R. D. Gunaratne is a member of the Department of Philosophy and Psychology at the University of Peradeniya. Sri Lanka.
It is well recognized that Naagaarjuna was, if not the greatest, then at least one of the greatest Buddhist philosophers of all time.  Drawing on the fruits of over five centuries of prolonged and often brilliant philosophical controversy among the Buddhist (and perhaps other) schools after the parinibbaana of the Buddha  and embracing the philosophy of `suunyataa based on the Praj~naapaaramitaa Suutras, he originated the Maadhyamika system, laying the foundation for the later super-structures of Mahaayaana. The "Maadhyamika-Mahaayaana" Buddhism spread, and having "naturalized" itself in the northern countries, such as Tibet, China, and Japan, it gave rise to such off-shoots as Zen, and became the other living tradition of Buddhism along with the Theravaada of the southern countries. Naagaarjuna "revolutionized" Buddhist thought, was considered a Bodhisattva,  and also had an impact on the development of Hindu thought, as can be seen in the work of `Sa^nkara.  He thus holds a central position not only in Buddhist thought but also in Indian philosophical thinking in general. 
Some of the central expositions of Naagaarjuna appear, both in the explicit examples and in the general structure of his thinking, to be bound up with catu.sko.ti, the tetralemma of the Buddhist texts. It is thus important to examine (1) how it was that Naagaarjuna came to make such extensive use of the catu.sko.ti; (2) the logical form of Naagaarjuna's catu.sko.ti; and (3) with that purpose and in what manner this "logical apparatus" was handled by Naagaarjuna in the exposition of his philosophy.
Of these problems, the logical form of the catu.sko.ti will be the central concern of this article. The detailed examination of this problem will enable us to discuss the other two topics and, it is hoped, throw some light on them as well. This study is based on Naagaarjuna's Muulamaadhyamakakaarikaa (hereafter, Kaarikaa or MK) and the catu.sko.ti occurring therein.
The logical structure of the catu.sko.ti has been well known to be one of the most perplexing problems in the study of Buddhist thought. Much has been written on it.  Sometimes it has even been considered an insoluble problem.  The main difficulties with the logical form of the cat.uko.ti arise due to the apparently self-contradictory nature of its third and fourth alternatives together with the fact that it is difficult to see the meaning of the fourth alternative unless it is taken as logically equivalent to the third. The problem is made more complex by the fact that the catu.sko.ti examples occur in various contexts in the literatures of different Buddhist schools from different periods. 
We begin with a preliminary discussion, which will indicate the direction in which formulation of the logical structure in question is sought. Part II will
recapitulate briefly two logical forms a and b, which the present writer, in a previous article,  used in the symbolization of the catu.sko.ti examples in the Pali Canon and which will be used in Part III, where it will be argued that the form of the catu.sko.ti is given by two parallel, but related, sets of symbolizations corresponding to two strands of thought which are shown to be woven into the Kaarikaa.
Some Preliminary Problems
The following could be some of the possible reasons for the use of the catu.sko.ti by Naagaarjuna for the exposition of his views.
A. The catu.sko.ti was already existent in the Buddhist (and other) literature and was a dominant mode of philosophical discussion. Further, in addition to considering the extant catu.sko.ti examples, Naagaarjuna applied the form to new problems as well.
The considerations in (A) are very probably true, but they do not indicate why Naagaarjuna used the catu.sko.ti deliberately and extensively as an "instrument" in the exposition of his philosophy. Specific reasons for its use by him could range from (B) to (E).
B. He used the catu.sko.ti as it could show that logical contradiction is inherent in the discussion of reality. In this case he would have to be considered as accepting the laws of thought at least tentatively.
C. He employed it to show the invalidity or nonrelevance of the laws of thought by ignoring them in the discussion of reality and thereby showing the futility of all "rational" discussion which uses the laws of thought. If this were the case, Naagaarjuna used the catu.sko.ti deliberately to underline his rejection of the laws of thought themselves (that is, the rejection of the logical apparatus itself), irrespective of any other considerations.
D. The catu.sko.ti was used by him as a dialectic which progressively leads one to truth.
E. The catu.sko.ti was used as an instrument of meditation.
It is clear that these positions need not be mutually exclusive. Limitations of space prevent any consideration of (D) and (E) here, although I think that both of these are possible interpretations of Naagaarjuna's use of catu.sko.ti and that consideration of them is necessary to get the overall picture of Naagaarjuna's effort in the Kaarikaa. (A) and (B) will come under consideration in Part III. Here in this part I shall take up (C). The discussion of (C) here will also lead us to a discussion of the forms by which the catu.sko.ti can best by symbolized.
The position in (C), namely, that Naagaarjuna purported (perhaps among other things) in his catu.sko.ti examples to ignore or reject the laws of thought, could be
considered under two cases. These are that he denied: (a) all the laws of thought, or (b) some, but not all of the laws of thought.
It seems unnecessary to examine (a) in detail as there seems to be fair consensus that Naagaarjuna (and the Maadhyamikas) did not purport to deny the laws of thought in toto. Indeed, it is generally agreed that Naagaarjuna made use of the law of noncontradiction in his arguments. 
If we agree that (a) is not the case, and that Naagaarjuna does not reject the law of noncontradiction, we can then proceed to (b), which is controversial. We now have to consider the cases of the laws of identity and excluded middle. But for the purposes of this article it is sufficient if we consider the case of the law of the excluded middle. 
It will be the contention of this article that neither did Naagaarjuna deny nor was it necessary for him to deny the law of the excluded middle. But Naagaarjuna's position in relation to this law has become problematic in the context of some contemporary views. I refer here, in particular, to Frits Staal's position,  but as Staal himself points out, he is not alone in taking this stand. 
Staal thinks that the Maadhyamikas reject the principle of the excluded middle.  Moreover, Staal gives a line of defense for the rationality (or the consistency) of the catu.sko.ti by way of a possible denial of this principle by the Maadhyamikas. And along with this we are made to consider the possibility that the Maadhyamikas denied the law of double negation, which is another statement of the law of the excluded middle.  It is important to examine this contention in view of the symbolizations and the interpretations which I advance in Parts II and III of this article.
Staal seems to use the consideration that the Maadhyamikas reject all the four catu.sko.ti alternatives as one base of his argument for the rationality of the Maadhyamika view -- and hence of the catu.sko.ti -- irrespective of the Maadhyamika position on the laws of the excluded middle (EM) and double negation (DN). This allows his argument, in the first instance, to be considered in the form of the following hypothetical disjunctive syllogism.
If the Maadhyamikas either negated all the four alternatives of the catu.sko.ti or denied EM and DN, then the Maadhyamika catu.sko.ti is rational. The Maadhyamika negated all the four alternatives of the catu.sko.ti. Hence the Maadhyamika catu.sko.ti is rational.
This, of course, is a valid syllogism, but it leaves his position vague. Further, Staal criticizes the solutions of the catu.sko.ti paradox offered by Raju, Robinson, Matilal, and others as not being satisfactory.  In such a context it is reasonable to consider that he is offering his views at least as a substitute for these solutions. We shall therefore look closely at the possibility and the justifiability of the assertion of either disjunct in the antecedent of the conditional above -- that is, the negation of all the alternatives, or the denial of EM, and their giving a satisfactory "solution" to the paradox of the Maadhyamika catu.sko.ti. 
