How do Mdhyamikas Think? Notes on Jay Garfield, Graham Priest and Paraconsistency

Several philosophers and Buddhist Studies specialists have taken up the question of where or whether the philosophers of the Middle Way school, i.e., Madhyamaka, use some form of deviant logic, or a logic which would not recognize fundamental theorems such as the law of double negation, the law of excluded middle and even the law of non-contradiction. Often this investigation is focused on the tetralemma (catukoi), with very varied results. In recent writings problems about excluded middle or the interpretation of negation in the tetralemma have tended to take precedence over earlier interests about Madhyamaka respect or non-respect for the law of non-contradiction. Indeed it's probably fair to say that, in Buddhist Studies at least, attributing contradictions to the Ngrjuna has increasingly fallen out of vogue, such an attribution or tolerance often being considered, by those of a philosophical bent, as tantamount to a disastrous trivialization of Madhyamaka as exclusively mystical or even irrational. Some would argue intuitively that contradictions are rationally unthinkable. Others would invoke a more sophisticated problem that anything and everything would follow from a contradiction so that all reasoning would become indiscriminatecontradictions thus could supposedly never be tolerated by rational individuals on pain of logical anarchy. In any case, the underlying idea then is that if the Madhyamaka is not to be trivialized as irrational and indeed I agree it should not be so trivialized , it would have to rigorously respect the law of non-contradiction.

Recently the Australian logician, Graham Priest has teamed up with the American philosopher, Jay Garfield, to significantly elaborate upon certain ideas that they attribute to the second century C.E. author, Ngrjuna. To do this they rely on paraconsistent logic, i.e., formalizations of logic that eliminate the spectre of anarchy by not allowing everything to follow from a contradiction. Amongst the several types of such paraconsistent logics developed in the current technical literature, Priest and Garfield opt for a radical type and maintain that there are some Ngrjunian arguments that can best be

interpreted as evidence of a logic that allows an acceptance of some true contradictions. In other words, Ngrjuna was (at least implicitly or in a reconstruction of his philosophy) an advocate of "dialetheism", i.e., the position that some contradictions are truefor some statement , & not- is true. Priest and Garfield's joint paper, "Ngrjuna and the limits of thought," certainly does not endorse a laissez-faire acquiescence in any and all contradictions; they do seek to argue that some statements of contradictions in Madhyamaka can be best taken as true, notably those along the lines of "the ultimate truth is that there is no ultimate truth" or "all things have one nature, i.e., no nature". These and other logically similar statements that are supposedly to be found in Western thinkers like Kant, Wittgenstein and Hegel, have the characteristic that Graham Priest has diagnosed as being at the "limits of thought", in that they involve totality paradoxes. The dialetheism comes in when we say that specific sorts of totalities, or "inclosures", exist and that there are at least some things which both are and are not in them.1 My own take: I can readily accept a limited type of paraconsistency in the Prajpramit and Ngrjuna, but full-fledged dialetheism seems to me unlikely Graham Priest and Jay Garfield seem to have read Tillemans (1999) as, like them, accepting Ngrjuna's "sincere endorsement of contradictions". Well, no doubt, finding out what that work`s svamata (rang lugs, own take) on paraconsistency might actually be is a difficult task, especially as my views evolved considerably since an earlier article. It's probably by now high time to set out as clearly as I can what I do accept.

In my introduction to Scripture, Logic, Language I had said: "I don't now know how to exclude that the Prajpramitstras are most simply and naturally read as having more or less the contradictions they appear to have. Indeed, that [Edward] Conze-[Jacques] May scenario fascinates me more and more."2

I was essentially imagining an attempt at a more or less literal and unhedged interpretation of certain passages in the Prajpramit-stras and in early Madhyamaka writers like Ngrjuna, an interpretation which would be independent of and even opposed to that of the later commentators. I found myself in a position where I could no longer rule out an interpretation of this sort on formal grounds or because all paraconsistency supposedly would be irrational or lead to unlimited anarchical implication. Indeed the prospect of trying to tread this paraconsistent path seemed to me worthwhile, even heady, in that it seemed to be an attempt to take the provocative and disturbing aspects of the Madhyamaka seriously, straight-no-chaser, and not explain them way with sophisticated ad hoc solutions or even massive additions to the texts designed to accomodate a type of prescriptive "common sense" about what was needed so that an author like Ngrjuna would supposedly be minimally rational.

In Scripture, Language and Logic, I had spoken about a natural and simple literal reading of passages in the Prajpramitstras that suggested acceptance of contradiction. I was thinking primarily of what can be called the "signature formulae" of the Vajracchedik-prajpramitstra.3 These are the oft-repeated statements throughout the stra that say that X does not exist or is not the case and that we therefore say that X does/is. E.g., the Buddha doesn't have any distinctive marks and that is why one says he does. Vajracchedik p. 24 (ed. M. Muller): buddhadharm buddhadharm iti subhte 'buddhadharm caiva te tathgatena bhit / tenocyate buddhadharm iti // "'The dharmas special to a buddha, the dharmas special to a buddha,' these the Tathgata has taught to not in fact be/have dharmas special to a buddha. Thus they are said to be dharmas special to a buddha." Leave aside the somewhat tricky question as to how we take the Sanskrit compound, abuddhadharm ca (as a bahuvrhi or as a tatpurua I tend to opt for the latter, as do most translations in Buddhist canons). In any case the simple and natural reading of the passage, deliberately neglecting commentaries, is to say that this signature formula is denying something and then later affirming it. We'll go into such statements, as well as the commentaries, in more detail below.

