The
Principles
of Reasoning
and
Forms
of Argument
in the
Early
Buddhist
Canon
Fumimaro Watanabe
It is mentioned that the extant Abhidhammas are very important from a logical point of view; especially the Kathavatthu and the Yamaka show us a variety of logical methods for dealing with propositions, or terms, presented for discussions). In the former we see a collection of more than 200 debates, which are refutation of propositions formalized by hypothetical statements, maintained by many schools of Buddhism. In the latter we see an enormous number of pairs of questions formalized by alternative state-ments and see the answers to these questions which are given throughout. In order to clarify the establishment of such logical forms, we must learn the principles of reasoning and forms of argument appearing in the Nika-yas.
The way of thinking of the early Buddhists was mainly based on the principle of contradiction. From a logical point of view, the principle of identity is equivalent to that of contradiction; however, it seems that the early Buddhists avoided the expression of emphatic affirmative; rather, they tried to give the expression lacking positive affirmative by the practical use of double negative (e.g. It is not the case that everything is not subject to change-aviparinama-dhamma)2). As the characteristic of the dialogue on
Dha-1) A. K. Warder, "The Earliest Indian Logic," Proceedings of the 25th Inter-national Congress of Orientalists, Vol. 4, (Moscow, 1963). Outline of Indian Philosophy (Dept. of East Asian Studies, The University of Toronto, 1967), pp. 59-62.
-476-mmas, we can see that there are the four methods of answering questions (parzhabyakaranas)3), in which the first method is to give a categorical rply or to answer directly in affirmative. This method is generally based on the principle of identity expressed by the formula of "(All) S is P." Most of the remarkable logical forms which we find in the Nikayas seem to be the statement founded on this principle. However, at the same time we cannot fail to see the fact that in the Nikayas there are statements which are expressed according to the principle of contradiction. This principle is that which forms the foundation of negative thinking, whilst the principle of identity is what forms the basis of affirmative thinking. The reason why the way of thinking of the early Buddhists was mainly based on the prin-ciple of contradiction is because the methods of Sanjaya's answer influenced more or less the early Buddhists. In a sense, the four kinds of possibilities of answer (catuskoti, tetralemma) coming out in the Nikayas are similar to Sanjaya's answers. Sanjaya's answers are: 1. It, is not thus for me (Evam pi me no), 2. It is not so for me (Tatha ti pi me no), 3. It is not otherwise
for me (Anniatha ti pi me no), 4. I do not say it is not (No ti pi me no) and 5. I do not say it is not not (No no ti pi me no)4). The four kinds of possi-bilities of answer used by the Buddha and his disciples are: 1. It is, 2. It is not, 3. Both and 4. Neither5). So, we could express San jaya's answers in bther words I. "Tatha"is contradictory to"annatha" II "An"natha"is contradictory to "tatha". Therefore, the relationship between them is: in case the one is "it is", the other is "it is not." III. "No ti" is a negative proposition of both items I and II. Therefore, this is "neither it is nor it is not." IV. "No no ti" is a negative proposition of item III. Therefore, this
2) S. III, 98-99.
3) As to this, see E. Maeda, A History of the Formation of Original Buddhist Texts (Tokyo, 1964), pp. 286-293.
4) D. I, 27, 59, M. I, 521, etc.
5) M. I, 486-7, Taisho 2, 245, 444, S. II. 112-3, Taisho 2, 81 a, etc. The Ajivaka maintained three sets of possible statements (trairasika): 1. It is, 2. It is
not and 3 Both (see A. L. Basham, History and Doctrines of the Ajivakas (London, 1951), p. 175.
-475-is "neither not it -475-is nor not it -475-is not." Apart from item IV, there -475-is no gainsaying the fact that the above possibilities of answers influenced the development of Buddhist doctrines-especially, the doctrine of voidness (sunya) of Nagarjuna. At any rate, we see that Saljaya's answers have so-mething in common with the four kinds of possibilities of answers.
From the above, we are inclined to think that the forms of argument in the Nikayas were built up, i.e. the forms of argument characterzed by a sorites, being indicative of hypothetical statements, not being indicative of categorical propositions. This point can be also understood from the fact that the Buddha admonished his disciples not to say "This alone is the truth, any other view is f ales (idam eva saccam mogham annam)6)." The most basic sorites expressing hypothetical judgement in the Nikayas is the for-mula: "From the existence of this, that becomes (imasmim sati idam hoti); from the happening of this, that happens (imassuppada idam uppajjati). From the non-existence of this, that does not become (imasmim asati idam na hoti); from the non-existence of this, that does not happen (imassa nirodha idam nirujjhati)7). And such a sorites of the most developed form is, we could say, the twelve paticcasamuppadass).
