Some Logical Aspects of Naagaarjunas System

·期刊原文
Some Logical Aspects of Naagaarjuna's System
By Richard H. Robinson

Philosophy East & West
Volumn 6, no. 4(October 1957)
P.291-308
(C) by University of Hawaii Press

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p.291

THE MAADHYAMIKA SCHOOL, founded by Naagaarjua
(2nd century A.D. ), has been known to modern
scholarship since the time of Emile Burnouf, over a
century ago. During the past six decades, it has been
studied by Indian, European, and Japanese scholars,
who have generally conceded that this school is
crucial for the history of Indian philosophy, both
Buddhist and non-Buddhist. Naagaarjuna has been
widely praised as a great dialectician. However, a
large residue of baffement has remained after each
attempt to elucidate the true message of the
Maadhyamikas. This is inevitable in the nature of the
case, since the pioneers have had to grapple with
more or less corrupt texts in Sanskrit, Tibetan, and
Chinese; to compare the Maadhyamikas with their
Buddhist, Naiyaayika, and Saa^mkhya opponents, whose
systems were almost equally ill-known; and to render
the Maadhyamika texts intelligible in terms of
Occidental philosophy.
The most productive period of Maadhyamika
studies commenced with the publication of Th.
Stcherbatsky's The Conception of Buddbist Nirvaa.na
in 1927. The ontological problem, the question of the
Absolute in the Maadhyamika system, then became
central. Louis de La Vallee Poussin, Stanislaw
Schayer, and others debated this theme somewhat
acrimoniously with Stcherbatsky. La Vallee Poussin's
death and World War II interrupted the debate. The
task of translating the Prasannapadaa was continued
by J. W. De long,(1) who also wrote the most lucid of
all articles on the Maadhyamika conception of the
Absolute.(2) T. R. V. Murti's The Central Philosophy
of Buddhism, published in 1955, continued the work of
Stcherbatsky and his opponent-colleagues, and brought
the "metaphysical" phase of investigation to its
point of maximum returns.
The "metaphysical" debate has exhibited extreme
variety of opinion, and the attempt to describe
Maadhyamika as an "ism" has led various people to
call it nihilism, negativism, monism, relativism,
irrationalism, criticism, and


(1)J. J. W. De Jong, Cinq chapitres de Ia.
Prasannapadaa (Paris: Paul Geuthner, 1949).
(2) J. J. W. De Jong, "Le probleme de I'Absolu dans
l'ecole Maadhyamika," Revue Philosopbique,. 1950,
pp. 322-327.

p.292

absolutism. Attempts to find transformulations based
on analogy with Western thinkers have not gone very
far. The most usual comparisons, those with Kant and
Hegel, are not apposite, because Kant's and Hegel's
structures differ too radically from any of the
Indian systems in question.
Several fundamental limitations of the
metaphysical approach are now apparent. It has tried
to find comprehensive answers without knowing the
answers to the more restricted questions
involved--such questions as those of the
epistemological and logical structure of the system.
Synchronic and diachronic considerations have not
been treated separately, with the result that
Naagaarjuna's system has not been clearly
distinguished from Candrakirti's. Writers have
generally taken the Maadhyamika statements out of
context and reshuffled them into some modern pattern,
with the result that the intrinsic structure of
argumentation has not been clearly discerned. An even
deeper weakness of the metaphysical approach is that
it seeks to answer our questions, rather than to
identify Naagarjuna's questions.
The present need is for sectional studies of the
Maadhyamikas, observing the priority of synchronic
studies over diachronic studies, and isolating
classes of problems for detailed inquiry. This is
similar to the recent trend in linguistics, where
more rigorous analysis and more closely controlled
reasoning have captured the field.
One topic which particularly needs separate and
detailed inquiry is the role of logic in Maadhyamika.
Stcherbatsky's views on this subject are based on
Candrakiirti's Prasannapadaa, which is centuries
later than Naagaarjuna and is the product of a time
when Indian logic was far more highly developed than
in Naagaarjuna's time. Murti has a lot to say about
"dialectic," but practically nothing to say about
formal logic. I quote the following passages to
illustrate the opinions on the role of logic which
representative writers have expressed.
1. Notwithstanding the somewhat monotonous
method by which he applies to all the conceptions of
Hiinayaana the same destructive dialectics, he never
ceases to be interesting, bold, baffling, sometimes
seemingly arrogant... However, it is only the
Hiinayaanist and all pluralists in general that need
to be afraid of Nagaarjuna's dialectics. He does not
assail, but extols the idea of the Cosmicaal Body of
Buddha He extols the principle of Relativity, and
destroys through it every Plurality, only in order to
clear up the ground and establish on it the unique,
undefinable (anirvacaniiya) Essence of Being, the
One-without-a-Second. According to the principle
monistic philosophy, consistently applied, all other
entities have only a second-hand contingent reality,they
are borrowed cash. The Maadhyamika denies the validity of
logic, i.e., of discursive conceptual thought, to
establish ultimate truth. On the charge that in doing so
he himself resorts to some logic, he replies that the
logic of common life is sufficient for showing that all
systems contradict one another that and our fundamental
conceptions do not resist scrutiny.(3)

