021-rationality

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RATIONALITY, ARGUMENTATION AND EMBARRASSMENT:

A study of four logical alternatives (catu.sko.ti) in Buddhist logic
By V. K. Bharadwaja

In   this   paper     I   shall   consider     several interconnected issues centering around the four logical alternatives (catu.sko.ti) in Buddhist logic which, it seems to me, involve    questions   of rationality,   argumentation,   and     philosophical embarrassment. It is my contention that philosophers who have worked in this area of Buddhist logic during the past fifty years or so have not faced these issues squarely. In their work, they show either an obsession with logic,[1] or a tilt in favor of the Inexpressible, [2] or have felt a       certain level of philosophical   embarrassment [3] while discussing them. Let me state these issues:

One: In the early Paali Buddhist literature we find (a) not only expressions "There is a next world" and "There is no next world" but also the forms "There is and is not a next world" and "There neither is nor is not a next world"[4], and (b) "The world is finite," "The world is infinite," "The world is both finite and infinite," and "The world is neither finite nor infinite".[5] There are two features   of these examples (a) and (b) : (1) Regarding them as a subject/predicate   form of statement, what is in question in (a) is the existence of the next world (the subject term) in each one of these four expressions; while in (b) the existence of the world, the subject term, is not in question; what is in question is whether or not the world is finite. (2) In both (a) and (b), four logical possibilities have been taken into account: affirmation,   negation,   both    affirmation    and      negation, and neither affirmation nor negation. These four possibilities have been historically called catu.sko.ti, and philosophers have taken upon themselves the task of explaining them, the question being as to how it is that Buddha, the Enlightened One, rejected each one of them.[6] Naagaarjuna exploits this rejection as a form of argumentation against his critics and opponents.[7] There is a vast historical gap between the date of the Buddha and the date of Naagaarjuna; yet when one reads Naagaarjuna's    works   one is surprised   by the similarity   between   his work and that of the Buddha in the formulation of the four alternatives and their systematic rejection.[8]

Two: Naagaarjuna is said to have held no thesis or philosophic position of his own on the grounds that he rejects each one of the the four possible alternatives and that he himself says that "he has no thesis of his own or no position to defend."[9] The question, however, is that if he has no thesis of his own to defend, then what is he doing? Is he engaged in vitaa,[10] a form of debate in which one is concerned only with refuting the opponent's thesis but not with establishing one's own? An affirmative   answer   to this   question    is "an embarrassment to the philosophers, " [11] however "useful and effective a philosophic method"[12] it may prove to be.

Three: The above two become issues only when we think that both Buddha, the    Enlightened    One,   and    Naagaarjuna,   the Maadhyamaka philosopher, were concerned with the Inexpressible. "'All things are void' is not a       proposition. It only expresses the Inexpressible with the help of the conventional truth. The real language    here   would   be silence."[13] Or, as Ramchandra Pandeya puts it: Since none of the four alternatives have been asserted, the question of their denial does not arise such that "if there be any reality, it cannot be expressed in terms of four ko.tis."[14]

I will discuss these issues one by one. My plan is as follows: First, I will pick up one or two major positions on each one of these issues and examine them in detail. My strategy is to take into account the context in which these issues make their maiden appearance; to draw important distinctions, like the one between different types of questions; to indicate the role which the Buddhists assign to denying each one of the four possible alternatives in order to reject the opponent's position; and finally to outline the conceptual framework within which both the Buddha and Naagaarjuna are operating. In the course of my argument I suggest that both argumentation and embarrassment presuppose a certain analysis of the concept of rationality which to my mind is too narrow to go with the sense in which we say that `man is a rational animal'.