Another style of argument in the Nikayas is the form of argument expressed by alternative judgement. Such a style of argument must have been important in discussing with non-Buddhists to decide which doctrine is proper to Buddhism, and also must have been useful in arranging many doctrinal topics (matikas) in Buddhism. Alternative propositions are com-pound propositions in which the components are connected by "or" or "either
or The components are called alternants and there may be two or more of them. And the interpretation of "either p or q" is treated as implying that one alternant or the other must be true. In other words, the most important thing is that either p is true or q is true, but not both of
6) M. II, 171, A. V, 173, Taisho 2,245c,, etc.
7) S. II, 28, M. II, 32, III, 63, Taisho 1, 723c, 2,98b, 100a, etc.
8) S. II, 1-2, 42-43, V, 338, M. III, 63-64, Vinaya I, 1, Taisho 2, 85a-b, 216a, 723c, etc.
them together. The "or" has exclusive sense. In the Nikayas, we see the following illustration9):
There are three feelings:1. happy feeling (sukha vedana), 2. unhappy feeling (dukkha vedana), and 3. feeling that is neither unhappy nor happy (adukkharn-asukha vedana). Whenever one feels item 1, one feels neither item 2 nor item 3. Whenever one feels item 2, one feels neither item 1 nor item 3. Whenever one feels item 3, one feels neither item 1 nor item 2.
From the standpoint of Buddhism, the above expression would be "All men feel either happiness or unhappiness or neither-happiness-nor-unhappiness (schematized by ((x) x is a man D ((x is a) or (x is b) or -(x is a v x is b))J ).
We can see that the forms of argument of the early Buddhists are characterized by hypothetical and alternative statements rather than cate-gorical ones. Let us introduce here the explanation of anicca, dukkha and anattan, which can be seen widely in the Nikayaslo):
Now, what do you think, monks? Is everything permanent or impermanent? Everything is impermanent, the Exalted One.
What is impermenent, is that happy or unhappy? That is unhappy, the Exalted One.
What is impermanent, unhappy, subject to change,-is it proper to regard that as This is mine. I am this. That is my self?
No, indeed, the Exalted One.
The starting-point in the above is Everything is either permanent or im-permanent (Schematized by (x) (Fx v-Fx)-Whatever x may be, x is perma-nent or x is not permaperma-nent). From the standpoint of Buddhism, the answer is
Everything is impermanent. Therefore, the next point is Everything is either happy or unhappy. In this case, the answer is of course Everyth-ing is unhappy. And the last point is Everything is either substantial or not substantial. The answer is Everything is not substantial." If we re-place "permanent" with P, "happy" with H and "subs-tantial" with S, the above argument could be schematized as follows:
9) D. I, 182, Taisho 1,110a.
10) The Khanda-samyutta (Vol. 3,1-188, e.g. 181, 182). The Salayatana-s. (Vol. 4, 1-204, e.g. 45, 47, 54, 106). Taisho 2, la-49a (e.g. 41c, 42a),
-473-(x) Px or -473-(x)-Px? (x)-Px*
(x) (-Px D Hx) or (x) (-PxD-Hx)? (x) (-PxD-Hx)*
(x) (-Px e-Hx D Sx)?-This answer is "No" because of the above two premisses (asterisks).
Hence, (x)-Sx.
As a whole, the above is schematized by (x) (-Px.-Hx D -Sx). If replac-ing -Px, -Hx and -Sx with the letters p, q and r to symbolize the state-ments, we can see the above form as the tautology called the principle of simplification: (p-qDr). The form p a q D r is equivalent to the form Cp D (q D r)), called the principle of exportation.