A solution to the problem of the catu.sko.ti should indicate how it was possible for generations of thinkers (and others) to have entertained the catu.sko.ti alternatives in spite of their seemingly contradictory or problematic nature.  It must be indicated at the outset that Staal's account does not properly address itself to this problem.
It is well known that there are counterexamples to the assertion that all the alternatives of the catu.sko.ti were denied by the Maadhyamikas. The very verse that he quotes,  as Staal himself notes, is a case in point. Robinson, too, noted this discrepancy.  For example, consider the verse
sarva.m tathya.m na vaa tathya.m tathya.m caatathya.m eva ca
naivaatathya.m naiva tathya.m etad buddhaanu`saasana.m. (MK XVIII.8)
This verse has been variously translated,  but I will here use the form, "everything is real or unreal or both real and unreal or neither real nor unreal" (Robinson, p. 56) as its translation. Staal writes that despite passages like the above, he would assume that the Maadhyamikas rejected all the four alternatives. 
Staal perhaps is hinting at a basis of explanation for the above verse when he suggests that the Maadhyamikas "rejected all the four clauses, which the Buddha had failed to approve"  (my italics). This is indeed a sound basis, but it stands in direct contradiction to the explicit assertion, "etad buddhaanu`saasana.m" of Naagaarjuna. For this states that in the just-mentioned catu.sko.ti all the alternatives are the teachings of the Buddha.
It is indeed true that, going by the early Buddhist literature, the Buddha had rejected most of the catu.sko.ti alternatives.  It is also true that the Buddha was silent in response to the alternatives in the avyaakatas -- all of which were expressed in catu.sko.ti form. But that is partly the problem here. The Buddha did not make the catu.sko.ti his instrument or "vehicle." But Naagaarjuna does. The Buddha was indifferent to the catu.sko.ti. But Naagaarjuna says that the Buddha asserted all the alternatives of some of the catu.sko.ti, like MK XVIII.8. Maadhyamika commentators like Candrakiirti "explain" or interpret how and why the Buddha asserted these positions.  Robinson considers this verse as an instance where the catu.sko.ti is used as a pedagogical device. Staal indicates no way in which such a counterexample could be accommodated, when he wants to maintain that all the alternatives are negated by the Maadhyamikas. Thus, not only is the suggestion unacceptable that the denial of all the four alternatives in the catu.sko.ti "dissolves" the paradox, but there are also instances in the Kaarikaa where Naagaarjuna asserts all the alternatives, for which Staal is unable to account.
We are then led to see whether the assertion of the other arm of his disjunction is justifiable and paves the way for a solution of the paradox. Here there is no clear evidence for Staal's assumption that the Maadhyamikas negated the law of the excluded middle.  The least one could say is that Staal is here on very controversial ground. It must be emphasized that to suggest that Naagaarjuna and
other Maadhyamika logicians did away with the law of the excluded middle is a major contention which should be fully authenticated and argued for rather than made in the face of good evidence which contradicts it.
I shall argue that the assumption of the negation of the law of the excluded middle (and of double negation)  is not necessary for a solution of the catu.sko.ti paradox and that the solution that Staal offers on these lines is based on certain misconceptions.
It is true that the assumption of the negation of EM and DN can make the fourth alternative a noncontradictory position and the third and the fourth alternatives nonequivalent. But if the idea of the negation of all the alternatives is used as a basis for the rationality of the catu.sko.ti, then there is no necessity to make the fourth alternative noncontradictory, and since, in any case, the third alternative is contradictory, this "improvement" of the fourth alternative seems to be of no particular use. Of course, it does serve the purpose of showing how it was possible to entertain both the third and the fourth alternatives as separate "corners" (ko.ti) of the tetralemma. But we would still be left with the problem of how it was possible for generations of thinkers seriously to entertain the contradictory third alternative. 
It is not necessary to go to the extent of "implanting" intuitionism to make the Maadhyamika catu.sko.ti rational and reasonable. Such a move would not only be incorrect, it would also not place the Naagaarjunian catu.sko.ti in a historical perspective much needed in order to understand it, a necessity which later sections of this article will indicate.
A startling observation by Staal that there is no textual support for the use of predicate logic (or quantification) in the catu.sko.ti examples -- and hence that Raju's views and Robinson's use of the Aristotelian A, E, I, O forms for the symbolization of the catu.sko.ti have no basis -- seems to me to be evidence of an incorrect understanding and formulation of the catu.sko.ti. This contention of Staal's needs closer scrutiny in view of what follows in this article.
It is not clear whether Staal is speaking only about the catu.sko.ti in later Buddhism (that is, Naagaarjuna or Maadhyamikas here). Many students, including the present writer, have quoted a number of catu.sko.ti that occur in early Buddhist texts which need the use of "all" or "some" to symbolize their meanings. Two of the clearer examples, even on the basis of the literal form alone, for instance, are:
"Some persons are tormentors of themselves," and
so on, 
"Things continue after detachment from and cessation of six spheres of experience," and so on. 
As Staal seems to be mainly concerned with the Maadhyamika, let us confine ourselves to the catu.sko.ti therein. But before we examine the Maadhyamikas catu.sko.ti to see whether there are no quantifiable sentences in them, it is worth mentioning that, since most of the catu.sko.ti examples are common to early and
later Buddhism along with some fundamental tenets of Buddhism,  it would be best for us to study the Maadhyamikas catu.sko.ti bearing in mind always its relationship with the catu.sko.ti in early Buddhism. It should also be noted here that not only Robinson, but other contemporary students of catu.sko.ti in early Buddhism and/or Maadhyamika, like Chi and Jayatilleke, have also used the Aristotelian or quantified forms, in addition to propositional calculus, to symbolize them. 
Staal interprets the Maadhyamika catu.sko.ti only in terms of propositional variables. To use the simple argument showing that all the Maadhyamika catu.sko.ti could not be symbolized in terms of propositional variables is to look at the very example which we considered earlier. This is MK XVIII.8. that is, "Sarva.m tathya.m ..." and so on, which we translated as "Everything is real," and so on. Now 'sarva.m' here refers, in Staal's own translation, to "everything," which is equivalent to "all things." How would it be proper to symbolize this in terms of a propositional variable, say "p"? With such textual contradictions staring us in the face, we are at a loss to see why Staal insists on the nonapplicability of quantification for the symbolization of any of the catu.sko.ti examples. 
This example shows that some of the Maadhyamika catu.sko.ti are analyzable in terms of predicate logic. There are others which, I think, call for symbolization in terms of predicate logic or class logic, though this might not be indicated in their literal form explicitly. Let us consider two such verses. The very first verse of the Kaarikaa is translated by Inada as:
At nowhere and at no time can entities ever exist by originating out of themselves, from others, from both (self-other), or from lack of causes. 
Now, these are actually the negated forms of the catu.sko.ti
"Things originate by themselves
Things originate by others," and so on. 