p.293

2. What Naagaarjuna wishes to prove is the
irrationality of Existence, or the falsehood of
reasoning which is built upon the logical principle
that A equals A.... Because two answers, assertion
and denial, are always possible to a given question,
his arguments contain two refutations, one denying
the presence, one the absence of the probandum. This
double refutation is called the Middle Path.(4)
3. Every thesis is self-convicted and not
counter-balanced by an anti-thesis. Why are all views
rejected! What is the principle on which it is done!
Any fact of experience, when analysed, reveals the
inner rift present in its constitution. It is not a
thing in itself; it is what it is in relation to
other entities, and these in turn depend on others.
This process thus proceeds indefinitely and leads to
a regress.(5)

Stcherbatsky maintains that Naagaarjuna
establishes a set of transcendental concepts through
his dialectic. Murti maintains that all theses are
refuted. Stcherbanky equates logic and discursive
conceptual thought. Liebenthal introduces the dubious
notion, not attested in Naagaarjuna's works, that the
rationality of Existence is built upon "the logical
principle that A equals A," despite the patent
contingency of any connection between logical
principles and ontological truths, and despite the
fact that the "logical principle" mentioned is nor
the basis of formal logic, but only a derived
theorem. (It is impossible to derive any of the
logical calculi from this so-called "principle.")
Liebenthal does not ask whether the probandum is a
term or a proposition, nor does he examine the sorts
of predicate which may be affirmed or denied of it.
Murti's statement that "Any fact of experience,
when analysed, reveals the inner rift in its
constitution" is misleading. It leads one to expect
that Naagaarjuna will examine faces of experience
empirically. But Naagaajuna examines, not facts of
experience, but extensional relations between terms,
between concepts and properties ascribed to them by
definition.
Murti's statement that "Every thesis is
self-convicted," besides raising again the classical
paradox of the Liar, is both vague and dubious. It is
not certain whether "thesis" is intended to mean a
proposition or a set of propositions; an assertion or
an inference; a proposition that may contain the
functor of negation or a proposition that does not
contain the functor of negation. Certainly some of
Naagaarjuna's ancient opponents were just as confused
as his modern interpreters, but, if we can reach
clear answers to some questions such as the above, we
may well find that Naagaarjuna was actually saying
something meaningful.
By "Every thesis is self-convicted," Murti may
mean "Every proposition

(3)Th. strcherbatsky, The Conception of Buddbist
Nirva.na (Leningrad: Publishing Office of the Academy
of Sciences of the U.S.S.R., 1927), pp. 46-47, p. 38,
n.3.
(4)"Walter Liebenthal, The Book of Chao (Peking:
Gatholic University Press of Peking, 1948), p.3O.
(5)T. R. V. Murrti, The Central Philosophy of
Buddbism (London: George Allen & Unwin
Ltd,1955),p.136.

p.294

is self-contradictory." Since this is not true of
tautologies, the proposition that "Every proposition
is self-contradictory" is false.
Clearly, the problem requires more precisely
formulated questions, and a rigorous methodology,
with consistent definitions of terms and delimitation
of fields of inquiry. The present article will
attempt no more than a limited contribution to a
limited section of the problem, namely, some
principles and constructions of logic observed in the
Muula-madhyamaka-kaarikas.
The first step toward a formal analysis of
Naagaarjuna was taken almost twenty-five years ago by
the Polish Indologist Stanislaw Schayer. The Polish
school of logicians commenced the scientific study of
ancient, i.e., Greek and Roman, formal logic.
Schayer, under the influence of Jan Lukasiewicz and
his pupils, studied modern logic and proceeded to
investigate ancient Indian logic in terms of it.
Unfortunately, he did not live to provide us with
a survey comparable to Lukasiewicz's Aristotle's
Syllogistic, or I. M. Bochenski's Ancient Formal
Logic, but his articles contain both methodological
principles and some valuable though fragmentary results.
In Ueber die Methode der Nyaaya-Forschurng,(6) he
offers a notational transcription of a stanza from
the Kaarikaas. In Altindische Antizipationen der
Aussagenlogik, (7) he broaches the question of
rules of inference employed by early Buddhist
dialecticians, and examines the Tetralemma (catu.sko.ti)
as a feature of propositional logic. Schayer's
criticisms of Stcherbatsky are incisive and just.
Murti makes no reference to Schayer's logical works.
Professor Hajime Nakamura, of Tokyo University,
took up Schayer's methodology, defending and further
applying it, in "Some Clarifications of the Concept
of Voidness from the Standpoint of Symbolic Logic.(8)
He presents the case for the superiority of modern
scientific, notational logic as an instrument for
investigating Indian logic. Notational statement
avoids the pitfalls and awkwardness of linguistic
statement and rhetorical logic. It does not
necessitate conversion of Indian forms into the
standard forms of traditional Western logic, but
clarifies the traditional Indian structure without
rrequiring reformulation. To Nakamura's points I may
add that modern logic asks a greater range of
questions and hence sharpens the observation of the
investigator.
The rest of Nakamura's article deals with
notationl transcriptions of some Maadhyamika
propositions and inferences, with what these reveal
about
--------------------------
(6)Stanislaw Schayer, Ueber die Methode der
Nyaaya-Forshung. Festshrft Winternitz Leipzig
Otta Harrassaowitz, 1932),pp.247-257
(7)Stanislaw Schayer, "Altindische
Antizipationen der Aussagenlogik." Bulletin
international de l'Academie Polonaise des Sciences et
philologie, 1933,pp. 99-96.
(8)Hajime Nakamura, "Kuukao no
kigo-ronrigaku-teki ketsumei, " Indogaku-bukkyogaku
Kenkyuu, No. 5, Sept., 1954, pp. 219-231.