In the early Paali Buddhistic literature,[15] four types of questions have been differentiated. [1]There are questions which ought to be explained categorically For example, to the question "Is form impermanent?" the answer is "Yes, it is." To the question "Is the world full of suffering?" the   answer is "Yes, it is." To the question "Does everyone die?" the answer is "Yes, everyone dies." These are questions which are clear in respect of        both syntax and semantics and which therefore are answered categorically. The Buddhists call them pa~nha eka.msavyaakara.niiya.[16] [2] Then there are questions which ought to be answered with a counter question. For   example, the question "Is consciousness a person's soul or is consciousness one thing and the soul another?" is responded to with a counter question "What do you take to be the soul?   "   The    Buddhists    call   them     pa~nha pa.tipucchavyaakara.niya.[17] [2] A third type of question is those that should be set aside. For example, the question "Will the Tathaagata live after his death or not?" is a question which is to be   set   aside. Such    questions   are   called pa~nha.thapaniiyo.[18] [3] The fourth    type   of question is those which ought to be explained analytically and then answered. For example, to the question "Are all human beings reborn?" the answer is "Some are and some aren't." Questions like these are called pa~nha vibhajjavyaakara.niya.[19] In the case of the fourth type, adequate specification, clarification, and analysis are required before these questions are answered correctly. For my purposes, two types of question are important: the first type of question to which a categorical answer is possible, and also is generally given; and the third type of question, those questions which are to be set   aside that    is, the eka.msa    and the .thapaniiya questions. The remaining two types of question require clarification and analysis but they are both askable and answerable affirmatively or        negatively as the case may be. The questions of evidence whether that evidence is analytic or empirical or whether it is of some other admissible kind of evidence are definitely relevant to the truth and falsity of their answers.

Consider first the .thapaniiya kind of question. A .thapaniiya question is one which is to be set aside. Jayatilleke sees in this type "a modern parallel   in the kind of questions   which the Positivist dismisses as meaningless and therefore unanswerable." [20] The question, however, is: "What is the criterion    by applying which a certain question is said to be set aside? One answer which Buddhaghosa gives is that a .thapaniiya question is "a question which ought not to be explained and which ought to be set aside on the ground that it was not explained by the Exalted one."[21] But as Jayatilleke observes: "This is not very helpful, for he is virtually saying that these questions ought to be set aside because they have been set aside by the      Buddha."[22] Buddhaghosa's position thus amounts to accepting the authority of the Buddha, an authority which even the Buddha himself did not regard as unchallengeable, and this is philosophically very embarrassing. We do need a criterion to tell a .thapaniiya from a .thapaniiya question.

Broadly, there are two different criteria for identifying a.thapaniiya question: (1) the pragmatic criterion and (2) the logical criterion. As regards the pragmatic criterion Jayatilleke observes: "These questions were 'to be set aside' (.thapaniiya) on pragmatic   grounds since belief in any of the        possible answers was considered irrelevant   and otiose for our purpose."[23] Here the parable of the arrow is relevant. The parable is designed to bring home the idea that what is important is giving urgent medical attention to the one who is shot with the arrow. Questions such as "Who shot the arrow?" are left to be answered later, when an inquiry into the incident is conducted.    In the context of inquiry, these questions   are both askable and      answerable; but in the context of giving urgent medical aid to the victim, they are irrelevant.

The    second   is the logical   criterion.    A .thapaniiya question is either (a) misleading in form, violating the logic of meaningful syntax and thus rendered meaningless, or (b) it is conceptually impossible   for us within   a given   conceptual framework to assign' truth values, true or false, to any answer given to it. Take, for instance, the question whether the Tathaagata will exist after death. An answer to it is classified as one of the avyaakata   theses [24] (which    we shall   discuss presently). From a logical Point of view, it should be possible to say that any one of the four alternatives is true. The possible alternatives are [1] 'Yes, it is the case', [2] 'No, it is not the case', [3] 'It is both the case and not the case', and [4] 'It is neither the case nor not the case'.

