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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 ^ ww 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, thenwA  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 negationwcannot  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.

We must seek some other  tack in order   to solve the puzzle, or look at it once again in order  to be sure what it really is.  To do this I will take into account   the  context  in  which  the  four  logical alternatives  are  rejected, and the purposes  which are achieved by rejecting  them.  The considerations which led this kind of rejection to transform itself into the prasa.mga  form of argument [82] will not be out of place  here.  In this  connection, to repeat, consider   the  (A) and  (B) types  of the  avyaakata theses:

             (A) (1) There is a next world
                    (2) There is no next world
                    (3) There both is and is not a next world
                    (4) There neither is nor is not a next world
and         (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.

The alternatives (1) through (4) in both (A) and (B) are answers to .thapaniiya questions, and the answers are avyaakata theses.  The questions are .thapaniiya, since   in each  one of them  at the same  time  a no kalla    question is involved.   Further, these alternatives  are not negated or denied but they are rejected.  The  alternatives   are rejected  by maa'h evam (do not [say] so), and not by no h'idam  (it is not so) The avyaakata theses are to be set aside, so the   rule  says  (A  vyaakataani  thaapitaani) .[83] Jayatilleke  writes:  "When  the  four  alternatives happened to be those of a .thapaniiya pa~nha   or   a  meaningless   question    all   four alternatives   were  rejected  rather  than  negated because the question in each of the alternatives was not   considered  to  be  a  proper  question  (kalla pa~nha)."[84] Jayatilleke  shows remarkable   insight  when  he says that   "Raju  and Bahm  have  therefore misdescribed [85] their  nature  as far as the   Paali Canonical  position  is  concerned  by calling  this doctrine  that of `four cornered  negation'  when it ought   properly   to  be  called    'four   cornered rejection'."[86] I fail to understand why Jayatilleke   did not follow  this important  insight but remained  obsessed  with treating  the avyaakata theses from a logical point of view exclusively. If  we  look  at  them   carefully   we  find   that  by characterizing them avyaakata  (unanalyzed, unexplained, unclear, incomprehensible) we legislate ourselves  out  from  being  in  a position  to  say whether  or not each  one of them  is true or false. Their  appraisal  in terms of truth  and falsity  is possible  only if we have criteria for their factual evaluation. But where are the criteria? We find them nowhere.  The alternative  for us is to reject   them and set them aside (.thapaniiya).

In a moral context  "avyaakata"  means  "neither good nor bad." In this sense "avyaakata"   is used to denote  what is "neutral"  in moral  contexts  where "what   is indeterminate"  (avyaakata) are acts which are neither good nor evil.[87] Jayatilleke   suggests that if we extend this application   of avyaakata  to any one of the four logical alternatives  in (A) and (B), we would like to say that the avyaakata  theses are logically  indeterminate  in the sense   of being neither   true nor false.  There are no criteria  for their factual  appraisal.  Nor perhaps  can there be any;  for  their  logical  status  is indeterminate.

Given this situation  we cannot  deny or negate them since  we  could  do  this  only  by presupposing   a certain   set   of  criteria   for    their   factual valuation.  In the absence  of some  methodological conceptual   framework   within   which  alone  their factual relevance  and appraisal is possible, we can only reject them, set them aside.

We do not reject  a theory  in a vacuum,[88] not least  an  avyaakata    thesis.   For  rejecting    an avyaakata  thesis, we need a framework  of criteria.

