On the Formal Arguments of the Akutobhaya

JOSEPH WALSER  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA INTRODUCTION Though the Madhyamaka school of Buddhism begins with Nagarjuna’s   a,  the world of Madhyamika with which most Mulamadhyamakak arik scholars are familiar begins with Buddhapalita (ca. 500 C.E.). Western scholars, for the most part, have been so accustomed to looking at early Madhyamika through the lens of the Buddhapalita – Bhavaviveka – Candrakırti debates on logic and method, that they tend to overlook the Madhyamika commentaries written prior to that debate – as if these earlier commentaries did not take a stand on Madhyamika doctrine and apologetics. There are only two such pre-Buddhapalita commentaries  a extant: the Chung-lun, by Vimalaks. a (or on the Madhyamakakarik _ Pingala), translated into Chinese by Kumarajıva in 5th century C.E.,  ostensibly by N and the Akutobhaya, agarjuna himself,1 translated into Tibetan in the 9th century under the patronage of King dPal lha bstan po by a translation team of the Indian Madhyamika, Jn~anagarbha and the Tibetan monk, kLu’i rgyal mtsan. Of these two commentaries, only the latter takes a stand on the syllogistic structure of Nagarjuna’s thought. Western scholarship on the Akutobhaya is scant. Max Walleser (1911) translated the text into German, but did not comment on it beyond his four page “forward”. In 1986, C.W. Huntington wrote a dissertation on  and created an edited edition the text-critical issues of the Akutobhaya, of the work. While his dissertation is in many ways invaluable, it devotes a sum total of two paragraphs to issues of doctrine and method  in the Akutobhaya. While I have no intention of entering into, much less settling, the  _ post – Buddhapalita svatantrika versus prasangika debates, I do believe that the Akutobhaya commentary can give us a picture of Nagarjuna’s logic that is perhaps closer to Nagarjuna’s own world view than can the commentaries of post – Dignaga India. In the following, I will attempt to show the ways that the formal argumentation of the Akutobhaya differs from that of post – Dignaga logic and seems to conform more closely to an earlier standard set by the early Nyaya and Sam . khya Journal of Indian Philosophy 26: 189–232, 1998. c 1998 Kluwer Academic Publishers. Printed in the Netherlands. 190 JOSEPH WALSER schools of logic. The result of this difference in logical methodology is subtle, but nevertheless has ramifications for Madhyamika doctrine. Since this article contrasts the formal logic of the Akutobhaya with that of the better known (post-Dignaga) commentaries on the   a,  I will first discuss the characteristics of these Mulamadhyamakak arik commentaries. In his commentary on the first verse of Nagarjuna’s text, Buddhapalita gives the following explanation to the statement, “things do not come into being from themselves”: _ po) were to arise, the arising of that entity would be Here, if some entity (dnos either from itself, or from another or from both – i.e., (from) the self and other; or would be judged2 to arise without a cause. When examined from all aspects [each point of view] is (still) not acceptable (mi h. thad). Why? “From itself” (bdag las)  has the meaning of saying “from its own self” (bdag n~id las = atmakatah . ). There (in the case of) some entities, there is no arising in its own self (bdag gi bdag n~id   la = atmakah . atmanah . ) because the arising of things [then] becomes pointless and because arising would [then] be endless. Thus, in the case of entities which exist by virtue of themselves another arising would be pointless. If another arising also exists [then] because there would never not be arising it is also not acceptable. Therefore, there are no such entities that arise in themselves.3 This seemingly innocuous explanation would become the focal point of a debate over the “correct” Madhyamika method of explanation that continues to occupy scholars today. The debate has been well rehearsed in a number of sources from Stcherbatsky onward,4 and I will present only the highlights here. The trouble begins in the 6th century,5 when Bhavaviveka objects to Buddhapalita’s explanation because he a) gives neither a reason nor an example for his argument and hence fails to employ a standard syllogistic form, b) does not refute the opponent’s possible objections, and c) he merely shows the negative consequence of one thesis thereby leaving open the possibility that the opponent might assume that the Madhyamika affirms its opposite.6 Bhavaviveka’s subcommentator, Avalokitavrata indicates that it is Bhavaviveka’s style of commentary that is traditional to the Madhyamika and Buddhapalita’s that is unusual. ‘Other’ refers to the elder (Sthavıra, gNas tran) Buddhapalita who is other than most of the many commentators on this treatise [on the Middle Way] – ranging from the honorable master [Nagarjuna] himself, the Elder Buddhapalita, Chandrakırti, Devasharma, Gun. ashirı, Gun. amati, and Sthiramati through to the master Bhavaviveka.7 In defending Buddhapalita against Bhavaviveka’s first criticism, Candrakırti claims that a Madhyamika does not need to, and indeed should not use an independent syllogism. His reasons for this are twofold. First, proper use of a syllogism requires that the subject and the predicate (of the thesis), the reason and the example, must each be acknowledged as existing by both the proponent and by the  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 191 opponent. The second objection is a corollary of the first; the object under discussion must be validly cognized by both parties. In order to properly argue the Madhyamika position, according to Candrakırti, one _ must use either a reductio ad absurdum (prasanga) argument or else an “other approved syllogism”. The difference between the two is that a _ is an argument without a formal structure (no thesis, reason, prasanga or example).8 An “other approved syllogism” is one that contains the proper members, but its reason and example are not necessarily accepted by the proponent, while they must be accepted by the opponent. While both syllogisms and reductio ad absurdum arguments existed well before the time of Nagarjuna, the logical theory which Bhavaviveka and Candrakırti take for granted was developed long after Nagarjuna. While Candrakırti and Bhavaviveka disagreed over whether or not a Madhyamika should use a syllogism, they did agree on what constituted a proper syllogism in the first place. Their disagreement was firmly grounded in the logical theories of Dignaga (480–540 C.E.). Though Dignaga’s system is difficult to summarize, there are two aspects of his thought that are relevant to the Bhavaviveka – Candrakırti debate. The first is Dignaga’s criteria for judging the formal validity of an argument. According to Dignaga, a syllogism should have three _ characteristics: a) the sign of the reason (linga) should be present in the subject of the thesis, b) the sign of the reason should be present in similar examples, c) the sign of the reason should be absent in dissimilar examples. That Bhavaviveka adheres to these criteria is evident from his mention of them in his works. However, for Bhavaviveka only the first two of these marks are important for an inference. It is the Madhyamika’s objective to prove that nothing exists ultimately – hence there can be no counter-example.9 Thus, for Bhavaviveka (following Dignaga’s criteria) a proper syllogism is one where there is a thesis  consisting of a locus (paks. a) and something to be established (pratijna)  (sadhya) in regard to that locus. Next comes a reason (hetu) consisting _ of a quality (linga) that must be both present in the paks. a and the   sadhya. Finally, there must also be an example (dr. s. .tanta) in which the  co-occurence of what is asserted in the reason (hetu) and the sadhya are generally accepted. I will take as a model of this kind of syllogism Bhavaviveka’s syllogism adduced for MMK 1.1:  do not originate from their causal [Thesis:] In ultimate reality, the inner ayatanas conditions, [which are] different [from them], [Reason:] because they are different [from those causal conditions]  [Example:] just as a jar [is different from the casual conditions of the inner ayatanas and so does not originate from them].10 192 JOSEPH WALSER Thus, when Bhavaviveka says that Buddhapalita’s arguments lack a reason he means, presumably, that the reason that Buddhapalita does give is not a proper reason according to Dignaga’s definition. The impropriety of the reason is because the subject of the thesis is “things”, and “pointlessness and endlessness” are not properties acknowledged to be present in “things”. On the contrary, “pointlessness” and “endlessness” are entailed in the contrary of the predicate of the thesis. In other words, if it were the case that any subject (“things” “balloons” “mobsters” etc.) arose from themselves, such an arising would be pointless and endless. Therefore the opposite of the counterfactual must be true – namely that nothing arises from its own self. On the other hand, in the alternative syllogism which Bhavaviveka offers, the reason can be said to be a property of the subject. From the standpoint of Western logic, the problem only seems to _ be a pseudo problem. What Bhavaviveka calls a prasanga argument is little more than a negative reductio ad absurdum argument with an unstated sub-argument. Once the thesis of the sub-argument is stated, the difficulties that Bhavaviveka points out are no longer problems. Yet, this does not really solve the problem for Bhavaviveka – as Candrakırti is quick to point out. Dignaga is also credited with making the distinction  anum   between making an inference for one’s self (svarth ana) and making  anum   an inference for someone else (pararth ana). He claims that the inference for another is merely expressing what one has found out to be true for oneself. Both Bhavaviveka and Candrakırti invoke this rule in criticizing the arguments of others. This rule forms the basis for Candrakırti’s claim that the Madhyamika cannot use a syllogism because what is true for a Madhyamika [namely that all things are empty] will not be accepted as true for the opponent. Either the opponent’s thesis or reason will appeal to something that is assumed to exist intrinsically or the Madhyamika will appeal to something’s lack of intrinsic existence. Either way there can be no commonly accepted thesis or reason on which to build an independent inference. Not all of Bhavaviveka and Candrakırti’s logical assumptions come out of Dignaga. One tenet which Bhavaviveka and Candrakırti hold in common as being central to Madhyamika philosophy is the belief that Madhyamika arguments negate a series of propositions without affirming their opposites. To explain this, Bhavaviveka borrows (and perhaps 11 alters) a distinction from the Mımam . sakas concerning negation. Bhavaviveka’s explanation occurs in his commentary on chapter 1   a.  verse 1 of Nagarjuna’s root text, the Mulamadhyamakak arik  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 193 The negation, “not from themselves”, (na svatah. ) should be regarded as having the meaning of a simple negation (prasajya-pratis. edha), because it is predominantly (gtso  anya),  negation. [This is so] because [Nagarjuna’s] intention is che ba, perhaps pradh  which is endowed with all to establish non-conceptual wisdom (nirvikalpaka-jn~ana) cognizable objects (jn~eya-vis. aya), by negating the net of all conceptual constructions  (kalpana).  If it is taken to be an implicative negation (paryudasa-pratis . edha), [then] because that is predominantly affirmation (vidhi), it would be distinct from our doctrine  [This is so] because [that implicative negation] would teach nonorigination (kr. tanta). by affirming that dharmas are unoriginated. For it is said in scripture that if one  one does not practice practices (spyod, root car) the nonorigination of Matter (rupa), the perfection of discernment.12 Both Candrakırti and Buddhapalita agree that it is necessary to make sure that each of Nagarjuna’s arguments did not imply its opposite.  They only disagree on whether an independent syllogism (svatantra _ prayoga) or a reductio ad absurdum (prasanga) argument should be used to this end. The disagreement on this second point led later Tibetan _ scholars to classify Madhyamikas into two groups, the prasangika and  antrika  svat depending on which kind of argument they upheld. Thus, the logical landscape occupied by post-Buddhapalita Madhyamikas was determined by the doctrines of formal verification defined by Dignaga and held in common with other schools of Buddhism, and by a doctrine specific to the Madhyamikas themselves – namely the doctrine that negative arguments should not imply a positive thesis. If Dignaga lived from 480–540 C.E. and Nagarjuna lived sometime in the second century,13 then we should expect the commentaries on the   a written prior to the sixth century to employ Mulamadhyamakak arik different criteria for formal logical validity. Having discussed the postBuddhapalita commentators’ use of Dignaga’s logic, I will now briefly examine logical sources prior to Dignaga in order to contextualize the  use of logic. Akutobhaya’s In order to make sense out of the formal logic employed in the  we need to look at some of the models of formal arguAkutobhaya, mentation available around the time that it was written. If we take the second century C.E. as a rough date for the writings of Nagarjuna, then the sources which are close to Nagarjuna are possible models for this kind of argumentation. The most important works which were written  followed by before the second century C.E. are the Caraka Samhita, 14  Sutra.  works such as the S. as. .titantra, and the Nyaya The second group of texts dating after the second century but before Dignaga presumably _   would be Asanga’s Bodhisattvabhumi, Vasubandu’s Tarkasastra, and 15 16   Sutra  . ya of V Vadavidhi, and the Nyaya Bhas atsyayana. 194 JOSEPH WALSER It would be convenient for dating purposes if these texts were to represent a nice linear progression of one logical theory being superseded by another. The history of thought is, unfortunately, not so linear. These texts come from several distinct traditions. The Caraka Samhita and the S. as. .titantra are Sam . khya texts, whose progeny are quite different  Sutra  from that of the Nyaya and its commentaries. While some texts respond to opposing positions, others, such as the early Sam . khya texts, do not. As a result, instead of one linear progression we have multiple lineages, each starting with a certain theory, with its defenders debating one another in defense of that view over the centuries. Furthermore, we cannot assume that just because a later text refutes an earlier theory that the adherents to that theory immediately abandoned it. It is more likely that at any given time there were a number of theories being held and defended by different groups of scholars. In order to construct a history, then, we must look at the theories represented in these texts as indicators that each theory had a certain circulation at the time it was written. With this in mind, I would like to present some of the Indian theories of logic and the forms of argumentation that went with them at the time of Nagarjuna.  