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Nagarjuna and Logic

To: soc.religion.eastern
From: W.F. Wong.
Subj: Nagarjuna and Logic (0000.ngrlgic.wfw)
Date: unknown

        Some time ago I made available the paper "Some Logical Aspects 
of Nagarjuna's System" by Richard H. Robinson (I shall abbrev. by R.R.) 
which appeared in _Philosophy East and West_ vol. VI, no. 4, p. 291. I 
was then fortunate enough to obtain from Tom McFarlane the paper 
"Buddhist Logic Expounded by Means of Symbolic Logic" by Hajime 
Nakamura (abbrev. H.N.) which appeared in the _Journal of Indian and 
Buddhist Studies_ vol, VII, no. 1, p. 395. I promised Tom that I will take it 
as a personal challenge to summarize these two papers for people on the 
net. Since then, I have the fortune to come across _Indian Buddhism_ by 
Hajime Nakamura (Prof. Nakamura, who is the director of the Institute for 
Asian Study at the University of Tokyo, is considered by many as the 
foremost authority of Indian and Buddhist philosophy in Japan. I have yet 
to have the karma to meet and listen to him.) and, more recently, _The 
Concept of Buddhist Nirvana_ by Th. Stcherbatsky (T.S.). (Both books are 
reprinted by Motilal Banarsidass Publishers of Delhi). While I am 
certainly no Buddhist scholar, I found these material to be so interesting 
that I will risk making a fool of myself by attempting to summarize their 
positions on Nagarjuna. Perhaps, this will touch off an interesting 
discussions and contributions by more knowledgeable netters.

Note : This is a very long posting. Please skip if you are not interested.

        Although it is appropriate that I should first do an introduction of 
Nagarjuna, lack of space and ability prevents me from doing so. However, 
there are lots of books written on him which the interested can find. 
Suffice it is to say that his philosophy was controversial both among his 
own contemporaries and the pioneering western Indologists. While 
Mahayana Buddhists honour him with the title of the "second Buddha" 
and 8 modern Japanese sects (including Zen, Pure Land, Sanron etc.) 
claim him as (at least one of) their founder, his opponents accuse him of 
being dogmatic, irrational and plain stupid. For example, T.S. mentions 
that "Vacaspatimisra is full of respect towards Buddhist logicians, but for 
the Madhyamikas he has only remarks of extreme contempt, he calls them 
fools". T.S. also mentions of Sankara (the founder of the Hindu Advaita-
Vendanta) because "the position of Sankara is interesting because, at heart, 
he is in full agreement with the Madyamikas, at least in the main line, 
since both maintain the reality of the One-without-a-Second, and the 
mirage of the manifold. But Sankara, as an ardent hater of Buddhism, 
would never confess that. He therefore treats the Madhyamikas with great 
contempt ..."

        But what actually did the Madhymikas say ? T.S. gave the 
following structure to the Buddhist schools :

        Vaibhasika and early schools - both samsara and nirvana real.
        Madhyamikas - both samsara and nirvana (separately) unreal.
        Sautranika - samsara real, nirvana (separately) unreal.
        Yogacara or Vijnanavada - samara unreal, nirvana real.

        T.S. served as the motivation of R.R. The important contribution of 
R.R. is to point out that since the method employed by Nagarjuna and the 
Madhymikas is dialectic, one can clarify the confusion if one examines his 
argument using modern logic. He first rebutes the thesis of T.R.V. Murti 
set out in his _The Central Philosophy of Buddhism_ (a well known thesis on 
the Madhyamika philosophy) and others who state that Nagarjuna's 
approach was to destroy all theories by their own tool, namely logic. And 
that his theory is a null-theory, because theories and logic are equated with 
discursive conceptual thoughts. (T.S. mentions that the sub-school 
Madhyamika-Prasangika which does exactly this - "destroy logic with 
logic".) This seens to be an apologist approach to the charge that the 
Madhyamikas are nihilists or negativists. 