p.295

the validity of Naagaarjuna's argumentation, and with
the suggestion that emptiness ('suunyataa) equals the
null class.
The present article includes a good deal of
Nakamura's material, which is acknowledged in
passing. However, my conclusions differ somewhat,
and a number of new questions are broached here.
In considering the formal structure of
Naagaarjuna's argumentation, I exclude epistemology,
psychology, and ontology from consideration. Such
extra-logical observations as emerge will be
confined to the concluding paragraphs of this
article.
Basic Theorems and Rules of Inference.

Naagaarjuna's knowledge of logic is about on
the same level as Plato's. It is pre-formal, and
consists of a number of axioms and rules of
inference which he manipulates intuitively, with
great dexterity but also with occasional error.(9)
Sometimes, however, these axioms are stated with
terms so generalized as to be virtual variables.
The three traditional "Laws of Thought" are no
longer considered the bedrock of deductive systems,
but it is still of interest to see whether Naagaarjuna
observes them, since he has been accused of
rejecting rationality.
The principle of contradiction is invoked
constantly throughout the Kaarikaas. It is stated in
general form in two places:
[1] "For entity and negation of entity do not
occur within a unity." (7.30)(10)
[2] "For real and non-real, being mutually
contradictory, do not occur in the same locus."
(8.7)
Applications of the rule with narrower values
for the terms are common:
[3] "For birth and death do not occur at the
same time." (21.3)
[4] "Nirvaa.na cannot be both entity and
non-entity, (since) nirvaa.,na is unconditioned, and
entity and non-entity are conditioned." (25.13)
[5] "For the two do not occur within one
place, just as light and darkness do not."
(25.14)(11)
[6] "He would be non-eternal and eternal, and
that is not admissible." (27.17)
The law of the excluded middle is twice invoked
explicitly:
[7] "Other than goer and non-goer, there is no
third one that goes." (2.8)(12)
___________________
(9)'Cf. R. Robinson, "Plato's. Consciousness of
Fallacy, Mind. 51 (1942), 97-114.
(10)"Number refer to chapter and 'sloka of
Louis de La Vall'ee Poussin, ed., Muula-madhyamaka-
kaarikaas, Bibliotheca. Buddhica. (St. Petersburg:
Imperial Academy of Sciences, 1903-1913), vol. IV.
(11)Nakamura,op. cit., p. 227a.
(12)Nakamura,op. cit., p. 228a.

p.296

[8] "Other than goer and non-goer, there is no
third one that stays." (2.15)
In other examples, "tertium non datur" is tacitly
assumed.
[9] "He who posits an entity becomes
entangled in eternalism and annihilism, since that
entity has to be either permanent or impermanent."
(21.14)
Since Naagaarjuna's argumentation relies on
numerous dichotomies, the principle of contradiction
is necessary to most of his inferences.
The law of identity (stated as an equation
rather than an implication in the passage of
Liebenthal's quoted above) is not explicitly stared
anywhere in the Kaarikaas. This is not surprising,
as the law would be meaningless to anyone who did
not possess a sophisticated notion of implication,
and would nor be of much use to anyone who was not
formulating a deductive system of logic. In this
connection, one should note Bochenski's statement,
"While we find no principle of identity in the
preserved writings of Aristotle, a whole book of
Metaphysics (III) is
devoted to the principle of contradiction."(13)
The hypothetical syllogism is Naagaarjuna's
principal form of inference. In is full form, it is
an argument composed of three propositions, but
Naagaarjuna, like other Indian dialecticians, values
brevity above formal completeness, and so leaves one
or two propositions of the inference unexpressed
whenever the reader can supply them from the
context. The two valid varieties of the hypothetical
syllogism---modus ponendo ponens, with affirmed
antecedent, and modus tollendo tollens, with denied
consequent-both occur, with sub-varieties, in the
Kaarikaas. However, modus tollens is the commoner.
A. Modus ponens
[11] "If time depends on entities, then wherever
there is no entity, there is no time. No
entity exists; (thus, if time depended on
entities) time would not exist anywhere."
(19.6)
This may be represented in notation as follows:
Let p = "time exists" q = "entity exists"

pq.. °q°p; °q; ★°p
The first half-verse states the rule of
denying the consequent and shows that Naagaarjuna
was aware to some degree of the principles of
conversion In the second, the antecedent of the
converted implication°q°pis affirmed, and the
consequent is accordingly affirmed.