Fortunately,  in  this  case  we  have  one  in  the conceptual framework of the Four Noble Truths.  This is   shwon    by   the   parable     of   the   arrow.        Differentiating    avyaakata  from  vyaakata  theses, Buddha, the Enlightened  One, remarks: The avyaakata questions are not answered (they are .thapaniiya) and the  avyaakata  theses  are rejected   (they  too are  .thapaniiya)   because  they  are  "not  useful,  not related   to  the  fundamentals   of  religion,  not conducive    to   revulsion,  dispassion,  cessation, peace,    higher    knowledge,   realization, and  Nirvana."[89]   Given  this,  I  shall  call  it  the pragmatic criterial framework in which the avyaakata questions and the avyaakata theses are rejected, set aside (.thapa~nya), not negated or denied.  Logic is not  relevant  here.  For, where  there  is  neither affirmation  nor negation nor inclusion or exclusion of both, what role  does  logic  have  to play? Both logic and the obsession  with logic, taking logic to be the only form of rationality, are to be set aside as  irrelevant.  The  catu.sko.ti,  which  has  been considered an "insoluble problem for centuries,"[90] simply  is nor a problem.  We saw logic   in it where there was none. The result: the problem was not susceptible  of solution  on the logical  plane.

Once things are put in their proper, natural  place, the problem simply ceases   to  be  a  genuine problem.[91] The catu.sko.ti and the rejection of each one of the four logical  alternatives  have  become  in the hands   of Naagaarjuna  "a very useful  and effective philosophic method,"[92] called the prasa.mga or the reduction form  of argumentation.[93] In using  this form of argumentation, the reasoner  or "the debater may have  no thesis  of his  own  or no position   to defend."[94]  In  this  connection,  Naagaarjuna  is frequently   quoted   as  saying:  "If  I  had   any proposition, then this defect would be mine. I have, however,  no  proposition.  Therefore, there   is  no defect  that  is mine."[95] On the face  of it, this way of argumentation is indeed "an embarrassment  to the philosophers."[96] The structure of this method of argumentation is as follows: We consider each one of   the   four    possible logical alternatives (catu.sko.ti)  and  reject  it  as  untenable. The function is to show that any philosophical  position can be shown to be logically  discrepant, for it can be stated exclusively  in terms of the four possible logical  alternatives, each one of which  is (or can be) easily rejected. Consider for example:

        (G) Things are not originated by themselves;
            Nor are they originated by others;
            Neither by both; nor without cause;
            Therefore, there is no origination.[97]
and, (H) Nirvaa.na is not an existent;
            Nirvaa.na is not a non-existent;
            Nirvaa.na  is not both  an existent  and also  a non-existent;
            Nirvaa.na  is  not  neither  an existent  nor   a non-existent.[98]

None of these four possible logical alternatives  is applicable  to nirvaa.na.   They are not upaadeya[99] in relation to nirvaa.na. The idea underlying (G) is that   everything,  whether  mental  or  material, is without an intrinsic nature (ni.hsvabhaava).[100] If  this is so, then saying(1) that some material  thing is produced, or saying (2) that some material  thing is  not  produced,  are   equally   the  result   of conflating   the category  of "production"  with  the category   of "material  thing."  The two categories, which   are    conceptually   different,  cannot    be logically combined in the way that they are combined in  (1)  and  (2).  Syntactically   (1) and  (2)  are correctly formed expressions, but semantically  they are  avyaakata  and  hence .thapaniiya   (unanalyzed, unexplained,  unclear,  and  incomprehensible,    and therefore  to be set aside).  Similarly  in the case of(H), the underlying  idea is that the category  of `nirvaa.na'   and  the category  of `existent   thing' have  been  conflated  in the  given   four  possible logical  alternatives, with the result that each one of the alternatives, though  syntactically   correct, is avyaakata semantically and hence to be set aside.This  reasoning  follows  the rule, namely, that the theses  which  are avyaakata  are   to be set  aside (avyaakataani thapitaani).

