The Logical Form of Catuskoti: A New Solution

·期刊原文
The Logical Form of Catuskoti: A New Solution
By R. D. Gunaratne
Philosophy East and West
vol. 30, No. 2 (April 1980)
pp. 211-239
Copyright 1980 by University of Hawaii Press
Hawaii, USA

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Author's Note: I wish in thank Dr. Merlin Peiris, Mr. S. V. Kasynathan and Mr. C. Vitanachchi of the University of Sri Lanka: the former two for suggestions on the improvement of the presentation of this article, the latter for help in the clarification of some Pali passages; Rev. Fr. Dr. Harold Panditaratna, Rector, National Seminary, Kandy, for directing me to some relevant material; Mr. Bandula Jayawardhana, of the Encyclopedia of Buddhism, Colombo, for drawing my attention to some problems in understanding the catu.sko.ti. I am solely responsible for the views expressed here.

The main purpose of this article is to present the logical form of catu.sko.ti (the four alternatives of the Buddhist texts) in a symbolization different from those so far suggested. These latter, it is argued here, are unsatisfactory and proposed here are a set of symbolizations which, hopefully bring out the most general and minimum logical relations that could be seen in the catu.sko.ti alternatives. The present study is based on the occurrences of catu.sko.ti statements in the Pali canonical literature and hence in early Buddhism. No claim of a study of catu.sko.ti in the Maadhyamika or later Buddhist literature is made here, although I feel that the logical form of catu.sko.ti, as suggested here, is general enough to cover its occurrences in the post-canonical literature as well.

The origin and development, the logical form and interpretation, as well as the applications of catu.sko.ti is a problem that has long interested students of Buddhism. Indeed, "the catu.sko.ti has been considered an insoluble problem for centuries." [1] During the present century, again a number of writers have commented on one or more aspects of this problem. [2] The most recent article on it is that by Alex Wayman in the January 1977 issue of Philosophy East and West. [3]

The problem will be dealt with here under the following heading: (1) catu.sko.ti and logic, (2) examination of the logical form of the catu.sko.ti statements, as given by earlier writers, (3) a new symbolization of the catu.sko.ti statements and (4) some issues in the interpretation of catu.sko.ti.

Catu.sko.ti and Logic
I shall comment here on certain views expressed by Professor Wayman on the use of symbolic logic to explicate the logical form of catu.sko.ti. Wayman, in his article, questions the use of symbolic logic to represent the catu.sko.ti statements.

A question of interest that he raises seems to be whether the "given" is "amenable" to symbolization. but what Wayman implies as the given is not quite clear in spite of his attempt at clarification. Is reality the "given"? Wayman's quotation from Weyl suggests this meaning. [4] On the other hand, Wayman also says, "In the case of catu.sko.ti the given is a rather considerable corpus of material in the Pali scriptures and then in Naagaarjuna's works, not to speak of contributions by later Asian authors. And there is the assumption that this corpus is at hand in a translated form of English sentences that are

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susceptible, in whole or part, to being converted from the natural form to the artificial language of a symbolic system." [5] Is, then, the "given" the relevant Pali and other literature?

Wayman contends that the structures in symbolic logic could not represent the "given." Whether the abstractions of standard logic could successfully present the structure of reality is no new problem, nor is it one raised only in connection with a specific area of discourse like the catu.sko.ti. A Bergson, Hegel, or Heraclitus could raise the same question on the structure of reality presented by modern science, insofar as the latter employs standard logic (and mathematics). One does not want to contest that our concepts, our logical and mathematical structures are "abstractions" and that these might not translate a "given" -- whether language or otherwise -- fully. What one fails to see is the point in Wayman's attempt to associate this problem with the use of symbolic logic only.

Further, the relevant point for Wayman's argument seems to be not whether symbols in mental operations are "detached" from reality or independent of the given (p. 5) but whether the structures developed using these symbols (that is, the mathematical, logical structures) could represent, or help us understand, reality. And in this respect, the astounding success of mathematics, as applied mathematics and as a major branch of modern science, [6] shows that the structures developed in mathematics could help us understand nature, at least in the scientist's sense.

What concerns us most in this study is whether catu.sko.ti has an isolable or a consistent logical structure. Such writers as Wayman seem to despair about eliciting this structure but my article attempts to establish that this structure does exist and is, in fact, isolable.

Examination of The Logical Form of The Catu.sko.ti Statements, as Given by Earlier Writers
The following are some of the more important views expressed by contemporary scholars on the logical form of the catu.sko.ti statements.

Catu.sko.ti statements ignore the Laws of Thought and hence are not understandable (Poussin). [7]

Catu.sko.ti statements, somehow, relate to the four Laws of Thought (Mrs. Rhys Davids, Barua). [8]

Catu.sko.ti statements constitute a mutually exclusive and together exhaustive disjunction which can be analysed in terms of a Boolean class algebra They are, to some extent, related to the Aristotelian Forms A, E, I, O (Robinson). [9]

Catu.sko.ti statements constitute a mutually exclusive and together exhaustive disjunction. These are not to be associated with the Jaina Syaadvaada or the fivefold assertions of the Skeptics which are systems of statements true from different standpoints. The catu.sko.ti can be analyzed in terms of either or both nonquantified and quantified propositions, and it is a "two valued logic of

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four alternatives" unlike the Aristotelian logic which is a two-valued logic of two alternatives (Jayatilleke). [10]

Catu.sko.ti statements do not always exhibit a consistent logical form. They must be understood by the purposes to which they were employed. We can distinguish two views here, namely,

There are three kinds of catu.sko.ti: (1) a disjunctive system, (2) an instrument of meditation on causation, and (3) an instrument of meditation on existence. It is a dialectic of negation which rejects reason and/or leads to truth. It can also be viewed as based on the idea of degrees of truth. The use of symbolic logic to explicate its logical form is analyzing it in an artificial or an alien language. The catu.sko.ti shows both prasajya and paryudaasa types of negations (Wayman). [11]

No symbolic or logical representation (except an intuitionistic one) fits the scheme of catu.sko.ti in general. The catu.sko.ti merely shows that as long as one's own view is held to be ultimate one can never avoid dogmatism. The catu.sko.ti is not a "Buddhist logic"; Buddhists are only its critics, and they reject it. It is a dialectic which makes use of the fact that four positions are possible in regard to any statement. The catu.sko.ti is applicable to metaphysical speculation only (Chi). [12]

I shall not discuss paragraphs two and three of this section, because these views seem to be obviously mistaken and have been adequately dealt with. [13] One aspect, that is, the use of symbolic logic in the explication of catu.sko.ti form, of (2.151) has already been commented on earlier in this article.

The purposes of this article call for some discussion of the symbolizations of catu.sko.ti by Robinson, Jayatilleke, and Chi; but some questions on the basis and the interpretation of catu.sko.ti need consideration before these symbolizations are taken up. The questions are: (1) whether the catu.sko.ti statements are to be considered as alternatives true from their respective standpoints, (2) whether they are based on a notion of degrees of truth, (3) what role catu.sko.ti plays in rejecting dogmatism and metaphysics, and (4) whether and how far it is a dialectic of negation leading to truth. These are, of course, questions which only partially fall under the problem of the logical form of catu.sko.ti. But these are also matters of importance when one discusses the logical form of the system. Thus, for example, a set of statements which are true from different standpoints is not normally called an exclusive disjunctive system.

Let us now consider (1) and (2). There are examples of catu.sko.ti in the Pali Canon in which only one of the alternatives was considered to be true. [14] Therefore the view that the catu.sko.ti alternatives are each true in turn from different standpoints does not seem tenable. [15] In view of this it is difficult to see how Wayman, having accepted that catu.sko.ti is a disjunctive system, accommodates, as he does, the Naagaarjuna position which considers catu.sko.ti as based on the distinction between inner and outer teaching and as constituting

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a dialectic which leads from the outer to the inner truth. Wayman suggests an interpretation to the canonical passage [16]:

Kim pan' -- AAnanda bkikkhu-sa.mgho mayi paccaa-si.msati? Desito AAnanda mayaa dhammo anantara.m abaahira.m karitvaa, na tatth' AAnanda Tathaagatassa dhammesu aacariya-mu.t.thi... [17]

which could support the contention that the Buddha practiced graded teaching and that Buddha's ultimate dhamma was one with "neither an inner nor an outer" -- expressible in the fourth alternative of the catu.sko.ti. On the contrary, this passage purports to tell AAnanda that the Buddha has no aacariya-mu.t.thi left; that is, he has withheld nothing from his disciples (and therefore that Buddha's teaching has no "inner-outer" in this sense). [18] There is no question of either graded or nongraded teaching here. Also the passage does not say that the dhamma that the Buddha taught is "with neither an inner or an outer," as Wayman suggests. [19] It is true, as Wayman says, that "Buddhaghosa ... insists that the Buddha's teaching was fittingly modified ... with the varying inclinations of both men and gods." [20] But Wayman misunderstands Buddhaghosa here. [21] The Theravaadin admits that the Buddha adjusted the topic or the technique of teaching to suit the learner. This does not mean that he adopted these methods to teach relative or graded truth. The case is similar to that of a teacher today adopting different approaches to the teaching of, say, mathematics to different students. Some students would find beginning with Euclidean geometry easier; others, perhaps, would learn faster if they start with the sets. Moreover, there is no evidence in the Pali Canon that the Buddha accepted as true more than one of the alternatives in any of the catu.sko.ti, even on different occasions. Whereas if Wayman's view of "graded truth" were correct, this has to be very much expected.