(13)I. M. Bochenski: Ancient Formal Logic
(Amsterdan: Norrh-Holland Publishing Company.
1951) p.38.

p.297

It is to be noted that the antecedents
affirmed by Naagaarjuna are negative propositions.
B. Modus tollens
The propositional form is pq; °q; ★°p
[12] "If cause-of-form existed disjoined from form,
then there would be an effectless cause; but
there is no effectless cause; (therefore,
cause-of-form does not exist disjoined from
form.)" (4.3)
[13] "Space does not occur previous to the
mark-of-space; if it existed previous to its
mark, it would involve the absurdity of its
being markless. (But no entity occurs without
its mark; therefore, space does not.) (5.1)
[14] "If present and future depend on the past,
then present and future should exist in past
time. (But they do not; therefore, they do nor
depend on past time.) " (19.1)
[15] "Since no unconditioned entity occurs
anywhere, if nirvaa.na were an entity,
nirvaa.na would be conditioned; (but nirvaa.na
is by definition unconditioned; therefore,
nirvaa.na is not an entity ). (25.5)
[16] "Nor does it obtain that the self is
other than the appropriation; for, if it were
other, it should be perceived without
appropriation; but it is not (so) perceived."
(27.7)
Naagaarjuna states the law of conversion to
which these inferences conform in 19.6 (example
(11), above).
C. Fallacy of the antecedent
In a number of instances, Naagaarjuna negates
the antecedent, thus violating the law of
conversion. The propositional form of this fallacy
is:

pq; °p; ★°q

Since Aristotle it has been recognized that this
fallacy contains all other fallacies.(14)
[17] "If fire and fuel were separated from each
other, fire, which is other than fuel, might
catch hold of fuel; (but fire does not occur
separate from fuel; therefore, it is false
that fire, which is other than fuel, catches
hold of fuel)." (10.7)
[18] "If something non-empty existed, then there
might be something termed empty; there is no
something non-empty, and so nowhere does there
exist a non-empty something." (13.7)(15)
[19] "If any non-arisen entity occurred anywhere,
then it might arise; but, since it does not
exist, the entity cannot arise." (7.17)(16)
---------------------------
(14) Bochenski, op. cit., pp. 35, 100.
(15) Nakamura, op. cit., p. 228b.
(16) Nakamura, op. cit., p. 229a.

p.298

Nakamura, in the article cited, advances the
 suggestion that these examples are fallacious from
the standpoint of traditional formal logic, but
valid in terms of the Boole-Schroder logical
algebra. If so, this would be of great moment both
for Naagaarjuna and for logic. Let us transcribe the
last three examples, then, and test this view.
[18] Let a = "something," b = "empty
ab≮0..ab≮0; ab=0; ★ab=0
ab=0is the contradictory ofab≮0but not
ofb≮0. Thus it is the antecedent which negated,
and an indeterminacy ensues. This inference is just
as wrong in notational as in rhetorical logic.
[19] Let a = "entity, " b = "arising."

ab≮0..ab≮0; ab=0; ★ab=0
The transcription reveals that (19) is
formally identical with (18) and therefore
fallacious for the same reason.
[17] Let a = "fire," b = "fuel," p = "fire catches
hold of fuel."

ab≮0..p, ab=0; ★°p

The transcription shows that the propositional
form (though no: the term-structure) of (17)
is identical with that of (18) and (19), and
that it, too, violates the law of conversion.
Instances of the categorical syllogism are of
comparative interest, but rather trivial otherwise.
[20] "The Buddha declared that all mis-taken
dharmas are illusory; All sa^mskaaras are
mis-taken dharmas; therefore, they are
illusory. (13.1)
This is the opponent's argument, not
Naagaarjuna's. It conforms to the mood
"barbara," MaP.SaM..SaP.
[21] "This action is of the nature of the passions,
and the passions do not exist in reality; if
the passions do not exist in reality, action
cannot exist in reality." (17.26)
This conforms to the mood "celarent, "
[MeP.SaM..SeP].
The protasis in the second sentence merely
repeats the second premise and establishes that an
inference is intended. It is not necessary to the
inference.

Definitions and Axioms
The foundation of Naagaarjuna's system is a
set of definitions, in which certain properties
(lak.sa.na) are ascribed to a term. For example:
pratiityasamutpaada (dependent co-arising)
[22] Dependent co-arising is without cessation,
without arising, without annulling, without
ever-existence, without oneness of object,