        The central thesis of R.R. is that Nagarjuna was in fact trying to 
establish certain theorems based on the basic Buddhist axioms. To do this, 
he was a master logician. After reading a little (very little) of the Mula-
madhyamika Sastra, I do feel that R.R. seems correct. Although not well-
organized, I can distinctly make out definitions, axioms, lemmas, theorems 
and corollaries - not unlike a rigourous mathematical thesis. R.R. then 
went on to give some of the basic definitions, axioms and inference rules 
used. Upon this careful analysis, I cannot help but feel the brilliance and 
sophistication of Nagarjuna (given the period he lived in).

        One of the main theorem of Nagarjuna which R.R. noted was that 
there is no such thing as a self-being (svabhava) and reality (tattva). The 
single most important definition introduced by Nagarjuna is that of 
SUNYATA. This term has been the source of numerous confusions (esp. 
for me). The problem is its translation into Chinese and English (the two 
languages accessible to me) as EMPTINESS or VOIDNESS. T.S. 
criticized this translation. The correct translation, according to him, should 
be RELATIVITY. This is made very clear by what Nagarjuna himself 
defined SUNYATA to be -

        "What is dependent co-arising (pratitya-samutpada), that we
          designate SUNYATA".

This single statement cleared a lot of my confusion. Why use this 
confusing term ? Firstly, its because its a linguistic necessity to distinguish 
dependent-coarising (which is the name of a phenomena or a property) and 
that which exhibits it. Secondly, it might have been a deliberate attempt to 
use a term which invokes religious feeling. At least for me, when face to 
face with suffering and desperation, the idea of "emptiness" invokes an 
unexplainable yet deep feeling in me.

        Arguably, dependent-coarising is one of the most basic of Buddhist 
axioms, one to which all schools of Buddhism will subscribe to (probably 
with different interpretation though). Nagarjuna's argument against self-
being is summarized by R.R. :

"Svabhava is by definition the subject of contradictory ascriptions. If it 
exists, it must belong to an existent entity, which means that it must be 
conditioned, dependent on other entities, and possessed of causes. But a 
svabhava is by definition unconditioned, not dependent on other entities, 
and not caused. Thus the existence of a svabhava is impossible."

The same attack was made of reality which was defined as that which do 
not obey dependent-coarising. Why this perculiar definition of reality ? 
The analogy given is that a thing which is dependent on other is not real in 
itself just like borrowed money is not real wealth. My feeling is that it is a 
similar confusion with that of sunyata - he had a clear definition of what 
the term is but confusion set in because of the connotations we have of the 
terms or the translations of them.

        Then came the shocker ... Nagarjuna concluded that there is no 
difference between Nirvana and Samsara. Why ? Because samsara is all 
that is dependent-coarising and since there is nothing that isn't (because
that which is - the selfbeing (svabhava) has been 'proven' to be non-existent), 
samsara must be (in set theory - that which is without a complement) the 
universe inclusive of nirvana. The implications of this single conclusion on 
Buddhism is, to me, incalculable and is Nagarjuna's single most important 
achievement. This brought about a crisis - what about Nirvana ? Was the 
Buddha lying when he spoke of nirvana ? Nagarjuna, being a devout 
Buddhist, did not shirk from this crisis. He, and others after him, went on 
to give a new interpretation of nirvana. What about the nirvana that the 
Buddha talked about ? To begin with, no one really knows what 
Sakyamuni spoke of. Even the Pali Canon whose proponents claim to be 
the original words of the Buddha contains clear instances of later 
additions, editing etc. just like any ancient text. The early Mahayanist 
rebels have always claimed that the original teachings of the Buddha have 
been corrupted in the Pali Canon. (Interestingly, the same criticism is 
leveled against the Mahayanist sutras.)

        On a few technical matters, R.R. points out that Nagarjuna had 
committed a well known mistake in logic - that of the fallacy of the 
antecedent. Briefly, the fallacy goes something like this : "If A is true then 
B is true; but A is false so we can conclude that B is false". In logic, if B 
is false, we may conclude that A is false (the contraposition) but if A is 
false, we CANNOT conclude anything about B. An example would be 

"If any non-arisen entity occurred anywhere, then it might arise; but, since 
it does not exist, the entity cannot arise."

