By Richard H. Robinson

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


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 wwwwwwwwwwww (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 wwwwwwwww (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" upq.. qڡp; q; pv 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 implicationuqڡpvis affirmed, and the consequent is accordingly affirmed. wwwwwwwwwww (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 upq; q; pv [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: upq; p; qv 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 A 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 ab0..ab0; ab=0; ab=0 uab=0vis the contradictory ofuab0vbut not ofub0v. 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." ab0..ab0; 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." ab0..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," uMaP.SaM..SaPv. [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 ab0 3 ab0.ab0(conjunction of I and O forms) O ab0 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" oneupq.rq:pvr:qv "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: u(x).AxBx. AxڡBxv 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 u Bx Ax v for u -Ax -Bx v (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.