Wayman might well be correct that, regarding the views on causation the four alternatives in the catu.sko.ti represent respectively the Saa.mkhya, the II`svaravaadin, the Nyaaya-Vai`se.sika and the Lokaayata views, [22] and that the Buddhists rejected all these four. What this goes to show is something about the origins of catu.sko.ti, and that the catu.sko.ti alternatives, as Jayatilleke also noted, [23] are drawn from views in existence then. But that is no reason they were not considered to be mutually exclusive and together exhaustive. On the contrary their being the views of rival or different schools may be the very reason for their being considered mutually exclusive.

Let us consider (3) and (4) now. Chi thinks that catu.sko.ti is used to reject metaphysical positions, [24] and Wayman also treats this aspect in his sections on catu.sko.ti and causation, and catu.sko.ti and existence. [25] The difference between these two writers seems to be that while Chi holds that all dogmatism and metaphysics is rejected by it. Wayman suggests that the catu.sko.ti, by rejecting the four views, leads the Buddhists to the real. [26] In any case, Chi's statements seem to stand in need of correction when he says, (1) that "catu.sko.ti

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is applicable to metaphysical speculation only" and (2) that "Buddhists are its critics" (and they reject it). [27] For there are examples in the Pali Nikaaya's such as the following:

Example 1. Cattaaro 'me Pessa puggalaa santo sa.mvijjamaanaa lokastmi.m, katame cattaaro: idha Pessa ekacco puggalo attantapo hoti, ... [28]

which do not seem to be classifiable merely as metaphysical speculation. Moreover, acceptance of one of the alternatives (that is, the fourth) seems recommended in this instance and, as such, all the alternatives are not negated, as Chi seems to suggest. The point of interest for us here is that if the Buddhists did not take this form of classification seriously they could not have accepted one of the alternatives at times or made a serious denial of all the four, more often. If and when the Buddhists negated (or rejected) all the four alternatives, what they negated (or rejected) are the particular applications of the classification with specific concepts applied to specific situations inadequately or incorrectly, [29] rather than the form of the classification itself. If one is rejecting the form of the classification itself one need not negate (or reject) the alternatives on the basis of the nonapplicability of the concepts employed, as, when in the answer to Timbaruka, the Buddha holds that the "caused by itself," and "caused by another" (of pleasure and pain) are misconceptions. [30] If and when the concepts were applicable and correctly used, the Buddha probably accepted one of the four alternatives, as the system is mutually exclusive and together exhaustive. At any rate, it would appear that catu.sko.ti as an instrument to reject metaphysical speculation and dogmatism gets emphasis not in early Buddhism but in the Maadhyamika systems.

I shall consider now the logical forms suggested for the catu.sko.ti by Robinson, [31] Jayatilleke, [32] and Chi. [33] Robinson says, "A typical piece of Buddhist dialectical apparatus is the tetralemma (catu.sko.ti). It consists of four members in a relation of exclusive disjunction ... these alternatives were supposedly exhaustive..." [34] He goes on to give the structure of the four propositions interpreting the third alternative to have the form 'some x is A and some x is not-A' and the fourth to be of the form 'no x is A and no x is not-A', where "x" stands for the attributes of the entity in question. On this basis he symbolizes the "tetralemma" and finds parallels in the Aristotelian forms as shown in the following table. [35]

Aristotelian forms Tetralemma
A: All x is A = 0 1. = 0
E: No x is A ab = 0 2. ab = 0
I: Some x is A ab 0 3. ab 0, 0 (I.O)
O: Some x is not A 0 4. ab = 0, = 0 (E.A)

Robinson takes the view that the fourth alternative is true when x is null. That Robinson's symbolization and interpretation is inadequate to meet the

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variety and the complexity of the catu.sko.ti statements is seen when we consider example 1, first alternative of which could be taken as

Example 1. Puggalo attantapo ... (that is, the person who torments himself, for example, the ascetic).

Since in Robinson's symbolization, x is an attribute of the entity in question, we would have to read 1 as "All the attributes of the person are attributes which torment himself." Such a translation does not read sound. Jayatilleke, [36] taking other examples, argued that such a translation does not always make sense and Robinson, [37] in a subsequent article, has recognized this difficulty. Moreover, as in the preceding example, the possibility of the fourth alternative being true, even when x is not null, is there. [38] Further, Jayatilleke correctly argued that Robinson should interpret all the Aristotelian forms existentially, if he is to give a disjunctive system.

Let us next consider Jayatilleke's renderings of the catu.sko.ti form. As we noted earlier Jayatilleke considers catu.sko.ti as a "two valued logic of four alternatives." [39] Jayatilleke first considered the catu.sko.ti sentences to be prepositional functions. In his later work he gives two symbolizations of the catu.sko.ti examples. One is "a corrected and a modified" form of Robinson's (quantified) scheme. The other is a modification of his earlier account based on prepositional functions." [40]

To take up the quantified form, Jayatilleke is correct to maintain that the four alternatives given by Robinson are not mutually exclusive. For when x is null and the fourth alternative E.A is true, the first and the second alternatives, which are respectively A and E, also are true, unless they are interpreted as existential.

Jayatilleke attempts to correct the defects in Robinson's formulation, but he himself commits mistakes. He symbolizes the four alternatives as follows, using x to mean the existential interpretation: [41]

(I) (x)A (II) (x)E (III) (x)I.O
(IV) -(x)AV(x)EV(x)I.O

While Jayatilleke is correct that these alternatives are mutually exclusive he seems to be giving the incorrect reason for (I) and (III) being so. He thinks that when A is given existential import, A and O are contradictories, [42] but given existential import to A and E, the two pairs A and O and E and I are only contraries. [43] Thus the reason given by Jayatilleke for I.O being false when existential A of E is true is wrong. Still, what is of interest to us here is that these relations do hold. [44] Jayatilleke's formulation of the fourth alternative which is instrumental in making his system exhaustive, is also unconvincing. Robinson's comment that "the Form 'X is neither Y nor non-Y' obviously requires further study, because neither Jayatilleke's work nor anyone else's accounts for the heterogeneity of the examples and identifies a common

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denominator" seems justified. [45] The most surprising thing is Jayatilleke's suggestion that the fourth alternative holds when there are no fx's that is, when the "class-x" is null. [46] Jayatilleke has rightly criticized Robinson for taking up this position, pointing out that there are instances in the Nikaayas where the fourth alternative seems approved of even when the subject class of a catu.sko.ti is not null. Thus, he referred to the catu.sko.ti which we have taken as example 1, where the fourth alternative can be speaking of an arahant ("who is neither a self-tormentor nor a tormentor of others"). [47] Indeed, only in a few of the catu.sko.ti one could consider the subject class null, the condition required by Robinson and Jayatilleke to be satisfied for the fourth alternative to be true. Since Jayatilleke also gives a symbolization of the four alternatives in terms of prepositional functions, there was a possibility for him to say that the cases where there are fx's and the fourth alternative is asserted have to be taken under this symbolization. But Jayatilleke has not taken or argued for such a view either. In any case, we shall find Jayatilleke's symbolizations using propositional functions unsatisfactory as well.

Let us now consider Jayatilleke's symbolization in terms of propositional functions. His original suggestion was to take the four alternatives as (I) X is A (II) X is not A (III) X is and is not A and (IV) X is neither A nor not A where A and not A are taken as contraries and not as contradictories. [48] In his later work Jayatilleke interprets the first three alternatives as (1) S is wholly P, (2) S is wholly non-P, (3) S is partly P and partly non-P. Again, as in the case of his symbolization in terms or quantified propositions, he takes the fourth alternative to be the negation of the disjunction of (I), (II) and (III). [49] He symbolizes these forms as follows:

(I) P (II) P (III) PP
(IV) -[PVPV(PP)]

Although these give a mutually exclusive and together exhaustive set of alternatives, this symbolization and interpretation also does not seem satisfactory from a number of points of view, namely:

(ai) Here again the fourth alternative is taken as the negation of the disjunction of the first three, giving it an arbitrary character.

(aii) His symbolization uses, four propositional variables p, p, p and p. It is not clear why Jayatilleke needs both and . Now stands for S is partly p. Also Jayatilleke accepts the convention that when p is true p is false (that is, when 'S is wholly p is true' is true, 'S is partly p' is false). Thus it is clear that while p and p are contraries, p and p are also contraries. Now, if p, that is, 'S is partly p' is true, it has to be the case that p, that is 'S is partly non-p' is also true, (as when is true, neither p nor p can be true, and so on). Similarly when is false p is also false. (that is, S is (only) partly p is false implies that 'S is (only) partly non-p' is false). Thus is superfluous logically. This shows that Jayatilleke's

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variables do not have any sound logical basis. I think that Jayatilleke's confusing logic and semantics is partly the reason for creating this situation. (bi) Jayatilleke does not indicate the example for which his quantified form applies and the examples to which his propositional function-form applies. (bii) We find that some of the examples in the canon cannot be meaningfully interpreted in terms of either the quantified or the propositional functions that he has suggested. For example consider:

Example 2: atthi sattaa opapaathikaa (There exist spontaneous beings.)
natthi sattaa opapaathikaa (There do not exist spontaneous beings.)
atthi ca natthi sattaa opapaathikaa (There do and there do not exist spontaneous beings.)
n'eva atthi ca na natthi ca sattaa opapaathikaa (There neither do nor do not exist spontaneous beings.) [50]

It does not seem easy to render these in terms of A, E, I, O forms and their combinations as suggested by Jayatilleke or Robinson. [51] Nor does it seem correct to use nonquantified propositions to symbolize it. The first alternative of this example, that is, "There exist spontaneous beings," has to be taken in one of the following senses.