p.299

without plurality of object, without arrival,
without departure (1. vandana).
[23] What is dependent co-arising, that we designate
emptiness. (24.18)
[24] He who sees dependent co-arising sees
suffering, origin, cessation, and way, (24.40)
tattva (reality)
[25] The mark of reality is that it is not
dependent on another, is calm, is not
figmented by fictions, is free from
imaginings, and without plurality of object.
(18.9)
 nirvaa.na
[26] That which is not abandoned, not obtained,
not annulled, not ever-existent, not
extinguished, and not arisen, is called
nirvaa.na (25.3)
[27] That which, when embodied (having
appropriated) or dependent, is the existent
that wanders to and fro; the same, when free
from appropriation and non-dependent, is
called nirvaa.na. (25.9)
suabhaava (own being)
[28] For own-being is unmade and not dependent
on another. (15.2)
[29] For the complement (alter-being) of a nature
(own-being) never occurs. (15.8)
Svabhaava is by definicion 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 svabhaava is by
definition unconditioned, not dependent on other
entities, and not caused. Thus the existence of a
svabhaava is impossible.
All subjects of negated propositions in the
Kaarikas belong to the svabhaava class.. The basic
argument is that if the variables of a proposition
art null, the proposition is not existentially true.
It cannot be inferred from this that, if the
variables are not null, the proposition is
existentially we, but the contingency that it might
sometimes be existentially true can be inferred. The
statement on emptiness and cogency (example 60)
states explicitly that a certain set of propositions
is true under certain conditions.
Negation
It is necessary to reiterate here that
epistemological questions are excluded from present
consideration, and that the question is not how
absences are cognized, but how the logical functor
of negation is understood.
A number of passages reveal that Naagaarjuna
maintained a concept of negation which at first
sight seems nonsensical.
[30] "If entity (presence) is not established, then
non-entity (absence)

p.300

is not established either, since by non-entity
people mean that alterentity (complement) of
entity." (15.5)
[31] "Independent of the pure there is nothing
impure in dependence on which we may posit the
pure. Therefore, the pure does not occur
either." (23.10)
[32] "If self, purity, permanence, and felicity
do not occur, then nonself, impurity,
impermanence, and suffering do not occur
either." (23.22)
[33] "If nirvaa.na is not an entity, it cannot be a
non-entity; where there is no entity, there is
no non-entity." (25.7)
[34] "Since the conditioned is not established, the
unconditioned cannot be established." (7.33)
[35] "If 'both eternal and non-eternal' were
affirmed, then 'neither eternal nor
non-eternal' might be affirmed." (27.18)
These examples seem to maintain that the
presence of the negation of any variable implies the
presence of that variable. However, it is more
likely that Naagaarjuna was thinking of a finite
extension and its complement, and excluding null and
universal terms from consideration. An entity
(bhaava) is by definition conditioned, and neither
universal ('saa'svata) nor null (uccheda). It has a
complement which is conditioned in the same way
except for the property of being absent when the
entity .is.present.A pacaphrase of (33) may
elucidate this.
"If nirvaa.na is not the finite extension of a
set of properties, then nirvaa.na cannot be
the finite extension of the absence of a set
of properties; in cases where a finite
extension does not exist, the complement of
that finite extension does not exist either."
The term "nature" (prak.rti equals svabhaava)
has no complement. (36) "If (anything's) existence
is due to its nature, its non-existence will not
occur, since the alter-entity (complement) of a
nature never occurs." (15.8)
That is, a nature is the class of properties
attributed to a class of terms Since they are
necessarily present throughout the range of the
subject or class of subjects, cases of their absence
do not occur.
If the extension of purity is the null class
or the universal class, then no part of the
universal class constitutes the class of pure
things, and no other part constitutes the class of
impure things.
Quantification
Many of Naagaarjuna's terms are explicitly
bound, and, since all his propositions seem to be
general it is necessary to supply quantifiers in a
number of propositions where they are not given.

p.301

Universal quantifications are effected both by
the functor all (sarvam) and by negation of an
existential functor (ka'scid, kadaacana, etc.)
[37] "For among existents, impermanence never does
not occur." (21.4)
[38] "Since no non-dependently-arisen dharma occurs,
no non-empty dharma occurs." (24.19)
[39] "Origin and dissolution do not occur without
entity." (21.8)
[40] "For nowhere does there occur any
unconditional entity." (25.5)
[41] "Since an entity does not (occur) without
aging-and-death." (25.4)
Existential quantifications are denied by
Naagaarjuna, since all the terms he is
repudiating are conceived as essences, and it is
absurd to maintain that the essence of a thing pertains
only to part of the thing.
[42] "If one part is divine and one part is human,
he would be both eternal and non-eternal; and
that is impossible." (27.17)
[43] "If one part were finite and the other part
were infinite, both finite and infinite would
pertain to the world; and that is impossible."
(27.26)
[44] "Nor does it obtain that one part of the body
(upaadaana) perishes, while the other part
does not perish." (27.27)
Assuming that bones do not decay, "one part of
the body perishes and one does not" is not an absurd
statement. But manifestly Naagaarjuna's point is not
the denial of common-sense assertions, but the
denial of the concept of entity (bhaava) and
own-being (svabhaava) which is commonly imposed on
the terms of common-sense assertions. The axiom is
"that is not one (entity) of which contradictory
attributes are predicated."(17)
Quantity has something to do with the two
extremes (the ever-existent and the annulled).
[45] "Ever-existence-that 'that which exists by
own-being does not' not exist'-and
annulment--that 'it does not exist now but
it existed formerly'are absurd." (15.11)
Eternalism asserts that "all A is B," while
annihilism asserts that "some A is B and some A is
nor B." Both views are rejected on axiomatic
grounds. The significant point is that the
distinction is one of the quantity of the terms.