KHYA SCHOOL FORMAL LOGIC IN THE EARLY SAM . Two of the candidates for being pre-second century logic texts, the Caraka Samhita17 and the S. as. .titantra18 are both Sam . khya texts. Of  treatment of logical theory and practice these two, the Caraka Samhita’s is brief and certainly not as nuanced as the S. as. .titantra. Whether this is because it is an earlier text or because it is primarily interested in practical matters is not certain. There does, however, seem to be a general agreement between the two texts on some basic issues. There are three features of early Sam . khya logic that are important for our purposes. Let us begin with the definitions that the two texts give for inference. The theory that seems to be behind their notion of inference is that inference comes to know its object through an appeal to some sort of connection. In Vars. agan. ya’s compilation of the S. as. .titantra19 inference is explicitly defined as the employment of such a connection. Inference is the establishment of a remainder by virtue of direct perception of a certain relationship (sambandha).20 In the same passage, the S. as. .titantra claims that it is by this relationship that one may infer what is not seen by appeal to a previously known  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 195 connection between what is seen and something which is not seen but which must be there for the connection to hold. Concerning these (connections), inference is due to some connection, the (perceptible) remainder of which is the cause of the establishment of the imperceptible thing to which it is connected.21 It is possible that the interpretation of inference as being based on the perception of some connection is set forth in the Carakasam . hita as well, although the interpretation there is somewhat ambiguous. The Carakasam . hita has the following definition of inference:  Inference (anumana) is the reasoning (tarka) relying on a logical connection (yuktyapeks. a); just like agni (is known) by ability of digestion, strength by the ability to exercise, sounds etc. by the grasping of words etc. [etc.]22 The ambiguity lies in the fact that the word yukti can mean either “reason” or “connection”. Sharma (1981) translates this compound “invariable concomitance”. However, this is a common translation for  “vyapti”, and thereby prejudices the reading of this sentence toward a term that was yet to be established at the time the text was written. I have chosen the translation “logical connection” playing on the ambiguity of the Sanskrit “yukti” meaning both to “connection” and “reason”. Furthermore, as modifier of tarka, yukti would be redundant if it held the former meaning (can tarka ever be divorced from yukti?). It is possible that this term “yukti” may have been used in an even more restricted sense. Pradeep Gokhale (1992) points out that elsewhere in the Caraka Samhita yukti is defined as: a cognition or cognitive faculty (buddhi) that sees the objects to be generated by the conglomeration of many causes : : : . Yukti can be construed more generally as a cognition or cognitive faculty by which one grasps the eternal causal laws governing any type of phenomena. The term yukti on the other hand literally means reasoning or application of (reason). If Caraka’s term yukti can be said to have both these shades of meaning, it can be interpreted as the reasoning involved in inductive generalization pertaining to causal laws. Since inductive reasoning generalization involves analogical reasoning : : : it is possible that Caraka uses the term yukti in the sense of analogical reasoning also.23 Logical connection receives much more attention in the S. as. .titantra  So important was the notion of these than in the Caraka Samhita. logical relationships that the S. as. .titantra contains a list of seven possible relationships which provide the basis for inference. The relation (’brel pa = sambandha?) of connected things is sevenfold: [Relation] _ po-artha24 ) of property and property-owner like 1) by means of the property (dnos a king and his servant or like purus. a25 and the prakr. ti. 2) by means of the property of original state (ran_ bzin = prakr. ti) and the changed thing – like milk and curd or the Prakr.ti and Mahat etc. 3) by means of the property of (material) cause and effect 196 JOSEPH WALSER like a chariot and its parts or like the prakr.ti26 etc. 4) by means of the property of (efficient) cause and effect27 like a potter and a pot or like purus. a and the instigation28 of prakr. ti. 5) by means of the property of a totality29 and its contents like a tree and its branches, etc. or like the great (elements) and sound, etc. 6) by means of the property of unification like ducks30 or like gun. as etc. 7) by means of the property of the one who harms the one who is harmed, like a snake and the weasel (or mongoose)31 or like parts and prakr. ti etc. which has parts.32 Claus Oetke (1996) sees these seven relationships as inferences themselves,33 but it is clear from the discussion which follows them that these relationships are merely the instruments by which inferences are made. In the S. as. .titantra’s syllogisms, the “reason” member manipulates the connection implicit in the thesis, while the “example” shows what the relationship is like. Later authors also employ the idea that an appeal to a relationship is involved in inferences, although they become more specific in exactly what constitutes a relationship. For instance, in the  . khya Karik  a of Isvarakr. s. n. a inference is said to be preceded by Sam 34 Asanga _ _ _ [knowledge of] a mark (linga) and a marked thing (lingin). reduces the number of relationships to five: one may make an inference _  from a sign (lingatas), from a thing’s intrinsic nature (svabhavatas), from activity (karmatas), from characteristic (dharmatas), or cause from 35 In the works of Vasubandhu, the definition of  effect (hetuphalatas).  the inferential relationship becomes more strict. In the Vadavidhi, he claims that the reason of a syllogism is established on the basis of an  ava”  36 ). “invariable concomitance” (“avınabh The second distinctive characteristic of Sam . khya logic is evident in an examination of its treatment of the five members of the syllogism. This brings us to the most important area of agreement between the Caraka Samhita and the S. as. .titantra. In describing the five members, the wording of the two texts is identical.37 In fact, the “iti” at the end of the definition in both texts of the five members in the S. as. .titantra suggests that both texts were quoting from the same source, or at least, that the definition was standard for the Sam . khya school. A translation of these members runs as follows:  is the assertion of what is to be proved. The reason (hetu) The thesis (pratijn~a)  The example is the is the statement of the connection to the evidence (sadhana).  is the uniting of what illustration (nidarsana) of that. The correlation (upasamhara) is to be proved and the example. The conclusion (nigamana) is the repetition of the thesis.38  . a) The Caraka Sam . hita claims that, “reason (hetu) is the cause (karan of understanding (upalabdhi), it is direct perception, inference, tradition, and analogy. What is understood by these reasons is reality”.39 For Caraka, the “example” functions merely to give rhetorical emphasis  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 197 to the connection between the locus and the inferendum established through the reason.  Example (dr. s. .tanta) is that which establishes understanding (buddhi) in both the fool and the wise. It describes what is describable [yo varn. yam . varn. ayati]. For instance: fire is hot, water is wet, earth is stable and the sun is an illuminator. Just as the sun 40 is an illuminator, so too the Sam . khya is also an illuminator. Compared to the exalted role given to the reason (i.e., “that which makes reality known”), the example seems secondary. This is further indicated by the fact that the example given is a metaphorical example and not necessarily a locus where the connection in question actually occurs. The description of the five members of the syllogism used in the Caraka Sam . hita and the S. as. .titantra seems straightforward enough. It is only by comparison to the more familiar definitions of the Nyaya school that we notice how distinctive this definition is. The first difference between the Nyaya definition and the Sam . khya occurs in the definitions of the reason and the example. The reason alone, according to Sam . khya, introduces the evidence which supports the thesis. The example merely reinforces this evidence. Compare this to the definition of the reason  Sutra  of Nyaya 1.1.34: “The reason is the means of establishing what  is to be established (sadhya) by virtue of its similarity to the example 41 In the Nyaya    (udaharan a)”. Sutra, the force of the syllogism is not . carried by the reason but by the example. The reason is only forceful insofar as it is similar to (i.e., has the same “quality” = “dharma” as) the example. While the Caraka Sam . hita and the S. as. .titantra may agree on the general theory of inference, the S. as. .titantra develops an elaborate typology of inference. The typology and the explanation of it constitutes the third feature of early Sam . khya logic that is relevant to later Madhyamika thought. This feature is, in fact, more prominent than the other two insofar as the S. as. .titantra was perhaps the first text to formulate a distinction between a direct syllogism and a reductio ad absurdum syllogism, or what would become in Buddhist circles the _ difference between svatantra-prayoga and prasanga. Both of these can be found under the discussion of “general inference”. General inference  anyodr  (sam . .s.ti) occurs when, for example, after having seen smoke and fire connected many times, one infers the concomitance of smoke and fire in general.42 Knowledge of this concomitance can then be the basis for two other  kinds of inference: inference prior to the fact (purvavat – inference from cause to effect) and inference after the fact (ses. avat – inference 198 JOSEPH WALSER from effect to cause). The former is a kind of prediction and hence is fallible due to being subject to a number of default conditions. The latter is a kind of analysis which is, at least in the Sam . khya’s own view, analytically true. It is only this general inference after the  anyato   . ses. avat), which, when verbalized, fact (sam dr. .s.tam anumanam utilizes the five-membered syllogism.43 There are two kinds of ses. avat     syllogisms – direct (vıta) and indirect (av ıta). The av ıta syllogism is essentially a reductio ad absurdum inference. The explanation that the S. as. .titantra gives for the distinction between direct and reductio ad absurdum inferences is significant and worth quoting at length along with the examples given for each: Direct proof results from its own nature. When a reason (hetu) does not take into consideration the other position [and the reason] is indicated by its own nature in accomplishing its objective, then it is called “direct”. When a reason is not other than this, [then] it is this. Therefore, the reason is only [presented] from [the argument’s] complement. [When] what is to be known is indicated in the proof, then [the proof] is called indirect. [For example:]  [= “Prakr. ti”] exists. Because the [mutual] association of [its] divisions Pradhana are seen. A mutual connection (samanvaya) is seen for the single class of internal divisions (which are) the internal cause and effect. [Application:] Those divisions which consist of the five internal causes – sound, touch, taste, form, and smell – [these] are merely the assembly of the three – pleasure, pain, and confusion. Why?  of the five. Courage, Because of there being a single cause (namely, the pradhana) affection, begetting, lightness, and serenity of pleasurable smell, form, taste, touch, and  of pleasurable (things). Hatred, trembling, supporting, sound are the cause (karyam) division, heat and desiccation are the cause of suffering. Difficulty, depression, revulsion, concealment, and desiring destruction are the cause of bewildered (things).  exists).44 (Therefore, pradhana It is a bit puzzling why this should be held up as an example of a direct syllogism with five members, when it is somewhat difficult to distinctly identify those members. Nevertheless, this is a direct syllogism because no reference is made to any opposing doctrine. Furthermore, the example in this syllogism seems to represent an advance over that of the Caraka Sam . hita in that the example put forward actually is an instance  of a mutual relationship within pradhana. Unlike Nyaya’s syllogisms, however, while an example is given, here there is no counter-example. After the discussion of the direct syllogism, the S. as. .titantra shows how the same thesis is established using a reductio ad absurdum inference. If the arising of the Manifest (vyakta) occurs in [something] non-existent, then unity  the results from a lack of an origin. Due to the lack of primary matter (pradhana), Manifest, which is only a generality, is without distinctions. Why? Because of the priority of a generality to particularity. Priority of generalities are distinctions seen in the world. It is just like the prior status of milk which is the absence of curds, whey, diluted curds, fresh butter, clarified butter, buttermilk and condensed45 milk. When there is non-existence there is no prior thing which exists; something which is  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 199 prior to particular manifestations (vyakti) should exist. Therefore, <it follows> only the generality is the Manifest which is without distinctions. This is not, however, the case. Therefore, the Manifest does not occur in the non-existent. Consequently, this Manifest occurs from primary matter.46 The verbiage of the syllogism notwithstanding, in this syllogism all five members of the syllogism can be easily located, and when this paragraph is compared with that of the direct syllogism, a definite pattern of argumentation emerges. The first sentence of this paragraph, “if the arising of the Manifest (vyakta) occurs in [something] non-existent, then unity results from a lack of an origin”, merely sets up the initial false assumption from which the negative proof will proceed, and it is not one of the five members of the syllogism itself. It is in the next sentence that we find the thesis [in italics]: “Due to the lack of primary  matter (pradhana), the Manifest, which is only a generality, is without distinctions”. The thesis is followed by the rhetorical question, “why?”  which introduces the reason. The reason asserts the connection (kasmat), of the thesis to the evidence. The reason here states that the general thing is always in a relationship of priority to the particular things. The example begins with a general statement and then a specific illustration: “Priority of generalities are distinctions seen in the world. It is just like the prior status of milk which is the absence of curds, whey, diluted curds, fresh butter, clarified butter, buttermilk, and condensed milk”. Notice here that the example is not a doctrine-specific example like the one used in the direct syllogism, but rather is an example illustrating the type of relationship that holds between “the original state and the changed thing” (relationship number two in the list of relationships above). The next sentence is the “application”, which brings the issue of nirvises. a (which is what is to be proved) together with the issue of priority (from the reason and example): “When there is non-existence there is no prior thing which exists; something which is prior to particular manifestations (vyakti) should exist”. The next sentence concludes by restating the thesis – “Therefore, <it follows> only the generality is the Manifest which is without distinctions (nirvises. a)”. The last sentence in the illustration exposes the false supposition of the syllogism (“if the Manifest occurred out of nothing”) and states the positive conclusion; “However, this is not the case. Therefore, the Manifest does not occur in the non-existent. Consequently, this Manifest occurs from primary matter”. Here, the relationship (sambandha) between the general thing and the particular manifestation, which is employed in the reason, is a relationship already entailed in the concept of prakr. ti; the reason merely invokes it. The relationship between milk and its by-products 200 JOSEPH WALSER is by definition the distinctive aspect of the relationship between prakr. ti and its manifestations (a la relationship number two listed above). In sum, there are three characteristics of early Sam . khya logic that have a bearing on Madhyamika logic: the use of the notion of relationship, a five-membered syllogism that places the burden of the proof on the reason rather than the example, and a direct and indirect syllogism both of which employ five members.  