(1) Some spontaneous beings exist. (2) A spontaneous being exists. (3) All spontaneous beings exist. (4) X is a spontaneous being which exists.

I indicate later that one possibility is that not all four alternatives in example 2 are universal propositions, but that, on a more plausible rendering, the first and the third alternatives are combinations of particular and universal propositions while the second and the fourth are universal propositions alone. On such a view neither (4) nor (1) above is a sufficiently correct rendering of it. (3) and (2), the latter considered as a variation of (3), are allowable on the first interpretation. Jayatilleke's (or Robinson's) forms using quantified propositions do not accommodate examples which have all the four alternatives as universals. They symbolize the third alternative as a conjunction of particulars. They also do not have the mechanism to handle examples where all the alternatives are particulars or an example which is given the second "interpretation" that I suggested for example 2.

Let us then consider whether such examples as 1 and 2 could be meaningfully symbolized by his nonquantified propositional functions. In the case of "Cattaaro 'me ... puggalaa ...," that is, example 1, Jayatilleke took "X is a person who torments himself," [52] and so forth, as giving equivalent logical sense. I shall show later that this rendering of Jayatilleke is allowable only with some qualification. It is likely that Jayatilleke thought example 1 as symbolizable in terms of nonquantified propositions. But it will be seen later that such a symbolization is inaccurate.

Even if we allow Jayatilleke's interpretation of example 1, such cases as example 2 do not seem amenable to symbolization in terms of his propositional functions. For there is much difficulty in interpreting some of Jayatilleke's

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symbolizations when applied to such examples as "atthi sattaa opapaathikaa" or "atthi paro loko," and so on, [53] where 'exist' is, at least apparently, the "predicate." It becomes difficult to see what the (III) and (IV) forms of the alternatives then mean. Jayatilleke's truth functional symbolizations give

(i) p (ii) p (iii) pp (iv) -[pVpV(pp)]

for the four alternatives and on this, the third alternative "atthi ca natthi ca paro loko" will read "Another (or a next) world partly exists and partly does not exist." The third alternative "Atthi ca natthi ca sattaa opapaathikaa" reads as "Spontaneous beings are partly existent and partly nonexistent." What sense could be attached to these renderings? Jayatilleke does not seem to have noticed this special problem with "existence."

In commenting on this interpretation of the IV-form of the propositional functional symbolization suggested by Jayatilleke. Robinson says, "I might suggest that when the subject is an admitted (prasiddha) entity, the interpretation is: In some respects, this world is not finite, and in other respects, it is not infinite." [54] Jayatilleke interpreted the third alternative here in a similar manner, that is, as "The world is both finite in some respect and infinite in another respect." [55] This seems close to the sense indicated in the text, [56] but whereas Robinson extended the same interpretation to the fourth alternative, Jayatilleke took the fourth alternative, in this case, as the position of a takkii, one who thinks that 'finite' and 'infinite' could not be predicated of the world. [57] Where predication was possible Jayatilleke interpreted a fourth alternative like "A person is neither happy nor unhappy" to say that the person (for example, an arhant) is in a neutral hedonic state. Robinson's interpretation above seems inspired by Buddha's sermon to Kaccaayana. (see notes 78 and 94 herein). Robinson goes on to say, "But "existent" and "nonexistent" are not logically the same as "happy" and "unhappy." The IV-form containing them does not mean "the world possesses a neutral ontological status." [58]

Here Robinson's position also raises problems. Robinson distinguishes between "the soul," "the Tathaagata after death" and so forth, on the one hand and "the world" and so forth, on the other on the basis that the former are not admissible subjects of predication in Buddhist doctrine, whereas the latter are. I fail to see much point in this distinction since what comes, for example, in the Brahmajaala Sutta are not discussions of the Buddhists but those of the Brahmins as recorded by the Buddhists. Next, given Robinson's interpretation, the third alternative (III) reads, "In some respects the world is finite and in some other respects the world is not infinite." Both the third and the fourth alternatives could mean the same thing if "not infinite" is taken as "finite" and the "some respects" in (III) is not necessarily the "some respects" in (IV). For then "some respects" in (III) could very well be the "other respects" in (IV) and the "other respect--" in (III) could well be the "some respects in (IV)." If that sense is given (III) and (IV) will mean the same thing. Of course,

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it is possible to render the III-form as "In some respects R1 the world is finite and in some respects R2 the world is infinite and the IV-form" as "In some respects R1 the world is not finite and in other respects R2 the world is not infinite." If we symbolize the (III) form here as pp the corresponding symbolization of (IV) form seems to be simply ~p~p and not Jayatilleke's ~ [pVpV(pp)]. Finally, the (III) form may be rendered as "In some respects R1 the world is finite and in some respects R2 the world is infinite" and the (IV) form as "In some respects R1 the world is not finite and in other respect R2 the world is not infinite." This will need four variables to symbolize it, and Jayatilleke's or Robinson's forms are obviously inadequate. [59]

Although Robinson's suggestion itself raises problems, what concerns us right here is that Jayatilleke's treatment of the fourth alternative runs up against serious difficulty when one considers examples where 'existence' occurs, in some form, in the predicates.

I am also in agreement with the observation of' Robinson that Jayatilleke's interpretation of the fourth alternative as the position where the predicates are not applicable makes it a rejection rather than a denial. [60] It would lead the (IV) form to being interpreted, for example, as, "It is meaningless to assert that it is meaningless to assert that the world is finite, is infinite or is both finite and infinite." [61]

Thus Robinson's formulation as well as both of Jayatilleke's formulations are far from being satisfactory. Before we leave this topic, it is well to consider attempts by R. S. Y. Chi to give some symbolic forms to represent the catu.sko.ti; [62] Chi gives different symbolic patterns to suit different types of examples of catu.sko.ti. It is instructive to consider here Chi's attempt also. The first example taken by Chi is:

I.a. some state of mind is dhyaana but not samaadhi.
some state of mind is samaadhi but not dhyaana, etc,

Chi notes here that this pattern involves neither contradiction nor contrariety and therefore seems irrelevant to the usual puzzle of the catu.sko.ti. Nevertheless, as he correctly says, "... this is the fundamental pattern of the four alternatives from the point of view of logical priority." Next Chi takes the following, and symbolizes it as shown, taking fa to mean that a is a self-tormentor and ga to mean that x is a tormentor of others.

I.b. some people torment themselves (Ex(fx~gx)
some people torment others (Ex(~fxgx))
some people torment both themselves and others (Ex(fxgx))
some people torment neither themselves nor others (Ex(~fx~gx))

Although I find Chi's analyses convincing up to this point, the rest of his formulations is not relevant for my discussion. In any case, some of these latter forms, Chi himself points out, are unsatisfactory.

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A New Symbolization Of The Catu.sko.ti Statements
In view of these considerations it seems necessary to see if one could get a minimal formulation (or symbolization) to suit the variety of catu.sko.ti examples, together with satisfactory interpretations or explanations of them. In this section I shall develop four symbolic forms , , , and  to symbolize satisfactorily the different catu.sko.ti examples. Of these  and  seem to be sufficient to "cover" the common types of catu.sko.ti examples.

Let us begin with an example which we have mentioned already.

Example 3. The world is finite. The world is infinite. The world is both finite and infinite. The world is neither finite nor infinite. [63]

In the case of this example, we saw Robinson suggesting that the fourth alternative should be interpreted as, "In some respects, this world is not finite, and in other respects it is not infinite." He also associates this interpretation with the sixth example below. He says "This is the case in the Sa.myutta Nikaaya in the famous discourse to Kaccaana, where it is stated that in one sense the world is not existent (because it ceases) and in another sense it is not non-existent (because it arises)." [64] This view, as we noted earlier, is close to the interpretation given in the canon and can be a consistent extension of Jayatilleke's potion regarding the fourth example given earlier, although Jayatilleke does not interpret the fourth alternative of that example in the way in which Robinson does. [65] However, we noticed earlier that neither Jayatilleke's nor Robinson's suggestions for a symbolization and interpretation of this example are satisfactory. And if the idea of "finite in some respect" and "infinite in another respect" is to be used, it is only proper to take the predicates here as different -- for finite in some respect, that is, say, finite in sense S1, is not even the opposite of being infinite in another respect, that is, say, being infinite in sense S2. These predicates are, by themselves, neither "contraries," nor "contradictories." They are not even "opposites." This suggests that we symbolize these predicates by two independent symbols. [66] On the other hand, no two of the catu.sko.ti alternatives can be true together -- that is, the alternatives are contraries. Accordingly, a cornerstone of the present analysis will be the representation of the catu.sko.ti "opposite concepts" by qualities characterizing two classes A and Band yet arriving at four alternative statements with these predicates which are mutually exclusive and together exhaustive. In the preceding case let us take A to stand for the class of all things which have finite aspects (finite directions) and B to stand for the class of all things which have infinite aspects (infinite directions). Taking x to stand for an individual we can now symbolize the four alternatives in example 3 using standard set theoretic notation, where '' stands for "is a member of" and is the complement of A and signifies class product, as follows:

(I) x A (II) xB (III) xAB (IV) x.