The Tetralemma
A typical piece of Buddhist dialectical
apparatus is the tetralemma (catu.sko.ti). It consists
of four members in a relation of exclusive
disjunction ("one of, but not more than one of,'a,'
'b,' 'c,' 'd,' is true"). Buddhist dialecticians,
from Gautama onward, have negated each of the
alternatives,
--------------
(17) This is not quoted in the Kaarikaas.

p.302

and thus have negated the entire proposition. As
these alternatives were supposedly exhaustive, their
exhaustive negation has been termed "pure negation"
and has been taken as evidence for the claim that
Maadhyamika is negativism. There is thus an
extra-logical interest in analyzing the form of the
catu.sko.ti.
[46] "Everything is either true, or not true, or
both true and not true, or neither true nor
not true; that is the Buddha's teaching."
(18.8)
[47] "He is not to be called empty, nor non-empty,
nor both, nor both-not; but for the sake of
designation he is called...." (22.11)
[48] "It is not said that after final cessation the
Blessed One is, or that he is not, or that
both, or that neither." (25.17)
[49] "If the man is the god, he is thus eternal; the
god would be unborn, since the eternal is
unborn. If the man is other than the god, then
he is non-eternal;
If the man is other than the god, succession
does not obtain.
If one part is divine and one part is human,
then he is both eternal and noneternal; and
that is not possible.
If 'both eternal and non-eternal' were
asserted, then 'neither eternal nor
non-eternal' might be asserted." (27.15-18)
The four alternatives, as expressed before
Naagaarjuna negates them, are given in example (46).
The formula is:
[Ax v °Ax v Ax.°Ax v°(Ax). °°(Ax)]
It is evident that the first two alternatives
ate to be quantified universally for 'x.' Example
(49) quantifies the third alternative existentially
for 'x. "Some x is A and some x is not A." I propose
to interpret the fourth alternative as: "No x is A
and no x is not A." This is true when x is null.
Schayer(18) transcribes the fourth alternative
[°p.°(°p)l "not-p and not-not-p." This is on the
assumption that the four alternatives are
propositional functions. However, it is apparent
that negations and conjunctions of the basic
proposition do not transcribe (49), and,if the terms
of the other examples are quantified in the same
way, do not transcribe them. "Not-p" is the
contradictory of "p," but "some x is A" is not the
contradictory of "some x is not A."
Nakamura(19) interprets the tetralemma
algebraically as: "a," "-a," "a-a" and "-(a-a)."
Since "a-a" equals "0" and "-a-a" equals "O," the
third and fourth alternatives are redundant and
senseless. However,if the subject
-------------------------
(18) Aussagenlogik, p. 93.
(19) Op. cit., p. 229.

p.303

is not totally distributed in either conjunct in
the third alternative, then this form need no
longer be considered redundant.(20)
Naagaarjuna's reason for negating each of the
alternatives is that its terms are null, as defined
by his opponents. The fourth alternative is true
when one of its terms is null, but not false when
the other term is non-null. It is probably for this
reason that Naagaarjuna rejects the fourth
alternative.
The tetralemma resembles the four Aristotelian
forms in some ways. Both sets comprise propositions
constructed from two terms and the constants
(functors) "all," "some," and "not." However, the
third and fourth alternatives of the tetralemma are
not simple propositions, but conjunctions. The
comparison may be tabulated as follows, using the
Boole-Schroder notation.

ARISTOTELIAN FORM TETRALEMMA

A ab=0 1 ab=0
E ab=0 2 ab=0
I ab≮0 3 ab≮0.ab≮0(conjunction of I and O forms)
O ab≮0 4 ab=0.ab=0 (conjunction of E and A forms)

Dilemmas
It is not surprising to find numerous dilemmas
in the works of an author reputedly "bold, baffling
and seemingly arrogant" The common form is the
"simple constructive" onepq.rq:pvr:q
"r" is generally "not-p," so that "p or r" becomes
"p or not-p."
The examples are illustrative but not exhaustive.
[50] "If own-being exists, other-being belongs
to nobody; if own-being does not exist,
other-being belongs to nobody." (13.4)
[51] "When nature exists, alteration belongs to
nothing; when nature does not exist,
alteration belongs to nothing." (15.9)
[52] "If the effect is born from the conjunction
of cause and preconditions, and if it exists
in the conjunction, then it cannot be born
from the conjunction; if the effect is born
from the conjunction of cause and
preconditions, and if it does not exist in the
conjunction, then it cannot be born from the
conjunction." (20.1,2)
[53] "If the cause is void of effect, it cannot
produce effect; if the cause is not void of
effect, It cannot produce the effect." (20.16)
-----------------------
(20) Stcherbastsky The Conception of Buddhist
Nirvaa.na, p.90, incidencally quantifies. the third
alternative of a tetralemma., but does nor remark on
what he has done. "He denies that they are identical
(with their causes), that they are different from
them, or that they are both (partly identical and
partly non-identical).