One can easily understand "things" here as "all things" in analogy with, for example, our taking "men" in "men are mortal" as "all men" in elementary logic.  It is thus seen that such examples in Naagaarjuna are perhaps best symbolized in terms of predicate logic or class logic. Of course, one could sometimes ignore these meanings and symbolize some of them by using propositional variables, but at least the fact that predicate logic could be used here cannot be denied by such moves.  Certainly, there are catu.sko.ti like "The Buddha (after his attainment of Nirvaa.na) exists, does not exist, both exists and does not exist, neither exists nor does not exist" which are apparently symbolizable in terms of propositional variables, without violation of the intended meaning in the text. Even here, it appears that what permits this use of the propositional variables is the fact that the subject term is singular -- that is, the sentences are of the form "Socrates is mortal," which is also symbolizable in terms of predicate or class logic. In any case, the symbolizations of these catu.sko.ti in terms of propositional
variables, in forms such as p, ~p, p ^ ~ p, and ~ p ^ ~ p (or ~ (p v ~ p)) lead to the paradoxes of the catu.sko.ti discussed earlier if the negation of the laws of thought EM and DN by the Maadhyamika is not assumed. It has been indicated here already that there is no sound basis to assume such negation and that even such an assumption would not show how the contradictory third alternative was entertained.
On the other hand, Parts II and III of this article will, it is hoped, show that all the catu.sko.ti of early and later Buddhism can be symbolized in terms of class logic, without leading to paradox, and that such symbolization will also bring out the historical continuity in the catu.sko.ti forms of early and later Buddhism and thereby that of Buddhist thought itself. This interpretation will also indicate how Naagaarjuna made the Kaarikaa an exposition of `suunyataa as well as of his philosophy of two truths, sa.mv.rti and paramaartha.
I outline here two symbolic forms a and b, which I developed for the symbolization of the catu.sko.ti in early Buddhism in a previous article.  These are introduced here to show how these forms and some derivations of them, which I call the "limiting forms" aN and bN, could symbolize the catu.sko.ti occurring in the Kaarikaa. Consider the catu.sko.ti
The world is finite
The world is infinite
The world is both finite and infinite
The world is neither finite nor infinite 
In order to symbolize this, let A stand for the class of all things which have finite aspects (finite directions) and B stand for the class of all things which have infinite aspects (infinite directions). Taking X to stand for an individual and using standard set theoretic notation, where Î stands for "is a member of" and A‾ is the complement of A and Ç signifies class product, the four alternatives of the above catu.sko.ti could be symbolized as follows:
That these four alternatives are mutually exclusive and together exhaustive can be seen from the following Venn diagram, where X1, X2, X3 and X4 indicate the position of x in the respective alternatives.
I termed this symbolization a and referred to
Symbolization (I) will mean, in this case, that the world has finite aspects (directions) but no infinite aspects (directions); (II) could be read to mean that the world has no finite aspects (directions) but has (only) infinite aspects (directions); (III) says that the world has both finite and infinite aspects (directions); and (IV) says that the world has neither.
I also translated (I) and (II) in this case as "the world is wholly finite" and "the world is wholly infinite," respectively, but "wholly finite" does not mean that "all the aspects (of the world) are finite." It means only that "no aspect (of the world) is infinite." For, the terms "finite" and "infinite" need not apply to some aspects, or even to any aspects, of the world, The form b applies to universal propositions. Consider the following examples.
The soul is wholly happy (Ekaanta-sukhii attaa hoti)
The soul is wholly unhappy (Ekaanta dukkhii attaa hoti)
The soul is happy and unhappy (sukhii-dukkhii attaa hoti)
The soul is neither happy nor unhappy (Adukkha.m asukhii attaa hoti)
In the same way that "Man is mortal" is a stylistic variation of "All men are mortal," "The soul is wholly happy" could be considered a stylistic variation of "All souls are wholly happy." And in my article I indicated that this is the rendering most appropriate to the lines of this catu.sko.ti in the Pali Canon. Thus this example can be written as:
All souls are wholly happy
All souls are wholly unhappy and so on
Considering that 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. The four alternatives in the catu.sko.ti just given can then be symbolized as:
This symbolization was termed b, and the four alternatives there were referred to as b1, b2, b3, and b4,, respectively. The following diagrams show that these alternatives are mutually exclusive and together exhaustive.
It is well known that Naagaarjuna inherited two great traditions of Buddhist thought -- the Abhidharma of early Buddhism and the Praj~naapaaramitaa Suutras of the Mahaayaana.  Naagaarjuna embraced the latter and criticized the former.
The springboard of much of the controversy among the Theravaada schools themselves and, indeed, between Mahaayaana and Theravaada was the avyaakatas.  The avyaakatas thus played a key role in the development of Buddhist schools. They were not only points of deviation between the two great traditions of Theravaada and Mahaayaana, they were also a link between them.  It is of central importance to us here that the avyaakatas occur in early Buddhism expressed in catu.sko.ti form. They were also, again in catu.sko.ti form, one of Naagaarjuna's main concerns. Thus it is the terms and the linguistic forms of the same catu.sko.ti of early Buddhism that Naagaarjuna reinterprets. The significance of these contentions will emerge as we go on. But we must note at this point that the context, the structure, and the text of the Kaarikaa show that it is a living dialogue of the `suunyataa philosopher with the Abhidharmavaadins. The Kaarikaa begins with the dedication to the Buddha, who has proclaimed the cessation of all phenomenal construction. It then goes on to expound this `suunyataa, by actually arguing against the other (that is, the Theravaada) positions. Sometimes it explicitly states the argument for the Abhidharmavaadin position and is followed by Naagaarjuna's reply to it.  The final two chapters -- that is, chapters XXVI and XXVII of the Kaarikaa -- go back directly to an analysis of the early Buddhist views. Moreover, most of the topics or subjects that Naagaarjuna discusses in the text, like dhaatu  or nirvaa.na,  are those that have been dealt with at length by the Abhidharma schools. Again, the Maadhyamika commentators on the Kaarikaa refer to the different points raised by a variety of early Buddhist schools which Naagaarjuna was presumably contesting. 
It is thus seen that there are two major strands of thought -- the early Buddhist and the Maadhyamika -- in the Kaarikaa. Naagaarjuna is implicitly or explicitly moving from one line of thinking to the other. The Theravaada views come as premises or contentions which the argument, now implicitly basing itself on the `suunyataa philosophy which runs as a thread in the background of the whole exercise, refutes, and in turn `suunyataa as the conclusion surfaces. 
Thus it seems reasonable to consider the catu.sko.ti in the Kaarikaa as being often laden with a "two-pronged" line of thinking. The two parallel views are intertwined. The contention in this article, therefore, is that each catu.sko.ti verse (or most) in the Kaarikaa be considered as carrying two interpretations and, hence, that each catu.sko.ti in the Kaarikaa is best given two symbolizations -- one corresponding to the early Buddhist and the other to the Maadhyamika sense of it.
On this basis the early Buddhist interpretation of the catu.sko.ti is present in all or most of the catu.sko.ti examples in the Kaarikaa as one of the two interwoven strands in them. Naagaarjuna, versed as he was in the controversies among the early Buddhist schools, in his attempt to resolve them, of course, in his own
terms, entertained these views as the hypothetical premises of his reductio arguments. It is by this technique, I suggest, that the Kaarikaa verses condensed the dhamma controversy and its Maadhyamika resolution into a succinct exposition of a reinterpreted Buddhism.