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That these four alternatives are mutually exclusive and together exhaustive can be seen from the following Venn diagram where x1, x2, x3, x4 indicates the position of x in the respective alternatives.

I shall call this symbolization form  and refer to

xA as 1, xB as 2, xAB as 3 and x as 4.

Symbolization (I) will mean in this case that the world has finite aspects (directions) but no infinite aspects (directions). That, in this case, the world is considered as not having infinite directions can be gathered from the lines in the Diigha Nikaaya which say that a path could be traced around the world as it is finite. [67] Symbolization (II) could be read now as "the world has no finite aspects (directions) but has (only) infinite aspects (directions). Symbolization (III) says that the world has both finite and infinite aspects (directions) and symbolization (IV), that the world has neither. Jayatilleke's treatment of the matter is different, and he complicates the problem by using the terms 'finite in all respects' and 'infinite in all respects' (note: the first alternative does not mean that the world is finite in all respects, for 'finite' need not apply to some characteristics of the world).

Sometimes we shall use the term 'wholly' in translating the first and the second alternatives as symbolized in the preceding. Thus, the first and the second alternatives in the foregoing example could be translated as, "The world is wholly finite" and "The world is wholly infinite," respectively. It must be emphasized that 'wholly finite' here does not mean that "all the aspects (of the world) are finite." It means only that "no aspect (of the world) is infinite." For, as just pointed out, the terms 'finite' and 'infinite' need not apply to some aspects of the world. Indeed, the fourth alternative could mean that 'finite' and 'infinite' do not apply to any aspect of the world.

A fair amount of catu.sko.ti examples in the Pali Canon have singular sentences -- that is, sentences which have singular nouns as their subjects, as for example, the sentence "The world is finite." We shall see later that all or most of these could be brought under form .

Let us consider a catu.sko.ti where universal sentences seem to be in order. The example is:

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Example 4. Ekanta-sukhii attaa hoti (The soul is wholly happy)
Ekanta-dukkhii attaa hoti (The soul is wholly unhappy)
Sukhii-dukkhii attaa hoti (The soul is happy and unhappy)
Adukkham asukhii attaa hoti (The soul is neither happy nor unhappy) [68]

'The soul' here clearly means all souls, that is, the sentences are stylistic variations of universals. Thus we read this example as:

All souls are wholly happy. All souls are wholly unhappy. All souls are happy and unhappy. All souls are neither happy nor unhappy.

Again, happy and unhappy are only "opposites." Let us represent the classes of all souls, all things with "happy aspects" and all things with "unhappy aspects" by X, A and B respectively. Let 0 be the null class. We then symbolize this example as follows:

We shall refer to this as symbolization  in which 1, 2, 3 and 4 respectively represent the four alternatives. The following diagram shows these alternatives to be mutually exclusive and together exhaustive. [69]

Our next problem is to see how far the other examples could be brought under these two forms. Let us first take examples where the subject is clearly singular.

Example 5.The world is eternal. The world is not eternal. The world is eternal and not-eternal. (The world is neither eternal nor not-eternal). [70]

Example 6.The world exists. The world does not exist. (The world exists and does not exist.) The world neither exists nor does not exist. [71]

Example 7.The Tathaagata exists after death. The Tathaagata does not exist after death. The Tathaagata exists and does not exist after death. The Tathaagata neither exists nor does not exist after death. [72]

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It is possible to use form  to represent both the fifth and the sixth examples above. Let now A be the class of all things which have eternal aspects. Let B be the class of all things which have non-eternal aspects. We can then symbolize "The world is eternal" by 1, i.e., xA which will now mean that the world has eternal aspects, but no non-eternal aspects. That is, the world is wholly eternal. 2, i.e., xB will similarly represent the alternative "The world is non-eternal," which gets interpreted as "The world is wholly non-eternal". The third alternative symbolized by 3, i.e., xAB, will mean that the world has aspects which are eternal and aspects which are non-eternal and the fourth, given by 4, i.e., x that the world has neither. [73]

Is there any basis for us to interpret the fifth example as we do here? The eternality of the world spoken of here seems to be that it has no beginning (that it, it has no pubbanta). Since it is possible to speak about eternality in relation to either end it follows that one could speak of eternality in terms of aspects which are eternal or non-eternal. [74] Thus the qualities characterizing the classes A and B are again only opposites. In considering the sixth example, let A be the class of all things having existent aspects and B be the class of all things having non-existent aspects. When read thus it would appear that A and B are classes with contradictory properties. But the situation is somewhat different. Existing here means always existing and non-existing means not always existing. We can now symbolize the sixth example by form . Given this form to it xA will mean that the world has existent aspects but no non-existent aspects, xB will mean that the world has only non-existent aspects but no existent aspects, xAB will mean that the world has both existent and non-existent aspects, and lastly, x will mean that the world has neither the existent nor the non-existent aspects.

This last interpretation is somewhat different from the one suggested by Robinson. [75] However, the sense that I have given to the term 'existent' is more appropriate. [76] Mrs. Rhys Davids, for instance, points out that, "According to B, Eternalists held that, 'in the conditioned world' once existing means always existing; annihilationists held that nothing existing persisted always ... Existence (atthitaa) is apparently understood in the Parmenidean sense: incapable of absolute dissolution." [77]

Also the following passage from the Buddha's sermon to Kaccaayana shows the Buddha referring to this, that is, the eternalists' sense of 'existence'. Buddha tells Kaccaayana:

Now he, who with right insight sees the uprising of the world, as it really is, does not hold with the non-existence of the world. But, he, who with right insight sees the passing away of the world as it really is, does not hold with the existence of the world. [78]

That what the Buddha here refers to is the eternalists' sense of existence is clear by the following words of the Buddha in the same sutta.

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Everything exists: this is one extreme. Nothing exists: this is another extreme. Not approaching either extreme the Tathaagata teaches you a doctrine by the middle... [79]

It would be seen that the statement "Everything exists" is possible only if the eternalists' sense of existence is assumed, that is, only if it is assumed that anything that has ever existed always exists.

Robinson's comment that the (IV) form of this example does not mean that "the world possesses neutral ontological status," points out the problem with 'existence' but does not help in solving the problem of interpreting this alternative. The solution, I think, lies in the interpretation that the world is neither existent nor nonexistent in a particular sense of 'existence', namely, that of the eternalist. This sense of 'existence' makes 'existence' a predicate.

Does this interpretation of 'exist' make examples five and six the same? This possibility cannot be ruled out, although there is reason for holding them as two separate examples. 'Eternal' and 'exist' could have, in addition to their common core of meaning, other associated meanings attached to each. For example, 'eternal' in example 5 could mean eternal with respect to pubbanta (see note 74). It is also possible that 'eternal' had more temporal flavor whereas 'exist' emphasized the fact of "no absolute dissolution." On the other hand, what was explicitly called eternal (sassata) in the Brahmajaala Sutta in the Diigha Nikaaya, could have been meant by a reference to the sense or 'exist' involved in the "right views" in the Kaccaayana Sutta in the Sa.myutta Nikaaya.

The seventh example can be symbolized by  and interpreted on the same lines as the earlier examples. Let A be the class of all things which have aspects which do not cease (after death). Let B be the class of all things which have aspects which cease (after death). Then, 'The Tathaagata exists after death' can be symbolized by 1, that is, xA; this will mean that none of the aspects of the Tathaagata will cease to exist after death: "The Tathaagata does not exist after death" by 2, that is, xB; This will mean that no aspect of the Tathaagata will continue to exist after death: "The Tathaagata exists and does not exist after death" by 3, that is, xAB; this will mean that some aspects of the Tathaagata will continue to exist while some other aspects will cease to exist after death. The fourth alternative, "The Tathaagata neither exists nor does not exist after death," symbolized by 4, that is, x, means that the Tathaagata does not have aspects which continue to exist after death or ceases to exist after death. Indeed this example being an avyaakata, the case seems to be that the categories 'exist after death', and 'not-exist alter death' do not apply to (any aspect of) the Tathaagata so that this is a rejection of the predicability of these categories of the Tathaagata.

It is not necessary for our interpretation that we take 'exist' in example 7 to mean the same as 'eternal', but this seems to be the meaning intended. For, in essence, the question is about the Tathaagata being eternal (in some sense). This

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is also seen by the fact that this question of existence (after death) is not raised in connection with "ordinary" (human) beings.

