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
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
logic, or a tilt in favor of the Inexpressible,  or have felt a
certain level of philosophical embarrassment  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", and (b) "The
finite," "The world is infinite,"
"The world is both finite and infinite," and "The world is neither finite nor
infinite". There are two features of these examples (a)
: (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)
(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. Naagaarjuna
exploits this rejection as a form of argumentation against his critics and opponents. 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.
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."
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, 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, "  however "useful and effective a philosophic
method" it may prove
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." 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."
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, four types of questions
have been differentiated.
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
and semantics and which
therefore are answered categorically.
The Buddhists call them
pa~nha eka.msavyaakara.niiya.  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.  A third type of question is
should be set aside. For example, the
question "Will the Tathaagata live after his
death or not?" is a question which is to
aside. Such questions are
called pa~nha.thapaniiyo.  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. 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
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."  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
one." 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."
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." 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
is conducted. In the context of
questions are both askable and
answerable; but in the context of giving urgent
medical aid to the victim, they are irrelevant.
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  (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  'Yes, it is the case',  'No, it is not the
case',  'It is both the case and not the case', and  'It is neither the case nor
not the case'.
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
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. 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
the female parent? " The question, for example, "Where does the
flame of a candle go to when it
is blown out?" is one which does not
admit a meaningful answer because it is based on a conceptual confusion
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?") The question thrives on the mistaken
syntactical similarity with another question like "Where
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.
is another type of
is regarded as "inappropriate" (na kalla) and  which, like the .thapaniiya
questions, is also set aside on the grounds
that it is "literally
meaningless." For example,
"What is decay and death and
of whom is this decay and death?" is
an inappropriate question;
it is a misleading
question to ask "Who feeds
on the food of
consciousness?" Both are examples of
improper questions (na kalla pa~nha).
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
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
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. 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. 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
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, and whether these commitments
are moral, intellectual, or philosophical will depend upon the type of
conceptual framework within which we operate.
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.
"analysed, explained, clear, comprehensible."
vyaakata question is
well-analyzed, explained, clear, and
comprehensible such that a
meaningful answer to it can be
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." I Shall call them unaskable questions. The question
'What is decay and death and of whom is the
decay and death?' and the question
`Who feeds on
the food of consciousness? ' 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. 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
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
alternatives may be false," 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."
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 
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. A, example  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 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
 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.
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
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.
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
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. An example
in which the
predicates are neither contrary nor contradictory  is as
(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.
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)
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, developed into "a very useful and effective
philosophic method" called
the prasa.mga form of argumentation, that is, the argument by reductio ad absurdum.
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)
far back as 1917
Poussin treated the four logical alternatives
(catu.sko.ti), as "a four branched dilemma"
of Buddhist dialectic. 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
non-existence. We are helpless."
I wish that Poussin had realized that the old
Aristotelian three laws of thought are the mark of human rationality (and on Leibniz' reckoning, even God could not violate
them in particular the
contradiction), and it does not matter whether a human being
is white, black, brown, yellow, or red.
reason, if for no other. I do not agree
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.
Rhys Davids 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
other words is A a chimera)?" 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. 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
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
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
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.
P. T. Raju's interpretation 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." 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 ("indescribable"), on the one hand, and with the `Sa^mkara Vedaantic
anirvacaniiya ("indefinable") , on the other, a
to my mind, is unwarranted and
misplaced. Richard Chi  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
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.
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. 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
Enlightened One, tackled the four logical alternatives by "not a rejection
by negation but a rejection by silence"
is noteworthy. Yet, logically, catu.sko.ti remains
a puzzle; and there
must be some way to
solve it. Chi mentions one tack suggested by Jayatilleke
 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. 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. 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.
In a way, Chi's solution is a reformulation of Jayatilleke's in the strictly formal logical
terminology of the Intuitionist logicians. 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.
operator "¡w" Boolean negation
operation and the operator "~" de Morgan negation. Unlike de Morgan negation, Boolean
that A & ¡wA entails B, and that ¡wA & (A v B) entails B.
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." 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." On this
interpretation of 'T','F','N', and 'B', using the
Morgan negation operation
(1) ~T=F (2) ~F=T (3) ~B=B (4)
we can use, on the said four values, Boolean negation operation ~ and get:
¡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
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'." 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." If
this is so, then even the Boolean negation¡wcannot be
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  will not be out of place here. In this connection,
to repeat, consider the (A) and (B)
types of the
(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
(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)
. Jayatilleke writes: "When the four alternatives
happened to be those of a .thapaniiya pa~nha or a meaningless question
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)." Jayatilleke shows remarkable
insight when he says that
"Raju and Bahm have therefore
misdescribed  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
rejection'." 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. 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
Given this situation we cannot deny
or negate them since we could do this only by presupposing
a certain set of criteria for
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, 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
by the parable
of the arrow.
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."
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," 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. 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," called the prasa.mga or the reduction form of argumentation. In using this form of argumentation, the reasoner or "the debater may have no thesis of
or no position to defend." 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." On the face of it, this way of argumentation is indeed
"an embarrassment to the
philosophers." 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
(G) Things are not originated by themselves;
Nor are they originated by others;
Neither by both; nor without cause;
Therefore, there is no origination.