Apparently,   the  avyaakata  theses  are  indeed correct from the ordinary language point of view.  Anybody who rejects a certain thesis in this way must have a certain criterial  framework within  which   he  is  operating, as   we  have  said earlier.   In the case  of Naagaarjuna, the framework is definitely  not that of formal  logic, for in his view, these are both avyaakata  and .thapaniiya.   Nor      is  his  framework   that  of  the  methodology   of empirical   knowledge  (pramaa.nas).  He accepts only two criteria of knowledge  (pramaa.nas): observation (pratyak.sa) and inference (anumaana).  He uses them to decide  whether  a certain  piece   of information gained observationally  or inferentially  is true or false.  But  in  the  case  of questions   about  (a) dependent  origination   (pratiityasamutpaada), (b) voidness (`suunyataa), and (c) nirvaa.na  he rejects the applicability of the pramaa.na methodology.[101] If I am right  in this  thinking, then three  things become apparent:

First, Naagaarjuna  regards (a), (b), and (c) as the constituents  of the conceptual framework within which he is operating  when he is engaged in arguing against his critics and opponents. He cannot be said to   be arguing  against  his  critics  in  a vacuum. Matilal  is mistaken  when he says that "the debater may have  no thesis  of his  own   or no position  to defend."[102] One  can indeed  regard  (a), (b), and (c)   as   axioms    or   the   presuppositions    of Naagaarjuna's  philosophical   thought,  constituting the background of his arguments against his critics.

Second, nirvaa.na is a way of looking at things. It  is   a  conceptual  style  (d.r.s.ti) .[103]  One develops   this   conceptual    style   by   way    of         understanding dependent origination (pratiityasamutpaada)  and  voidness  (`suunyataa) .

Hence,   in  the  case  of  nirvaa.na,  the  question whether   nirvaa.na is an existent  or not simply does not arise.  And, once you have this conceptual style (d.r.s.ti), all questions concerning origination and nonorigination, and so forth become  irrelevant  and need to be set aside.

Third, Naagaarjuna's  argumentation, at the same time, works within the concepfual  framework  of the Four Noble Truths.  Being a Buddhist, he cannot, and in fact  he does  not, give  it up.[104] So he says: "All things  prevail  for him for whom this voidness prevails. Nothing  prevails  for  him  for  whom voidness does not prevail.”[105]

In fact, in Naagaarjuna's thought, all three are interconnected; (a) dependent     origination (pratiityasamutpaada),  (b) voidness  (`suunyataa), and (c) nirvaa.na constitute the conceptual  framework F1 within  which  he is operating.  The  aim  is  to develop  the  nirvaa.na    d.r.s.ti  or  the nirvaa.na conceptual style.  This aim is equally well achieved if the conceptual  framework  F2 of the  Four  Noble Truths   is accepted;  and Naagaarjuna  does  operate within   this   framework [106]  also.   Within   the framework   F2 the avyaakata  theses are set aside on pragmatic grounds of dharma; but with respect to the framework  F1 they are rejected  on the grounds that within  F1 the four  possible  logical  alternatives become avyaakata  theses, and outside  the framework they   make  no sense.  The  ordinary  language  does permit  them, but  within  Naagaarjuna's  conceptual framework  F1 they  are  to be set  aside  as  being external to the framework.  However embarrassing  it might be to the philosophers, neither  formal   logic nor the methodology  of empirical  knowledge  can be said to be relevant for an adequate understanding of the so called problem of catu.sko.ti.


1.  Archie J. Bahm, "Does Seven-Fold Predication Equal Four Cornered  Negation  REversed?" Philosophy East  and West  7, nos.  3 and 4 (October  1957  and January 1958): 127-130; Richard S. Y.  Chi, Buddhist Formal Logic (London: The Royal Asiatic  Society  of Great  Britain  and Ireland;   sold by Luzac and Co., Ltd., 1969);  Mrs.  Rhys Davids, "Logic (Buddhist),"