One example which is of an uncommon type, but which, I think, could be accommodated under the symbolization  in practice, is example 1, namely, "cattaaro 'me Pessa puggalaa santo sa.mvijjamaanaa lokasmi.m ... ekacco puggalo attantapo hoti..." and so on. Let us consider, what at first sight may seem to be the possible logical senses of this:

There are four types of persons found in the world.
(1) Some persons are tormentors of themselves
(yet) Some (other) persons are tormentors of others
(yet) Some (other) persons torment themselves and others
(and yet) Some (other) persons neither torment themselves nor torment others

(2) If we take any particular individual person say, P, it is the case that,
(either) P is a person who torments himself
(or) P is a person who torments others
(or) P is a person who torments himself and others
(or) P is a person who neither torments himself nor torments others (where 'or' stands for strong disjunction).

Since the Pali passage clearly intends to categorize persons, a version of it with all the alternatives as universals obviously cannot fulfill this intention. Version (1) is, ordinarily, satisfactory. Indeed the PTS translation is,

Pessa, these four kinds of persons are found in the world. What four? ... some person is a self tormentor, ... some person is a tormentor of others ... some person is both a self-tormentor ... and a tormentor of others ... some person is neither a self-tormentor ... nor a tormentor of others...

The list is clearly intended as an exhaustive classification of persons on the bases of tormenting themselves and tormenting others, it also seems to be, when read in context, intended as a mutually exclusive classification. [80] In a way, form (2) brings out the logical characteristics of this example more easily than form (1). But the apparent "singular sentence appearance" of form (2) is deceptive, [81] for P is a variable in effect.

The next point about this example is that the two characteristics "torments himself" and "torments others" seem to be just opposites (and no more). They are, by themselves, neither "contraries" nor "contradictories." Thus we can represent the class of all "tormentors of oneself" and the class of all "tormentors of others" by two symbols A and B. [82]

Although a strict symbolization of the alternatives of this example, with the intended meaning of the first interpretation above, could be given using predicate calculus, [83] it seems best to opt for a more simple symbolization, such as , if it sufficiently satisfies our needs here. Let us explore this possibility.

If x is an individual, U, the universe of persons, and A and B, the classes of all self-tormentors and all tormentors of others, respectively, we may symbolize the four alternatives of this catu.sko.ti all together in the following way.

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xU(xAxBxABx)............. ()

where '', '' are the logical constants of implication and strong disjunction respectively. Of course, to this we will have to add the rider that U≮O where O is the null class, since the alternatives in question are existential.

If we are ready to overlook the universal nature of the preceding symbolization and also that x there, though standing for an individual, is standing for any particular individual, we can use  to symbolize this example. For let us take a particular individual I, in U. Then we can correctly write

IAIBIABI........................()

Indeed, () is derivable from () by something like universal instantiation. [84] We can thus use the disjuncts in () as our alternatives. But these disjuncts, when I is replaced by x, are

(I) xA, (II) xB, (III) xAB, and (IV) x

which are 1, 2, 3 and 4, respectively. Therefore, use of  to symbolize example 1 seems allowable.

Let us now take the examples which are best given universal interpretation.

(8) There is another world. There is no other world. There is another world and no other world. There is neither another world nor no other world. [85]

(9) The soul has form. The soul is formless. The soul has and has not form. The soul neither has nor has not form. [86]

(10) The soul is finite. The soul is infinite. The soul is both (finite and infinite). The soul is neither (finite nor infinite). [87]

(11) One's suffering is wrought by one's self. One's suffering is wrought by another. One's suffering is wrought by one's self and by another. One's suffering is wrought neither by one's self nor by another. [88]

(12) Things continue after complete detachments from and cessation of the six spheres of experience. Things do not continue after complete detachment from and cessation of the six spheres of experience. Things continue and do not continue after complete detachment from and cessation of the six spheres of experience. Things neither continue nor do not continue after complete detachment from and cessation of the six spheres of experience. [89]

(13) The soul is identical with the body. The soul is not identical with the body. [90] (The soul is identical and not identical with the body. The soul is neither identical nor not identical with the body.)

(14) The soul has one mode of consciousness. The soul has many modes of consciousness. The soul has limited consciousness The soul has infinite consciousness. [91]

In the eighth example, the statement "There is another world," means that a being is born again or will continue in another life after death. Again we may take that X is the class of all beings, A is the class of all things which have aspects which continue to exist or are reborn after death and that B is the class

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of all things which have aspects which do not continue to exist or are not reborn after death. We can then symbolize this example by the form .

Examples (9) and (10) on this rendering will consist of universal propositions. "All souls have form," and so forth, and "All souls are finite," and so forth. Let X be the class of all souls. Then if A is the class of all objects which have (aspects with) form, B is the class of all objects which (have aspects which) are formless, then example (9), can be symbolized by . Again, if A is the class of all objects which have finite aspects and B is the class of all objects which have infinite aspects, then,  can symbolize example (10).

Similarly, examples 11 and 12 can be symbolized by . In the former, X is the class of all beings, A is the class of all beings each of whose suffering is (or has aspects) caused by itself, B the class of all beings each of whose suffering is (or has aspects) caused by another. In the latter X is, again, the class of all beings, A the class of all beings which have aspects which continue after complete detachment from and cessation of the six spheres of experience and B the class of all beings which have aspects which cease to continue after complete detachment from and cessation of the six spheres of experience. There is some similarity or content between this last example and example 7 which we symbolized by . Example 13, an avyaakata in which only the first two alternatives occur in the literature, can again be symbolized by . In this case, X is the class of all souls, A the class of all things which have aspects identical with (those of) body and B the class of all things which have aspects which are not identical with (those of) body. Moreover, a very plausible rendering of example 14, which appears difficult to interpret, can be given on the basis of the present symbolization. For, let A be the class of objects which have one mode of consciousness. Let B be the class of objects which have many but finite modes of consciousness. Then, 1, that is, says that the soul has one mode of consciousness, 2, that is, says that the soul has many modes of consciousness, 3, that is, says that the soul is in the class which has one and many but finite consciousness. This is to say, soul is in the class which has limited consciousness. 4, that is, says that the soul is outside the class of one and the class of many but finite modes of consciousness. Since one and many but finite covers everything outside infinite, this gives the meaning that soul is in the class of infinite modes of consciousness which agrees perfectly with the fourth alternative, "the soul has infinite consciousness." Finally, let us take example 2 which seems problematic. This example is

There exist opapaathika beings. There do not exist opapaathika beings. There exist and do not exist opapaathika beings. There neither exist nor do nor exist opapaathika beings. [92]

First, on interpreting atthi (that is, exist) in the sense that to 'exist' means to exist always and without dissolution, we can symbolize this example by  on the following further consideration.

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There is reason to render "There exist spontaneous beings" as "all spontaneous beings exist" and so on, that is, on the same lines as "All souls are (wholly) happy" and so forth, and not on the lines of "Some persons torment themselves" and so forth. The reasons for the last form to be inappropriate are: (i) the second alternative "Natthi sattaa opapaathikaa," in any case, is a universal negation, so that an interpretation with all four alternatives as particulars seems inappropriate; (ii) the third alternative and the first alternative can be true together if both these are taken as particulars without further qualification.

Therefore, proceeding on the lines suggested, if A is the class of all objects with aspects which exist (in the sense of the eternalist) and B is the class of all objects with aspects which do not exist (in that sense) and X is the class of all opapaathika beings, then 1, that is, , will represent that all opapaathika beings (wholly) exist; 2, that is, , that no opapaathika beings have any aspects which exist; 3, that is, , that all opapaathika beings have aspects which exist and aspects which do not exist and 4, that is, , that all opapaathika beings have aspects which neither exist nor do not exist.

Generally, the canonical literature seems to assume that there are opapaathika beings. [93] Since the canonical literature seems to assume the existence of opapaathika beings, it is reasonable to suppose that the question handled in this catu.sko.ti example is not a question about the existence simpliciter of opapaathika beings but the existence, in the sense of the eternalist, of the opapaathika beings. (Of course, whether the class of opapaathika is null or not a Buddhist could reject all four of the alternatives since 'exist' or 'not exist' in the sense of the eternalist is not acceptable to the Buddhist.) [94]

Although there is thus some basis to accommodate this catu.sko.ti under form  one could also look at it differently. It has not been necessary to give a specific meaning to 'exist' (like that of the eternalist) in our treatment of examples except example (6) where 'exist' is applied to the world. (Note: In example 7 it was not necessary to understand 'exist' as 'eternal' although it made sense to do so.) There is good reason, as we pointed out, to take 'exist' in example 6 in the sense of the eternalist. Still, one could question the plausibility of such an interpretation in examples like the preceding one. One could also take the position that "There exist opapaathika beings" does not mean that "all opapaathika beings exist," but that "there are opapaathika beings," that is, it means that some opapaathika beings exist (in the usual sense of 'exist').

We are thus led to give a symbolization, which we shall call , that might be more appropriate for this example. Let X be the class of all beings, A the class of all beings with opapaathika aspects, and B the class of all beings with non-opapaathika aspects. Symbolization  then, is:

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The following diagrams show that these are mutually exclusive and together exhaustive positions, as far as the class of beings is not null.