We thus begin with the contention that each catu.sko.ti occurring in the Kaarikaa is given two symbolizations, one reflecting its logical structure corresponding to the early Buddhist interpretation and the other corresponding to the Maadhyamika interpretation. It will be found that these structures are different but closely related. It is suggested that the logical form of one strand of thought (that corresponding to the early Buddhist analysis) in the Naagaarjuna catu.sko.ti can be understood as given by a or b, introduced in Part II of this article. The parallel set representing the Maadhyamika interpretation will be what could be called "limiting" cases of a and b, where the class B is identified with the complement class of A, that is, A‾. These forms I shall term aN and bN, respectively.
We first take up the feasibility of using a and b for the purpose suggested. I have argued that the early Buddhist catu.sko.ti examples similar in form to, for example, "Nirvaa.na is real," and so on (which could be obtained from MK XXV, verses 4 to 16), could be symbolized by a. For if x stands of nirvaa.na, A for the class of objects with all real aspects, and B for the class of objects with all unreal aspects, we can symbolize this catu.sko.ti by:
It is suggested here that the symbolization corresponding to its early Buddhist interpretation of this catu.sko.ti in the Kaarikaa could be considered to have the form given here. Indeed it can be argued that Naagaarjuna considers (and rejects) an interpretation tallying with this symbolization. Contemporary commentators have noticed that Naagaarjuna is here considering the early Buddhist view. Thus, for example, Stcherbatsky comments: "If nirvaa.na were both real and unreal then final deliverance would be both real and unreal together. This could not be possible." He also says,
Probably the Vaibhaa.sika theory about the dharma-svabhaava is here alluded to. According to this theory some lifeless residue of the sa.mskaaras or dharmas remain in Nirvaa.na. but their manifestation (dharma-lak.sa.na) is stopped forever. We would then have in Nirvaa.na sa.mskaaras somehow existing and non-existing at the same time... 
On such an interpretation, Naagaarjuna considers the position exemplified by a, although he rejects it on the basis of his own interpretation, which we shall indicate later.
Again, the catu.sko.ti, which I have used in introducing the form a in Part II, that is, "The world is finite," and so on, which occurs in the Diigha Nikaaya, is seen to be negated in the Kaarikaa when we consider in conjunction the verses 21, 25, and 28 of its last chapter. Inada, for example, notes this when he writes, "He also goes on to show the absurdity involved in trying to assign partial characteriza-
tion to one realm and another partial characterization to yet another realm as, for example, speaking of partially limited and partially unlimited worlds."  This shows that these catu.sko.ti, and others like them in the Kaarikaa, can be symbolized by a. For what Naagaarjuna is denying in these catu.sko.ti are exactly the early Buddhist doctrines.
Again, consider "sarva.m tathya.m na vaa tathya.m," and so on (MK XVIII.8), which we quoted in full earlier on. This is translated as "everything is real or unreal or both real and unreal or neither real nor unreal; this is the adapted instruction of the Buddha." Now if X stands for the class of all things, A for the class of all real things, and B for the class of all unreal things, we may symbolize this by b, that is, by:
That this symbolization brings out at least the Maadhyamika considerations, if not Naagaarjuna's, is clearly seen when we consider the Middle Treatise commentary on this verse, which Robinson translates as follows:
As for "everything is real," when you analyse
the real-nature of the dharmas, (you find that) they all enter the absolute truth, are all
equal, are all of one mark, that is, they are markless....
As for "everything is unreal," when the dharmas have not entered the real mark, they are contemplated analytically one by one, and they are all (seen to) have nothing real in them.
As for "everything is both real and unreal," there are three classes of living beings -- superior, medium and inferior. The superior contemplate the marks of the dharmas as "not real and not unreal." The medium contemplate the marks of the dharmas as "all both real and unreal." The inferior, because their powers of knowledge are shallow, look on the marks of the dharmas as "partly real and partly unreal....
As for "(Everything) is not real and not unreal," (the Buddhas) declared "not real and not unreal" in order to refute "Both real and unreal." 
The first two paragraphs of this commentary indicate clearly that the class of dharmas which are real does not necessarily exclude the class of dharmas which are not real (indeed both predicates apply to "everything") -- hence a class and its complement cannot be used to symbolize this situation. This justifies our use of the two classes A and B in the symbolization of this catu.sko.ti.
It is also of interest to consider whether the Maadhyamika catu.sko.ti, could be considered as asserting the different alternatives from different standpoints and, if so, whether this could lead to a "relativist" position like that of the syaadvaada. The question is important as it raises the applicability to the Maadhyamika catu.sko.ti of my symbolizations a or b, which give disjunctive systems. Would it be the case that "The superior contemplate the marks of the dharmas as 'not real and not unreal'..."(and so on) amounts to saying, "From one (person's) standpoint the dharmas are not real and not unreal and from another (person's) standpoint the dharmas are real and unreal"?
Even if asserted from different standpoints or by different persons, the position above is not a relativist stand. It is only one alternative which is considered true at a certain time or by a particular group; hence the system is disjunctive. It is also important to note that although MK XVIII.8 ascribes all four positions to the Buddha, there is no evidence that the Buddha asserted all or even one of them. The suggestion could only be that the Buddha asserted the different alternatives while preaching to different groups. Thus we are able to accommodate in our symbolization b even the interpretation of MK XVIII.8 given by Candrakiirti in Prasannapadaa. In this interpretation, first, the Buddha speaks of dharmas as if they are real, in order to lead beings to venerate his omniscience. Next, he teaches that phenomena are unreal, because they undergo modifications. Thirdly, he teaches some hearers that phenomena are both real and unreal: real from the point of view of worldlings but unreal from the point of view of saints. To those who are practically free from passion and wrong views, he declares that phenomena are neither real nor unreal, in the same way that one denies that the son of a barren woman is either white or black. 
This ascription to the Buddha of "graded instructions" or the view that the four assertions were made (preached) to different groups of people by the Buddha is irrelevant for the possible symbolization of these by b. For, again, even as an upaaya the Buddha is asserting only one alternative at a time (maybe for a particular group).
These considerations indicate that one possible set of interpretations of the catu.sko.ti could be symbolized by the forms a or b, even in the light of Maadhyamika commentaries on the tetralemma in the Kaarikaa. It seems that in the case of examples like "sarva.m tathya.m," and so on, the same logical form, that is, b, could be made to represent both the early Buddhist and the Maadhyamika interpretation. But a and b would, in general, symbolize the early Buddhist strand in the Kaarikaa catu.sko.ti. Interwoven with the early Buddhist strand or in superposition with it there is an another strand of thought implied in the Kaarikaa. The whole exercise in the Kaarikaa is to propound or expound `suunyataa by suggestion or implication. The `suunyataa view is ringing in its background. Sometimes it is implied, or else verbally asserted. While still being at the sa.mv.rti level, the Naagaarjunian standpoint is used in the Kaarikaa to criticize the early Buddhist pluralism as well as to point towards the `suunyataa, the paramaartha. This is the most prominent of all the strands in the Kaarikaa and the form which centrally draws our attention here. We shall now try to untangle this strand and proceed to formulate two symbolizations which bring out its logical structure.