FORMAL LOGIC IN THE EARLY NYAYA The Nyaya articulation of the syllogism diverges from that of early Sam . khya in a number of ways. One of these has already been mentioned above. Whereas the early Sam . khya syllogism places the most emphasis on the reason, the early Nyaya syllogism places the most emphasis on the example. Furthermore, in Nyaya there are two kinds of example: the positive example and the negative example.47 This seemingly subtle difference between Nyaya and Sam . khya concerning the role of the example results in a profound difference in the ways the two systems operate. The significance of this example-based syllogism as found in  Sutra  the Nyaya has been discussed at length by Claus Oetke (1996) in his article, “Ancient Indian Logic as a Theory of Non-Monotonic Reasoning”. Oetke argues that the Nyaya form of inference functions differently from a Western categorical proof in that it assumes certain default, or “normality” conditions. Oetke tries to show that all of the syllogisms of the earliest strata of theories concerning the nature of inference in India assume a certain number of these normality conditions – conditions that, if violated, render the syllogism invalid. For instance, if I see smoke on a mountain directly after a rainfall, I would infer the presence of fire on that mountain by assuming the absence of wet smoldering wood (which would still produce smoke even though there would no longer be a fire).48 One could imagine an almost infinite number of conditions such as “absence of wet wood” which must be fulfilled before one could be sure that an inference of fire from smoke were true. The fact that these syllogisms, unlike the categorical syllogism, require default conditions that are not themselves stated in the syllogism means that the number of additional cases to which the syllogism can be extended is necessarily limited to cases covered by the default. For this reason, according to Oetke, these syllogisms are non-monotonic.49  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 201 Oetke sees the warrant for the default conditions (which are subject to revision) as the function of the “example” and “correlation” members of the five-membered syllogism. In his interpretation the example: : : : possesses the function of giving an empirical foundation and justification of (relevant) normality-assumptions. The fourth member [the correlation], on the other hand, can be understood as expressing the claim that the entity which is concerned in a particular case fulfills the relevant normality conditions.50 Whereas the Sam . khya syllogism establishes what is necessarily true of certain relationships, the Nyaya syllogism establishes what is most probably true given the present situation’s similarity to a known, controlled situation. The second major difference of interest to this study is the difference between early Sam . khya and Nyaya regarding direct and reductio ad absurdum arguments. In the S. as. .titantra the direct and indirect arguments are put on equal footing and there seems to be little value distinction made between them. In Nyaya texts, on the other hand, we find many discussions of the relationship between these two types of argumentation as well as assessments of their relative values. It appears that for early Nyaya, the direct syllogism was primary and the reductio ad absurdum argument was seen to be derivative at best. This view was justified in two different ways according to whether the interpreter comes before Dignaga or after.  Sutra  This view was probably first articulated in the Nyaya itself.  Immediately after discussing the parts of a syllogism proper, the Nyaya  Sutra takes up a different variety of inference which is called “tarka”. Like the Sam . khya avıta syllogism, tarka bears a strong resemblance _ to the Madhyamika prasanga arguments.51 The verse in question can be rendered as follows:  a]  When there is a meaning, a fact which is not-clearly known, there is an inference [uh (called) “tarka” for the purpose of true understanding by means of a [subsequently] produced reason.52 Coming as it does at the end of a section discussing the five-membered syllogism, we should expect tarka to be distinguished somehow from the . a of inference which has been explained in the preceding proper praman verses. The distinction turns out to be one of usage. Although a certain subject may be established by inference, there may be aspects of the subject which are still in doubt. These doubts take the form of “x subject either has the characteristic of y or not-y”. This additional characteristic may be established by a further reason in addition to the initial reason establishing the first inference. 202 JOSEPH WALSER We get much more information about tarka, or “reductio ad absurdum reasoning” from the commentaries. Vatsyayana has the following to say: Further, how is this (tarka) for the purpose of true knowledge and not merely true knowledge itself? Because of [its nature as a] restriction. It confirms by means of the resulting reason which is one of two possible dharmas. It neither causes discernment (na vyavasyati) nor does it settle or resolve, nor does it make certain that this is exclusively this [dharma]. How is it “for the purpose of knowledge of reality”? Real knowledge is produced  at),  and due to the characteristic of from the pure, from proof, from inference (uh  the subject of true knowledge, on account of the immediately confirming (abhyanujn~a) . a.53 preceding praman Implicit in this section is a distinction between inference proper . a anumana  expressed in a five-membered syllogism) (i.e., the praman  occurs in the and its derivative – reductio ad absurdum. Anumana case of true knowledge itself while reductio ad absurdum reasoning merely provides us with the significance of that true knowledge. Thus,  comes first in order to give us in Vatsyayana’s explanation, anumana discernment and certainty concerning the subject of inquiry. It is only when doubts arise about details of an already established subject that this initial knowledge may then by refined further through a process of eliminating extraneous or false characteristics of the subject through an examination of the implications already present in the subject. This refinement is also a kind of inference. It is, however, not a self-sufficient inference, but rather an inference which relies on information already . a for its validity. established by a bona fide praman Vatsyayana gives the following example of a reductio ad absurdum syllogism: The knower who knows some object to be understood, desires to know “that experiencer” (lit. the enjoyer). That person thinks: “does it have an origin or is it beginningless?” In the case of an object (artha) being considered, the reality of which is presently not known, a reason is arrived at from assenting to a certain dharma, [then] that dharma is understood. If [the experiencer] is beginningless then it will experience the result of the performance of (its own) action. The subsequent [production] of false cognitions, mistakes, activity, birth and suffering is the reason for what precedes it. When there is destruction of the latter there is release (apavarga) due to the absence of an immediately preceding cause. This would be the release   If the knower has a beginning then, this [release from sam from sam . sara. . sara] would not exist. Moreover, a produced knower would be connected with the feelings, awareness (buddhi) sense-faculties [of only one] body. The [experiencer would not experience the result] of the performance of its own actions. [The experiencer] having been produced, there would be no results produced. The experienced result of the performance of one’s own action does not exist for anything which is ended or which is [simply] not existing. For [such an experiencer], there would be no perpetual  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 203 unjoining and joining to more than one [body]. Wherever one sees a non-occurring  a and tarka.54 reason and accepts this [there] is said to be the characteristic of uh Notice that in this kind of inference, an example and an application are not necessary, because the subject and the predominant characteristics of what is to be proved are already understood from a direct inference. The argument draws out implications of a thesis which is opposite to the one actually stated in order to show that any thesis other than the one stated will be false. In an “either-or” situation, this procedure will remove any lingering doubt concerning which characteristics truly belong to the subject being examined. Long after Dignaga, Uddyotkara employs a slightly different justification to support the traditional Nyaya critique of reductio ad absurdum arguments. [Some suggest that:] “a reductio ad absurdum argument [tarka] is like a true inference  due to its being dependent on the recollection of the connection between [anumana] the mark and the marked-thing”. This is not so, because you do not perceive the essential nature of reductio ad absurdum reasoning. Reductio ad absurdum reasoning is not at all the dependence on the recognition of the connection between the mark and the marked-thing. How so? Because neither of the two are recognized. Wherever both are recognized (the dharmin and the confirming dharma) inference occurs. [By contrast] where there is _ that is the the recognition of the dharmin alone and no recognition of the linga, domain of reduction ad absurdum reasoning. Therefore, [reductio ad absurdum’s] _ _ and the linga is not dependence on memory of the relation between the lingin  occurs when there is both the apprehended dharma and the appropriate. Anumana recognized dharmin; again this is not reductio ad absurdum. On the contrary, reductio ad absurdum occurs by having understood the other [the opposite] : : : .55 In short, every reductio ad absurdum argument employs (implicitly) a sub-argument with a thesis opposite the initial thesis. Using Dignaga’s first criterion for formal validity, the character of the proposed reason in a reductio ad absurdum argument is not present in the stated thesis, but rather in its (unstated) opposite. Hence, as it stands, the reason contradicts the thesis. Bhavaviveka seems to adopt something similar _ _ argument to the Naiyayika stand on the prasanga. For him, a prasanga must be contraposed in order to be stated as a syllogism. This is implied in his commentary on 2.19:  [Verse:] If a goer were just the same as [his] going (gamana), The identity (ekıbhava) of agent and action/object (karman) would follow : : : . _ the [Bhavaviveka] Thus because here [in MMK 2–19] there is a prasanga-argument, original meaning (prakr. ta-artha) can be negated; and [the verse] has the meaning of a statement in which a reversed meaning is manifest. For example, [it is like the following argument:] If sound were permanent, it would follow that a jar would also be permanent; but it is not maintained that a jar, which is made [and] impermanent, is permanent. Therefore, 204 JOSEPH WALSER [Thesis:] sound is impermanent, [Reason:] because it is made, [Example:] like a jar. Therefore here, by virtue of the meaning of [that] statement [in which a reversed meaning is manifest], the syllogism is: [Thesis:] In ultimate reality, goer and going are not just the same, [Reason:] because they are agent and action/object, [Example:] like the cutter and the cut (bcad pa).56 THE AKUTOBHAYA Having set out some of the basic features of Indian logic that were available models between the second century and the fifth century C.E., I will now examine the formal arguments of the Akutobhaya with regard  logic, I will to these features. To illustrate the form of the Akutobhaya’s focus on the second chapter which investigates motion as this is the chapter with which perhaps most scholars are familiar, and because it is held up by Nagarjuna’s root text to be paradigmatic of his method. That this chapter is to be taken as paradigmatic can be seen through references to it throughout the text. There are four such references: MMK. 3.3 “The example of fire is not appropriate for the proof of seeing. That which has seeing is proved by (the example of) ‘what has been traversed, what has not yet been traversed, and what is presently being traversed’ ”.57 MMK. 7.14 “(Origination) is neither presently arising, arisen or not yet arisen. How can it not arise? This has been explained by means of ‘what has been traversed, what has not yet been traversed, and what is presently being traversed’ ”.58 MMK. 10.13 “Fire does not exist in fuel nor does fire come from (something) else. Here, in the case of fuel, the rest has been said by (the example of) ‘what has been traversed, what has not yet been traversed, and what is presently being traversed’ ”.59 MMK. 16.7 “If bonds exist prior to the bondage, they could bind freely or at will. But this is not so. The other matters have already been discussed with respect to ‘what has been traversed, what has not yet been traversed, and what is presently being traversed’ ”.60 By stating the parallels between these later chapters and chapter 2 in this way, Nagarjuna’s root text indicates that there is something about the form of the argument in chapter 2 which should serve as a model or pattern for any subsequent argument. That the Akutobhaya uses syllogisms is by no means obvious. As far as I know, no scholarship in a Western language has examined the logical aspect of this work in any depth. An idiosyncratic feature of  as opposed to the later commentaries with which we the Akutobhaya, are more familiar, is that its author never introduces his or her own syllogism, as Bhavaviveka sometimes does, to justify Nagarjuna’s verse. On the contrary, the Akutobhaya treats each of Nagarjuna’s verses as  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 205 an enthememe – a syllogism with one or two members missing. It takes words from the verse in question and rearranges them to fit a certain syllogistic structure by filling in the parts of the argument that are missing. The fact that the commentary on each verse appears to incorporate so much of the verse itself – often times only adding a word or a phrase here and there has led both Jaques May and C. Huntington (1986) to characterize the work as merely a “simple gloss”.61 Exactly how the Akutobhaya reworks the original text becomes apparent when we translate one of Nagarjuna’s verses along with its commentary and underline all of the phrases that are taken verbatim from the verse (the verse itself, I will double underline). This way it will become apparent which words are Nagarjuna’s and which words are added by the commentary. Using this method, I will show that not only does the Akutobhaya actively comment on Nagarjuna’s root text, but that its agenda seems to be to uncover a certain syllogistic structure of the verses themselves. In such an analysis, we find clues as to what was expected of a syllogism at the time the text was written and can finally place this text relative to other logical texts of its time. Let us begin with the first verse of the second chapter: 1. What has been traversed is not being traversed. What has not yet been traversed is not being traversed. What is being traversed,62 apart from what has been traversed and what is not yet traversed, is not being traversed.63 [Commentary:] What has been traversed is not being traversed. Because of completed going (son_ zin). Because an action is not admitted to be in what is devoid of action. What has not yet been traversed is not being traversed, because that is not traversed. There is also no going in what is being traversed. Because there is no thing being traversed, apart from what has been traversed and what is not yet _ 65 traversed, which is being traversed.64 Just like a lamp and illumination (snan). In translating this passage, I have not added any words that have no counterpart in the original Tibetan, in order to give the reader a sense of sparsity and the somewhat mechanical nature of parts of this commentary. The commentary on this verse separates Nagarjuna’s words into three arguments. It begins with a verbatim quotation from the first sentence of Nagarjuna’s verse, “what has been traversed is not being traversed”. The next two phrases are the contribution of the commentator. The first, “because of completed going”, is a dependent clause governed by the word “because” (phyi) which is subordinate to the quoted sentence. This phrase is followed by another “because” phrase; “because an action is not admitted to be what is devoid of 206 JOSEPH WALSER action”. This phrase ends with the particle, “’o” denoting the end of a thought. The style of the commentary is clipped: quote-comment-quotecomment and so on. Compare this extremely terse writing style with  first chapter and one the more conversational style of the Akutobhaya’s quickly begins to suspect that the shift in style is purposeful. If we take Nagarjuna’s first two assertions from the verse to function as theses, then we may make the provisional assumption that the conjunction “because” introduces the reason or support of that thesis. In fact, there seems to be a somewhat repetitive use of markers indicating the function of certain phrases. For example, in addition to the normal use of ablative phrases to introduce the reason, many of the arguments also introduce the reason with the rhetorical question “why? (Tibetan: “ci’i phyir ze na” lit. “if  66 Similarly, when a you should ask, why is it?” = Sanskrit “kasmat”). conclusion is given, the commentary will usually introduce it with a “therefore” (“de’i phyir”). Finally, all of the examples are introduced with “just like : : : ”67 (“bzin”). When I say that I take the identification of these phrases as parts of a syllogism “provisionally”, it is because this structure of argumentation appears frequently in the Akutobhaya and yet if we assume that every ablative phrase (or every rhetorical, “why?”) denotes a formal “reason”, then we may fall into the trap of finding syllogisms where there are none. The first argument is a good illustration. I have argued that the first sentence is a thesis and that the next two are reasons. If this were to be a syllogism like any that we have examined so far, the reason should be followed by an example. It is not. Instead, the Akutobhaya launches into another argument. We must decide whether the Akutobhaya employs a slightly different understanding of formal logic or whether these are not cases of formal reasoning at all. While I will investigate the Akutobhaya using the former possibility as my working hypotheses, the problem is made more difficult by the fact that the author of the Akutobhaya never identifies any arguments claiming it as a syllogism. The second sentence of the verse is treated much the same as the first. This is not, however, the case with the third sentence of the verse. Here the commentary provides a thesis statement which was not present in the verse itself: “there is no going in what is being traversed”. The commentary inserts a “because” in front of the quoted third sentence. This arrangement of quotation and comment effectively makes the third sentence of the verse the reason for an unstated thesis provided by the commentary. Finally, there is the phrase, “like a lamp  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 207 and illumination”,68 which functions as an example, presumably, for all three arguments. Our reconstruction of the entire commentary on verse one will look as follows: 1a. [Thesis:] What has been traversed is not being traversed (at present). b. [Reason:] Because of completed going; because an action is not admitted to be in what is devoid of action. 