eternal, because of (its) nature of being a product. "
Group III comprises those lingas that reside in all sapaksas and in
(7) Some scholars interpret the second character as the requirement that a valid linga must reside only in sapaksas and the third character as the requirement that a valid linga must not r€side in any vipaksas. In other words, they consider these two characters as logically equivalent. But so far as Dignaga's theory is concerned their interpretation is not correct. I shall discuss this point in a separate article.
(8) Everything is the object of cognition in some way or other. Threfore the nature of being the object of cognition resides in all sapaksas and in all vipaksas.
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some vipaksas, like the linga when we argue"Sound is the effect of human effort, because of (its) non-eternality.
Group IV comprises those lingas that reside in no sapaksas and in all vipaksas, like the linga when we argue"Sound is eternal, because of (its) nature of being a product."
Group V comprises those lingas that reside in no sapaksas and in no vipaksas, like the linger when we argue"Sound is eternal, because
(10) of (its) audibility."
Group VI comprises those lingas that reside in no sapaksas and in some vipaksas, like the linga when we argue"Sound is eternal, cause of [its) nature of being the effect of human effort."
Group VII comprises those lingas that reside in some sapaksas and in all vipaksas, like the linga when we argue"Sound is not the effect of human effort, because of [its) non-eternality."
Group VIII comprises those lingas that reside in some sapaksas and in no vipaksas, like the linga when we argue"Sound is non-eternal, because of (its) nature of being the effect of human effort."
Group IX comprises those lingas that reside in some sapasas and in some vipaksas, like the linga when we argue"Sound is eternal, cause of [its) penetrability."
Of these nine groups of lingas only those lingas that belong to the second and the eighth groups are the valid lingas, because it is only they that lack neither the second nor the third character. Those lingas that belong to the fourth and the sixth groups, i. e. the lingas that lack both second and
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third characters, are called viruddha, i. e. incompatible, because they (9) Here I used the word"some" in the sense of not all but some.
(10) Audibility belongs to sound only. Therefore it resides neither in sapaksas nor in vipaksas. It is important to note that sound itself is not a sapaksa
though it possesses the dharma eternality.
(11) Some eternal things, e. g. the ether, are penetrable, but some eternal things, e. g. atoms, are not penetrable. Therefore, penetrability resides in some sapaksas.
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A Note on the Methodology in the Study of Indian Logic (H. K.)
prove the fact asserted in the paksa (the paksa in the first sense). Again,
those lingas that belong to the other groups, i. e. the lingas that lack one
of the two characters, are called anaikantika, i. e. indefinite, because they
neither prove nor disprove the paksa.
Thus Dignaga classified lingas into valid, incompatible and indefinite;
and I hope that my above statements have given the reader an idea of
how it was possible for Indian logicians to build up a system of rogic on
such techniques as "dharma, ""dharmin, ""linga"
etc. Before I bring this
article to a close, I should like to make one more remark, i. e. the remark
concerning the possibibility of acquiring new concepts and a new way of
thinking from the study of Indian logic. Notice Aristotelean logicians make
no distinction between the functions of the copula"is" in the proposition
"Socrates is mortal" and that of the copula"are" in the proposition"All
human beings are mortal." The reason why they make no distinction
between the functions of these two copulas is that the distinction between
the membership relation and the subclass-class relation is not known to
them. However, what the proposition"Socrates
is mortal" really says is
that Socrates is a member of the class of mortal beings, and what the
proposition"All human beings are mortal" really says is that the class of
human beings is a subclass of mortal beings; thus there is a clear-cut
distinctinction between the functions of these two copulas. Modern
mathe-matical logicians make this distinction; they use the symbol"s" for
mem-bership relation and the symbol"C"
for subclass-class relation. And
though from a somewhat different angle, Indian logic also gieves a hint to
this distinction. In Indian logic the relation between entities are of two
kinds, namely, the relation of a dharma to its dharmin and the relation of a
dharma to another dharma."There
is a fire on the hill" and"Because of
(its] smoke," for example, express the former relation, while"Wherever
there is smoke there is a fire""Wherever
there is no fire there is no
as Dignaga's theory is concerned, this interpretation is not right. See my
smoke" express the latter relation. The former relation corresponds -if we are allowed to use the word "corresponds" -to the membership
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relation and the latter to the subclass-class relation. Suppose we had not as yet developed mathematical logic, the study of Indian logic might well have given a hint to the progress of logic in this respect; however, we should not forget that this kind of contribution is possible only when we conduct our study of Indian logic according to the method I have propounded throughout this paper. If during the study of Indian logic we were to interpret it by using the terminology of Westenn logic, there is little possibility that we could learn anything really new, for in that case we merely would be reviewing Western logic as applied to Indian logic.
* I do not deny that it is the brain which is trained in Western logic that can find jewels in Indian logic. All I want to say, therefore, is that in the field of the study of foreign systems of thought the deepest philosophical studies must always be preceded by rigid philological studies, and that only through such philological studies we can learn really new things from foreign systems of thought.
*I here express my deepest gratitude to the Rackefeller Foundation. The central concepts in this paper were formed during my study in U. S. and
India as a fellow of the Foundation. (1952-53)
(13) Mathematical logic expresses the relation A is a member of the class B by "A E B," and the relation B is a subclass of the class C by" (x) ((x E B) (x E C))." If we translate the latter formula literally into words it will become as follows. "Whatever x may be, if x is a member of the class B, then x is a member the class C." If we read the symbol" E " as "possesses the dharma" instead of "is a member of the class" and substitute "the hill" for "A", "smoke" for "B," and "fire" for "C," "A E B" will become "The hill
possesses the dharma smoke "and "(x)((xεB)=⊃(xεC))"will become " Whatever x may be, if x possesses the dharma smoke, then x possesses
the dharma fire." The reader thus must have found a closer parallelism between Indian logic and mathematical logic than between Aristotelean logic and mathematical logic in this respect. (The fact that Indian logicians understand the expression "Sound is non-eternal" as informing the fact that the dharmin sound possesses the dharma non-eternality may be a difficulty with the above explanation of parallelism. For, if what is really meant by "Sound is non -eternal" is the fact that any sound (not a particular sound) possesses the dharma non-eternaliy, the expression "Sound is non-eternal" should be understood rather as informing us of the fact whatever possesses the dharma sound-ness possesses the dharma non-eternality. Perhaps Indian logicians' analysis did not go thus far. Or, perhaps there were some other reasons. Nevertheless, the fact that in Indian logic the relations between entities are of two kinds is a good enough hint to the distinction between the membership relation and the subclass-class relation.)