Let us begin by considering one main reason for Naagaarjuna's rejection of the third alternative. This reason, as explicitly given by him repeatedly, is that the concepts in question are contradictory and hence cannot be asserted of the same thing. In a verse that we considered earlier (MK XXV.11) it was asserted that nirvaa.na cannot be both real and unreal because reality and unreality cannot be together. This is expressed clearly in MK XXV.14, which could be rendered as:
How can nirvaa.na represent
(The place) of reality and non-reality together
As light and darkness in one spot
They cannot simultaneously be present 
Again, in (MK VIII.7) we come across the verse:
kaaraka.h sadasadbhuuta.h sadasatkurute na tat
parasparaviruddha.m hi saccaasaccaikata.h kuta.h
which could be rendered as "A completed-incompleted doer cannot create a completed-incompleted deed. For, since they are mutually contradictory, how could the completed and incompleted states coexist as one"? Thus it is seen that the concept pairs real/unreal and completed/incompleted are taken as contradictory. Hence the sentences "Nirvaa.na is both real and unreal" and "The completed and incompleted coexist in one" have been considered self-contradictory statements.
At this point it is important for us to see clearly how it was that Naagaarjuna rejected the third alternative of the catu.sko.ti, considering it as a contradiction. First let us note that the catu.sko.ti occurring in Naagaarjuna's works are those of the more general (or metaphysical) type -- like the avyaakatas -- dealing with predicates like "real," "eternal," "persistence in the past," or "finite," and so on, and not ones involving predicates like "happy" and "unhappy." In early Buddhist literature these contradictories did not necessarily make the catu.sko.ti alternative self-contradictory, as has been shown by our symbolizations a or b and in the discussions in my previous article. This was possible on the basis of a pluralism; for example, on the basis of their theories of the dharmas. It was indicated earlier that Naagaarjuna himself considers this early Buddhist position in its own terms, but shifts to his own position in the argument to reject it. To see what happens, consider an example like "All souls are happy," and so on, which we symbolized by b. Here we note that our interpretation rules out, for example, the possibility of the third alternative (that is, "All souls are happy and unhappy") being read as "Some souls are happy and some souls are unhappy."
Thus symbolizations a or b envisage that either the singular thing (Nirvaa.na, the world, and so on) or each particular member in a collection or class of objects forming the subject (for example, each soul) is predicted of either characteristic envisaged in the opposite predicates in the third catu.sko.ti alternative. That is, both predicates are invariably found in each and every soul in this case.  Naagaarjuna's predication not only calls for each and every object in the class to have the characteristics predicated of the class; it goes further. The position could be introduced first by noting an interesting observation made by Robinson on this predication. He says:
It is a striking feature of the Stanzas that all predicates seem to be asserted totally of the whole subject. Existential quantifications are denied because the discussion is concerned, not with the denial or affirmation of commonsense
assertions such as, "Some fuel is burning,
and some is not," but with the concepts of own-being and essence. What
pertains to part of an essence must of course pertain to the whole essence.
Many of Naagaarjuna's terms are explicitly bound and universally quantified. The usual quantifying expressions are "all," and "not" anything/anyone/anywhere/anywhen. 
In early Buddhism the different or "opposite" characteristics or dharma marks were considered to be able to coexist in the same object.  A situation of that nature has no room in Naagaarjuna's philosophy of relativism and `suunyataa. The minimum that is required for Naagaarjuna's account seems not to be the strong position that there are no different aspects or qualities in an object but that if there are different qualities in an object, then each of these qualities has to be one with the object through and through. This disallows contradictory predicates being predicated of the same thing.
Thus, although there can be two classes A and B, where A is the class of all things with real aspects and B is the class of all things with unreal aspects, the members of A and B will have to be different; that is, the same member cannot belong to both A and B. For the opposite will say that some objects have both "being real" and "being unreal" through and through or else have both of them as essences. That cannot be, for "real" and "unreal" cannot be in the same place at the same time. If the two predicates exist in one thing they have to be one with that thing and with each other. But how could "real" and "unreal" be one with each other? This is the basis on which Naagaarjuna says that nirvaa.na cannot represent the place of reality and nonreality simultaneously. 
This makes the two classes A and B mutually exclusive and "real" and "unreal" contrary predicates. I shall now argue that it is proper to consider the classes A and B corresponding to predicates like "real" and "unreal" as having been considered by Naagaarjuna also to be together exhaustive.
What has to be shown is that "real" and "unreal" cannot be denied together of an object, according to Naagaarjuna. That would amount to showing that "not real" and "not unreal" could not be asserted of the same object. That this was Naagaarjuna's view is seen by the following considerations.
Naagaarjuna was aware that there is logical similarity between the third and the fourth alternatives. Thus, for example, in the case of the predicates "limited" and "nonlimited," he says:
If both the limited and the non-limited could be established (concomitantly) then, similarly, neither the limited nor non-limited could also be established at will. 
This clearly indicates that while limited and nonlimited could not be predicated together (as this leads to contradiction), "neither the limited nor the nonlimited" also could not be predicated of a thing (as this also leads to contradiction). For the argument, in effect, says that if you establish one contradic-
tion (the third alternative), you could prove the other contradiction (the fourth alternative).
The argument is general enough, and this shows that
(X is) real and (X is) unreal
as well as not (X is) real and not (X is) unreal
are contradictions, making "real" and "unreal" contradictory predicates. This shows that A (the class of all objects with real aspects) and B (the class of all objects with unreal aspects) are mutually exclusive and together exhaustive. Thus B reduces to A‾, the complement of A.
That Naagaarjuna considered real and unreal as exhaustive of the universe of discourse is strikingly seen in verses 15 and 16, in the examination of nirvaa.na. Inada renders these verses as
15. The proposition that nirvaa.na is neither existence nor nonexistence could only be valid if and when the realms of existence and nonexistence are established.
16. If indeed nirvaa.na is asserted to be neither existence nor nonexistence, then by what means are the assertion to be known?
Verse 15 indicates that for the fourth alternative to be asserted in this instance, that there is a realm (that is, an area of discourse) outside the realms of existence (real) and nonexistence (nonreal) should be shown. Verse 16 says that there is no way of understanding the assertion that nirvaa.na is neither existence nor non-existence. This indicates that Naagaarjuna considers this statement not to be referring to anything in the universe of discourse; that is, its "reference" is outside the universe of discourse. This position is very significant and illuminating when one takes into account the fact that of all things, nirvaa.na was, and is even today, considered to be one of the few concepts in Buddhism which Buddhists have "defined" or "understood" in terms of "neither existence nor nonexistence."  Naagaarjuna refuses to understand this, since such a sentence, if seriously asserted, takes us beyond the universe of discourse, that is, beyond language. Of course, that is exactly what he meant to do -- to lead us beyond language and to paramaartha of nirvaa.na. He is really killing two birds with this one shot. For, on the one hand, he is showing the "closedness" of language and its inability to give meaning to nirvaa.na or paramaartha. On the other, he uses this argument to reject the fourth alternative. For the discussion, though purported to direct one to the paramaartha level, has to be maintained at the sa.mv.rti level (to avoid paradox), as Naagaarjuna explicitly acknowledges. That is why the contradiction (and the nonunderstandability) helps Naagaarjuna to reject it.