2a. [Thesis:] What has not yet been traversed is not being traversed (at present). b. [Reason:] Because that is not traversed [yet]. 3a.[Thesis:] There is also no going in what is being traversed (at present). b. [Reason:] Because there is no thing being traversed, apart from what has been traversed and what is not yet traversed, which is being traversed (at present). c. [Example:] Just like a lamp and illumination. With a thesis, a reason and an example thus established, it remains to be shown what kind of syllogism it is. In this instance, there is really no question that the relationship between the thesis and reason is that of _ a direct syllogism rather than that of a prasanga. In this verse, there is no counterfactual assumption made in the thesis which is subsequently disproved in the course of the argument. Furthermore, the reason is sound even by Dignaga’s first criteria; absence of going (which is the characteristic of the reason as well as a characteristic of what is to be proved) is actually present in the subject of each thesis. We find this exact same structure of argumentation after verse 8. Not all of the arguments in the commentary, however, are as straightforward as those that come after verses 1 and 8. The commentary on verse three contains another direct syllogism, though we have to work harder to reconstruct its reasoning. 3. How will a traversing which is in what is being traversed be suitable,69 when what is being traversed which is devoid of going is not at all suitable?70 [Commentary:] [Thesis:] Here, a traversing which exists in what is being traversed is not suitable. Why? _ par [sic] gzun_ ba” [Reason:] Because it is not suitable to grasp (“mi nes that which is presently being traversed of a non-existent going. [Example:] Like the son of a barren woman.71 208 JOSEPH WALSER Like the commentary on the first verse, the commentary on verse 3 also transposes the verse into a formal argument. Jaques May (1959) claims that Nagarjuna’s use of the “katham . : : : upapatsyate” construction   denotes censure following Pan. ini’s rule at As. .tadhy ay ı 3.3.143–4. 72 While the rule does not, in fact, accurately apply to this particular construction of Nagarjuna’s,73 the Akutobhaya nevertheless transposes the first statement of the verse from a rhetorical question into a proper thesis statement. In the thesis, “what is being traversed” (bgom pa) is the dharmin and the untenability of “a traversing” (‘gro ba) is the dharma. The reason asserts that the untenability of the dharma (which is to be proved) is present in the dharmin because “what is being traversed” is already without going (a thesis which was already established in the commentary to verse one). Implicit in the reason is the fact that a thing which is traversed but which is devoid of going is a contradiction, and therefore cannot be a proper locus for any dharma, especially one that asserts the suitability of motion. The example, “like the son of a barren woman”, illustrates this point by using a stock Madhyamika phrase indicating the non-existence of something which is a contradiction in terms. In addition to direct syllogisms, the Akutobhaya also employs reductio ad absurdum syllogisms. Probably the best example of this can be found in the commentary on verse 6. If two goings are concluded, it would follow that there are two goers. Because, without a goer going is not possible.74 [Commentary:] [Thesis:] Here, if two goings are concluded, it would follow that there are two goers. Why? [Reason:] Because, without a goer, going is not possible. [Conclusion:] And a conclusion of two goers and two goings is not desired. Therefore, it is not reasonable to say that going exists in what is presently being traversed. [Example:] Like cutting off [a second] head.75  of Nagarjuna’s verse are used verbatim as Here, the first two padas a thesis in the commentary, just as the last two are quoted as a reason. This argument fulfills the criteria for a reductio ad absurdum syllogism because the reason (“a goer without a going”) is neither a property of two goings nor of two goers. The reason is justified in that from two goings there must be two goers because otherwise a contradiction of a goer without a going would ensue. Therefore, the characteristic of the reason is actually a property of the opposite of what is asserted as the reductio ad absurdum thesis.  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 209 While some of the arguments in the Akutobhaya are clearly direct syllogisms and others are clearly reductio ad absurdum, there are some passages that appear to reconstruct Nagarjuna’s verse into a formal argument, but one whose character as direct or reductio ad absurdum is either ambiguous or mixed. Though there are no striking examples of a mixed syllogism in chapter 2, an example can be found in the commentary on verse 14 of chapter 7. It is neither presently arising, arisen or not yet arisen. Why does it not arise? This has been explained by means of ‘what has been traversed, what has not yet been traversed, and what is presently being traversed.76 : : : How it does not arise, is explained through “what has been traversed, what has not been traversed, and what is being traversed”. If so, how then? It is explained: [Thesis:] An entity [already] arisen does not arise. Why?  would follow, [Reason1 :] Because an infinite regress [anavastha] [Reason2 :] and because there is no action in what as been done/made.77 In this reconstruction, the Akutobhaya takes non-arising as a thesis from the verse and justifies that thesis with two reasons. The first reason constitutes a reductio ad absurdum argument: an “ensuing infinite regress” is neither a property of “an entity” nor of “not arising”. An “ensuing infinite regress” is a property of the opposite of the thesis stated, namely, “an arisen entity”. The second reason supports the thesis in the manner of a direct syllogism insofar as “an entity” has the property of “something already done/made” and “arising” is an action. There seems to be a pattern to the order of the type of arguments. This statement may be somewhat preliminary, due to the fact that some of the arguments are ambiguous as to whether they are direct or reductio ad absurdum. Nevertheless, one can reasonably argue that the formal arguments that come after verses 1, 8, 14, 15, 22 and 23 employ direct syllogisms. Out of these verses, verses 1, 8,14, 15 and 22 introduce new topics: 1 introduces the “what has been traversed : : : ” [etc.], 8 introduces the goer going, 14 introduces the beginning of going, 15 introduces the staying of going, and verses 18–22 introduce the goers relationship to motion [gati as opposed to gaman. a]. The remaining verses are either reductio ad absurdum arguments or ambiguously direct.  In either case, it is significant in light of the discussion in the Nyaya  Sutra that the direct syllogisms are used to introduce new topics while the reductio ad absurdum syllogisms are reserved for addressing doubts left by the initial syllogism. From the syllogisms investigated so far, it is clear that the formal arguments of the Akutobhaya essentially have only three members. The conclusion and the example which come at the end of verse 6 210 JOSEPH WALSER do not belong exclusively to that verse, but rather to the series of arguments from verse 1, part 3 onward. In fact, there are a number of places in chapter 2 where conclusions are stated,78 but these usually are conclusions to a string of arguments and not conclusions to any single syllogism. For this reason, we cannot say that the Akutobhaya employs a conclusion as a regular member of its syllogistic structure. Furthermore, the Akutobhaya does not seem to be consistent in the number of members of the syllogisms it employs. While its basic structure employs three members, it is also characteristic of this commentary to eliminate one or more of these members. For example, the commentary on chapter 2 verse 10 only employs a thesis and reason, while the commentary on verses 19–21 and verse 25 have nothing but an example. The pattern that is used most often, however, is to argue for each verse using thesis and reason and to place an example at the end. The attribution of the term “syllogism” to an argument stating a fact and then stating a reason may seem dubious when no example is stated, and certainly this practice cannot be applied in all such cases. Nevertheless, looking back at chapter 2 verse 1, it is defensible to say that the first and second “thesis” and “reason” are part of a formal structure and that the example at the end serves all three arguments. In other words, the author of the Akutobhaya may have thought that the examples were necessary, but not for each argument. The fact that the examples are not attached to every argument  indicates the secondary importance of the example for the Akutobhaya. For the most part, the weight of each argument has to be carried by the thesis and the reason. This suspicion is deepened by the fact that each chapter ends with an isolated example – often isolated from any formal argument – which bears little relation to what is being said and leaves the reader with the impression that the examples may be something of an afterthought. This concern about the examples in the Akutobhaya is echoed in the work of C.W. Huntington. The problem, as Huntington  sees it, lies in the fact that in the sections of the Buddhapalitavr . tti and the Chung-lun that seem to have been lifted verbatim from the  the examples are missing. Huntington writes: Akutobhaya,  Short summary illustrations : : : are extremely common in ABh [the Akutobhaya],  and conspicuously absent from BP [the Buddhapalitavr . tti] and CL [the Chung-lun]. The fact that both BP and CL consistently omit just these examples from passages (or entire chapters) that are otherwise lifted verbatim suggests that the text of the ABh was not absolutely fixed during the first several hundred years of its circulation; rather, we may quite reasonably assume that both BP and CL utilized an earlier (or simply different) recension of the Indic source of ABh – one that did not include these illustrations.79  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 211 While the examples may very well be later additions, the fact remains that regardless of when the examples were added to the text, they were added in such a way that they make the arguments read like syllogisms. It is the formal arguments of the text in its final recension that we are investigating here. On the other hand, in some cases, it looks as if the example had to have been an intrinsic part of the original text. Using the same technique as I have in translating Akutobhaya chapter 2, I will translate the commentary on verse 31 of chapter 7.80 The cessation of a non-existent thing is also not possible. Just like a second head is not decapitated. [Commentary:] [Thesis:] The cessation of a non-existent thing is also not possible. Why? [Reason:] Because it doesn’t exist. [Example:] Just like a second head is not decapitated.81 Here, Nagarjuna’s verse itself presents what appears to be a thesis statement and an example; the reason is assumed. This reading is supported by the Akutobhaya reconstruction of the verse, which provides  the missing reason, and places the last two padas in the place of the example. Even if we accept Huntington’s hypothesis that the examples were added at a later time, this particular example must have been in the original commentary because it is a part of the verse. The fact that the rest of the formal arguments of chapter 2 follow this model (of thesis, reason, example) lends support to the authenticity of the examples. In short, the Akutobhaya interprets Nagarjuna’s logic as operating with a three-membered syllogism, in which the example is optional (hence, stressing the role of the reason). In Madhyamaka Schools in India, Peter Della Santina (1986) speculates about the origins of Indian logic. He claims that the first kind of syllogism in India only had two members – a thesis and a reason. More elaborate syllogisms were devised later, first with three members and then with five. Santina claims that while Nagarjuna must have been aware of the three membered syllogism, “which was in common use at this time : : : [he] singularly refrains from using it in any of his major works”.82 On the other hand, Santina does find quite a number of “proto-syllogisms” (two-membered) in Nagarjuna’s work.  representation of N While the Akutobhaya’s agarjuna’s logic supports Santina’s claim that Nagarjuna felt quite free using a two-membered syllogism, it does not support his claim that Nagarjuna never used a   a 7.31, quoted three-membered syllogism (as in Mulamadhyamakak arik above). In fact, if we were to defend Nagarjuna’s authorship of the  then we could strengthen this claim to, “N Akutobhaya, agarjuna used 212 JOSEPH WALSER the three-membered syllogism freely”. Also, the historical claim that Santina makes concerning the development of the syllogism in India is mistaken. In light of early Sam aya, it seems likely that the . khya and Ny five-membered syllogism came first, and that one of the later traditions reduced the number of members to either two or three.83 Though the Akutobhaya uses a three-membered syllogism, it is of a variety that does not seem to have been used elsewhere. While many of the syllogisms whose mark is present in both the subject and the  predicate (similar to the first of Dignaga’s trirupyahetu), there is no indication of a positive and negative example84 – a fact which sets it off _ from the syllogisms of Nyaya, Vasubandhu, Asanga, Dignaga and so on. Furthermore, each of the previously mentioned groups consider it necessary for the example to illustrate an actual locus where the alleged relationship is generally agreed to occur. Taking the first argument as an illustration, a “lamp and illumination” is not an instance of a locus where going is bereft of what is gone over. It is, on the other hand, an instance where something already established (illumination or whatis-gone-over) has no need of a initial establishment (by way of light or going). In other words, the examples of the Akutobhaya do not illustrate commonly accepted cases where the dharma to be established and the establishing dharma are known to occur together (as they are in other schools’ syllogisms) rather they illustrate analogous cases of the type of relationship found between the thesis and the reason (similar to Caraka Sam avaviveka also . hita and S. as. .titantra?). Thus, while Bh uses a three-membered syllogism with only one example, his examples do tend to be loci where the dharma present in the reason is known to occur (hence, his examples are more like Dignaga’s). While the syllogisms of the Akutobhaya may have something in common with those of the Sam . khya, it is more likely that the author used the three membered-syllogism with this kind of example because only these members could be found within Nagarjuna’s root text itself. From what has been pointed out so far concerning the formal nature of the arguments employed in the Akutobhaya commentary, we can make several conclusions. First of all, the Akutobhaya uses arguments that are definitely direct syllogisms, those which are definitely reductio ad absurdum syllogisms as well as some that are ambiguous. However, while most of the chapters of the Akutobhaya exhibit some of these arguments, it should be noted that chapter 2 is somewhat unusual in the number of such arguments. Chapter 1, for example, contains no formal arguments at all; it consists primarily of definitions of terms used in the verses. Nevertheless, the density of the arguments in the  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 213 second chapter can, I believe, be explained by the primary importance given to its arguments in the root text itself. The second point is that the syllogisms that the Akutobhaya produces differ from both the Sam aya syllogisms in that they do . khya and the Ny not employ anything resembling a “correlation” member or a “conclusion” member. In using a three-membered syllogism, they bear a superficial resemblance to the syllogisms used by Bhavaviveka. However, Bhavaviveka, who was an admirer of Dignaga, used examples which fulfilled Dignaga’s second criteria for a valid argument (i.e., “the sign of the reason should be present in similar examples”). The syllogisms  however, do not seem to assume anything of the of the Akutobhaya,  writings of Dignaga (there are no positive and negative examples, the reductio ad absurdum arguments assume information which the speaker does not believe) or of Bhavaviveka (there are no separate syllogisms – only those implicit in the verse itself). Third, the reductio ad absurdum syllogisms in the Akutobhaya partly follow the Nyaya model in being employed only after an initial direct syllogism in order to remove doubts and partly follow the Sam . khya model in employing distinct members of a syllogism. One is tempted to say that the author of the Akutobhaya understood this kind of argument to be secondary to the direct syllogism. However, while the Nyaya example of a reductio ad absurdum argument put forth by Vatsyayana avoids using the five members of an argument, the Akutobhaya argument employs the same members of a syllogism for both direct and reductio ad absurdum arguments. In this regard, it follows the model similar to that set up by the S. as. .titantra. Fourth, while there are no arguments without a thesis and a reason, there are some arguments without an example. Furthermore, the examples often seem to be placed throughout the chapter somewhat randomly.  