But, on the Buddhist   view, none of the four alternatives "fits the case" (upeti). To say that the Tathaagata exists after death does not fit the case; that he does not exist after death does not fit the case; that he exists and does not exist after death does not fit the case; that he neither exists nor does not exist after death does not fit the case.[25] When each   of the four possible alternatives is rejected, then within the context in which the question is asked, one obvious conclusion is that it is not possible to answer the question "Does the Tathaagata exist after death? " This possibility   is not empirical; and one is led to surmise that it involves logical and conceptual   confusions for instance, having a good syntax grammatically but semantically having a result that is a meaningless sentence like "The Taj Mahal is kind to people who visit it" or an unaskable question like "Is the father the female parent? " The question, for example, "Where does the flame of a candle go to when it is blown out?"[26] is one which does not admit a meaningful answer because it is based on a conceptual   confusion   of two distinct    logical concepts. (It is interesting to observe that in the early Paali Buddhistic texts an exactly similar example is given. Compare "This fire in front of you, which has gone out, in which direction has it gone?")[27] The question thrives on the mistaken syntactical similarity with another question like "Where do I go when I fall sick?" The second question is perfectly meanirigful while the first is incomprehensible. The second admits of a perfectly meaningful answer while the first does not.

There is another type of question which is regarded as "inappropriate"   (na kalla) and [28] which, like the .thapaniiya questions, is also set        aside   on the grounds    that   it is "literally meaningless."[29] For example, "What is decay and death and of whom is this decay and death?"[30] is an inappropriate question;    it is a misleading question   to ask "Who   feeds    on the food of consciousness?" Both are examples of inappropriate, improper questions (na kalla pa~nha).[31]

I said earlier that questions of the first type, namely, the questions which ought to be explained categorically, raise a special problem about the logical status of their answers. To a question of this type like "Is the world full of suffering?" the categorical answer is "Yes, the world is full of        suffering." What is the logical status of this answer? Regarded as an empirical statement or an unrestricted empirical generalization it is patently false. But for Buddha, the Enlightened One, it is true with absolute certainty. And we shall see later that his answer to this question is one of the      fundamental constituents or presuppositions of the Buddhist conceptual framework. As such, it may be said, it is either analytically true or the question of its truth or falsity within that framework simply does not arise. The only question one can ask about it is "Why after all should we accept this statement that the world is full of suffering as true?" And there is all the difference in the world between saying(1) that a statement S is true and saying (2) that S is accepted to be true. (1) may be a good reason for (2), but it need not be: and from (2), (1) need not follow. Besides, the reasons for (1) need not be the reasons for (2) and conversely also.[32] The question "Why after all should we accept that the world is full of suffering?" is external to Buddha's conceptual framework; and it is decidable on grounds of pragmatic considerations only.[33] Such considerations may not be regarded as rational in the narrow sense of the word "rational," the sense in which giving reasons for the truth of a statement is being rational. But, all the same, they are not irrational, either, for they concern and take into account the reasons for accepting the statement to be true. They involve a necessary reference to our aims, motives, and   purposes, to our values, commitments, and concerns, and even to our aesthetic considerations, like   simplicity    and   elegance.    In    Carnap's terminology[34] such questions are external and not internal to the Buddhist conceptual   framework. However, I disagree with Carnap on the point that only because external questions cannot be answered within the given linguistic framework, their answers must be analytically true with respect to the framework. To my mind, they need not be, and in fact they are not analytically true. The statement that the world is full of suffering is not analytically true; rather it expresses our commitments,[35] and whether these commitments are moral, intellectual, or philosophical will depend upon the type of conceptual framework within which we operate.

There is a distinction between vyaakata and avyaakata questions. In the early Paali Buddhist literature we come across four questions which have been characterized as avyaakata. "Vyaakata" means "analysed, explained, clear, comprehensible."[36] Thus   a    vyaakata   question   is    well-analyzed, explained, clear, and comprehensible such that a meaningful answer to it can be given within the conceptual    framework in which it occurs.    The question is both askable and answerable within that framework. It is not a .thapaniiya question, a question which is to be set aside. Given the types of questions we have enumerated and differentiated, all questions other than the improper ones (na kalla pa~nha) and those   that    are to be set aside (.thananiiya   pa~nha) fall within the range of vyaakata questions. The questions which are to be set aside need to be differentiated from those that are improper or misleading. An improper question (na kalla pa~nha) is to be set aside on the grounds that it is "literally meaningless."[37] I Shall call them unaskable questions. The question 'What is decay and death and of whom is the decay and death?'[38] and the   question    `Who   feeds   on    the   food   of consciousness? '[39] are improper and misleading questions. They are questions "which are suggested by the grammar of the language but which give or imply a false or distorted picture of the nature of reality.[40] This feature of na kalla questions shows that they form a proper subset of.thapaniiya questions. But then what is the differentia of na kalla questions?