1 says that there are beings with opapaathika aspects (and not having non-opapaathika aspects) that is, there are "wholly" opapaathika beings, but no "partly" opapaathika beings. What this could mean, we shall see in a moment. 2 says that there are no opapaathika beings. 3, that there are "partly" opapaathika beings but no "wholly" opapaathika beings. The "wholly" and "partly" could be understood thus: chance or spontaneous beings are beings which are "uncaused." Now this is usually taken to mean that they have no parents. But they could possibly be "caused" by, say, Brahma's wish. If such is the case, they could be partly "uncaused" or partly opapaathika, in the sense that they are without parents but not wholly "uncaused." If they are not caused in any sense at all, then they could be fully "uncaused" or wholly opapaathika. Indeed, opapaathika literally means something like "dropped." As we noted earlier, the devas and brahmas were opapaathika, in general. Passages in the Brahmajaala Sutta, where the births of brahmas and so on, are narrated, show how they "drop from different planes." Such births are without parents bur are "caused" by factors like greed. [95] (In  what we seem to be doing is talking of "cause and no cause aspects" of beings instead of the eternal and non-eternal aspects of them talked of in using .)

Some Questions in The Interpretation of Catu.sko.ti
In this section, I wish to take up, very briefly: the problem of distinguishing among (4.11) the acceptance of the fourth alternative, the negation of all four alternatives, the thapaniiya or the rejection of all the four alternatives of the catu.sko.ti, [96] and avyaakata questions; the relevance of the paryudaasa-prasajya negations and the view of degrees of truth to the understanding of the catu.sko.ti; the relevance of the origins and the historical development of the catu.sko.ti and the dialectic to the interpretation of the catu.sko.ti. The observations made in this section are only preliminary.

There seem to be examples where the Buddha opted for the fourth alternative. Our example 1 seems to be a case in point. The very nature of the fourth alterna-

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tive has complicated the problem of distinguishing between the acceptance of the fourth alternative and the negation and the rejection of all the four alternatives. Acceptance of the fourth alternative as, for example, in the case of "The person who neither torments himself nor torments others" seems to be the case when the predicates involved (and hence the alternatives) give a fair account of the actual situation but the alternative acceptable to the Buddhist is the one which lies outside the predicate concepts -- that is, the one in which the negation of the concepts are predicated.

Acceptance of the fourth alternative appears "akin" to the negation or rejection of the predicates, thus making it a more difficult case to distinguish from the latter. Take, for example, the Kaccaayana Sutta. When the Buddha says that a person with right insight cannot hold with either the existence or the nonexistence of the world, does it mean that the Buddha opts for the fourth alternative? It reads almost as if the Buddha was accepting the fourth alternative, but this, in fact, is not the case (I feel that this appearance of the fourth alternative was partly instrumental in the later Buddhists' using the catu.sko.ti as a dialectic leading to the `suunyataa view and so on). In the Kaccaayana Sutta the Buddha is only rejecting the "right views" presented by groups like the eternalists. This is clear from his words:

Grasping after systems, imprisoned by dogmas is this world, Kaccaayana, for the most part. And the man who does not go after system-grasping ... (and) does not think, "It is my soul! ... is not perplexed." [97]

The Buddha here is rejecting these categories and coming out with his causal theory of pa.ticcasamuppaada.

There are cases in which all the alternatives are negated and the answer "It is not so" (na h' idam) is given. Such a case is the following:

Example (15).
[Is it the case that] one attains the goal by means of knowledge.
[Is it the case that] one attains the goal by means of conduct.
[Is it the case that] one attains the goal both by knowledge and conduct.
[Is it the case that] one attains the goal without knowledge and conduct. [98]

(This can be symbolized and interpreted using form .) Jayatilleke points out that, in this case, the answer is "no" to each of the alternatives because "while 'knowledge' and 'conduct' are necessary conditions for final salvation, they are not sufficient conditions." [99] Thus the negation of all the four alternatives with the answer na h' idam seems given in cases where, although the two predicate concepts involved are applicable to the situation (or the class of objects) spoken of in the subject, none of the alternatives gives a sufficiently correct or true picture or analysis of the situation.

The thapaniiya pa~nha or the cases in which the four alternatives are "rejected" usually with the answer 'maa h' evam' that is, "do not say so," seem to be those where the predicates are not applicable to the subject (or sometimes, possibly

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where the subject class is empty). For instance, this occurs in the example of "pleasure and sorrow as originating from oneself or others." [100]

In this last case, which comes in the Timbaruka Sutta, Buddha relents Timbaruka's use of concepts because of the way he has distinguished between the experiencer and the experienced. A similar case is found in the Kassapa Sutta. [101]

We note that in the case of avyaakata questions, the subject class is, philosophically, a broad or a basic concept -- the world, the Tathaagata, the soul. It is possible that the Buddha considered that answering these questions was not helpful, but could be rather unhelpful to the understanding of the true nature of these subjects or reality it is also possible that the Buddha's standpoint was that the natures for which descriptions are attempted in these are not understandable conceptually but only "realized" otherwise. [102]

Matilal, [103] Staal, [104] and Wayman [105] mention the possible understanding of catu.sko.ti in terms of the prasajya-pratisedha (where the predicate is denied), for example, "The flower is not red" and paryudaasa (where a term is denied or where the denial is by implication), for example. "The flower is not-red" or "If it is blue it is not white." Matilal maintains that when the catu.sko.ti is interpreted as prasajya-pratisedha "the apparent contradiction of the joint negation of the four-alternatives will disappear." That the catu.sko.ti is of prasajya-type, but that that interpretation does not resolve the contradiction is maintained by Staal whose view here is correct in my opinion. In any case, this distinction, if at all, seems to help understand the Maadhyamika uses of catu.sko.ti which do not fall within the scope of this article. The view that the catu.sko.ti alternatives are based on an idea of degrees of truth (sa.mv.rti and paramaartha) also seems to be applicable to only later Buddhism. [106] The same comment applies to the suggestion by Wayman that catu.sko.ti also has a role in meditative practice.

The symbolizations (and the interpretations) which I suggested, on the other hand, deal with the canonical catu.sko.ti forms, and there is good justification for these symbolizations. First, I think that it is reasonable to believe that the Buddhist catu.sko.ti evolved from the "standpoint views" of Jaina Syaadvaada and the fivefold negations of the skeptics. [107] These involved a "standpoint view" and the ideas of opposites and negations. The Buddhist catu.sko.ti is not "a standpoint view," but it seems reasonable to hold that it is a dialectic which evolved from the two earlier systems.

It is possible that the development of the dialectical aspect of the catu.sko.ti also had some connection with the Buddhist view of reality as flux. But, as suggested earlier, I feel that the dialectical element in the catu.sko.ti in early Buddhism is perhaps more a result of the development of the catu.sko.ti from the Syaadvaada or Jaina and the fivefold negations of the skeptics. Murti writes,

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"Dialectic" is a term used generally but incorrectly, to any closely reasoned argument or refutation ... there must be at least two-viewpoints or patterns o interpretation diametrically opposed to each other... [108]

Some form of dialectic seems to be involved in both the early and the later catu.sko.ti examples. But, except perhaps for possible similarities in logical form, it seems best not to give the same interpretation to the examples in the Pali Canon and the post-Naagaarjuna occurrences of these examples. [109] The catu.sko.ti system in early Buddhism, even if it did evolve from the Syaadvaada and earlier systems, reflects the philosophy of early Buddhism -- whereas, Naagaarjuna and others interpreted the catu.sko.ti to suit the philosophy of later Buddhism. Early Buddhism avoids the two extremes of affirmation and negation. Its philosophy is a dependent origination -- where "things are, as well as not."

In a dialectical view a predicate is considered in relation to another predicate which is the "opposite" of the first. This has been a lead which I have followed in my symbolization. Following it, I preferred to consider the catu.sko.ti alternatives not as given by one predicate, its negation or contrary, and the positive or negative combinations of these, but as given by two predicate concepts characterizing two classes, A and B, because these predicate concepts are only "opposites" in most cases. These opposite characteristics could inhere in the same object or the same group of objects (and this is characteristic of a dialectic), but it could be that only one or none of them is found in any particular object or set of objects. Still, what is important dialectically is that one characteristic is taken into consideration with -- or against -- an opposite characteristic. The second point of interest for us here is the negation aspect of dialectical argument which is seen in catu.sko.ti. Thus alternative (I) is an assertion which when negated leads to alternative (II); alternative (III), in a sense, negates both (I) and (II), but it could be described even by the jargon that (III) is a synthesis of (I) and (II). Alternative (IV) is a more complicated form of negation, but still, one could look at it as a culmination of a dialectical process. The last seems to be the view of Matilal and others, who are more concerned with the Maadhyamika dialectic which ultimately rejects reason in the realization of the `suunyataa. The dialectical aspect is there in early Buddhism, but it is not developed as a process which generally progresses toward some goal. Nonetheless it plays one concept against its opposite and helps to deny absolutism and "realize" the middle path.