arguments place more These three facts indicate that the Akutobhaya’s emphasis on the reason than the example, hence, coming much closer to the early Sam aya. . khya notion of syllogistic function than the Ny  interpretation of N In short, the Akutobhaya’s agarjuna’s logic is that it operates with a three-membered syllogism, in which the example is optional (hence, stressing the role of the reason). Finally, like Sam . khya, the arguments of the Akutobhaya rely heavily upon relationships that are established a priori. Its arguments merely point out facts that are entailed in the relationship itself, and the example is an illustration of the type of relationship invoked in the reason. These arguments, then, are not cases of non-monotonic reasoning, but are analyses of what is true a priori of certain relationships. For example, 214 JOSEPH WALSER the second chapter is about going, and so the notion is broken down into its component parts and subject to analysis. The Akutobhaya then  examines the components in terms of their relations vis-a-vis one another, but the reader already knows that the terms exist to one another in the relationship of “composite” and “component”, echoing the relationship between a chariot and its parts in the S. as. .titantra (number 3 in the list of relationships). Composites and components do not exist without one another.85 Hence, the notion of going necessarily entails motion, the space/time that is crossed, and something which goes. By the same token, the terms cannot be identical to one another or there could be no relationship. From the standpoint of Sam . khya logic, this procedure is similar not only to the relationship between a chariot and its parts 86 but also to what is involved in a sam . bhava inference. Whereas the Sam . khya used the relationship of composite and component to prove the existence of prakr. ti, Nagarjuna uses this same relationship to prove dependent-origination/emptiness. According to the S. as. .titantra any inference is contingent upon a relationship which is invoked in the reason. Thus, while Western scholars have tended to focus on the aspects of mutuality or reciprocity in general in Nagarjuna’s works, when we look at the arguments in the context of early Indian logic it becomes apparent that Nagarjuna’s arguments involve a specific kind of mutuality – namely that of reciprocity as a function of composition. Thus, what we have seen so far is that the formal arguments of the Akutobhaya share some of the features of Nyaya logic and Sam . khya logic, but retains some features which are found in neither of these two nor in the post-Dignaga Madhyamika commentaries. Having established  we are now in a these features of the arguments of the Akutobhaya,  position to inquire as to whether the Akutobhaya presents any difference in interpretation from these other commentaries. If the Akutobhaya does indeed incorporate elements of the Nyaya and Sam . khya models of inference, we should inquire into the significance  Before Bh of negation in the Akutobhaya. avaviveka’s explanation of the two kinds of negation, the author of the Akutobhaya might be excused for assuming that all these negative arguments did imply something which was not explicitly stated (i.e., that Nagarjuna’s arguments, taken  as a group would be an examples of “implicative-negation” paryudasapratis. edha). This should come as no surprise. Many recent articles have   pointed out that verses 29 and 30 of the Vigrahavyavartan ı should not be interpreted to say that Nagarjuna has no thesis (as Candrakırti is wont  syllogisms have enough similarity to do). Further, the Akutobhaya’s  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 215 to the indirect syllogism of the S. as. .titantra to assume provisionally  that there is a reductio ad absurdum assumption (the abhyupagama  siddhanta) which is to be proven false by the indirect method. We find that in the Akutobhaya many positions are negated, but never in such a way as to violate the “law of excluded middle”. Unlike the  later commentaries which try not to affirm any thesis, the Akutobhaya’s arguments demarcate a false assumption which is the basis for all of its apparent paradoxes. The opposite of this assumption can then be seen as the unstated thesis which each of the arguments establish. The false assumption at the root of all the arguments in chapter 2 is that component terms have an independent existence. Independent existence implies that the connected terms must exist as either identical to or   a different from each other. The dilemmas of the Mulamadhyamakak arik merely point out the contradictions or infinite regresses that result from this problematic assumption. The Akutobhaya does, in fact, hint at this problematic initial assumption. Verse 4 of the root text points out that if one posits a going, then the implied counterpart (i.e., “what-is presently-being-traversed”) of that going itself would be devoid of going. The Akutobhaya commentary on this verse gives an explanation which does not occur in the other commentaries. 4. For the one who [maintains that there is] a going (gamana) for what is being traversed, it follows that what is being traversed is devoid of going (gati) because what is being traversed is really not understood.87 [Commentary:] [Thesis:] Here, in the thesis of the one who maintains there is a going in what is being traversed, for that one it follows that there is no going in what is being traversed. The significance of what has been said is that (then the going) would be independent (“ma bltos pa”88 ). Why? [Reason:] Because that which is presently being traversed is understood.89 [In other words,] due to the attachment to this statement (“tshig”, i.e., latching onto “what is presently being traversed”). That also is not desired. [Conclusion:] Therefore, “going exists in what is presently being traversed” is not reasonable. [Example:] Like a cripple.90 Instead of explaining the first half of the thesis (i.e., why it follows that there is “non-going” in “what-is-presently-being-traversed”) the commentator explains that the attribution of going to its corresponding counterpart would indicate that going and its counterpart were independent (ma bltos pa) of one another.91 The addition of the ‘independence’ interpretation onto the thesis indicates that independence had been unintentionally assumed in attribution of “going” to “what-is-presently- 216 JOSEPH WALSER being-traversed” when, in fact, this attribution is really just a judgment implicit in the connection of a subject with a predicate. The commentary gives two reasons why this hypostatization comes about. On the one hand, one really understands what-is-presently-being-traversed (e.g., as I am moving, I am aware of the floor which is stationary). On the other hand, there is a sentence that gives expression to that fact of cognition, a sentence in which “going” is attributed to “whatis-presently-being-traversed”. The two sources of knowledge produce contradictory responses.   a investigates are therefore Terms that the Mulamadhyamakak arik neither the same nor different. The commentator sets out this thesis  explicitly before chapter 2 verse 18 and lets the Mulamadhyama a’s  own verses (18–21) stand in for the reason (hetu). It concludes kakarik with an example which is one of the stock examples in Madhyamika for  two mutually related entities – “father and son”. Beyond the Mulamad a’s  own arguments the Akutobhaya commentator gives a hyamakakarik further argument which is somewhat cryptic but nevertheless suggestive: [Thesis:] Going is not possible (mi srid pa). [Reason:] Because of that [going] itself.92 In light of the preceding argument (that goer and going are neither the same nor different because they are mutually related like a father and son) the thrust of the argument here seems to be that going in any of its manifestations is not possible as long as it is treated as something existing in itself (non-dependently). The last piece of evidence I would like to consider with regard to an unstated assumption is the commentary on the last two verses of chapter  . ) goer and going do 2. Here the root text claims that a “real” (sadbhutah  . ) goer not traverse the three passages, nor do an “unreal” (asadbhutah and going. This would normally be considered to be exhaustive of all options, but the commentary does not interpret it so. The commentary  . ” means “established as independent” (anapeks. a) claims that “sadbhutah  . ” means “non-existent” (nasti).  and that “asadbhutah If both of these lead to false conclusions then the obvious middle position between the two would be simply to say that only as dependent (apeks. a) can a goer go, i.e., to say that the component terms of going exist in a relation of mutual-conditionality or reciprocal implication. By this reading, it is the independent or the non-existent passages that do not exist. They only appear to be independent in the manner of a circle of fire created by whirling a torch on the end of a rope appears as an independently existing thing.93  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 217 If the Akutobhaya indeed interprets the negations of the root text as implicative negations, then how does it interpret the classic instances of Nagarjuna’s tetralemma such as in chapter 18 verse 8? Here, we find that the Akutobhaya consistently distributes the terms of the tetralemma either between different levels of truth or between different people. The commentary on chapter 18 verse 8 has been held up as an example of the way the Akutobhaya distributes the terms. Everything is suchness [tathyam . ], not suchness, both suchness and not suchness, neither suchness nor not suchness. “Everything is suchness”; [this is] because there is no contradiction with conventional  = tha sn~ad kyi bden pa] [such as] sense objects like [visible] truth [vyavaharasatya  atanas  like the eye etc. “[Everything is] non-suchness”, because, form etc., and ay whereas it is illusory appearance relying on ultimate truth it is imperfect nature  = no _ bo n~id yongs su ma grub pa], [and also] because, it [aparinis. pannasvabhava does not exist in the way that it appears. “[Everything is] suchness and not suchness” because of being dependent on some aspect of the two truths. “Everything is neither suchness nor non-suchness” because of there being no mental construction in regard to the reality of all dharmas in all kinds of yoga at the time of abhisamaya. Alternately: “everything is suchness” is the teaching [given] by the Blessed One which is to be understood in order to [effect] the relinquishment of the obscuration of the klesas. It has the unshakable characteristic of being devoid of [the concepts] “me”  atana  = skye mched]. “[Everything is] and “mine” and of the inner and outer fields [ay non-suchness” due to the [apparent] possession of a self which has the characteristic of consciousness, and due to the existence of the concept “mine”. [Hence] the agent listens, thinks and meditates. “[Everything is] both suchness and not-suchness”,  or the world. “[Everything is] depending on the convention of either the Agamas neither suchness nor not suchness”. Because of the non-arising of all dharmas in the aspect of ultimate truth there occurs consciousness having mental discrimination and in the same [world] there occurs the realm devoid of discrimination. [The first] is determined to be non-suchness by way of its aspect as an entity and [the second] is determined to be suchness. [Hence,] what exists, in this way [also] does not exist.94 Given what has been said so far, it should be apparent that the Akutobhaya does assume that the root text has something like a thesis. The thesis is that there is no thing that exists independently. All assertions that assume the independent existence of that which is asserted are denied in order to show that the initial assumption is false. Dependent existence is then held up to be the middle position between false extremes of independence and non-existence. Alternately, we could say that all things exist within and are nothing apart from the relationship of “composite and component” in which they are found. Keeping in mind that the topic   of the root text of going and coming is first introduced in the namask ara which reiterates the relationship of the middle way to the teaching of  dependent-origination (pratıtyasamutpada), we would not be far off to assume that by showing how all cases assuming independent existence of the factors involved in motion lead to unwanted consequences. 218 JOSEPH WALSER The opposite (unstated) thesis is affirmed – namely that the various factors of motion exist only as dependently-originated. The arguments  of this chapter were perhaps meant to call to mind the many sutra passages teaching dependent-origination by way of negating apparent logical opposites (such as “everything exists” and “everything does not exist”). The relationship of composite and component (along with the illustration of the chariot and its parts) is one that is often referred to in Buddhist literature – usually with reference to the five aggregates.95 The only doctrinal innovation of early Madhyamaka is to connect these two teachings through a logical procedure. CONCLUSION Nagarjuna’s appeal in the West has been largely due to the fact that he seems to arrive at some counterintuitive conclusions from logical methods. Our understanding of Nagarjuna’s logical methods, however, derives from the various commentaries through which we read him. As the result of certain historical circumstances most of us tend to read Nagarjuna through the lens of Candrakırti and Bhavaviveka, but there are earlier commentaries which present a slightly different picture of Nagarjuna’s logic. From the standpoint of the earliest commentary  we can see that the arguments on Nagarjuna’s text, the Akutobhaya, of Nagarjuna’s text were not seen as defying logic in any way nor as coming to counterintuitive conclusions. On the contrary, the Akutobhaya presents Nagarjuna’s arguments as following a definite method and as coming to a conclusion that does not conflict with the teaching of dependent-origination in Buddhist scripture. ACKNOWLEDGMENT I would like to thank my wife, Radha Subramanyam, without whom this article would not have been possible. NOTES The authorship of the Akutobhaya commentary has traditionally been ascribed to Nagarjuna himself, although this attribution has been hotly debated since the time of Tson_ ka pa. It seems that the arguments on either side of the issue are the same today as they were for pre-modern scholars. For a full discussion of the arguments on both sides of the issue see Huntington (1986), pp. 124–194. The highlights of the arguments on both sides are as follows: 1  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 219 1) At the end of every chapter in two of the four recensions (in Peking and Narthan_ but not in the sDe ge or Cone) the following statement is appended – “[Chapter  a commentary on the Mulam    a by adhyamakak arik title] from the Akutobhaya,  arya Arya  Nagarjuna [Chapter # ]”. As Huntington points out there the Ac is some ambiguity (in Tibetan as in this English rendering) as to whether this phrase means that Nagarjuna wrote the Akutobhaya merely that he is the author    a of which the Akutobhaya is a commentary. This adhyamakak arik of the Mulam same phrase appears in all of the recensions of chapter 27. 