Encyclopaedia  of Religion  and  Ethics  (New  York: Charles Scribner's Sons, 1926), vol.  8, p.  133; K. N.  Jayatilleke, Early Buddhist  Theory of Knowledge (London: George  Allen & Unwin Ltd., 1963;  reprint, Delhi: Motilal  Banarsidass, 1980) (hereafter  cited as  Early  Buddhist  Theory) ;  P.    T.  Raju,  "The Principle    of  Four-Cornered   Negation   in  Indian Philosophy,   "   The   Review    of   Metaphysics   7 (1953-1954)   :   694-713    (hereafter    cited    as "Four-Cornered  Negation") ;  Richard   H.  Robinson, "Some   Logical  Aspects  of  Naagaarjuna's  System," Philosophy  East and West 6, no.  4 (January  1957): 291-308;  St.   Schayer, "Altindische  Antizipationen der Aussagenlogik," in Studien zur indischen  Logik,        Extrait  du  Bulletin  de l'Academie   Polonaise  des  Sciences et des Letters cracovic (1933), p.  93: and R. D. Gunaratne, "The Logical Form of Catu.sko.ti: A New Solution," Philosophy  East  and West 30, no.   2 (April 1960): 211-239  (hereafter  cited as "Logical Form").  Gunaratne  offers a vehement defense of the application  of formal logic (including  set theory) to  catu.sko.ti   statements    whose  structure,  he insists, is isolable  and can be given   a consistent interpretation.  He tends  to reject  Alex  Wayman's view expressed  in his article "Who Understands  The Four   Alternatives    of   the   Buddhist    Texts? " (Philosophy  East and West 27, no.  1 (January 1977)        (hereafter cited as "Who Understands?"): 3-21). that after    all  it  may  be  "hazardous    and  probably contraindicated  to apply  symbolic  logic"  (p.5)  without reservations to catu.sko.ti. My own position lends    support   to  Wayman's    view   vis   a  vis Gunaratne's.

2. Ramachandra Pandeya,  "The    Logic of Catu.sko.ti  and  Indescribability," in  his  Indian Studies  in Philosophy  (Delhi: Motilal Banarsidass, 1977), pp.  89-103  (hereafter  cited  as "Logic  of Catu.sko.ti") ;  T.   R.   V.    Murti,  The  Central  Philosophy  of  Buddhism  (London:  George  Allen  & Unwin.  1955). Observe in this connection Richard S. Y. Chi's remarks in his article "Topics on Being and Logical Reasoning" (Philosophy East and West 24, no. 3  (October  1974) :  298):  "After  many  years  of       dispute, I still  think  that  Murti's  view on this subject  is  the  right  one"  (hereafter  cited  as "Topics on Being").

3.  B.  K.  Matilal, The Logical Illumination of Indian Mysticism  (Oxford: Oxford University  Press, 1977;  reprint, New Delhi: Oxford University  Press, 1978) (hereafter cited as Logical Illumination).

4. Jayatilleke, Early Buddhist Theory, p. 134.

5. Chi, Buddhist Formal Logic, p. 161.

6. As in note 1 above.

7.     Naagaarjuna's   Madhyamaka-`saastra    and Vigrahavyaavartani, Buddhist Sanskrit  Texts No.  10 (Darbhanga: The Mithila  Institute  of Post-Graduate Studies   and Research  in Sanskrit  Learning, 1960). For an English  translation  of the latter work, see Kamaleswar  Bhattacharya, The Dialectical  Method of Naagaarjuna    (Vigrahavyaavartani)  (Delhi:  Motilal Banarsidass, 1978) (hereafter  cited  as Dialectical Method).

8.    Wayman, "Who Understands? "    p. 15. "Naagaarjuna, in the matter   of the  catu.sko.ti  is heir  to and  the   continuator  of teachings in the early Buddhist  canon  (in Paali, the four Nikaayas; in Sanskrit. the four AAgamas."

9.     Matilal,   Logical    Illumination,    and Vigrahavyaavartani.

10.  The Nyaaya Suutras of Gotama, translated by Satisa  Chandra Vidyabhusana;  reprint, New  Delhi: Oriental   Books Reprint Corporation, 1975;  Matilal, Logical  Illumination;  Chi, "Topics   on  Being," p. 295.