Thus for the purposes of Naagaarjuna's philosophy and his rejection of the alternatives, it is necessary to understand the "opposite" concepts in the alternatives as given by complementary classes. The forms of the catu.sko.ti on this interpretation can be considered as limiting cases of a or b, where B is the complement of A, that is, A‾. The two classes now become A and A‾, and the form
aN corresponding to a will be
The corresponding form bN of b is:
where U is the universe class and O‾=U.
The preceding gives the two forms aN, and bN of the Naagaarjuna catu.sko.ti, which are parallel to a and b, respectively. It is contended here that it was in terms of these "limiting" forms aN and bN that Naagaarjuna interpreted and rejected the catu.sko.ti alternatives.
There is the question whether it is correct to consider that all the catu.sko.ti in the Kaarikaa are best taken as having both of the interpretations a and aN or b and bN. It is neither necessary, nor wished here, to make such a claim. A fair number of catu.sko.ti examples, like "Nirvaa.na is real," and so on (a and aN,) and "Things are (not) originated by themselves," and so on (b and bN), could be given both the early Buddhist and the Maadhyamika interpretation. In the particular case of the verse "Everything is real," and so on (MK XVIII.8), it appears that, while the early Buddhist interpretation is different from the Maadhyamika interpretation, both interpretations could be accommodated in b only. We shall have occasion to return to this verse shortly.
This leads me to consider whether both pairs of forms a and aN and b and bN are necessary for consideration of the catu.sko.ti in the Kaarikaa or whether there is any context in which both these groups of catu.sko.ti could be considered as symbolizable by one pair of forms only. For example, consider the catu.sko.ti "All things are originated by themselves," and so on. "All things" could be considered to mean, in the Naagaarjunian context, the "world" and be considered as one. We could then well use the symbolizations a and aN, for this catu.sko.ti instead of the b pair. For example, we have just symbolized "Nirvaa.na is real," and so on, by a and aN. Naagaarjuna holds that there is no difference between nirvaa.na and sa.msaara as they are both the same thing. In such context it may be allowable to consider "all things" as the "one world" and symbolize the above catu.sko.ti by a and aN But such analyses seem to assume a Naagaarjunian monism, a question which I shall avoid here. 
While one may consider the possibility just mentioned, both pairs of forms a and b are necessary to understand Naagaarjuna's conception better even at this
level. Moreover, only bN could get reduced to aN here; that is, only in the "Naagaarjunian" or the "second" interpretation could the catu.sko.ti in the Kaarikaa be so reduced, as the first strand gives the early Buddhist conception which will need form b to symbolize the catu.sko.ti just given as well as others like "All things are real," and so on.
The two-strand interpretation of the catu.sko.ti of Naagaarjuna is justified by a few considerations, which I mention next. First, as we saw, it really brings into focus the generally agreed fact that Naagaarjuna is criticizing and denying the early Buddhist positions in his work directly or indirectly from the point of view of `suunyataa philosophy. Thus it happens that he moves to and fro between the early Buddhist conception and the `suunyataa conception in his work. This view also links early Buddhism and the Mahaayaana views through the origin of the Maadhyamika system.
There is a deeper factor which justifies this two-strand interpretation in the double position of the philosophy of Naagaarjuna, that of sa.mv.rti and paramaartha. The Kaarikaa is, in a sense, an exemplification of this position of two truths. Although the Kaarikaa itself, since it is expressed in concepts, is something in the sa.mv.rti sphere, what it expounds is the paramaartha. It thus contains, in that sense, the paramaartha truth. Moreover, the sa.mv.rti is contained in the paramaartha. The Kaarikaa, while being an exposition of the paramaartha, is designed to include the sa.mv.rti truth as well. Thus the early Buddhist position which is sa.mv.rti is contained in the `suunyataa position, which is the paramaartha.
It also shows immediately why a verse like MK XVIII.8, that is, "Everything is real," and so on, occurs as a buddhaanu`saasanam and is affirmed (or at least not denied) in the Kaarikaa. The four alternatives of this catu.sko.ti corresponded to certain early Buddhist interpretations of the buddhavacana. One aspect of these interpretations is that the third alternative could mean "everything is partly real and partly unreal." This is the view of the inferior (beings) according to the Middle Treatise Commentary. We find that this is absorbed into the Maadhyamika interpretation, which is based on graded instruction and/or the understanding of different levels of beings.
Thus the sa.mv.rti or lower-level truths are accommodated in the final truth, in the paramaartha of the Buddha. What is asserted in this particular verse is not (only) the sa.mv.rti and the paramaartha truth, but (also) the way of instruction of the Buddha. That is why this is given as the buddhaanu`saasanam and asserted, a position which looks anomalous to writers like Staal with their interpretation, as we saw. The interpretation that I have outlined is also able, thus, I think, to solve the perplexing problem of the anomaly in the assertion of MKXVIII.8. 
I think it best to recount certain material in the history of Buddhism to indicate that the suggestions that I have made so far are, far from being radical, the most natural interpretations. The best known catu.sko.ti examples, the avyaakatas, seem to have been questions put to various religious leaders by disputants as ready reckoners of each system.  It seems to be thus that the Buddha was made to face
these questions.  In general the Buddha seems to have discouraged these questions and their form, at times pointing out that they are not relevant or by maintaining silence altogether. 
It is clear that after the parinibbaana, the passing away of the Buddha, the avyaakatas played a role in the development of the various Buddhist schools. For unlike areas where the Buddha had categorically stated his views, the avyaakatas left room for manipulation by different disputants in inferring what was implied by the silence of the Buddha. Again, as the avyaakatas were questions raised as ready reckoners by various groups, the questions would have continued well after the parinibbaana of the Buddha. These deal with apparently fundamental metaphysical questions, like whether eternalism or annihilationism are true -- answers to which could support different philosophical schools.
The two main Buddhist schools that Naagaarjuna came into contact with were the Sarvaastivaadins and the Mahaasa^nghikas. The former were the conservative school while the latter led to the Mahaayaana. The Sarvaastivaadins were pluralists who accepted the svabhaava of the primary dharmas, together with the arising and passing away of the conditioned dharmas like the pudgala. The Mahaasa^nghikas, on the hand, criticized the pluralism of the Sarvaastivaadins and accepted `suunyataa, which meant that all dharmas were conditioned and existent only relative to each other.
The controversies between the Sarvaastivaadins and the Mahaasa^nghikas flowed through the Praj~naapaaramitaa Suutras, and Naagaarjuna was, in a sense, only vindicating these suutras and their doctrines through his exposition.  It is natural that the Kaarikaa also carries these controversies in it. Some of the key statements in the controversy were in the avyaakatas, which were already in catu.sko.ti form. The catu.sko.ti statements were certainly not considered outright self-contradictories by the early Buddhist or other groups. They were considered to be meaningful by them. Naagaarjuna was well versed in the interpretations which made them meaningful, but at the same time he wanted to contest all these views. And Naagaarjuna has to be considered as stating the early Buddhist position as part of the dialogue in early Buddhist terms if that position was to be "demolished" or overthrown by him in his work.