2) The attribution of this work to Nagarjuna becomes much more explicit in the colophon (present in all four editions) where it is stated that the text of   adhyamakavr the Akutobhaya Mulam . tti was composed by Nagarjuna. [Ibid., 129–130.]    a (those of adhyamakak arik 3) Of the three primary commentaries on the Mulam Buddhapalita, Bhavaviveka, and Candrakırti) none mention that Nagarjuna wrote an auto-commentary on his verses. In the case of Candrakırti, the absence of any mention is especially noticeable. The first mention of an auto-commentary    a is to be found in Avalokitavrata’s (7th cent) adhyamakak arik to the Mulam  ıpat. ika (Ibid., 134–136). Finally, the Akutobhaya is mentioned Prajn~aprad    a in Atısa’s adhyamakak arik by name as an auto-commentary to the Mulam  ı papan~jika (Ibid., 137). Bodhimargaprad 4) Huntington’s main thesis is that the Akutobhaya is the ur-source (or one recension of the ur-source) utilized without explicit acknowledgment by both Buddhapalita _ or Vimalaks. a). He demonstrates this and the author of the Chung-Lun (Pingala, point through an exhaustive comparison of the two texts.  We know that the Buddhapalitavr . tti incorporates lines, passages, and almost  Moreover, the relationship of Akutobhaya entire chapters from the Akutobhaya.  to Chung Lun confirms the fact that the Buddhapalitavr . tti borrowed from the Akutobhaya and not the other way around. Thus the Akutobhaya certainly existed in the mainstream of early Madhyamaka exegesis where it was both known and used by at least one of the three great Indian commentators on    a.  Even if it is not an auto-commentary, it was still adhyamakak arik the Mulam employed as a commentary – and an important one at that. [Ibid., 147.] 5) One of the main arguments against this text being an auto-commentary is the  presence in chapter 27 (also present in the Chung Lun and Buddhapalitavr . tti) of  Catuh. sataka. Tson_ ka pa and others have objected a quotation from Aryadeva’s that the Akutobhaya could not have been an auto-commentary because it would have been unusual for one of the only quotations in the entire work to be from the author’s student. 6) Huntington translates a section from the Bak ‘bum of Go rams pa bsod nams sen_ ge refuting the attribution of this work to Nagarjuna. Among the other arguments previously mentioned, there is an additional argument that, “: : : this commentary’s explanation of dependent-origination : : : does not quite agree with [that found in] the other commentaries, which entails the unacceptable consequence that these commentators are contradicting Nagarjuna himself” (Ibid., 156). Huntington claims that there is any difference in the interpretation of the Akutobhaya and the other commentaries, based on the opinion of Akira   ulamadhyamaka-vr Saito (Buddhapalita-m . tti, 1984, Ph. D. Dissertation, Australian National University, Canberra) that there are only five verses where the Akutobhaya  and the Buddhapalitavr . tti differ in their interpretations. He further claims that these five divergences are “: : : attributable to nothing more than a different syntactical reading of the verse in question”. My findings suggest otherwise –    a chapter 2, last verse. adhyamakak arik cf. the interpretation of Mulam 220 JOSEPH WALSER Another source that is not mentioned by Huntington is a rather cryptic comment in Avalokitavrata which suggests the existence of a commentary of Nagarjuna himself (see below, note 8). 2 _ = Sanskrit “kalpana”.  Tibetan “gran” 3 cf. Poussin (1903–1913) 1–4. “acaryabuddhapa litastvaha j na svata utpadyante _ bhavah. ’tadutpadavaiyarthyat ’atiprasangados . acca j na hi svatmana vidyamananam . padarthanam . punarutpade prayojanamasti j atha sannapi jayeta ’na kada cinna jayeta ’iti jj”. 4 One of the best treatments of this debate can be found in Hopkins (1983), pp. 41–530. But also see Lopez (1987), passim. 5 I am taking Ruegg’s date of c. 500–570. cf. Ruegg (1981), p. 61. 6 Bhavaviveka’s objections are quoted in Candrakırti’s Prasannapada as follows: “atraikadus. an. amahuh. tadayuktam. hetudr. s. t.antanabhidhanat j paroktados. apariharacca _ akyatvacca prakr. tarthavparyayen. a viparıt[artha] sadhyataddharmavyaktau prasangav parasmadutanna bhava janmasaphalyat janmanirodhacceti kr.tantavirodhah. syat.” Poussin (1903–1913), pp. 14–15. 7 Translated, Hopkins (1983), p. 462. 8 _ The issue of whether a prasanga argument is an invalid argument or whether it can stand on its own is picked up again by Dharmottara and Prajn~akaragupta, two  arttikam.  For a full discussion of this later commentators on Dharmakırti’s Pramanav debate cf. Takashi (1993), passim. 9 Lopez (1987), p. 165: “Here, from among the three modes of the sign, the mode in which [the sign] is opposed to the dissimilar class is not indicated. Here, only the two modes of the reason that I wish to propound are designated. The property of the subject [i.e., that earth and so forth are products] is exhausted in that which exists only in the similar class, not even a minute particle of the other – the existence of entityness – exists. Therefore, the dissimilar class does not exist. This, an example and a reason of the counter [pervasion] from the dissimilar class are not indicated here. Peking Tripitaka (hereafter “P.”) 5256, vol. 96 28. 1.6–8”. 10 Translation from Ames (1993), p. 223. 11 For a discussion of the early history of this distinction see Staal (1962), passim. 12 Translation from Ames (1993), p. 221. 13 This seems to be the generally accepted date. For an annotated bibliography of works discussing Nagarjuna’s date see Ruegg (1981), note 11, pp. 4–6. A fuller discussion of these theories can be found in Murty (1971). In this book, Murty gives three common reasons supporting the second century date. First of all, most of the atavahana kings was the friend to whom Nagarjuna’s sources agree that one of the S atavahana kings came to an end  ı is addressed. The reign of the S letter, the Ratnaval in 218 C.E., thus giving us one end of a bracket. Second, Murty notes that all of the sources agree that he was a great commentator of the Prajn~aparamita literature, and was a devotee of Amitabha Buddha. In light of the fact that the earliest possible   a Prajn~aparamit a (the first of the authorship and popularization of the As. .tasahasrik   ıvyuha  Sutra  avat (the first of the Amitabha Prajn~aparamita texts) and the Mahasukh texts) is around 100 C.E., this provides us with a lower extreme. The third piece of evidence that places Nagarjuna in the second century is the fact that many sources attribute the renovation of the Amaravati stupa to him. If he was indeed responsible for this, then archaeological information would confirm a date sometime in the latter half of the second century and the first half of the third, as the stupa was reconstructed then. While some of his evidence is problematic (for instance, there is no reason to assume that the Amitabha cult began with the texts devoted to him, nor can we assume based on one verse in the Suhr. lekkha and some late legends, that Nagarjuna was a devotee of Amitabha), most scholars agree that Nagarjuna wrote sometime in this period.  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 221 More recently, Shohei Ichimura (1992, 1995) has reexamined the evidence for the date of Nagarjuna, and has come up with the earlier dates of 50–150 C.E. by connecting him with Rudradaman. 14 Or, at least, shortly thereafter. 15 _ lived sometime around the late fourth – early fifth Vasubandhu and Asanga centuries. (For a discussion of the debate over Vasubandhu’s dates cf. Anacker, (1984), introduction. 16 ca. 450–500 C.E. source, Potter (1977), p. 9. 17 Priyavat Sharma [Sharma (1981), pp. vi–viii] suggests dates for Caraka sometime between 5th century B.C.E. and 2nd century C.E. Since the terminus ad quem is the date that is more relevant to this study, we shall focus on it. He claims that, due to  Sutra  and the doctrinal content, the Caraka Sam . hita is older than both the Nyaya  . khyakarik  a,  both of which he ascribes (without discussion) to the second century Sam C.E. Though this date seems somewhat vague in light of some questions concerning the dates of the latter two texts, it is probably not far off. Sharma rejects the claim of Sylvan Levi that Caraka was the court physician for Kanis. ka (ca. second century) on the grounds that 1) Kanis. ka associated only with Buddhists, 2) Caraka was (by tradition) a mendicant and would not have accepted the “bondage of royal court” (p. ix), and 3) Asvaghos. a never mentions Caraka who would have been his colleague. While it is true that Asvaghos. a does not mention   a-s  on which the author of the karik Caraka by name, he does mention Atreya, Caraka comments (see Cowell, 1894: p. 9). Hence, our best guess is that the Caraka Sam . hita and the logical theories on which it comments were extant circa the time of Nagarjuna. 18 There is a great deal that is not known about this work and its author. First of all, the name of the author there are a number of different versions: “Vars. agan. ya”, “Vr.s. agan. a”, “Vr.s. agan. avıra”, “Vars. agan. a”. For a discussion of the identity of this author see Larson (1987), pp. 131–135. In this chapter, I will use the first of these spellings. Larson also writes concerning the date of Vars. agan. ya: “Regarding the date of Vars. agan. ya, it would appear that Frauwallner’s suggestion that he lived around 300, errs on the side of being too late. Frauwallner’s reconstruction of the revised form of the S. as. .titantra need not be the work of Vars. agan. ya himself but may well be,  . agan. ah  . of Yuktidıpaka). rather, the work of the ‘followers of Vars. agan. ya’ (the vars Vars. agan. ya himself, then, might be placed back in the second and possibly even the first century of the Common era, a date that would correlate nicely with the reference to Vars. agan. ya in the Moks. adharma. Also, an early date for Vars. agan. ya would make plausible Vacaspati Misra’s claim in his Tattvakaumudı (under SK 47)  is attributable to Bhagavan Vars. agan. ya, an that the expression ‘pan~caparva avidya’  utra,  expression that appears, interestingly as the twelfth utterance in the Tattvasamasas and is quoted, even more interestingly, at XII.33 in Asvaghos. a’s Buddhacarita (from the first century of the Common Era)” [Ibid., 136]. In addition to the discussion quoted above, even if Vars. agan. ya had lived around 300, as Frauwallner claims, the S. as. .titantra that is attributed to him is not claimed to be an original work, but rather a redaction of the fundamental doctrines of the Sam . khya tradition, and thus much of its material should be ascribed an earlier date than that of its redactor. 19 Collected and edited in Frauwallner (1958). 20 Ibid., 123: “sam . bandhad ekasmat pratyaks. ac ches. asiddhir anumanam”. 21 _ sum las> lhag Ibid.: “de dag la ji ltar <srid pa bzin> ’brel pa gcig las <mnon _ sum ma yin pa’i ’brel pa can grub pa’i rgyu gan_ yin pa de rjes su dpag pa ni mnon pa’o jj”. 22 Translation mine. Text: “Athanumanam – anumanam . nama tarko yuktyapeks. ah. ; yatha 222 JOSEPH WALSER – agnim . jaran. asaktya, balam . vyayam asaktya, srotradıni sabdadigrahan. enetyevamadi.” Sharma (1981), p. 363. 23 Gokhale (1992), p. 221. 24 In context, we can assume, as does Frauwallner (who translates this artha as Verhaltnis), that the property is a relationship. 25  gtso bo dan_ skyes bu. Gtso bo could translate either atman, gun. a, or pradhana  would be acceptable although (= prakr. ti). In the context, either gun. a or pradhana the latter makes more sense. 26 sn~in_ stobs could mean either prakr. ti or gun. a. 27  . ”. Frauwallner reconstructs this phrase as “nimittanaimittikabhavah 28 Frauwallner has Tatigkeit for ’jug pa, which is not correct in context. 29  Reading tsam po, along with Frauwallner, as matra. 30 _ pa. Frauwallner reads this as nor _ ba, which means “the grunting of pigs”; nor _ pa, on the other hand means “duck” (Sanskrit (Cakravaka).  nor Monier–Williams explains that, “the couples are supposed to be separated and to mourn during the  night.” [Monier-Williams, s.v. “Cakravaka.”] 31 Chandra Das also gives the translation “stone-fox”, see, Das (1995) s.v. “Sbre”. 32 Frauwallner (1958), p. 123. Translation mine. Text: “ ‘brel pa rnams kyi don _ pos dan_ j rgyal rnams kyi ‘brel pa ni rnam pa bdun n~id de j nor dan_ bdag po’i dnos pa dan_ bran bzin dan_ j gtso bo dan_ skyes ba bzin te j ran_ bzin dan_ rnam ’gyur gyi _ pos ni j zo dan_ ’o ma bzin dan_ j gtso bo dan_ chen po la sogs pa bzin no jj dnos _ pos ni j sin_ rta dan_ yan lag bzin dan_ j sn ~in_ stobs la sogs pa ’bras bu dan_ rgyu’i dnos _ pos ni j rdza mkhan dan_ bum bzin te j rgyu mtshan dan_ rgyu mtshan can gyi dnos pa bzin dan_ j skyes bu dan_ gtso bo’i ’jug pa bzin no jj tsam po dan_ tsam po can _ pos dan_ j yal ga la sogs pa dan_ sin_ bzin dan_ j sgra la sogs pa dan_ ’byun_ gyi dnos _ ~in_ _ ba lta bu dan_ j sn pos ni j nur ba chen po bzin na jj lhan cig spyod pa’i dnos _ pos ni j sbrul dan_ sbre mo stobs la sogs pa bzin no jj gnod bya gnod byed kyi dnos bzin dan_ j yan lag dan_ yan lag can du gyur pa’i sn~in_ stobs la sogs pa bzin no jj” Ibid. 33 “The S. as. .titantra presents, however, the problem that the wording of the text does not make explicit what precisely has to be the initial information serving as the basis of inference and what exactly are the propositions to be inferred. If we take only the first “mundane” example exemplifying the connection of “master and his belongings” quite a large number of possibilities emerge as alternative reconstructions of the inference concerned : : : ”. Oetke (1996), p. 517, note 2. 34 _ _ u rvakam ngip verse 5: “: : : trividhamanumanamakhyatam j tallingali aptasrutiraptavacanam . tu jj” [Jha (1965), p. 19]. 35 Wayman (1958), pp. 34–35. 36 This term is also used by the Vaises. ika, Prastapada as well as by later Nyayas. 37 Compare: Caraka Sam . . hita in Sharma (1981), p. 360: “tatra sadhyavadharan. am pratijn~a, sadhanasamasavacanam. hetuh. , tannidarsanam . dr. s. t.antah. , sadhyadr. s. t.antayor ekakriyopasam. harah. , pratijn~abhyaso nigamanam iti : : : ”. My translation. ~a, sadhanaS. as. .titantra in Frauwallner, p. 125: “tatra sadhyavadharan. am . pratijn samasavacanam . hetuh. , trannidarsanam . dr. s. .tantah. , sadhyadr. s. t.antayor ekakriyo~abhyaso nigamanam iti : : : ”. pasam . harah. , pratijn 38 Sharma, Ibid. 39 Text: “Atha hetuh. – hetur namopalabddhika ran. am . ; tat pratyaks. am . , anumanam, aitihyam, aupamyamiti; ebhir hetubhir yad upalabhyate tat tattvam. (Sharma (1981), 361.) Translation mine. 40 dr.s. t.anto nama yatra murkhavidus. am . buddhisayam . , yo varn. yam . varn. ayati j yatha agnirus. n. ah. , dravamudakam. , sthira Pr.thivı, adityah. prakasaka iti; yatha adityah. prakasakastatha samkhyajn~anam . prakasakamiti jj Ibid., 361.  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 223 Tailanga (1984), p. 40: “udharan. a sadharmyat sadhyasadhanam. ”. “rjes su dpag pa ni rnam pa gn~is te j bye brag mthon_ be dan_ spyi mthon_ ba’o _ ba ni j gan_ gi tshe me dan_ du ba ’brel pa mthon_ nas du jj de la khyad par mthon ba de kho nas me de kho na’i yan_ dan_ yan_ de me de kho na ’di’o zes yod pa n~id du rtogs par byed pa’o j spyir mthon_ ba ni gan_ ’ga’ zig tu du ba dan_ me ’brel par mthon_ nas dus phyis du ba tsam mthon_ ba las me spyir rjes su dpag pa’o j”. Frauwallner translates this as: “Davon liegt Sehen dem Besconderen nach vor, wenn man Feuer und Rauch verbunden gesehen hat und nun immer wieder durch denselben Rauch dasselbe Feuer als vorhanden erkennt, (indem man denkt:) “Das ist eben dieses Feuer”. Sehen dem gemeinsamen nach liegt vor, wenn jemand einmal Rauch und Feuer verbunden gesehen hat und nun in spaterer Zeit durch das Sehen des blosen Rauches Feuer im allgemeinen erschlißt” (Ibid., 128). 