- and, (H) Nirvaa.na is not an
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.
None of these four possible logical
alternatives is applicable to nirvaa.na.
They are not upaadeya in relation to nirvaa.na. The idea underlying (G)
that everything, whether mental or material,
is without an intrinsic nature (ni.hsvabhaava). 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
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
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).
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
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
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. 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
or no position to
defend." 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)
. One develops this conceptual
style by way
understanding dependent origination
(pratiityasamutpaada) and voidness (`suunyataa)
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. So he says: "All things prevail for
him for whom this voidness prevails. Nothing prevails for him for whom
voidness does not prevail.
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  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,
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.
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)
T. Raju, "The Principle
of Four-Cornered Negation
The Review of
Metaphysics 7 (1953-1954) : 694-713 (hereafter cited
as "Four-Cornered Negation")
H. Robinson, "Some Logical Aspects of Naagaarjuna's System," Philosophy East and West 6, no. 4 (January 1957):
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
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
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
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
4. Jayatilleke, Early Buddhist Theory, p.
5. Chi, Buddhist Formal Logic, p. 161.
6. As in note 1 above.
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).
Wayman, "Who Understands? "
p. 15. "Naagaarjuna, in the matter
of the catu.sko.ti is heir to
continuator of teachings in the
early Buddhist canon (in Paali, the four Nikaayas; in Sanskrit. the
Matilal, Logical Illumination, and Vigrahavyaavartani.
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.
13. Bhattacharyya, Dialectical Method
14. Pandeya, "Logic of
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
Sayings, 5 vols. (London: Paali Text Society, 1932-1936).
16. Jayatilleke, Early Buddhist Theory, pp.
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.
Nikaaya, 3 vols., ed. V. Trenkner and R. Chalmers (London:
Pali Text Society, 1948-1951), 1.486; I. B. Horner, trans.,
Sayings, 3 vols. (London: Pali Text Society,
1954-1959); R. Chalmers, trans., Further Dialogues of the Buddha, 2 vols. (London: Pali Text
K. E. Neumann, trans.,
Gotamo Buddho's aus der mittleren Sammlung Majjhimanikaago, vols. 1 and 2
26. Ludwig Wittgenstein, The
Blue and Brown Books (Oxford: Basil Blackwell, 1958), p.
Nikaaya, I. 487.
28. Jayatilleke, Early Buddhist Theory, p.
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).
Carnap, Meaning and Necessity, 2 ed. (Chicago: University of Chicago Press, 1956).
35. Michael Polayni, Personal Knowledge:
Towards a Post-Critical Philosophy (London: Routledge & Kegan Paul, 1958).
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
37. Jayatilleke, Early Buddhist Theory, p.
42. Ibid., p. 293.
Bertrand Russell, "On
Denoting, " in
Contemporary Readings in Logical Theory, ed. I. Copi and J. Gould (New York: Macmillan
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).
Early Buddhist Theory, p. 335.
46. Ibid., p. 340.
47. Chi Buddhist Formal Logic, pp.
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.
54. Matilal, Logical Illumination, p. 18.
55. Louis de La Valle Poussin,
of Nirvaa.na (Cambridge:
Cambridge University Press, 1917), p.111.
56. 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").
Bertrand Russell, History
of Western Philosophy,
1st ed. (London: George Allen and Unwin Ltd.,
1946), 2nd ed. (1961), the chapter on Leibniz,
59. Mrs. Rhys Davids, "Logic
Buddist," p. 133.
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
65. Ibid., p. 702.
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.
68. Ibid., p. 161.
69. Ibid., p. 162.
71. Jayatilleke, Early Buddhist Theory, pp.
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
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 
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.
Early Buddhist Theory, p. 343. For Jayatilleke's own
solution of the problem, see pp. 333-346.
1974, Richard Chi came out with the
"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
(ibid., p. 298).
75. See L. E. J. Brouwer
and A. Heyting's work on Intuitionistic logic.
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
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.
Nikaaya, I. 426.
84. Jayatilleke, Early Buddhist Theory, p.
87. Dhammasa^nga.ni, ed. E. Muller
(London: Pali Text Society, 1885); Jayatilleke,
Early Buddhist Theory, p. 355.
Wittgenstein, On Certainty (Oxford: Basil
89. Majjhima Nikaaya, I. 431; Jayatilleke,
Early Buddhist Theory, p. 357.
90. Chi Buddhist Formal Logic, p. vii.
Ludwig Wittgenstein, Philosophical Investigations, 3rd ed. (New York: The Macmillan
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.
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.
the Paali expression "upeti" ('fits the case').
100. Naagaarjuna's Madhyamaka-`saastra.
stanzas 24 to 34.
Matilal, Logical Illumination, pp. 16-19.
Also compare Chi, "Topics on Being," p. 295.
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
Transcribed for Buddhism Today by
Bhikkhuni Lien Hoa