The occurrence of catu.sko.ti in the avyaakatas in early Buddhism was perhaps not the only or the main reason for Naagaarjuna's persistent and willing use of the form in his work. It seems reasonable to conjecture that Naagaarjuna saw the potential in this form not only for use in his argument, but also as a form to which all positions could be succinctly condensed. He probably saw it also as an instrument or rather a weapon to be used both to prepare the ground for his philosophy, cutting down the rival views, the key positions of which were already "summarized" in the avyaakatas and the other early Buddhist catu.sko.ti, and by suggestion to bring home the `suunyataa position, which is nonconceptualizable.
I have already suggested that in his brilliant use of the catu.sko.ti, Naagaarjuna was really going for much more. In the Kaarikaa, Naagaarjuna was doing something
deeper than what is apparently seen (or generally recognized) as his attempt there. He was, in a sense, practicing in his own work the very preaching involved therein. For he was not only demolishing the sa.mv.rti of the early Buddhist and establishing the paramaartha of the Maadhyamika, but was also incorporating the sa.mv.rti in the paramaartha in the verses themselves. That is to say, he was making the Kaarikaa a "living" embodiment or a practical example of the position, "the paramaartha captures and incorporates the sa.mv.rti." The Kaarikaa thus makes a concrete case for the view of two truths where the higher truth embraces (or is inclusive of) the lower.
As if all this were not enough, Naagaarjuna also uses the catu.sko.ti as a means by which the Kaarikaa verses would lead one from the sa.mv.rti to the paramaartha truth through a process of dialectical progression in thought and through meditation on the nature of things as "exposed" in the text. A discussion of these aspects is necessary for, and would add greatly to, the realization of the creative genius of Naagaarjuna in the handling of the catu.sko.ti form, but space does not permit me to enlarge on them here.
The author wishes to make the following clarifications: (I) The term "early Buddhism" is used roughly to mean non-Mahaayaana Buddhism. It is also called Hiinayaana in the literature. No distinction is made here between what some would consider early Buddhism proper or primitive Buddhism and later non-Mahaayaana schools of Buddhism. (2) Ç is the logical symbol used for conjunction. The rest of the symbols need no special mention.
1. See, e.g., Walpola Raahula, Zen and the Taming of the Bull (London: Gordon Frazer,1978), where he writes: "Naagaarjuna, perhaps the boldest thinker of the Buddhist masters ... took up this idea of `suunyataa and, with his tremendous genius, further developed it into such dizzy heights that now it is considered as Naagaarjuna's philosophy" (p. 81).
2. Cf. Kenneth K. Inada, Naagaarjuna -- A Translation of His Muulamaadhyamakakaarikaa with an Introductory Essay (Tokyo: The Hokuseido Press, 1970); Inada writes of the Abhidharma period: "Ideologically speaking, no other period in Buddhist history ... could ever match the level of activity as recorded during this period" (p. 6).
3. See, e.g., Richard H. Robinson, Early Maadhyamika in India and China (Madison, Wisconsin: The University of Wisconsin Press, 1967), p. 21.
4. Cf. Ashok K. Gangadean, "Naagaarjuna, Aristotle and Frege on the Nature of Thought," in Nathan Katz, ed., Buddhist and Western Philosophy (New Delhi: Sterling Publishers, 1981); he writes: "`Sa^nkara, the great dialectician of the Advaita Vedaanta tradition, was influenced by Naagaarjuna and developed this model in the form of adhyaasa" (p. 239). Also see T. K. V. Murti, the Central Philosophy of Buddhism (London: George Allen and Unwin, 1955), p. 56.
5. Cf. Robinson, Early Maadhyamika, p. 3. Some of the views expressed by me in this paragraph are in accord with those expressed by Frits Staal. See Frits Staal, Exploring Mysticism (Penguin, 1975), p. 41, where he writes: "Naagaarjuna, one of India's great philosophers ... the father of Maadhyamika, the grandfather of Ch'an and the great grandfather of Zen...." See also Inada, who notes the "closeness or perhaps an ultimate identity, in the final analysis, of the foundations of Zen and `Suunyavaada" (Naagaarjuna, p. 81).
6. See R. D. Gunaratne, "The Logical Form of Catu.sko.ti: A New Solution," Philosophy East and West 30, no. 2 (April 1980): 211-239. In particular, see note 2 on p. 235.
7. Ibid., p. 211.
8. See e.g., ibid., p. 214.
10. Thus, for example, a writer like Robinson, who thinks that no laws of thought are denied by Naagaarjuna, as well as writers like Staal and Chakrabarti, who think that some laws of thought are denied by the Maadhyamikas, agree that the law of noncontradiction is not denied by him. See Robinson, Early Maadhyamika, p. 50; Staal, Exploring Mysticism, pp. 41-44; and Sitansu S. Chakrabarti, "The Maadhyamika catu.sko.ti or Tetralemma," Journal of Indian Philosophy 8, no. 3 (September 1980): 304.
11. Robinson, in Early Maadhyamika (pp. 51-52), maintains that the law of identity was not denied. The question of the nondenial of the law of identity raises some deeper philosophical questions about the position of Naagaarjuna, but these are not directly relevant for us here.
12. Staal, Exploring Mysticism, pp. 47, 51.
13. Ibid., p. 51.
14. Ibid., p. 57. See also Chakrabarti, ("The Maadhyamika catu.sko.ti, pp. 303-304), who clarifies the position.
16. Staal, Exploring Mysticism, pp. 45 ff.
17. The view that all of the alternatives of the catu.sko.ti are denied by the Maadhyamika is, of course, not a novel position. It has been asserted, even in contemporary times, by writers like Murti. R. S. Y. Chi has suggested that Buddhists in general (not only the Maadhyamikas) were the critics of the catu.sko.ti and that they did not assert any of the catu.sko.ti alternatives. See R. S. Y. Chi, "Topics on Being and Logical Reasoning," Philosophy East and West 24, no. 3 (July 1974): 298.
18. Robinson, who was familiar with the catu.sko.ti in early Buddhism as well as in the Maadhyamika of both India and China, for example, was well aware of the Maadhyamika rejection of all the alternatives in most of the catu.sko.ti (Robinson, Early Maadhyamika, p. 56), which is, in fact, the most apparent thing in Naagaarjuna's work. But that rejection was never even considered as a possible resolution of the catu.sko.ti paradox by him.
19. Staal, Exploring Mysticism, p. 44.
20. Robinson writers, "In all the examples so far, all four lemmas are to be rejected. If this were always so, then the tetralemma would be simply a more comprehensive and emphatic way of denying all forms of own-being. However, it has another use -- as a pedagogical device" (Early Maadhyamika, p 56).
21. See, e.g., Staal, Exploring Mysticism, p. 44; Robinson, Early Maadhyamika, pp. 55 and 56; and Inada, Naagaarjuna, p. 115.