The attempt to use one concept and its contradictory or "contrary" in the catu.sko.ti predicates seems a mistake. It has not resulted in producing a general and consistent formulation which could present the logical form of catu.sko.ti. Attempts to understand and symbolize the catu.sko.ti using one predicate has made the students blind to the possibility of using more than one predicate concept in the alternatives. It looks as though to use two concepts in the

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predicates of the catu.sko.ti alternatives in the attempt to give it form is to throw the baby away with the bath water. My symbolization shows that this, in fact, need not be the case. In the first place since the predicates seem to be contradictories, contraries, "opposites" and so on, in a very general symbolization, to take the concepts as separate seems justified. Next, in logic concepts are given extensional meaning, and the same object (or same set of objects) cannot come under a concept and its negation. But the catu.sko.ti examples need to satisfy seemingly such situations. This was further justification for employing two predicate concepts which really characterize two classes A and B. Moreover, in catu.sko.ti it is the alternatives and not so much the predicates which exclude each other. And it has been possible, in this article, to give symbolizations using two predicate concepts which makes the four alternatives mutually exclusive and together exhaustive.

The present formulation maintains the distinction between the logical form of catu.sko.ti and its interpretation. This distinction between logic and semantics is not clear in analyses like that of Jayatilleke. Jayatilleke's and Robinson's renderings at times use the same symbol for what are in effect two or more concepts. [110]

It might be helpful to compare my locutions like "A is the class of all objects having finite aspects" with Robinson's quantification of the subject class, in terms of its attributes, [111] and Jayatilleke's and Robinson's use of terms like "In some respects (the world is finite...)," [112] and so on. Robinson took the first alternative as "All X is A," "where x stands for the attributes of the entity in question," but this, we noted, was not plausible. I am myself using the idea that the entity in question has different aspects but I am not quantifying the subject in terms of its aspects (or attributes). Unlike Robinson and Jayatilleke, I am recognizing that to say that the world is finite in some respects and infinite in others is really to predicate of the world not one but two terms.

In this article, I have only attempted to show that the catu.sko.ti examples occurring in the Pali canonical literature could be consistently symbolized by a few formulae and interpreted to be meaningful within the setting of early Buddhism. I think that this symbolization could be used for the Maadhyamika and later catu.sko.ti examples since many of the catu.sko.ti examples in early and later Buddhism are the same, but their interpretations are possibly different. My brief comments on the interpretation of the catu.sko.ti in early Buddhism were made partly to justify my approach to the symbolization. Interpretation of the catu.sko.ti of the Maadhyamika and later Buddhism, and the uses to which it was put by the Mahaayaanists need a more comprehensive study and I have not undertaken that difficult task here.

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NOTES
1. See Richard S. Y. Chi, Buddhist Formal Logic (London: Royal Asiatic Society of Great Britain and Ireland, 1969), Foreword, p. viii.

2. Among them the following: Louis de La Vallee: Poussin. The Way of Nirvana (Cambridge: Cambridge University Press, 1917), p. 111; C. A. F. Rhys Davids, Logic (Buddhist), Encyclopedia of Religions and Ethics, ed. James Hastings, vol. 8, p. 133; B. M. Barua, A History of Pre-Buddhistic Indian Philosophy (Calcutta: University of Calcutta, 1921), p. 47; T. R. V. Murti, The Central Philosophy of Buddhism (London: Allen & Unwin, 1955), pp. 121 ff; P. T. Rajju, "The Principles of Four-cornered Negation in Indian Philosophy," Review of Metaphysics 7:694-713; K. N. Jayatilleke, "Some Problems of Translation and Interpretation II," Ceylon University Review 8 (1950): 45-55 (hereafter cited as Jayatilleke I); Early Buddhist Theory of Knowledge (London: George Allen &. Unwin, 1963, mainly pp 333-35l (hereafter cited as Jayatilleke II); "The Logic of Four Alternatives," Philosophy East and West 17, no. 1 (hereafter cited as Jayatilleke III); Archie Bahm, "Does Seven-Fold Predication Equal Four-cornered Negation Reversed?" Philosophy East and West 7; Nos. 3-4; R. H. Robinson, "Some logical Aspects of Naagaarjuna's System," Philosophy East and West 6 (1957) pp. 291-308 (hereafter cited as Robinson I); "Mysticism and Logic in Seng-Chao's Thought," Philosophy East and West 8 (1958-1959): 99-120 (hereafter cited as Robinson II); Early Maadhyamika in India and China (Madison: University of Wisconsin Press, 1967) pp. 50ff (hereafter cited as Robinson III); "Early Buddhist Theory of Knowledge," Philosophy East and West 19 (1969): 69-81. (hereafter cited as Robinson IV); Shooson Miyamoto, "The Logic of Relativity as the Common Ground for the Development of the Middle Way," Buddhism and Culture, ed. Susumu Yamaguchi (Kyoto, 1960), pp. 67-68; B. K. Matilal, Epistemology, Logic and Grammar in Indian Philosophical Analysis (The Hague: Mouton, 1971, pp. 162-165; Ninian Smart, Doctrine and Argument in Indian Philosophy (London: George Allen & Unwin, 1964), pp. 35, 197; Richard S. Y. Chi, Buddhist Formal Logic, pp. 156-163 (hereafter cited as Chi I); "Topics on Being and Logical Reasoning," Philosophy East and West 24, no. 3 (hereafter cited as Chi II); Fritz Staal, Exploring Mysticism (Berkeley and Los Angeles: University of California Press, l975). pp 45 ff; Jayatilleke and/or Robinson refer also to the following: Schayer, "Altindische Antizipation der Aussagen Logic," in Studien zur Indischen Logik, Extrait du Bulletin de l'Academie Polonaise des Sciences et des Lettres cracovic (1933) (Jayatilleke II, p. 350; and Robinson I, p. 302; idem, IV. p. 76): Hajime Nakamura, "Kukan no Kigo-ronrigaku-teki Kaimei" (Some clarifications of the concept of voidness from the standpoint of symbolic logic), in Indegaku Bukkyoogaku Kenyuu (1954), and "Buddhist Logic Expounded by Means of Symbolic Logic, Indegaku Bukkyoogaku Kenyuu (1958) (Robinson IV, p. 73).

3. Alex Wayman, "Who Understands the Four Alternatives of the Buddhist Texts," Philosophy East and West 27, no. 1.

4. Wayman, p. 5.

5. Loc. cit.

6. Confer Paul Bernays, "Mathematics as a Domain of Theoretical Science and of Mental Experience," Logic Colloquium '73, ed. J. C. Shepherdson (Amsterdam: North-Holland Publishing Company, 1975), p. 4.

7. La Valle Poussin, p.111.

8. Mrs. Rhys Davids, p. 133; Barua, p. 47.

9. Robinson I, p. 303; idem, III, p. 57.

10. Jayatilleke II, pp. 339ff.; and idem, III, pp. 82ff.

11. Wayman,. pp. 4ff.,14ff.

12. Chi II, pp. 295-298; also see Muurti, pp. 121ff.

13. Confer Jayatilleke II, pp. 383-385; also Robinson IV, p. 73; and Chi I, p 156.

14. Majjhima Nikaaya (hereafter cited as MN) I, p. 341. See below, Example 1. All references to Pali texts and their translations are to PTS editions, unless otherwise specified.

15. Confer, Jayatilleke, p. 46. Also Wayman, says, "Jayatilleke has shown that various systems of four alternatives found in the early Buddhist texts are in a disjunctive system whose role seems to be that when one of the alternatives is taken as 'true' the rest are certainly false" (p. 6). Robinson

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(IV, p. 77), also considers catu.sko.ti a mutually exclusive, together exhaustive system. See also Chi II, p. 297.

16. Wayman, pp. 8-9.

17. Diigha Nikaaya (hereafter cited as DN) II, p. 100.

18. Keeping aacariya-mu.t.thi is generally a common practice mentioned about the guru in Indian schools. See also Murti, p. 47.

19. See Wayman, p. 9, where the relevant section reads, more fully but the same scriptural passage from the traditional, last sermon of the Buddha could be taken differently than it usually is, and perhaps consistently with Naagaarjuna's verse (that is, Maadhyamika Kaarikaa VIII, 8) as Candrakiirti understood it. That is because the original Paali (Diigha Nikaaya II, 100) reads: mayaa dhammo anantara.m abaahira.m karitvaa (By me was the dhamma preached without inner, without outer). The phrase "without inner, without outer" can be restated as "with neither an inner nor an outer."
And then just as the "neutral feeling" (neither pleasure nor pain) is not either pleasure or pain, so also one could not determine if the Buddha's doctrine was either inner or outer. On the other hand, Buddhaghosa, in his commentary Sumangala Vilaasinii makes it clear that 'anantaram-abaahiram' refers to the fact that the Buddha did not have an "inner-outer" distinction in his teaching, either as far as his dhamma or as far as the people to whom the dhamma was taught were concerned. Wayman does not recognize that what the phrase "without inner, without outer" qualifies is not the dhamma but the way he (that is, the Buddha) taught the dhamma. For the passage reads not just mayaa dhammo but desito ... mayaa ... dhammo ... na tath ... aacariya-mu.t.thi.