H.N. suggest that Nagarjuna may not be using traditional logic but rather 
logic algebra. R.R. thinks that it is not so.

        The other difficulty that R.R. clarified is that concerning negation. 
The example he raised is 

"If nirvana is not an entity, it cannot be an non-entity; where there is no 
entity, there is no non-entity."

This statement seems contradictory at first. R.R. points out that we run 
into a contradiction if we assume that entity is a universal term and non-
entity is its null complement, i.e. everything is an entity. If "entity" is a 
finite set A that possess some property and "non-entity" is the finite set B 
that does not have that property, that we can reinterprete the above as :

"If nirvana is not A, it cannot be B (because) if A does not exist, B does 
not exist too."

To clarify the above, lets suppose A is a red house and B is a non-red 
house. If in the entire universe, there isn't such a thing as a red house, then 
there is also no such thing as a non-red house. Or one who is coloured-blind
from birth and who have never seem red would never know what "not red" means.

        Given these two difficulties, it is not surprising that Nagarjuna is 
so often misunderstood as dogmatic or nonsensical. R.R. then went on to 
the problem of the tetralemma - "true, not true, both true and not true and 
neither true nor not true". Neither R.R. nor H.N. seems to be able to make 
sense out of it except to say that it resemble Aristotelian logic.

        In concluding, R.R. first noted that "it is doubtful whether 'positive' 
or 'negative' have anything to do with the meaning of 'emptiness', except 
as signalling emotional acceptance or rejection." He also stated that "there 
is no evidence that Nagarjuna 'uses logic to destroy logic'. He makes 
mistakes in logic, but does not deny any principle of logic. He asserts that 
a certain set of propositions - the Buddhist doctrines - is true under a 
certain condition, that of emptiness, and false under another condition, that 
of own-beingness. ... He simply refutes all theories of own-being."

        H.N. is much harder reading for me. The main reason is that the 
symbolism he used does not seem modern (i.e. they are not the ones' I 
learned) and so a lot of the equations are very vague to me. Notheless, I 
shall try to summarize this paper. The paper, in fact, precedes R.R.'s who 
quotes it extensively. 

        H.N. starts with the observation that ideally logic should be a 
universal language where everyone from any background can do cross 
discussions meaningfully without the cultural baggages. Unfortunately, 
this is not the case. He then states his intention as "let us try to treat and 
express Buddhist logical thought by applying to it the mathematical form 
of symbolic logic. Then the inconsisitencies and the important differences 
will be seen between this and the present day logician's general 
interpretations." This sets the tone for the entire paper, i.e. academic.

        H.N. begins by pointing out that the ancient systems of logic are 
usually biased the grammar and vocabulary in which they were expressed 
in. He then goes into the technical issues of mapping Indian logic to 
symbolic logic and compares it to Aristotlean logic. He then went on to 
discuss the 5 member syllogism used in Indian logic. This is the so-called 
Old Logic or Nyaya which was commonly used by all schools, Buddhist and
non-Buddhist. However, Dignaga, the great Buddhist logician, later modified 
it to found the so-called Buddhist New Logic. The 5 member syllogism is :

(1). Proposition (pratijna) - Q(a) - eg. there is fire on the hill.

(2). Reason (hetu) - P(a) - eg. because there is smoke.

(3). Exemplification (drstanta) - Forall(x).P(x) -> Q(x) - whatever shows 
smoke shows fire.

(4). Application (upanaya) - P(a) -> Q(a) - this hill smokes.

(5). Conclusion (nigamana) - Q(a) - therefore, there is fire on this hill.