Both types of questions are those which are to be set aside.    Both   types   are    grammatically well-formed also. The two may be differentiated on the grounds that while a na kalla question is either improper or misleading, a .thapaniiya question is set aside    (a)   on    the   strength    of    pragmatic considerations   formulated on the lines of the parable of the arrow, or (b) on logical grounds with respect to (i) that any answer to them fails to fit the case (upeti) and (ii) that any answer to them results in an avyaakata thesis. Besides, the kind of response which they evoke would differentiate a na kalla from a .thapaniiya question. In the case of na kalla   questions, "all   four   of    the   logical alternatives may be false,"[41] but these questions are not to be treated as .thapaniiya since they have been categorically answered.The   Nikaayas distinguish between the two types by using the formula `maa h'evam' (do not [say] so) for all the four alternatives of a .thapaniiya question, while in the case of na kalla questions, "the usual negation 'no h `idam' (it is not so) is used for each of the four alternatives."[42]

We have said above that any answer    to a .thapaniiya question results in an avyaakata thesis, a thesis which is unanalyzed, unexplained, is not clear, and is incomprehensible.    Such a thesis broadly is of two types: first, that which affirms or denies the existence of the nominatum [43] of the      subject   term, and   second, that   which, while presupposing the existence of the nominatum of the subject term, affirms or denies a certain predicate of it.[44] A, example [45] of the first type is:

     (A) (1) There is a next world

            (2) There is no next world

            (3) There is and is not a next world

            (4) There neither is nor is not a next world

In (A) it is the existence of the next world which is affirmed in (1), denied in (2), both affirmed and denied in (3), and neither affirmed nor denied in (4). An example[46] of the second type is:

        (B) (1) This world is finite

            (2) This world is infinite

            (3) This world is both finite and infinite

            (4) This world is neither finite nor infinite

There are other examples of avyaakata theses; but the difference between them as in (C) below is in terms of the subject and the predicate chosen in a given context; or, as in (E) below, the difference is in terms of the contrary   or contradictory predicates affirmed or denied of the subject. An example [47] of (C) is as follows:

         (C) (1) The soul is identical with the body

               (2) `The soul is different from the body

               (3) The soul is both identical    with   and different from the body

               (4) The soul is neither identical with nor different from the body.

Here in (C), if(1) through (4) are regarded as subject-predicate forms of the statement, then the difference between (B) and (C) is in the particular subject and predicate chosen in a given context.

From the logical point of view, formally there is no difference between (B) and (C).

           (D) (1) The Tathaagata exists after death

                  (2) The Tathaagata does not exist after death

                  (3) The Tathaagata both exists and does not exist after death

                  (4) The Tathaagata neither exists nor does not exist after death.[48]

In (D) as in (A) the existence of the nominatum of the subject term is affirmed in (1), denied in (2), both affirmed and denied in (3) , and neither affirmed nor denied in (4). An example of (E) is as follows:

             (E) (1) The soul is happy

                   (2) The soul is unhappy

                   (3) The soul is both happy and unhappy

                   (4) The soul is neither happy nor unhappy

Here in (E) the predicates affirmed or denied of the subject in (1) through (4) are contrary and not contradictory.[49]   An   example    in   which   the predicates are neither contrary nor contradictory [50] is as follows:

              (F) (1) The goal can be attained by knowledge

                    (2) The goal can be attained by conduct

                    (3) The goal can be attained by both knowledge and conduct

                    (4) The goal can be attained   by neither knowledge nor conduct.