20. Wayman, p. 10.

21. Buddhaghosa, Atthasaalinii I, p. 248; idem, II, pp. 318-319.

22. Wayman, p. 11.

23. Jayatilleke II, p. 344.

24. Chi II, p. 297. See also the last paragraph of p. 296.

25. Wayman, pp. 10ff.

26. Wayman, p. 13; also the following on p. 14, "Such passages undoubtedly support the frequent claim that the Maadhyamika rejects all 'views'. But note that views here are of existence, not of causation; and that Naagaarjuna elsewhere adheres to the view of dependent origination, which in Buddhism would be counted as a 'right view' (samyag-d.r.s.ti)."

27. Chi II, p. 298.

28. MN, p. 341.

29. See later, pp. 28ff.

30. Sa.myutta Nikaaya (hereafter cited as SN) II, p. 18.

31. Robinson I, p. 303; idem, III, p 57.

32. Jayatilleke, I, pp. 53-55; idem II, pp. 339ff., idem III, pp. 69-83.

33. Chi I, pp. 156-162.

34. Robinson III, p. 57.

35. Robinson I, p. 303.

36. Jayatilleke III, pp. 77-78.

37. Robinson IV, p. 75.

38. Jayatilleke II, p. 351, makes this point also. There he also noted that the first alternative is not always a universal affirmative proposition. Robinson (IV, p. 74) felt that this last comment needed clarification. Examples like "Puggalo attantapo" are best not rendered as universal affirmatives, as I suggest later. But I agree that Jayatilleke's example there, that is, "This world is finite" and so on, given Robinson's interpretation, ceases to be a clear counterexample to Robinson's view that the first alternative is an A proposition.

39. Jayatilleke II, p. 350.

40. Jayatilleke III, pp. 71ff.

41. Op. cit., pp. 74-75.

42. Jayatilleke III, p. 76 says, "We have already seen that when (1) is true, (2) and (3) are false," and here he is referring to p. 75, where he says "When A is true ... O being the contradictory of A is false and therefore the conjunction I.O is false ... when E is true ... since the contradictory I is false, I.O would be false."

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43. Confer, for example, P. F. Strawson, Logical Theory (Methuen, 1952), p. 170; A. Ambrose, and M. Lazerowitz, Fundamentals of Symbolic Logic (New York: Holt, Rinehart and Winston, 1962), pp. 241 ff.

44. Jayatilleke III, pp. 74-75, also makes an incorrect statement when he says, "It is generally admitted by modern logicians that the relationship among the Aristotelian forms A, E, I, O in the traditional square of opposition holds only if they are given an existential interpretation." On this, again, see Strawson, p. 165.

45. Robinson IV, p. 75.

46. Jayatilleke III, p. 75.

47. Jayatilleke II, p. 351. See MN I, p. 341 ff.

48. Jayatilleke I, p. 55; idem, II, pp. 343 ff. In the latter "S is P" is used instead of "X is A."

49. Jayatilleke III, p. 79.

50. DN I, p. 39.

51. Confer Chi I, p. 161, commenting on his examples VIa and VIb as "really puzzling and controversial" ones.

52. Jayatilleke III. p. 70.

53. Jayatilleke II, p. 342. See later, example 8.

54. Robinson IV, p. 75.

55. Jayatilleke II, p. 341.

56. See DN I, p. 25, where the third alternative is "explained" as "the world is limited in the upward and downward directions, but infinite across."

57. Jayatilleke II, p. 341.

58. Robinson IV, p. 75. As Robinson notes, "happy" and "unhappy" are predicated of the soul and not of a person, in the Sutta. Jayatilleke is here treating a modified example.

59. Robinson's own observations seem appropriate here. See Robinson IV, pp. 75-76, "Semantic multivalence hovers around most of the instances, and is only occasionally marked by qualifiers such as 'in some respects'. Where if anywhere is the border between logic and semantics? And is it justifiable to call this fourfold form logical at all, when one term can be used in two senses, and when the predicates are so diverse -- contradictories, contraries, opposites, and mere differents? But unless each term is used in the same sense throughout the four alternatives, multiple standpoints are in fact involved."

60. For this distinction between denial and rejection, see later.

61. Robinson IV, p. 74.

62. Chi I, pp. 156-163. Chi II suggests that no consistent form is possible for this system. Although he seems mistaken in this, he correctly admits that he was wrong in comparing the catu.sko.ti with intuitionism (Chi II, p. 297).

63. DN I, pp. 22-23.

64. Robinson IV, p. 75.

65. Jayatilleke II, pp. 340-341.

66. Confer, Chi I, p. 157, where he characterizes the catu.sko.ti predicates using two symbols f and g.

67. DN I, pp. 22.

68. DN I, p. 31.

69. We may also symbolize them by the quantified forms

(I) (x) (fx(gx~hx))
(II) (x) (fx(~gxhx))
(III) (x) (fx(gxhx))
(IV) (x) (fx(~gx~hx))

where f, g, and h stand for the characteristics of being a soul, being happy and being unhappy respectively. 70. DN I, pp. 13ff. The IV form is not seen here, but appears in later literature. This is an avyaakata. See also Murti, p 38. 71. SN II, p. 5. The III-form is not given there. The IV-form of this example is referred to in Robinson IV, p. 75.

70. DN I, pp. 13ff. The IV form is not seen here, but appears in later literature. This is an avyaakata. See also Murti, p. 38.

71. SN II, p. 5. The III-form is not given there. The IV-form of this example is referred to in Robinson IV, p. 75.

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72. DN I, p. 27.

73. We can illustrate this by the following case. Let a being have one or both or neither of soul and body. Let the soul be eternal, and the body noneternal. Now 1 will say that this being is all soul, 2 that it is all body, 3 that it is both body and soul, and 4, that this being has neither soul nor body. In this last case it can be that the being is not existent or that, for example, it is a being which has neither soul nor body, but a mind, which is, say, "a stream of consciousness."

74. See Murti, p. 38n.3. Also see DN I, pp. 16ff. Indeed, in the earlier example, finite and infinite was sometimes taken in the texts as referring to the pubbanta and not as speaking of spatial limitation (compare Murti) but in some example, the spatial aspect is made explicit (for example, DN I, p. 23).

75. See above, p. 12.

76. 'B' here refers to Buddhaghosa. Note that this example occurs in the discussion of eternalists and others, in Brahmajaala Sutta.

77. Mrs. Rhys Davids, PTS translation of Sa^myutta Nikaaya II, p. 12n.3.

78.Op. cit., pp. 12-13.

79. Op. cit., p 13. Note also that Buddha is here referring to the "right view" of other teachers. For Kaccaayana is asking "Lord, we hear the phrase, 'right view, right view.' Now how far is there a 'right view?'" (op. cit., p. 12).

80. "There are four types of persons in the world" carries that sense.

81. Jayatilleke probably has interpreted this example as consisting of singular sentences when he took it in the form, "X is a person who torments himself" and so on, see Jayatilleke III, p 76.

82. Confer, Chi I, p. 157, where Chi symbolizes these very characteristics by f and g.

83. Let f, g and h be the qualities of being a person tormenting oneself and tormenting others. We could then represent the first alternative of example 1 by:

Ex[fx(gx~ hx)](x) [(fx(gx~ hx))
{f(x)~ ((hx~ gx) V (hxgx) V (~ hx~ gx))}]

where '~', '', '', and V stand for the constants of negation, implication, conjunction, and weak disjunction and (x) and Ex for universal and existential quantification. The other alternatives could be similarly symbolized.

84. Confer, D. Kalish, and R. Montague, Logic: Techniques of Format Reasoning (New York: Harcourt Brace and World, 1964), p 99.

85. DN I, p. 27.

86. Ibid., pp.31-32.

87. Ibid.

88. SN II, pp. 19-20.

89. A^nguttara Nikaaya (hereafter cited as AN) II, p. 161.

90. MN I, p. 157. Only the first two alternatives of this avyaakata occurs in the literature usually.

91. DN I, p. 31.

92. DN I, p. 27.

93. Indeed, the devas and the brahmas were often taken as opapaathikas. The Brahmajaala Sutta, where this example occurs, makes reference to such births.

94. Note that this again is an example coming in the Brahmajaala Sutta, where what is 'reported' is the discourse of the brahmanas.

95. See, for example, DN I, chapter II, pp. 17ff.

96. See Jayatilleke II, p. 347, who makes this distinction between negation and rejection. See also Robinson's comment on Jayatilleke's "apparently sharp distinction" in Robinson IV, p 74.

97. SN II, PTS translation, p. 13.

98. See Jayatilleke II, p. 347.

99. Loc. cit. Although Jayatilleke speaks of "an apparent violation of the Law of Exclusion" here, there does not seem to be such a violation in this example given by Jayatilleke.

100. SN II, pp. 19-20.

101. SN II, pp. 22-23.

102. Confer, for example, Murti, pp. 44-50.

103. Matilal, p. 164.

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104. Staal, pp. 45ff.

105. Wayman, p. 16.

106. See Matilal, pp. l52ff., and D. Sharma, The differentiation Theory of Meaning of Indian Logic, pp. 34ff.

107. Confer, Jayatilleke II, p. 344. Jayatilleke does not rule out connections between the sceptic's logic and catu.sko.ti. See also Bahm.

108. Murti, p. 124.

109. Confer, Jayatilleke III, pp. 81-82.

110. In example, see preceding pp. 12ff.

111. Robinson III, p.57.

112. Robinson IV, p. 75.