11. Matilal, Logical Illumination.

12. Ibid.

13. Bhattacharyya, Dialectical Method

14. Pandeya, "Logic of Catu.sko.ti."

15.  A^nguttara Nikaaya, 5 vols., ed.  R. Morris and E. Hardy (London: Paali Text Society. 1885-1900); F.  L. Woodward and E.  M. Hare, trans., The Book of the  Gradual   Sayings, 5 vols.  (London: Paali  Text Society, 1932-1936).

16.  Jayatilleke,  Early  Buddhist  Theory,  pp. 281-283.

17. Ibid.. p. 287.

18. Ibid., p. 288.

19. Ibid., p. 281

20. Ibid., p. 287.

21. Ibid., p. 288.

22. Ibid., p. 288.

23. Ibid., pp. 288, 274.

24. Ibid., pp. 471-476.

25.  Majjhima Nikaaya, 3 vols., ed.  V. Trenkner and  R.   Chalmers   (London:   Pali  Text   Society, 1948-1951), 1.486;  I.  B.  Horner, trans.,   Middle       Length Sayings, 3 vols.  (London: Pali Text Society, 1954-1959); R. Chalmers, trans., Further Dialogues of the Buddha, 2 vols.  (London: Pali Text   Society,

1888);   K.  E.  Neumann,  trans., Die  Reden   Gotamo Buddho's aus der mittleren Sammlung Majjhimanikaago, vols. 1 and 2 (Leipzig, 1896-1900).

26.  Ludwig  Wittgenstein, The   Blue  and  Brown Books (Oxford: Basil Blackwell, 1958), p. 108.

27. Majjhima Nikaaya, I. 487.

28. Jayatilleke, Early Buddhist Theory, p. 292.

29. Ibid.

30. Ibid.

31. Ibid.

32.  G.  E.  Moore, Principia Ethica (Cambridge: Cambridge University Press, 1903), chap.  5;  V.  K. Bharadwaja,   Naturalistic   Ethical  Theory  (Delhi: University of Delhi Press, 1978).

33.  Rudolf Carnap, Meaning and Necessity, 2 ed. (Chicago: University of Chicago Press, 1956).

34. Ibid.

35. Michael Polayni, Personal Knowledge: Towards a  Post-Critical  Philosophy  (London:  Routledge  &  Kegan Paul, 1958).

36.    Vaman  Apte,  Sanskrit  English  Practical Dictionary (Poona: Prasad Prakashan; reprint, 1977). Richard Chi, in "Topics on Being," mistranslates the Sanskrit "avyaak.rta" as "inexpressible" (p.  296). See  Apte's  Dictionary.   Avyaakata    is  Paali  of Sanskrit     avyaak.rta.    It   means    "unanalysed, unexplained, incomprehensible."

37. Jayatilleke, Early Buddhist Theory, p. 292.

38. Ibid.

39. Ibid.

40. Ibid.

41. Ibid.

42. Ibid., p. 293.

43.    Bertrand   Russell,  "On    Denoting, "  in Contemporary Readings in Logical Theory, ed. I. Copi and J. Gould (New York: Macmillan Company, 1967).

44.  G. Frege, "Sense and Nominatum," and P.  F. Strawson, "On Referring."  in Copi  and Gould, eds., Contemporary  Readings  in  Logical  Theory; Saul Kripke,    Naming   and   Necessity    (Oxford:  Basil Blackwell, 1972).

45.  Jayatilleke, Early Buddhist Theory, p. 335.

46. Ibid., p. 340.

47. Chi Buddhist Formal Logic, pp. 158-159.

48. Ibid.

49. Ibid.

50. Ibid.

51. Naagaarjuna's Vigrahavyavaartani.

52. Matilal, Logical Illumination, p. 17.

53. Ibid., p. 18, Th.  Stcherbatsky, The Central Conception  of Buddhism  and The Meaning of the Word "Dharma" (Reprint, Delhi: Motilal Banarsidas, 1970), p. 22.