Any    example   in   which    the   predicates    are contradictory is the same as (B) or (C) above. In my discussion, I will restrict myself to the forms (A) and (B) only. From the logical point of view, it is the (A) and (B) forms which are interesting and not the others at least so it seem to me. The theses (l) through (4) in both (A) and (R)are avyaakata theses. The questions to which they are answers are .thapaniiya to be set aside. In both (A) and (B) each one of the four logical alternatives   is rejected. This form of rejection, at the hands of Naagaarjuna,[51] developed into "a very useful and effective philosophic   method"[52]   called    the prasa.mga form of argumentation,[53] that is, the argument by reductio ad absurdum.[54]

What are we to make of the rejection of each one of the four logical alternatives? The ground cited for the rejection is that none of the alternatives fits the case (upeti) .    As far back as 1917 Poussin[55] treated the four logical alternatives (catu.sko.ti), as "a four branched dilemma" of Buddhist dialectic.[56] He believes that it violates the law of contradiction. He writes: "Indians do not make a clear distinction between facts and ideas, between ideas and words; they have never clearly recognized the principle of contradiction. Buddhist dialectic has a four branched dilemma: Nirvaa.na is existence, or non-existence, or both existence and non-existence, or neither    existence     nor non-existence. We are helpless."[57] I wish that Poussin had realized that the old Aristotelian three laws of thought are the mark of human rationality (and on Leibniz' reckoning,[58] even God could not violate     them in    particular    the    law    of contradiction), and it does not matter whether a human being is white, black, brown, yellow, or red.

For this reason, if for no other. I do not agree with Poussin that Indians, if they are rational enough, have violated the law of contradiction in     rejecting each one of the four logical alternatives. Anyway, Poussin was puzzled about the structure of catu.sko.ti, and he found himself helpless    to understand it. But he need not have despaired so very much about it.

Mrs. Rhys Davids[59] calls the rejection of the four logical alternatives "Laws of Thought." She writes: "The import of a number of terms is set out, usually in dichotomic division but sometimes in the distinctively Indian method of presenting the by us so called Laws of Thought thus, Is A B & If not, isA not B? If not, is A both B and not B? If not, is A neither B nor not B (in other words is A a chimera)?"[60] She regarded the rejection of the second and the third alternatives as an assertion, respectively, of the law   of contradiction and the law of excluded middle.[61] Mr. B. M. Barua agrees with Mrs.Rhys Davids but makes the bold statement of calling all four logical alternatives the four laws of thought. He says: "These are in their application to propositions:

        1. (If A is B), A is B

        2. A cannot be both B and not B

        3. A is either B or not B

        4. A is neither B nor not B" [62]

It needs little argument to point out Mr. Barua's logical folly. One tends to agree with Jayatilleke that the contentions of both Mrs. Rhys Davids and Mr. Barua, that the four logical alternatives are laws of thought, are equally fantastic. Buddha, the Enlightened One, was not interested in asserting logical    truths or inconsistent    statements   in rejecting any one or all of the four alternatives.

Mr. Barua's construal of the rejection of the fourth alternative as an assertion of the law of double negation    is beyond   comprehension, as it does violence to the common sense and logic that we have learnt from the cradle.[63]

P. T. Raju's interpretation[64] of the rejection of the catu.sko.ti alternatives reduces to this: Each one of the four logical alternatives is about the `suunya (void), which in mathematics means 'zero'. He writes "Zero is the quantity of which all the four alternatives are denied: it is neither positive, nor negative."[65] To my mind, this is an assertion which is the least illuminating; and it turns out to be identical with what was to be analyzed,   explained,   and     made    clear,   the analysandum.   Besides, Raju makes mistakes like conflating   the   Buddhist    notion   of avyaakata ("unanalyzed, unexplained,     unclear,     and incomprehensible") with   the   Jaina    notion of avaktavya[66] ("indescribable"), on the one hand, and with   the `Sa^mkara   Vedaantic    notion   of anirvacaniiya ("indefinable") , on the other, a reading which, to my mind, is unwarranted and misplaced. Richard Chi [67] seeks to analyze the four logical alternatives in terms of the first-order functional   calculus.    He   utilizes   the truth functional logic also when and where this adds to clarification.   This is an admirably    effective approach. He opines that if one keeps apart the different levels of truth and the different points of view, the so-called puzzle about the rejection of the four logical alternatives does not arise.[68]