p.304

[54] "If effect is endowed with real own-being,
cause produces no effect; if effect is not
endowed with real own-being, cause produces no
effect." (20.21)
[55] "Origin and dissolution of the empty do not
take place; origin and dissolution of the
non-empty do not take place." (21.9)
[56] "When the latter is extinguished, the former
entity is not cogent; when the latter is not
extinguished, the former entity is not
cogent." (21.18)
[57] "If the world were finite, there could not
be another world; if the world were infinite,
there could not be another world." (27.21)
Note that this "simple constructive" form
consists of two implications, one of whose
antecedents must be affirmed. The above examples
illustrate Naagaarjuna's use of modus ponens. They
observe the rule of affirming the antecedent, and so
are formally correct. The designation "simple
constructive" may seem inappropriate to dilemmas
whose consequents are all negations, but
"constructive" refers to the propositional
structure, and not to the mood of the terms.
Naagaarjuna eschews affirmation of terms, but he
does afffirm propositions.
The next example, though of the same
propositional form as the preceding ones, is
exceptional in that the first "horn" is the
opponent's objection, while the second one is
Naagaarjuna's reply.
[58] (Opponent): "If all this (world) is empty, then
there is no arising and perishing, and no
one's nirvaa.na through abandonment or
cessation is asserted.
(Naagaarjuna) : "If all this (world) is
non-empty, then there is no arising and
perishing, and no one's nirva.na through
abandonment or cessation is asserted."(25.1, 2)
The opponent wishes to deny the
antecedent--emptiness of everything--and
advances his implication in the expectation
that the consequent will be denied by
Naagaarjuna, who, however, advances a
counter-implication with contrary antecedent
but identical consequent.
The way of escape from the consequences of
these dilemmas is to "take them by the horns,"
to repudiate the definitions which they
presuppose. In so doing, one rejects the whole
set of propositions. which Naagaarjuna calls
"views" (d.r.s.ti), and arrives at the meaning
of emptiness.
[59] "Emptiness was declared by the Victors as the
expeller of all theories; they declared that
those for whom emptiness is a theory
(d.r.s.ti) are incurable." (13.8)

p.305

Emptiness and Nullity
Most discussion of 'suunyataa has centered on
whether it is a "positive or a "negative" concept,
on whether it has a transcendental significance or a
nihilist one. La Vallee Poussin held that the
central conception of Maadhyamika is an "absolu a
base d'inexistence," which theory Stanislaw Schayer
underwrote. (20) D. T. Suzuki says,(21). but we must
remember that the Mahaayaana has its positive side
which always goes along with its doctrine of
Emptiness. The positive side is known as the
doctrine of Suchness or Thusness (tathataa). The
La^nkaavataara is always careful to balance
'Suunyataa with Tathataa, or to insist that when the
world is viewed as 'suunya, empty, it is grasped in
its suchness. Naturally, such a doctrine as this
goes beyond the logical survey based on our
discursive understanding as it belongs to the realm
of intuition."(22)
In other words, this solution of the riddle
doesn't make sense. Even though we were to admit
that some nonsense is meaningful, attempts to blame
"discursive understanding" for failure to answer the
unanswerable would still be suspect prima facie.
Questions should not be pronounced rationally
insoluble until the full range of rational
possibilities has been considered. It is doubtful
whether "positive" and "negative" have anything to
do with the meaning of "emptiness," except as
signalling emotional acceptance or rejection. Nor
are we further ahead for the knowledge that
emptiness is transcendental, or nihilist, unless we
know the configuration of qualifications within
which such concepts have meaning.
The possibilities of a formal, non-intuitive
definition of emptiness deserve exploration. One
such definition, suggested by Nakamura,(23) is that
emptiness equals the null class. The same author,
however, suggests that other possibilities are
worthy of consideration.
My interpretation is one not listed by
Nakamura, and derives from the following key
passage.
[60] "For that of which emptiness is cogent,
everything is cogent; for that of which
emptiness is not cogent, nothing is cogent."
(24.14) Here "everything" means "all mundane
and transmundane dharmas," that is, "all true
predicables in the Buddhist domain of
discourse." It manifestly does not mean
predications about rabbithorns and
tortoise-hairs.
--------------
(21)Stanislaw Schayer, "Das mahaayaanistische
Absoluturm nach der Lehre der Maadhyamikas" Orien-
talische Literaturezeitung,1935,p.413.
(22) D. T. Suzuki Studies in the Lankavatara
Sutra (London: George Routledge & Sons, Ltd., 1930),
p.446.
(23) Op. cit., p. 230.