43 This distinction between non-verbalized inference without a formal syllogism and verbalized inference with a syllogism could perhaps be the basis for Dignaga’s  anum   ana) and inference for another distinction between inference for one’s self (svarth  anum   ana). The S. as. .titantra does not, however, take this distinction to the (pararth conclusion that what one tells to others must correspond to what one has inferred for oneself. 44 Frauwallner, p. 125: tes. am . yad etat samanyato dr.s. t.am anumanam . ses. avat, es. a hetur atındriyan. am . samadhigame. tasya prayogaopaca ravises. ad dvaividhyam, vıta avıta iti. svaru pad vıtasiddhih. . yada hetuh. parapaks. am avyapeks. ya svenaiva ru pen. a karyasiddhav apadisyate, tada vıtakhyo bhavati. parises. ad avıtasiddhih. . yadanedam ato ’nyatha sambhavati, asti cedam, tasmat parises. ato hetur evayam ity avadharya karyasiddhav apadisyate, tadavıtakhyo bhavati. vıtasya vakyabhavah. pan~capradesah. , pratijn~a hetur dr.s. t.anta upasam . haro nigamanam ~a, sadhanasamasavacanam iti. tatra sadhyavadharan. am . pratijn . hetuh. , tannidarsanam . dr.s. t.antah. , sadhyadr. s. t.antayor ekakriyopasam. harah. , pratijn~abhyaso nigamanam iti. purastad vıtasya prayogam . nyayyam . manyate, pascad avıtasya. asti pradhanam, bhedanam anvayadarsanat. adhyatmikanam . karyakaran. atmakanam vaks ekajatisamanvayo dr.s. t.ah. . <adhyatmikah. karyatmikanam . . amah. .> adhyatmikah. karyatmaka bhedah. sabdasparsarasarupagandha h. pan~ca trayan. am . sukhaduh. khamohanam .    sanniversamatram. kasmat? pan~canam [sic.?] ekak a ryabh a v a t. sukhanam . . sabdasparsarasaru pagandhanam _ . prasadalaghavaprasavabhis. vangoddhars . arprıtayah. karyam, duh. khanam . sos. atapabhedopas. t.ambhodvega padves. ah. , mu d. hanam . varan. asadanapadhvam . sanabaibhatsyadainyagaurava n. i usw. 45 . a and kurcik  a both seem to mean “inspissated milk”. cf. Monier-Williams, kilat . a” and “kurcik   a”. s.v., kilat 46 Frauwallner, pp. 125–126. “yadi vyaktasyasata utpattih. , yonyabhavad _ . . pradhanabhavat samanyapu rvakatvad vises. an. am. samanyapu  rvaka hi ekatvaprasangah loke vises. ah. [sic] : : : dr.s. t.ah. , tadyatha ks.ırapurvaka dadhimastudrapsanavanıtagr.taris. t.akilat.akurcikabhavah. . na tu asati bhavah. kascid asti, yat purvaka vyaktivises. ah. syuh. . tasmat samanyamatram idam . vyaktam . nirvises. am ity etat <prasajyate>. na tu idam . tadr.k. tasman nedam . vaktam asata utpadyate. parises. yat pradhanad evedam . vyatam utpadyate : : : ”. 47  Sutra  1.1.36 and 1.1.37. Cf. Nyaya 48  Indeed, the problem of how to exclude such exceptions (upadhi) from an inference was an abiding interest of Navya-Nyaya. See Phillips (1995), pp. 142–146. 49 Phillips independently arrives at the same conclusion. In his analysis of the “fire-syllogism” he concludes the following in reference to Nyaya interpretation of it: 41 42 224 JOSEPH WALSER The logic is deductive, although the premises are arrived at inductively. The reasoning is, then, defeasible or non-monotonic. That is to say, new information can affect the warrant of the general premise – i.e., the premise expressing invariable concommitance, or (literally) “pervasion,” vyapti, between two things x and y : : : . Reasoning based on an assumption of vyapti can in principle be defeated. The Naiyayikas here as elsewhere are fallibilists; pervasions are only fallibly known [Ibid., 55]. 50 Oetke, 479. 51  arttikat   ıka,  Vacaspatimitra talks about the function atparyyat Indeed, in his Nyayav _ Visvanatha’s Vr. tti, states that, “It [tarka] has five of tarka in terms of prasanga. _ [deduced] varieties due to the different kinds of the faulty consequence (prasanga) or the purpose of refuting the opponent: [namely:] having self as a basis, mutual dependence, circular reasoning, and infinite regress”. ~cavidhih. , See Tarkatirtha and Tarkatirtha (1985), p. 325: “sa cayam . pan atmasrayanyonasraya-cakrakanavastha-tadanyabadhitarthaprasangabhed _ at j”. 52  Sutra  1.1.40, Tailanga (1984), p. 45: avijn~atatattve ’rthe karan. opapatNyaya titastattvajn~anarthamuhastarkah. . 53 ~anartho na tattvajn ~anameveti j anavadharan. at “katham . punarayam . tattvajn anujanatyayamekataram. dharmam . karan. opapattya na tvavadharayati ~anartha na vyavasyati na niscanoti evamevedamiti j katham . tattvajn iti tattvajn~anavis. ayabhyabujn~alaks. an. anugrahodbha vitaprasannadanantaram. praman. asamarthyattattvajn~anamutpadyataityevam. tattvajn~anartha iti j” Ibid p. 47. 54 ~ata jn ~atavyamartham ~asa j sa kimutpat yo ’yam . jn . janıte tam . ca bhojanıyeti jijn tidharmako ’nutpattidharmaka iti vimarsah. jj vimr.syasmane ’vijn~atattve ’rthe yasya dharmasyabhyanujn~akaran. amupapadyate tamanujanati j yady ayamanutapttidharmakh. , tatah. (sva)kr.tasya karmanah. phalamanubhavati jn~ata rvasya pu rvasya duh. khajanmapravr. ttidos. amithyajn~ananamuttaramuttaram . pu  apavargo j sam s a r karan. amuttarottarapaye tadanantarabhavadapavarga iti syatam . . utpattidharmake jn~atari punarna syatam j utpannah. khalu jn~ata dehendriyabuddhivedana bhih. sambadhyata iti nasyedam . svakr. tasya karman. ah. phalamutpannasca bhutva na bhavatıti tasyavidyamanasya niruddhasya va svakr. takarman. ah. phalopabhogo nasti tadevam-ekasyaneka-sarırayogah. sarıraviyogscatyantam . na syaditi yatra karan. am-anupapadyama nam . pasyati taccanujanati so ’yamevem. laks. an. a uhastarka ityucyate j Ibid. pp. 46–47. 55 _ _ ngasambandhasmr anumanam . tarkah. lingali . tyapeks. atvat anumanavat j na tarka_ _ ngasambandhasmr svarupanavabodha t; naiva lingali . tyapeks. astarkah. j kathamiti? dvayasyanadhigateh. j yatra dvayamadhigamyate dharmı sadhanadharmasca _ adhigatirasti tatranumanam . pravartate, yatra punarddharmima tradhigatirna ling _ _ ngasambandhasmr sa tarkavis. ayah. iti j tasmat lingali . tyapeks. atvamanupapannam j anum anam . dharmi gata dharmopalabdhau pravartate na punas tarkah. , tarkastvanyagatadharmadars anenapi pravartate : : : [Tarkatirtha (1985), p. 328] 56 Translation from Ames (1995), pp. 322–323. 57 “na paryapto ’gnidr.s. t.anto darsanasya prasiddhaye j sadarsanah. sa prayukto gamyamana-gatagataih. jj” Poussin (1903–1913), p. 114. 58 “notpadyamanam . notpannam . nanutpannam . katham . cana j utpadyate tad akhyatam . gamyamanagatagataih. jj” Ibid., 157. 59 “agacchaty anyato nagnir indhane ’gnir na vidyate j atrendhane ses. am uktam . gamyamanagatagataih. jj” Ibid., 211. 60 rvam “badhnıyad bandhanam. kamam . bandhyat pu . bhaved yadi j na casti tac ches. am uktam . gamyamana gatagataih. jj” Ibid., 291–292. Translation of this verse is from Inada (1993), p. 103. 61  is, as May puts it, ‘a simple gloss’. Even in what probably “[The Akutobhaya] represents a relatively late recension, the Tibetan translation most often contains only  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 225 very rudimentary grammatical or etymological exegesis. It is certainly an altogether less sophisticated text than its successors, and may well have originally been an oral  a-s  that the two were never considered commentary so closely aligned with the karik in isolation from one another”. Huntington (1986), p. 148. 62  as “gegenwartiges Throughout his translation, Walleser (1911) translates gamyamana Gehen,” despite the fact that it may refer to the substratum of going. 63 The Sanskrit from the Prasannapada reads: “gatam . na gamyate tavad agatam . na eva gamyate j gatagatavinirmuktam. gamyamanam . na gamyate j” Poussin (1903–1913), p. 92. There is some disagreement among the commentaries as to how to interpret this last  (source: Candra word, gamyate. Buddhapalita glosses it as gzun. du med pa –agrahya (1990), p. 2089). This interpretation is followed by Bhavaviveka, and Avalokitavrata glosses gzun. du med (is not grasped) as dmigs su med “is not apprehended”. See Ames (1995), p. 339 n. 36. The Akutobhaya and the Chung-Lun have no hint of this interpretation in their commentaries. 64 The Tibetan translation of the verse takes “gamyate” in the sense of “to understand” and thus renders it “shes par mi ’gyur ro”. So does the Peking edition of the  Interestingly, “shes pa” appears nowhere in the Akutobhaya commentary Prasannapada. on this verse. 65 P. 5229, vol. 95, p. 41b “re zig son_ la ’gro ba med j ma son_ ba la ’an_ ’gro ba med j son_ ba dan_ ma son_ ma gtogs par j bgom ba ses par mi ’gyur ro jj ’di la re zig son_ ba la ’gro ba med de j son_ zin pa’i phyir te j bya ba dan_ bral ba la bya ba mi ’thad pa’i phyir ro j ma son_ ma la yan_ ’gro ba med de ’gro ba med pa’i phyir ro j bgom la yan_ ’gro ba med de j son_ ba dan_ ma son_ ba dag ma gtogs par bgom pa med pa’i phyir te j mar me tan_ snan_ bzin no j” 66 The rhetorical device of asking “why?” and proceeding to answer the question is a common feature of philosophical texts of this time, for instance there are quite a  ı. Though in most number of these in the auto-commentary on the Vigrahavyavartan other texts this does not necessarily indicate a syllogism, there does seem to be a  correlation in the Akutobhaya. 67 Compare this convention with that of Bhavaviveka who introduces his examples with, “for example : : : ” [“dper na: : : ”]. 68 Presumably this example refers to Nagarjuna’s own discussion of the example of   a 7.9–13 and at Vigrahavyavartan  ı arik a lamp and illumination at Mulamadhyamakak 34–39. 69 There is some disagreement among modern translations concerning the difference between upapatsyate and upapadyate. Inada [(1993), p. 44] ignores the difference and translates both as “is possible”. Tachikawa seems to be aware of apdifference and translates the verse by using two different definitions of the term upa pad – “to be possible” and “to exist”: “How is it possible that there is [the action of] traversing on the point being traversed? For if there is not [the action of] traversing, the point being traversed cannot exist”. [Tachikawa (1974), p. 6] Upapatsyate, however, is unequivocally of the periphrastic future, defined by Whitney as follows: “The periphrastic future is defined by the grammarians as expressing something to be done at a definite time to come : : : . It is especially often used along with sva tomorrow”. [Whitney (1891), p. 338] Upapadyate, on the other hand, is present tense middle voice of the same verb. Hence, the second pada should be in the future tense while the fourth pada should be in the present tense. This difference is also suggested by the Tibetan “ji lta bur na ’thad par ’gyur” / “bgom pa ’thad pa med phyir”. Both May and Walleser translate it accordingly: Comment le mauvement s’appliquer-t-il [en tant que predicat] au mouvement actuel, puisqu’un mouvement actuel sans mouvement [inherent] est tout a fait irrationnel? 226 JOSEPH WALSER [May (1959), p. 55] Wie wird als gegenwartiges Gehen nicht moglich ist? (Walleser (1911), p. 16.) 70 The Sanskrit of this verse according to Poussin’s edition reads, “gamyamanasya dvigamanam. katham . namopapatsyate j gamyamane dvigamanam . yada naivopapadyate  jj” [Poussin (1903–1913), p. 94]. However, the version on which the Akutobhaya comments is slightly different. The Tibetan reads: “bgom la ’gro ba yod par ni / ji lta bur na ’thad par ’gyur // gan_ tshe ’gro ba med pa yi / bgom pa ’thad pa med  ıpa, phyir ro jj” The Akutobhaya version of this verse is supported by the Prajn~aprad and the Chung-lun. Inada [(1993), p. 44] also mentions that there is confirmation of this reading in the Ta-ch’eng-chung-kuan-shih-lun. These readings as well as Tucci’s Sanskrit manuscript supports a reading of “vigamanam. ” instead of “dvigamanam. ” [de Jong (1978), p. 36]. 71 “bgom la ’gro ba yod par ni ji lta bur na ’thad par ’gyur j gan_ tshe ’gro ba med pa yi j bgom pa ’thad pa med phyir ro j ’di la bgom pa la ’gro ba yod pa mi ’thad _ par gzun_ ba mi ’thad de j ci’i phyir ze na j ’di ltar ’gro ba med pa’i bgom pa nes pa’i phyir te j mo gsam gyi bu bzin no j” P. 5229, vol. 95, p. 42a. cp. Huntington (1986), p. 263. 72 “Sur l’emploi optionnel du present, du futur ou de l’optatif dans une phrase interrogative exprimant un bl^ame, v. Pan. . III.3.143–144.” Jaques May (1959), p. 5, note 18. 73 Pan. ini’s rule states that: [3.3.143] “katham . ” conjoined with a present indicative _ verb optionally denotes blame or censure (garha).  Pan. ini 3.3.144 (lat. ), or optative (lin) states that a declined form of “Kim . ” conjoined to a future (lr. .t) verb also denotes censure. [Cp. Katre (1987), pp. 311–312.] In this verse, katham . is conjoined with a future tense verb – a case which is not covered by the rules cited. Nevertheless,  reconstruction certainly seems to be in the spirit of Pan. ini’s rule. the Akutobhaya’s 74 Sanskrit dvau gantarau prasajyete prasakte gamanadvaye j gantaram . hi tiraskr.tya gamanam . nopapadyate j [Poussin (1903–1913), p. 96].  and of the Cone and sDe dGe versions of the The Tibetan of the Prasannapada, third pada say, “gan. phyir ’gro ba med par ni” The Peking of the Akutobhaya is correct, “gan. phyir ’gro po med par ni”. 75 “’gro ba gn~is su thal gyur na j ’gro ba po yan_ gn~is su ’gyur j gan_ phyir ’gro po med par ni j ’gro ba ’thad par mi ’gyur phyir j [42b] ’di la ’gro ba gn~is su thal bar ’gyur na ’gro ba po yan_ gn~is su thal bar ’gyur te j ci’i phyir ze na j gan_ gi phyir ’gro ba po med par ’gro ba ’thad par mi ’gyur ba’i phyir ro j ’gro ba gn~is dan_ gro ba po gn~is su thal bar ’gyur ba de ni mi ’dad de j de’i phyir bgom pa la ’gro ba yod do zes bya ba de rigs pa ma yin te j mgo bcad bzin no j” P. 5229, vol 95, pp. 42a–42b, Huntington (1986), p. 265. Walleser translates “mgo bcad” as “ein abgeschlagenes Haupt” [Walleser (1911), p. 17] While it is true that “mgo” can mean “height”, a better rendering would be “head” using Nagarjuna’s own example at MMK 7.31 as a model. There, the example indicates that because one does not have second head, it is impossible to cut it off.  at MMK 7.31: “mgo gn~is Buddhapalita explains this (better than the Akutobhaya) pa la ji ltar ni / bcad du med pa de bzin no / med pa la ci zig ’gag par ’gyur te / ’di ltar mgo gn~is pa med par bcad par mi nus pa bzin no j” [P. 5242, vol. 95, p. 221b] = “ ‘Just like cutting a second head is not possible’ What would be the purpose of eliminating something that doesn’t exist? Hence, for example, it is not possible to cut off a non-existent second head. “Applied to this, the example means that because there is no second going a second goer associated with that going is not possible (i.e., in order for there to be a second cut there must be first a second head)”. 76 “notpadyamanam . notpannam . nanutpannam . katham . cana j utpadyate tad akhyatam . gamyamanagatagataih. jj” Poussin, p. 157.  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 227 “skyes dan_ ma skyes skye bzin pa j ji lta bur yan_ skyed mi byed j son_ dan_ ma son_ bgom pa yis j de dag rnam par bsad pa yin j : : : ji ltar skyed par mi byed pa de ltar ni son_ ba dan_ ma son_ ba dan_ bgom pa dag gis de dag rnam par bsad zin to _ ji ltar ze na j bsad pa j re zig dnos _ j de yan po skyes pa ni skyes par mi byed de j ci’i phyir  ze na j thug pa med par thal bar ’gyur ba’i phyir dan_ j byas pa la bya ba med pa’i phyir te j” P. 5229, vol. 95, p. 54b, Huntington, 313–314. 78 cp. verses 4, 6, 8, 14, 17ab. 79 Huntington (1986), p. 23. 80 Italicized words are those which are quoted verbatim from the verse itself. Unitalicized words represent insertions of the commentary. 81 _ po med par gyur pa la ’an_ j ’gag pa ’thad par mi ’gyur ro j mgo gn ~is pa “dnos _ pa med pa la yan_ ’gag pa ’thad par la ji ltar ni j gcad du med pa de bzin no j dnos mi ’gyur te j c’i phyir ze na j med pa’i phyir te j ji ltar mgo gn~is pa la bcad du med pa de bzin no j” P. 5229, vol. 95, p. 58b, Huntington, pp. 328–329. 82 Santina (1986), p. 54. 83 Arnold Kunst (1939) credits the Buddhists in general and Nagarjuna in particular for the trend of reducing the number of members of the syllogism. 84 Shohei Ichimura, in a number of articles has claimed that the manipulation of positive instantiation is the driving force behind Nagarjuna’s dialectic. In an early article [Ichimura (1980), pp. 7–15], he claims that the principle of dual instantiation  and in a more recent article was first expressed among Buddhists in the Katthavattu, [Ichimura (1995)], he finds further support for this claim in the presence of two examples in the Fang-pien-hsin-lun (a text ostensibly by Nagarjuna himself). While there is no space to examine each of his arguments, let me make two observations.  there are arguments against opposing First of all, while it is true that in the Katthavattu sides of the same issue, the opposing arguments are held by those with different sets of assumptions. Thus, the opposing arguments are examples of “rejoinder” more than they are examples of dual instantiation. Second, while the Fang-pien-hsin-lun does talk about two kinds of examples, there is no indication that these two are the same positive and negative examples mentioned in the Fang-pien-hsin-lun. Taisho volume 32, no 1632 p. 23c states: and might be best translated as “complete” and “incomplete” examples, but, to my knowledge, these  characters are not Chinese equivalents of the Sanskrit anvaya and vyatireka. 