By making up a diagram, we can grasp all the more the characteristic of the forms of argument expressed by a sorites which is indicative of
hypothetical judgement:
A bold-faced line indicates a direct relation, and dotted lines vertical and horizontal indicate indirect relations. The letter A is related to the letter B, B is related to C,...and E is related to F. Such a relation is a direct re-lation. At the same tithe, the letter A is related indirectly to C, D, E and F. In other words, each letter is related to every other letter both directly and indirectly. The teachings which the Buddha preached in regard to a
A B C D E F
-472-sorites being indicative of hypothetical judgement can be, we would say, clarified only by understanding clearly the direct and indirect relations. This can be realized from the fact that the Buddha made use of the words Dhammacakkhu and Yathabhutam in the explanation of his doctrine. The former means "the eye of wisdom" and the latter, "as it really is." If one understands only the direct relation indicated by a bold-faced line, one has just a scientific eye. On the other hand, if one understands the direct rela-tion and at the same time understands indirect relations, one has the eye of wisdom and can see everything as it really is. In the same way, we would say that to realize truly the dependent origination which is a central concept in Buddhism is in fact to realize systematically the fact that all phenomena are composed of involved relations. In this respect, the 12 (or 9) paticcasamuppadas are the most representative of the real logic of rela-tions, because they make clear the relationships between the origination and the cessation of unhappiness. What we call here the real logic of re-lations does not mean the logic of rere-lations in modern logic. As can be realized from the diagram above, the characteristic of a sorites which is indicative of hypothetical judgment is that direct relations (a bold-faced line) and indirect relations (dotted lines) are realized simultaneously. Let us see the following illustration1l):
To him who has discerned the elimination of the five obstacles (nivaranas), a great delight (pamujja) arises; to him who is greatly delighted, joy (piti) arises; to him who is joyous, the body becomes tranquil; to him who has a tranquil-body, happiness arises; to him who feels happy, his thought (citta) comes to one-pointedness (samadhiyati).
This can be expressed by the term "if...., then", i.e. "If one elimi-nates the five obstacles, then a great delight arises....and "If one feels happy, then one's thought comes to one-pointedness." If using the letters p, q, r, s, etc. to symbolize the statements, and replacing the letter A of the diagram with "p", the letter B of it with "q", the letter C of it with CYO, we can see that p is related directly to q, and at the same time
11) ID. I, 182, Taisho 1,110a.
-471-p is related indirectly to r and so forth. From such relations, it is possible to derive at least a mixed hypothetical syllogism and a pure hypothetical syllogism. In this case, the direct relation between p and q, or the direct relation of p, q and r always becomes a premiss (or premisses), and the indirect relations of them can be regarded as the conclusion.
Now, by using diagrams, let us demonstrate the above fact. In a mixed hypothetical syllogism affirmative12>, the following diagram can be drawn:
Diagram A:
p p D q (shown by a bold-faced line.)
q p (a point of intersection between dotted lines horizontal and vertical.)
Hence, q (a point of intersection between a dotted line vertical and a bold-faced line horizontal.) A noteworthy point here is that the direction of the arrow is always as shown if the conclusion is affirmative and true, because the following form is invalid logically: p q, q hence, p. In this connection, we must know that the form p q, -p hence, -q is also invalid. However, the form p q, -q hence, -p is valid. In such a case we can view it by making a diagram as follows:
The left side means that any conclusion is always negative and true.
The right side means that any conclusion is always affirmative and true.
Diagram B:
p p
-q
q
In case the conclusion is negative and true, the direction of the arrow al-ways comes up.
Pure hypothetical syllogisms are arguments in which all three propo-sitions are hypotheticals. On this we can draw the following diagram:
12) e.g. see the explanation of "birth" and "old age" in the Mahatanhasank hayasutta (M. I, 261).
-470-Diagram C: p pDq q r q J r Hence, p D r
In the same way as diagram A, the direction of the arrow must always come down; if it does not, the conclusion will be, even though affirmative, fales13). In connection with the most basic valid form of pure hypothetical syllogism mentioned above, it would be possible to enumerate additional forms of pure hypotheticals if we allow each proposition to appear either affirmed or denied, and of these some, like the following, will be valid:
1. p D q, r D -q hence, p D-r 2. qDr, -qDp hence, -pDr 3. qDp, rDq hence, -pD-r
But traditional logic deals chiefly with the first valid form (which is indi sated by diagram C). This can be also applied in examining statements of the Nikayas as well as of Abhidhamma texts.
Moreover, from a sorites which consists of direct and indirect relations, the forms such as p m q D r, p-q r D s and the like can be obtained. These forms are composed of a compound proposition. on the whole, we would say that in a sorites based on hypothetical judgement various forms of argument are involved, in so far as such a sorites is called the real logic of relations.
Thus, the logical analysis of dialogues (suttas) teaches us without fail the structure of the Buddha's teachings and the forms of argument in the Nikdyas14). And we can clarify the development of Abhidhamma
philoso-phy.
13) e.g. the following forms are invalid: 1. p D q, r Dq, hence, p D r. 2. q:)p, q D r, hence, p:)r. 3. q D p, r D q, hence, p J r.
14) e.g. Potthapada-sutta (D. I), Payasi-s. (D. II), Patika-s. (D. III), Samma-ditthi-s. (M. I), Rathavinita-s. (M. I), Mahavedalla-s. (M. I), Aggi-Vaccha-gotta-s (M. I), etc.