54. Matilal, Logical Illumination, p. 18.

55.  Louis  de  La  Valle  Poussin, The  Way   of Nirvaa.na  (Cambridge: Cambridge  University  Press, 1917), p.111.

56. Ibid., p.111.

57.  Ibid., p.  111.   See also  F.  J.  Hoffman, "Rationality  in Early  Buddhist  Four  Fold Logic," Journal  of  Indian  Philosophy  10, no.  4 December 1982): 309-337 (hereafter cited as "Rationality").

58.    Bertrand   Russell,  History    of  Western Philosophy, 1st ed.  (London: George Allen and Unwin Ltd., 1946), 2nd ed. (1961), the chapter on Leibniz,

pp. 563-576.

59. Mrs. Rhys Davids, "Logic Buddist," p. 133.

60. Ibid.

61. Ibid.

62.  B.  M.  Barua, A History  of Pre-Buddhistic Indian Philosophy  (Calcutta, 1921;   reprint, Delhi: Motilal Banarsidass, 1970), p. 47.

63.  For  a  different  line  of  criticism, see Jayatilleke, Early Buddist Theory, pp. 334-336. Also see,  for some other attempts to solve the so-called problem  of  catu.sko.ti, Bahm, "Does  Seven-Fold?"; Wayman, "Who Understands?"; Hoffman, "Rationality"; Gunaratne, "Logical Form"; and Shosun Miyamoto, "The Logic  of Relativity  as the common  Ground  for the Development  of  the  Middle  Way," in Buddhism  and Culture, ed.   Susumu Yamaguchi (Nakano Press, 1960), pp. 67-68.

64. Raju, "Four-Cornered Negation."

65. Ibid., p. 702.

66.  For a clarification  of the Jaina notion of avaktavya see V.  K.  Bharadwaja, "The Jaina Concept of  Logic," Indian   Philosophical  Quarterly  9, no. 4(Jaly 1982): 363-375.

67. Chi, Buddhist Formal Logic, pp. 156-163.

68. Ibid., p. 161.

69. Ibid., p. 162.

70. Ibid.

71.  Jayatilleke,  Early  Buddhist  Theory,  pp. 333-346.

72.  Chi, Buddhist Formal Logic, pp.  vii-ix. He writes: The  catu.sko.ti  has been  considered  an insoluble problem  for centuries.   In December  1967, I read a paper ("A Tentative  Solution to the Problem of Four Corner  Negation") at  the  University  of  Chicago, which  I believe  solves  the problem.  The solution depends    on     applying      Bertrand      Russell's vicious-circle    principle  and  my  explanation  of "unavoidable  mistakes,  "  namely, "under   cultural circumstance  x, a mistaken theory y is inevitable." The  paper  is  unmanageable  in  length  and  needs further revision: it will appear as an article.  For the  moment, I can  only  say  that  it corrects  my earlier  explanation  of the  catu.sko.ti  which  is erroneous.  (pp. vii-ix of his Foreward [1968] to his Buddhist Formal Logic(1969). Observe also change in his position reflected in his article "Topics on being and Logical Reasoning," pp. 293-300.

73.  Jayatilleke, Early Buddhist Theory, p. 343. For Jayatilleke's  own solution  of the problem, see pp. 333-346.

74.  In 1974, Richard  Chi  came  out  with  the thesis  that   "Buddhist  logic  belongs  to strictly conventional  two-valued  logic" ("Topics on Being," p.  297), that he had made a "mistake  by comparing catu.sko.ti  with intuitionism"  (p.  297), and that  "the  subject  of  catu.sko.ti...    is  not  at  all `Buddhist   logic'"(p.  298).  Having  said  this, he tends to subscribe  to T.  R.  V.  Murti's view, and adds:  "As   a  matter   of  fact,  catu.sko.ti    is applicable   to  metaphysical    speculations   only" (ibid., p. 298).