85 bhava: “Similarly what happens in the case Cf. Vatsyayan. a’s explanation of sam . of [sam . bhava] is that, the Composite and the Component being related to one  the cognition of another by the relation of invariable concomitance (avinah=avin), the former gives rise to the cognition of the latter; and is only a case of inference”. Translation, Jha (1984), p. 886. Text: tatha carhapattisambhavabhavah. vakyarthasam . pratyayenanabhihitasyarthasya pratyanıkabhavad grahan. am arthapattir anumanameva avinabhavavr. ttya ca sambaddhyayoh. samudayasamudayinoh. samudayenetarasya grahan. am . sambhava tadapyanuma nameva j [Tailanga (1984), p. 101]. 86 This is somewhat peculiar because we do not normally consider what-is beinggone-over to be a part of “going”. Yet, it is still something that is necessarily entailed in the notion of going. This is perhaps more acceptable if one thinks of being in a boat on a river. From one perspective the boat is moving, but form another the shore is moving. 87   . gamanam Sanskrit gamyamanasya . yasya tasya prasajyate / .rte gater gamyamanam  . hi gamyate gamyamanam [Poussin (1903–1913), p. 95]. Inada choses to translate p the derivatives of pra san~j as “a fallacy results”. While this may work in context, it seems to me to assume a special definition of the term which is unwarranted. p Pra san~j simply means to be connected or to logically follow from something.  necessaire”. Hence, I follow Walleser’s “zutreffen” and May’s “consequence 77 228 JOSEPH WALSER The last pada of the Akutobhaya reads gamyate in the sense of “is known” following the interpretation given by the commentary below. This translation is the  same as that of Buddhapalitavr . tti and the Prajn~apradıpa (P. 5229, vol. 95, p. 42a 1. 4, P. 5242, vol. 95, p. 190b ll. 5–6, and P. 5253, vol. 95, p. 78a ll. 2–3, respectively] “bgom pa khon_ du chud phyir ro”). Candrakırti, without any comment, goes against this interpretation and takes this last pada as ‘because what is being traversed is  amam    a also ignore ulamadhyamakak arik traversed’. The Chung-Lun, and the Prajn~an this secondary meaning of the word gam (cf. Bocking (1995), pp. 120–121 and Prasannapada and Pmmk. “bgom la ’gro ba yin phyir ro” /). 88 Tibetan = “ma bltos pa” translates Sanskrit “anapeks. a”; cf. chp. 10.3, (Huntington (1986), p. 348). The Tibetan seems to be a literal translation meaning “what is not seen” or perhaps even, “what is irrelevant”. Monier-Williams (s.v.) has “disregarding”, and “irrelevant” as definitions for “anapeks. a”, but Apte’s “independent” and Bothelink’s “Unabhanigkeit” seem to be more to the point here. Walleser translates it following Bothelink. Huntington points out that the Cone and Derge editions prefer “ltos ba”, while the Peking edition uses “bltos pa”. This variation is not significant for our purposes. 89  The reason here is taken from the last three padas of the verse which in Tibetan reads: “gan_ gi phyir bgom pa khon_ do chud pa’i phyir te”. The Tibetan translators render “gamyate” in its secondary meaning of “is understood”. My decision to _ par zhen pa” follow the Tibetan in translating this was made based on “mnon (“abhinivisyate”) in the next line which is a paraphrase of the previous sentence. 90 P. 5229, vol. 95, p. 42a: “gan_ gi bgom la ’gro yod pa j de yi bgom la ’gro med par j thal ba ’gyur te gan_ gi phyir j bgom pa khyon_ du chud phyir ro j ’di la gan_ gi phyogs la bgom pa la ’gro ba yod par ’dod pa de’i bsgom pa la ’gro ba med par thal bar ’gyur te j ma bltos par ’grup par ’gyur ro zes bya ba’i tha tshig go ci’i phyir ze na j gan_ gi phyir bgom pa khon_ du chud pa’i phyir te j tshig ’di la _ par zen pa’i phyir ro j de yan_ mi ’dod de j de’i phyir bgom pa la ’gro ba yod mnon do j zes by ba ni rigs pa ma yin te j grum po bzin no j” cp. Huntington (1986), p. 264. 91 This interpretation for this verse seems to have only been used in the Akutobhaya and in the Chung-lun. See Bocking (1995), p. 121. 92 ’gro ba mi srid pa de n~id kyi pyir” P. 44a 1. 8, Huntington, 273. 93 The Akutobhaya author was not the only commentator to pinpoint the problem underlying the dilemma in verse four as lying in the independence of goer and going. The Chung-lun approaches the problem from the other direction. If someone says that in the already-gone and the not-yet-gone there is no going, but that a going really exists in the moment-of-going, this person is in error. If the moment of going existed independently of the dharma of going, then they would not be interdependent. Why is this? If you assert that there is a going in the moment-ofgoing, this implies two operations, but this is not so in reality. Therefore you cannot say that there is a moment-of-going separate from going. [translated by Bocking (1995), p. 121. Italics mine] Clearly, from the italicized portion of this passage the Chung-Lun commentator assumes that goer and going are interdependent. Although the Chung-Lun does not seem to have the same penchant for syllogisms as does the Akutobhaya it nevertheless does share a number of interpretations which are not shared by the later commentaries.   and “asadbhuta” in the last A notable similarity is the definitions for “sadbhuta”  verse, which is roughly equivalent to those given in the Akutobhaya. “Definitely fixed” means having real existence from the beginning and not arising on account of a dharma of going.” : : : “Not definitely fixed” means really non-existent from the beginning”.  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 229 94 “thams cad yan_ dag yan_ dag min j yan_ dag yan_ dag ma yin n~id j yan_ dag min _ rgyas bstan pa’o j thams cad yan_ dag ces bya ba ni min yan_ dag min j de ni sans mig la sogs pa skye mched rnams dan_ gzugs la sogs pa’i yul rnams tha sn~ad kyi bden pa dan_ mi ’gal bar yod pa’i phyir ro j yan_ dag min zes bya ba ni don dam _ bo n ~id yons _ su ma grub ba’i phyir ji ltar bar rten nas byun_ ba sgyu ma bzin du no snan_ ba de ltar yod pa ma yin pa’i phyir ro j yan_ dag yan_ dag ma yid n~d ces bya ba ni j bden pa gn~i ga’i rnam pa la bltos pa’i phyir ro j yan_ dag min min yan_ dag min zes bya ba ni j mdon par rthogs pa’i dus na rnal ’byor pa rnam pa thams cad du chos thams cad kyi de kho na la rnam par mi rtog pa’i phyir ro j yan_ na thams _ pa’i sgrib pa span_ ba’i cad yan_ dag ces bya ba ni j bcom ldan ’das kyis n~on mons phyir nan_ dan_ phyi rol gyi skye mched bdag dan_ bdag gi dan_ bral ba’i mtshan n~id gyo ba med pa ses byar bstan pa dag yin no j yan_ dag min zes bya ba ni rnam par ses pa’i mtshan n~id kyi bdag gis bdag dan_ bcas pa’i phyir dan_ bdag gi yin pa’i phyir byed pa por brjod pas n~an ba dan_ sems pa dan_ bsgom par byed pa dag yin no _ dag yan_ dag ma yin n ~id ces bya ba ni ’jig rten dan_ bstan chos kyi tha sn ~ad j yan [tha skad?] la bltos pa dag yin no j yan_ dag min min yan_ dag min zes bya ba ni j don dam pa’i tshul gyis chos thams cad skye ba med pa’i phyir  ses ba rnam par _ rtog pa dan_ bcas pa dan_ rnam par rtog pa med pa’i spyod yul n~id du ’gyur ba dnos po’i tshul gyis yan_ dag pa ma yin pa n~id du rnam par brtags pa dan_ yan_ dag pa n~id du rnam par brtags pa gan_ yin pa de lta bu med pa yin no j” P. 5229, vol. 95, pp. 83a – 83b, cp. Huntington (1986), pp. 436–437. For a discussion of the various commentaries on this verse see Ruegg (1977), pp. 37–39. 95 This discussion bears a number of similarities to the simile of the chariot explained  by Vajira Bhikkhunı, in the Sam . yutta Nikaya: [Mara asks:] By whom was wrought this ‘being’ [satta]? Where is he who makes him? Whence doth a being arise? Where doth the being cease and pass away?: : : [Vajira Bhikkhunı:] ‘Being’! Why dost thou harp upon that word? ‘Among false opinions, Mara, hast thou strayed. Mere bundle of conditioned factors, this! No ‘being’ can be discerned to be. For just as, when the parts are rightly set, the word ‘chariot’ ariseth [in our minds], So doth our usage covenant to say: ‘A being’ when the aggregates are there. Nay, it is simply Ill that rised, Ill that doth persist, and Ill that wanes away. Nought beside Ill it is that comes to pass, Nought beside Ill it is that comes to pass, Nought else but Ill it is doth cease to be. Then Mara the evil one thought: ‘Sister Vajira knows me’ and sad and sorrowful he vanished there and then. [Translation: (Kindred Sayings, vol. 1, pp. 169–170.) Text: “Kenayam . pakato satto kuvam . sattassa karako, Kuvam . satto samuppanno kuvam . satto nirujjhatıtikinnu satto ti paccesi mara dit.t.higatam . nu te j _ arapun ~jo yam palabhati jj suddhasankh . nayidha sattu _ ara hoti saddo ratho iti j yatha hi sangasambh evam . khandhesu santesu hoti satto ti sammuti dukkham eva hi sambhoti dukkham. tit.t.hati veti ca j nan~n~atra dukkha sambhoti nan~n~am . dukkha nirujjhati  (Sam (PTS) vol. 1. 135) . yutta Nikaya, jj Also, cf. Milindapan~ho: “I, revered Nagasena, am not telling a lie, for it is because of the pole, because of the axle, the wheels, the body of the chariot, the yoke, the reins, and because of the goad that ‘chariot’ exists as a denotation, appellation, designation, as a current usage, as a name.” [Milinda’s Questions, vol. 1, (1963), p. 37.] 230 JOSEPH WALSER ~ca pat.icca The Pali runs as follows: “Naham . bhante Nagasena musa bhan. ami, ısan akkhan~ca pat.icca cakkani ca pat.icca ratho ti sankha saman~n~a pan~n~atti voharo namam . pavattatıti” [PTS version p. 27]. The central message of Vajira Bhikkhunı’s speech that one’s soul should be denied existence in favor of its parts (i.e., the 5 skandhas). The crucial difference occurs in the statement, “The wheel, etc., : : : is [similarly] a designation depending on parts”. The emphasis here is that each part is not ultimate, but is also composite. In short,  not only is the composite thing without an ultimate identity (“pudgala-nairatmiya”)  but its component parts are similarly composite = (“dharma-nairatmiya”). REFERENCES The Book of Kindred Sayings (Samyutta-Nikaya) (1992). Rhys Davids, C.A.F. and Woodward, F.H., trans. New York: Oxford University Press. Milinda’s Questions (1963). Horner, I.B., trans. London: Luzac & Company, Ltd.  ıpa: A Translation of Chapter One: Ames, William (1993). ‘Bhavaviveka’s Prajn~aprad  – Part One’, Journal of Indian “Examination of Causal Conditions”, (Pratyaya) Philosophy 21(3), 209–257.  ıpa: A Translation of Chapter Ames, William (1995). ‘Bhavaviveka’s Prajn~aprad Two: “Examination of the Traversed, The Untraversed, And That Which is Being Traversed” ’, Journal of Indian Philosophy 23, 295–365. Anacker, Stephan (1984). Seven Works of Vasubandhu: The Buddhist Psychological Doctor. Delhi: Motilal Banarsidass Publishers Private Limited.  arjuna  in China: A Translation of the Middle Treatise. Bocking, Brian (1995). Nag Lewiston, NY: The Edwin Mellen Press. Chandra, Lokesh (1990). Tibetan-Sanskrit Dictionary Based on a Close Comparative Study of Sanskrit Originals and Tibetan Translations of Several Texts. Kyoto: Rinsen Book Co. Cowell, E.B. (1894). ‘The Buddha-k^arit^a of Asvaghosha’, in Buddhist Maha^ya^na Texts. New York: Dover Publications Inc, 1969. Das, Sarat Chandra (1995). A Tibetan-English Dictionary with Sanskrit Synonyms. Delhi: Motilal Banarsidass Publishers. Frauwallner, E. (1958). ‘Die Erkenntnislehre Klassischen Sam . khya-Systems’, Wiener Zeitschrift fur die Kunde Sud- und Ostasiens 2, 84–139. Gokhale, Pradeep (1992). Inference and Fallacies Discussed in Ancient Indian Logic  and Buddhism). Delhi: Sri Satguru Publications. (with special reference to Nyaya Hopkins, Jeffrey (1983). Meditation on Emptiness. London: Wisdom Publications.  and Early Indian Madhyamaka. Huntington, Clair W. (1986). The “Akutobhaya” Ph.D., University of Michigan. Ichimura, Shohei (1980). ‘A Study of the Madhyamika Method of Refutation,  Journal of the International Especially of Its Affinity to that of Kathavatthu’, Association of Buddhist Studies 3(1), 7–15. Ichimura, Shohei (1992). ‘Re-Examining the Period of Nagarjuna: Western India, A.D. 50–150’, Journal of Indian and Buddhist Studies 40(2), 1073–1079. Ichimura, Shohei (1995). ‘The Period of Nagarjuna and the Fang-pien-hsin-lun (or  . daya  sastra)’,  Journal of Indian and Buddhist Studies 43(2), 1033–1028. Upayahr  arjuna:    a A Translation of this Mulamadhyamakak arik Inada, Keneth K. (1993). Nag with an Introductory Essay (reprint ed.). Delhi: Sri Satguru Press. _ und Prasangavipary _  bei Dharmakirti und Seinen aya Iwata, Takashi (1993). Prasanga Kommentatoren. Vienna: Arbeitskreis fur Tibetische und Buddhistische Studien.  ON THE FORMAL ARGUMENTS OF THE AKUTOBHAYA 231  Jha, Mahamahopadhyaya Ganganath (1965). The Tattva Kaumudi: Vacaspati Misra’s  . khya-Karik  a.  Poona Oriental Series, vol. 10. Poona: Oriental Commentary on the Sam Book Agency.  . ras of Gaut. ama with the ut Jha, Mahamahopadhyaya Ganganath (1984). The Nyaya-S . ya of Vat . syayana   . ika of Ud. d. yot. kara, translated into English and the Vart Bhas    . ika-T  Udayana’s art With Notes from Vachaspat . a.tparyaıka’, . i Mishra’s ‘Nyaya-V . yachandra. Delhi: Motilal Banarsidass. ‘Parishud. d. hi’ and Raghuttama’s Bhas  Indo-Iranian Journal de Jong, J.W. (1978). ‘Textcritical Notes on the Prasannapada’, 20(1–4), 25–60 (#s. 1/2) and 217–252 (#s 3/4).  ı of Pan . ini. Austin: University of Texas Press.  ay Katre, Sumitra M. (1987). As. .tadhy Kunst, Arnold (1939–1940). ‘The Two-Membered Syllogism’, Rocznik Orientalistyczny 15, 72–83.  . khya: A Dualist Tradition in Indian Philosophy. Larson, Gerald (ed.). (1987). Sam Princeton: Princeton University Press.  Ithica, New York: Snow Lion Lopez, Donald (1987). A Study of Svatantrika. Publications. May, Jaques (1959). Candrakırti Prasannapada Madhyamakavr. tti: Douze chapitres   d’une introduction, de notes accompagnes traduits du sanscrit et du tibetain,  Paris: Libraire D’Amerique et et d’une edition critique de la version tibetaine. D’Orient. Monier-Williams, S.M. (1899). A Sanskrit-English Dictionary Etymologically and Philologically Arranged with Special Reference to Cognate Indo-European Languages. Delhi: Motilal Banarsidass (1990).  arjuna.  Delhi: National Book Trust. Murty, K. Satchidananda (1971). Nag Oetke, Claus (1996). ‘Ancient Indian Logic as a Theory of Non-Monotonic Reasoning’, Journal of Indian Philosophy 24, 447–539. Phillips, Stephen H. (1995). Classical Indian Metaphysics: Refutations of Realism and the Emergence of “New Logic”. La Salle: Open Court. Potter, Karl H. (ed.). (1977). Indian Metaphysics and Epistemology: The Tradition  _ sa Princeton: Princeton University Press. ses. ika up to Gange of Nyaya-Vai   as  (Madhyamikas   arik utras) Poussin, Louis de la Valee (1903–1913). Mulamadhyamakak  arjuna  avec la Prasannapada Commentarie de Candrakırti. Osnabru ck: de Nag Biblio Verlag (1970). Ruegg, David Seyfort (1977). ‘The Uses of the Four Positions of the Catus. kot.i and the Problem of the Description of Reality in Mahayana Buddhism’, Journal of Indian Philosophy 5, 1–71. Ruegg, David Seyfort (1981). The Literature of the Madhamaka School of Philosophy in India. Wiesbaden: Otto Harrassowitz. Santina, Peter Della (1986). Madhyamaka Schools in India: A Study of the Madhyamaka  ngika _  and Svatantrika Philosophy and the Division of the System into the Prasa Schools. Delhi: Motilal Banarsidass.  Agnivesa’s Treatise Refined and Annotated Sharma, Priyavat (1981). Caraka Sam . hita:  (text with English translation), Priyavrat by Caraka and Redacted by Dr. dhabala Sharma, ed. and trans. Banaras: Chaukhambha Orientalia. Staal, J.F. (1962). ‘Negation and the Law of Contradiction in Indian Thought: a Comparative Study’, Bulletin of the School of Oriental and African Studies University of London 25, 52–71. Tachikawa, Musashi (1974). ‘A Study of Buddhapalita’s Mulamadhyamakavr. tti’, Nagoya Daigaku Bungakubu Kenkyu Ronshu 63 (Dec. 9), 1–19.  utras  with Tailanga, Mahamahopadhyaya Gangadhara Sastri (1984). The Nyayas  ayana’s  . ya and Extracts from the Nyayav  arttika  Bhas and the Tatparyatıka Vatsy (2nd edn.). Delhi: Sri Satguru Publications.  sanam: Taranatha Nyaya-Tarkatirtha and Amarendramohan Tarkatirtha (1985). Nyayadar  ayana’s  . ya, Uddyotkara’s Varttika,    Bhas Vacaspati Misra’s Tatparyat With Vatsy . ıka 232 JOSEPH WALSER  & Visvanaatha’s Vr. tti (2nd edn.). New Delhi: Munshiram Manoharlal Publishers Private Limited. Wallesser, Max (1911). Die Buddhistische Philosophie in iherer geschichtlichen  arjuna.  Heidelberg: Carl Entwickling: Zweiter Teil – Die mittlere Lehre des Nag Winter’s Universitatsbuchhandlung. _ Journal of the Wayman, Alex (1958). ‘The Rules of Debate According to Asanga’, American Oriental Society 78, 29–40. Whitney, Dwight W. (1891). A Sanskrit Grammar, Including Both the Classical Language and the Older Dialects, of Veda and Brahmana (2nd edn.). Leipzig: Breitkopf and Hartel. Department of Religious Studies Loyola University New Orleans, U.S.A.