22. Staal, Exploring Mysticism, p. 44.
24. See, however, Gunaratne, "The Logical Form," p. 215. The example here, namely, Cattaaro 'me Pessa puggalaa sa.mvijjamaanaa lokasmi.m, ... ekacco puggalo attantapo hoti, etc., seems to give a catu.sko.ti where all four alternatives could be asserted as true, while the last alternative could be the one that a person is recommended to achieve.
25. See, later, in Part III of this article.
26. See note 20, preceding.
27. In spite of instances of violations of the law which Staal, referring to the work of Mayer and Schayer, considers as evidence to the contrary, the Maadhyamikas seem to have accepted the law in principle. Thus a writer like Robinson does not consider that they negate the law of the excluded middle. He writes (Robinson, Early Maadhyamika, p. 57): "The law of the excluded middle is invoked explicitly in some places: A goer does not go, and a non-goer does not go; what third other than goer and non-goer goes?" (Prasannapadaa, p. 97).
28. It is not clear whether Staal considers that the law of double negation was accepted (or denied) by the Maadhyamika in view of his following statement, namely, "If we reject the fourth clause, as the Maadhyamika philosophers did, we are forced to accept the principle of the excluded middle. But we do not have to, since denying the denial of an excluded middle only implies the excluded middle if we accept the principle of double negation, which is itself equivalent to the excluded middle" (p. 47).
29. Robinson saw this problem clearly, for he notes: "It would be very curious if early dialecticians from Maalu^nkyaaputta and Vachchagotta onwards had framed questions in two modes which they interpreted in a manner that they knew to be absurd" (p. 57). Moreover, Staal is not the first scholar to take this idea of using Brouwerian intuitionism as a help in understanding the catu.sko.ti. R. S. Y.
Chi, who clearly showed the roles of the laws of contradiction, excluded middle, and double negation in the catu.sko.ti, toyed with this idea far back in the sixties. See Chi, Buddhist Formal Logic (Royal Asiatic Society, 1969), pp. 161-163. Chi realized later on that it was both incorrect and not very helpful to have used "intuitionism" for a solution of the catu.sko.ti paradox (Chi "Topics on Being," p. 297).
30. Gunaratne, "The Logical Form," p. 215.
31. K. N. Jayatilleke, Early Buddhist Theory of Knowledge (London: Allen & Unwin 1963), p. 347. Also see Gunaratne, "The Logical Form," p. 227.
32. See Raahula, Zen, pp. 15-23, for a piece which shows some of the relations between Zen and Theravaada beautifully. See Part IV of this article for some of the broad points of contact between schools in the early development of Buddhism. See also the introductory chapters in Inada, Naagaarjuna, and in B. L. Suzuki, Mahaayaana Buddhism (London: Allen & Unwin, 1981).
33. See Chi, Buddhist Formal Logic and "Topics on Being," and Jayatilleke, Early Buddhist Theory, chap. 7. See Gunaratne, "The Logical Form," for a discussion of symbolizations given by Robinson, Jayatilleke, and Chi and an indication of the problems involved.
34. Staal, Exploring Mysticism, p. 45.
35. Inada, Naagaarjuna, p. 39.
36. Chi, in "Topics on Being," for example, puts down the same verse in the following form:
Things are not originated by themselves;
Nor are they originated by others;
Neither by both; nor without cause;
Therefore there is no origination. (p. 159).
37. See Gunaratne, "The Logical Form," p. 223.
38. A similar example is MK XXII.11, which Inada (Naagaarjuna, p. 134) translates as:
Nothing could be asserted to be `suunya, a`suunya both `suunya and a`suunya and neither `suunya nor a`suunya. They are asserted only for the purpose of provisional understanding.
39. Gunaratne, "The Logical Form," p. 223.
40. This catu.sko.ti occurs in early Buddhist literature as well as in the Kaarikaa. But here I am only recapitulating the form developed for the symbolization of the early Buddhist case. See Digha Nikaya I, PTS translation, pp. 22-23; compare also with the Kaarikaa XXVII, verses 21, 25, and 28.
41. The reader is referred to the original article for further details and justifications of these symbolizations.
42. See, e.g., Inada, Naagaarjuna, pp. 4 ff.
43. See, e.g., Murti, Central Philosophy of Buddhism, pp. 36 ff.
44. See the discussions later in this part.
45. E.g., MK X, verses 6 and 7.
46. MK V.
47. MK XXV.
48. See, e.g., Stcherbatsky, The Conception of Buddhist Nirvaa.na (Leningrad: Academy of Sciences of the USSR, 1927), in which is included a translation of Candrakiirti's commentary on MK.
49. Some of my observations in the last four paragraphs are borne out, for example, by the views expressed by Inada when he writes:
"In this chapter and the final one to follow, Naagaarjuna goes into the analysis of Hiinayaanistic doctrines... The discussion is Hiinayaanistic... But the doctrine must be seen under a new light when Naagaarjuna discusses it, i.e., within the backdrop of his doctrine of `suunyataa and pratiityasamutpaada... " (Naagaarjuna, p. 160. See also p. 164).
50. Stcherbatsky, Conception, p. 199, note 3.
51. Inada, Naagaarjuna, p. 164.
52. Robinson, Early Maadhyamika, p. 56.
54. Compare Stcherbatsky, Conception, p. 76.
55. Indeed, of the examples I considered in my earlier article there were only two that lent themselves to interpretations which could give particular sentences, and those I symbolized by the
forms a and g (Gunaratne, "The Logical Form," pp. 226-227 and 229-230). In the Naagaarjuna catu.sko.ti the rare particular sentences which one comes across in early Buddhist catu.sko.ti do not seem to occur.
56. Robinson, Early Maadhyamika, p. 54.
57. This position has been noted by Staal also; see Staal, Exploring Mysticism, p. 48.
58. See MK XXV.
59. Inada, Naagaarjuna, p. 171.
60. See, e.g., E. J. Thomas, The History of Buddhist Thought (London: Routledge & Kegan Paul, 1933), p. 121.
61. I should emphasize that my analysis here did not use the idea of a monism in the Kaarikaa.
62. See, Robinson, Early Maadhyamika, (p. 55). But Robinson's contention that this occurrence is just a pedagogical use of the catu.sko.ti is not a sufficient explanation. Note also that Naagaarjuna does not make this assertion and leave matters there. He goes on in the verses immediately following it (that is, MK XVIII.9 ff) to indicate how this verse is acceptable at the `suunyataa level by giving what tathavasya lak.sa.na.m or characteristics of reality there are at the paramaartha level.
63. See Bhikku ~Naa.naananda, Concept and Reality in Early Buddhist Thought (Kandy: Buddhist Publications Society, 1971).
64. The Buddha would have been aware of these controversies after his six-year-long search with different gurus. But in the literature the questions are put to him directly by such inquirers as Kaccaayana, Maalu^nkyaaputta, and Vacchagotta.
65. See David Kalupahana, Causality. The Central Philosophy of Buddhism (Honolulu, Hawaii: University Press of Hawaii, 1970), p.143.
66. See Kalupahana, Causality. In chapter 7, he gives some interesting analyses of the developments which led to Naagaarjuna's position.
AUTHOR'S NOTES: The author wishes to express his thanks to the editor of Philosophy East and West and to the two anonymous readers for helpful comments on an earlier draft.