75. See L. E.  J.  Brouwer and A. Heyting's work on Intuitionistic logic.

76.  Nuel D.  Belnap, Jr., and J.  Michael Dunn, "Entailment   and    the   Disjunctive   Syllogism." Contemporary  Philosophy  I, ed.  G.  Floistad  (The Hague:   Martinus  Nijhoff  Publishers,  1981), pp. 337-366 (hereafter cited as "Entailment").   See also J.  M.  Dunn, "Intuitive  Semantics  for Firstdegree Entailments    and  Coupled   Trees."    Philosophical Studies 29 (1976): 149-168, and Nuel D. Belnap, Jr., "A Useful Four-valued Logic," in J.  M.  Dunn and G. Epstein.  eds., Modern Uses of Multiple-valued Logic (Dordrecht: D. Reidel Publishing Co., 1977).

77. Belnap and Dunn, "Entailment," p. 342.

78. Ibid., p. 342.

79. Ibid., p. 343.

80. Ibid., p. 343.

81. Ibid., p. 345.

82. Matilal, Logical Illumination, pp. 16-18.

83. Majjhima Nikaaya, I. 426.

84. Jayatilleke, Early Buddhist Theory, p. 346.

85. Ibid.

86. Ibid.

87. Dhammasa^nga.ni, ed. E. Muller (London: Pali Text  Society, 1885);  Jayatilleke,   Early  Buddhist Theory, p. 355.

88.  Ludwig Wittgenstein, On Certainty  (Oxford: Basil Blackwell, 1969).

89. Majjhima Nikaaya, I. 431; Jayatilleke, Early Buddhist Theory, p. 357.

90. Chi Buddhist Formal Logic, p. vii.

91.      Ludwig    Wittgenstein,    Philosophical Investigations, 3rd  ed.  (New  York: The  Macmillan Company, 1968).

92. Matilal, Logical Illumination, p. 17.

93. Ibid., pp. 16-17.

94. Ibid., pp. 16-19.  Also compare Chi, "Topics on being."

95. Bhattacharya, Dialectical Method, p. 23.

96. Matilal, Logical Illumination, p. 16.

97. Buddhist Formal Logic, p. 159.

98. Naagaarjuna's Madhyamaka-`saastra, chap. 25, Kaarikaas. 3, 4, 5, 7, and 8.

99.  Compare the Paali expression "upeti" ('fits the case').

100. Naagaarjuna's Madhyamaka-`saastra.

101.   Naagaarjuna's  Vigrahavyaavartani, stanzas 24 to 34.

102.   Matilal, Logical Illumination, pp.  16-19. Also compare Chi, "Topics on Being," p. 295.

103.   Richard Chi seems to translate  "d.r.s.ti" as "dogmatism" ("Topics on Being," p.   296). I agree with him that it is hard to find an English  synonym

for "d.r.s.ti." But, then, "dogmatism" won't do;  "a way of looking  at the world"  or "a point   of view" are better synonyms.

104. Alex Wayman has this important insight when he writes: "the four Noble Truths  have been a basic ingredient   of  Buddhist    thinking  and  attitude" (Wayman,   "Who  Understands,"  p.  10).  And, again, "Naagaarjuna, in the matter  of catu.sko.ti, is heir to and the  continuator   of teachings  in the  early Buddhist canon" (Wayman, ibid., p. 15).

105.  Naagaarjuna's  Vigrahavyaavartani,  stanza LXX.

106.  In fact, the two frameworks  F1 and F1 can easily be shown to be essentially  one.  The line of argument in that case will be that the framework   of the four Noble Truths undergoes linguistic   mutation at  the  hands   of  Naagaarjuna,   as  a  historical development,  into   the   framework    of  dependent origination,   voidness,    and   nirvaa.na.   (This, however, forms the subject of another paper.)

Transcribed for Buddhism Today by Bhikkhuni Lien Hoa


Updated: 15-1-2001

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