Suppose, however, that all four alternatives are denied one and the same subject at the same level of truth and from the same point of view; then the puzzle does arise.[69] How is it possible to negate all four logical alternatives simultaneously? This problem, of course. explains de la Vallee Poussin's         helplessness: but at the same time it cries out for a satisfactory solution. Chi's observation that Buddha, the Enlightened   One, tackled the four logical alternatives by "not a rejection by negation but a rejection by silence" is noteworthy.[70] Yet, logically, catu.sko.ti remains a puzzle; and there must be some way to solve it. Chi mentions one tack suggested   by Jayatilleke [71] to   construct   a solution utilizing the notions developed in the many valued logics of Lukasiewiez and Lobochevsky but Chi himself does not offer a solution to the puzzle on these lines.

Instead, utilizing L. E. J. Brouwer and A. Heyting's Intuitionistic negation operator, he formulates the four logical alternatives as (1) p (2) ¡wp (3) p ^ ¡wp (4) ¡wp ^ ¡w¡w p.

And there he stops.[72] Chi's own solution has quite an affinity with Jayatilleke's solution of the problem of catu.sko.ti. The core of Jayatilleke's thesis    is that we treat not-P (in the four alternatives) as   the    contrary   and   not    the contradictory of P. He writes: "We maintain that the   proposition, natt.hi paro loko, should according to its context be treated as the contrary and not the contradictory of atthi paro loko despite linguistic      form.[73] Chi exploits   the notion of contrary negation as found in the Intuitionistic logic and reformulates the four logical alternatives so that they could be denied simultaneously.[74] In a way, Chi's solution is a reformulation of Jayatilleke's in the strictly formal logical terminology of the Intuitionist logicians.[75] The value of this sort of solution has implications for the methodology to be employed in the study of Buddhist logic. This, however, is an independent topic which I do not propose to investigate in this paper.

Let us call the operator "¡w" Boolean negation operation and the operator "~" de Morgan negation. Unlike de Morgan negation, Boolean negation has properties such that A & ¡wA entails B, and that ¡wA & (A v B) entails B.[76]

The idea of Boolean negation originated in the semantical contexts of relevant logics; but it can be discussed   in the context of a four valued semantics. The motivation for Belnap was to "devise an effective    logic   for computers    (mechanical question-answering systems) to use when there is a real risk that the data-base from which answers to questions    are    to     be   inferred    may     be inconsistent."[77] The four values used are:

                   T(rue) F(alse) B(oth) N(one)

`T' represents the case in which the person has been told about a certain sentence S that it is true but has not been told that it is false; 'F' when he has been told that S is false but not told that it is true;'N' when the person has not been told anything: and 'B' when the person has been told both that S is true and also that   S is false."[78] On this interpretation of 'T','F','N', and 'B', using the Morgan negation operation

              (1) ~T=F (2) ~F=T (3) ~B=B (4) ~N=N

we can use, on the said four values, Boolean negation operation ~ and get:

                        (1) ¡wT=F (2) ¡wF=T

(1) and (2) behave the same way as in the case of the operation of de Morgan negation: but (3)¡wB = N, and (4)¡wN = B. Here (3)¡wB = N will mean something like this: "If a sentence A is marked as both true and false, then¡wA cannot be marked as true, since in order for this to be the case it would have to be that A is not marked as true (but it is). And similarly A cannot be marked as false since then A would have to be not marked as false (but it is). So A must be marked as None."[79]

Similarly, justification can be given for ¡w N = B. Belnap   and Dunn   remark: "In a nutshell, the difference between ~ and ¡w would seem to be that ~ is a kind of 'internal' negation, whereas ¡w is a kind of 'external' negation. ~ A might be read as 'A is false', whereas ¡wA should be read as 'it is not the case that A is true'."[80] But then how are we to understand "not" in a given context? For, we have made intelligible Boolean negation (¡w)in terms of de Morgan negation (-) . Given this situation, ordinarily    the   distinction     between ¡w and ~ collapses so much so that ¡w is understood in terms of ~ only and "so we have only one kind of negation after all."[81] If this is so, then even the Boolean negation¡wcannot be employed with advantage over other alternative interpretations given in terms of de Morgan negation to solve the centuries old puzzle of catu.sko.ti.