p.306

Let x= "everything" (all mundane and
transmundane dharmas), A = "empty," and B = "is
cogent." The transcription then reads:
(x).AxBx. Ax°Bx
Thus "x is empty" and "x is cogent" are equivalent.
(24)
If we substitute "... is cogent" for "... is empty"
wherever the subject is a "dharma," the result is a
list of propositions which are basic Buddhist
doctrines and which are not in the least "nihilist."
Another key passage is:
[61] "We declare that what is dependent co-arising,
that is emptiness; it serves as a designation;
it is identical with the Middle Path." (24.18)
Dependent co-arising is emptiness, and
therefore it is cogent. Emptiness is by
definition "absence of own-being (svnbhaava)."
The entire point of Naagaarjuna's argument is
that the class of entities that possess
own-being is null. Thus the class of empty
phenomena, pratiitya-samutpaada, is the
complement of the own-being, or null, class.
The "emptiness" class has "designations" as
members, and some designations are cogent Thus
the emptiness class is not null, but is
co-extensive with the universal class.
Further Logical Questions
A goodly number of topics and examples have
not been mentioned here. My examples are all from
Naagaarjuna's Muula-madhyamaka-kaarikaas. His other
works, particularly the Vigrahavyaavartanii are
important, too. It would also be worthwhile to
examine Aaryadeva's writings and the commentaries
separately, to elucidate L. de La Vallee Poussin's
statement that "There are Maadhyamikas and
Maadhyamikas."(25) Questions in the comparative
field have been ignored here, except for occasional
references to Greek logic, though the comparison of
forms and principles instanced in Naagaarjuna with
Indian theoretical logic is exceedingly important.
Even within the domain of monosystemic
analysis, many topics have been ignored here. I have
confined investigation to inferences of the primary
rank, though the Kaarikaas exemplify architectonic
structures of a dozen or more primary inferences. I
have ignored the possibility of a modal logic in
Naagaarjuna, though certain words could be construed
as modal functors. I have not gone into the arguments
which are concerned with transitive
--------------
(24) The proof of equivalense is omitted. It may be
effected by substituing  Bx  Ax  for 
-Ax  -Bx 
(25) Harvard Journal of Asiatic Studies, III, (1938).
150.

P.307

and reflexive relations, though if one could
separate the metaphysical from the logical in these
statements they would probably throw a good deal of
Light on Naagaarjuna's concept of identity. This
article has made relatively slight use of the
resources of modern logic, but it is possible to
transcribe the Kaarikaas entirely, chapter by
chapter, into logical notation, thus bringing to
light formal features which do not appear from the
consideration of examples taken out of context and
listed topically. In short, the logical analysis of
Naagaarjuna is far from complete.
Philosophical Afterthoughts
There is no evidence that Naagaarjuna "uses
logic to destroy logic." He makes mistakes in logic,
but does not deny any principles of logic. He
asserts that a certain set of propositions-the
Buddhist doctrine--is true under a certain
condition, that of emptiness, and false under
another condition, that of own-beingness. It is not
right to say that "Naagaarjuna denies the validity
of logic... to establish ultimate truth." He simply
refutes all theories of own-being. This refutation
ipso facto establishes right understanding. This
does not constitute "irrationalism," since it merely
refutes by rational means a manifestly irrational
notion.
It is not meaningful to call Naagaarjuna's
system "negativism" because he uses the functor of
negation frequently, unless one is willing to call
Plate's or Hume's philosophy "conjunctivism" because
they use "and" frequently.
With at least some wrong questions obviated,
philosophical inquiry can pursue genuinely
productive ones. Schayer's remarks that existence
and entity are ineluctably spatial and extensional
in Indian thought should be heeded.(26) We should
remember that early Indian thinkers had great
difficulty. in distinguishing concretions from
abstractions. We are prone to forget that our term
"existent" comprises a multitude of abstractions,
and that our predecessors struggled hard to arrive
at the conception of intangibles, which is
explicitly ruled out of consideration by some Indian
schools. Naagaarjuna's contemporaries were infintely
less sophisticated than Kant's. Their problems were
simpler, their concepts were fewer, and their
devices for handling concepts were much cruder. It
is not that they were worse thinkers than the
moderns, but simply that they were earlier. It is in
this milieu that Naagaarjuna's reasoning should be
appraised. I believe that when this environment has
been analyzed and taken into account, his stature
will appear greater, and his system much less
barbarous and baffling than it has seemed hitherto.
The 'Suunyavada is in fact a kind of theory of
fictions. The concept of
-------------------------
(26) Op. cit., OLZ. 1935.pp.405-406.

P.308

designation (praj~napti) provides a way of handling
abstracts without concretizing them, or assigning
ontological value to them. This understanding of the
process of abstraction is perhaps the greatest
achievement of Indian Buddhist philosophy. The
obstinate resistance that this theory met in India
is due to the realist schools' belief that all the
parts of a true statement must be true knowledges
corresponding to existent objects.
The questions asked by modern investigators of
Naagaarjuna have often been too fancy, too abstruse,
and not specific enough to permit piecemeal
verification. But surely,in the "Age of Analysis,"
we should be able to free ourselves from Baroque
philosophical methods.The most promising comparisons
are not between Kant and Hegel and the Indians,but
between Aristotle's predecessors,particularly the
Eleatics and Plato,and the Indians. We could learn
much from the best modern studies on the
Pre-Aristotelians.
It is also worth while to compare Indians
thinkers and Scholastics.Naagaarjuna, for
instance,could well be compared with William of
Ockham, since his system bears certain resemblances
to Nominalism,and it would be valuable to study in
detail the Indian parellels to the controvesy about
universals.