>From the point of view of Aristotlean logic, (4) and (5) are redundant. 
H.N. do not think so. He mentions Russell's theory of apparent variables :

        (Forall(x)(P(x) -> Q(x)).and.P(a)) -> Q(a)

In other words, (4) and (5) was useful (but not absolutely necessary) in 
that it explicitly instantiating the formula (P(x) -> Q(x) where x is 
universally quantified) with the instant a. He went on to postulate that 
Dignaga's reform of Old Logic is no more that the introduction of Russell's 
theory, i.e. formulating the whole argument into a single statement and 
thus implicitly eliminating (4) and (5). 

        The second section examines the application of logic to the idea of 
SUNYATA. H.N., like R.R., thinks that all the controversies and 
confusion surrounding Nagarjuna can be solve by using symbolic logic so 
as to remove the linguistic component from his discourses. For example, 
the problem of the equivalence (eg. between nirvana and samsara) can be 
solve by rendering his assertion to logic : "when there is an 'x' which 
depends upon 'y', it cannot be said that 'y' is different from 'x'." If 
expressed in logic, it is : Forall(x, y). xRy -> ~(x <> y), i.e. if x is 
related to y, then it is not the case that x is not equal to y. He also went 
on to formalize dependent co-arising (pratitya samutpada) as expressed in the 
Mulamadhymika sastra as

                Forall(x, y).xRy -> ~(x<>y).and.~(x=y)

But wait ... the above can be transformed to (using standard logic)

                Forall(x, y).xRy -> ~~(x=y) .and. ~(x=y)
        =>      Forall(x, y).xRy -> (x=y) .and. ~(x=y)
        =>      Forall(x, y).xRy -> FALSE

By the definition of '->', this means that xRy == FALSE ! What can this 
mean ? H.N. then postulate that SUNYATA == FALSE. (Note that this 
'FALSE' is strictly a logical quantity and readers should not give it the 
usual connotation associated with 'falsehood'. The actual term used in 
H.N. is '0'.) This would be consistent with the definition of SUNYATA, 
that it is that which have dependent-coarising. This may also be another 
reason why the term SUNYATA is used : it denotes "null" or the "empty 

        H.N. also points out the fallacy of the antecedent using the 
following as an example :

"If there is something that is non-void (A), then there probably is 
something that is void (B). However there isn't anything exisiting that is 
non-void (~A). Then where is such a thing as void ? (~B)"

Again, we find the mistake of A-> B .and. ~A -> ~B. 

Next, on the issue of the tetralemma, H.N. thinks that the third and fourth 
alternatives "has substantially no logical meaning". But he went on to say 
that "in the Madhymika school, as things could not be expressed 
absolutely as being and again not understood absolutely as nothing, the 
theory of the Middle way of neither being nor non-being was set forth 
which is thought to carry the same purport as the theory of dependent 
origination."  He concludes this section by noting that if his postulate is 
correct, i.e. SUNYATA = 0, then there is a big problem in that in modern 
two-value logic, '0' does not correspond to anything existent and in fact 
expresses falsehood. He suggests that may be multi-value logic may have to be
called in to resolve this problem. If this is true, then it would certainly be 
another major achievement for Nagarjuna.

        The next section deals with the logic of Dignaga. I do not 
understand enough of the archaic symbolism that he used to be able to 
summarize it. In any case, its outside the scope of this posting ;-) But his 
conclusion on Dignaga's contribution is worth noting.

        "Dignaga denied the existence of universals, and asserted that they 
were nothing but fictions constituted merely by excluding what is other. 
According to him words express only relations or mutual negation; a 
concept is made only by negating what is other than it."

        The above summarizes the two papers plus with some additions 
from T.S. The major thrust of both papers is that a better understanding of 
the philosophy of Nagarjuna if using standard logic the linguistic 
component is eliminated. While this may remove the religious element 
from his discourses, they contend that it will clarify the underlying 
message. As T.S. said, while the Madhymikas gave is no longer in existence, 
their philosophy, i.e. the philosophy of SUNYATA, forms the basis of all the
Mahayanist schools today. Therefore, the approach of H.N. and R.R. may be
necessary to unravel the confusions surrounding such an important philosophy.

with Metta,

W.F. Wong.


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