As for Ngrjuna, I was only secondarily thinking of his use of the tetralemma: what impressed me was a natural, more or less literal interpretation of his system in the sixfold logical corpus (rigs tshog drug). At some points (e.g., in his Ratnval) he endorses various Buddhist doctrinal positions (e.g., karmic retribution etc.) and at other points (i.e., in the Mlamadhyamakakriks) clearly denies that there are any such things at all. The fabric of his system, again neglecting commentaries, seems to suggest contradictoriness not unlike that to be found in the signature formulae of the Vajracchedik: such and such is said to be so in certain texts, chapters, etc. and elsewhere, or even in the same paragraph, is said not to be so.

My own mentor, Jacques May, had already many years ago applied some Hegelian notions to Ngrjuna and had seen Ngrjuna's dialectic as a continuous and endless Aufhebung (sublation) of provisional contradictory positions. Edward Conze had also held a view on the Prajpramit as accepting contradictions. Although I couldn't see myself furthering the exact same perspectives that they were promoting, I did think that the debate about paraconsistent approaches, a debate that had gone out of fashion in Buddhist Studies, should be profitably revived. That has now happened with Graham Priest and Jay Garfield and it is, I think, something of a liberating experience to be able to talk seriously about Madhyamaka and Prajpramit in these terms, even if, as we shall see, I don't share their enthusiasm for dialetheism in Buddhism. Priest and Garfield on Ngrjuna Although a natural account of the signature forumulae of the Vajracchedik and the fabric of Ngrjuna's six works seems to go have him endorsing the truth of at some point and endorsing the truth of not- at another, we never, to my knowledge, find a clear textual endorsement of the truth of the conjunction, and not-. My intuitive skepticism about dialetheism in Ngrjuna is thus obviously going to clash with Graham Priest's and Jay Garfield's interpretation. We thus need look in more detail at why Priest and Garfield thought that there were indeed true contradictions (i.e. true conjunctions of and not- ) in the Madhyamaka and what exactly would be problematic in such a reading of Ngrjuna.

Let's be clear on a point of method: attributing such and such a type of logic to an author like Ngrjuna is primarily a matter of rational reconstruction. If we are going to cite texts, and I certainly think we should, the onus has to be heavily on their interpretation, context and rational reconstruction the mere words by themselves prove virtually nothing. So far, I think, Priest, Garfield and I would agree, and I would have no problems with their characterization that what they are doing with Ngrjuna "is .. not textual history but rational reconstruction."4 Indeed, if we look at the two candidates for paradox that they give, these statements are certainly not quotations from Ngrjuna. The first one, i.e., "The ultimate truth is that there is no ultimate truth", is in effect arguably a consequence or paraphrase of several passages in the Mlamadhyamakakriks and in that way can perhaps be claimed to be the thrust of Ngrjuna's philosophy, if not actually his words.5 The second, i.e., "all things have one nature, i.e., no nature", is in fact close to an historically attested interpretation of some passages in Madhyamakakriks XV about the three characteristics of any intrinsic nature: non-fabricated, independent of other things (nirapeka paratra) and always fixed. It is especially Candrakrti's interpretation of these passagesnotably his Prasannapad on XV.2that brings in the idea that Ngrjuna does not just refute intrinsic natures, but accepts that there is at least one such non-fabricated, independent and unchanging fixed nature of things, viz., their emptiness (nyat).6

I shouldn't go into very many technical details here about how Priest and Garfield formally present the paradoxes that they see in Ngrjuna; I'll confine the presentation of inclosure schemata to a long footnote. 7 In any case, Priest and Garfield claim that the Ngrjunian paradox is one like set theoretical paradoxes, where in the case of some totality, or "limit of thought", defined in a certain way, there will be objects that both are included within it and are outside it. They argue that if we suppose with Ngrjuna that all things are empty, then the totality of empty, i.e., natureless, things will itself have a nature (i.e., being empty) and that this nature will be both in and not in the totality of empty things. Formulated as an inclosure paradox it does look potentially interestingly similar to other such paradoxes, like those of Cantor and Russell.

The connection with other logical paradoxes would itself be quite important as it would serve in part to answer a charge that these Ngrjunian paradoxes are simply "rhetorical paradoxes" along the

lines of "The Golden Rule is that there is no Golden Rule", "I can resist everything except temptation" and other such cute duplicitous sayings that are no more than attention grabbers.8 Undeniably there is a penchant for such enigmatic, provocative styles of expression in Indian philosophy, so that it would be silly to say that every use of words in an apparently contradictory fashion in a Sanskrit text is a case of an author embracing dialetheism or saying something exotic of logical interest. The saving grace of Priest's and Garfield's Ngrjunian paradoxes, if they are right, would be that they would both be cases of a wider East-West phenomenon, i.e., inclosure paradoxes, and would thus not be simply a matter of provocative style. They would supposedly be logical paradoxes in the same way that Russell's paradox and Cantor's are.

Although the Ngrjunian paradoxes would be interesting for comparative philosophers in that they would be East-West discoveries of consistency problems with totalities, I see two major problems in seeing totality paradoxes as playing a significant role in Ngrjuna's thought, i.e., philosophical problems and historico-textual problems.

Let's take philosophical considerations first. One problem is that these paradoxes would only happen in very specific areas: the biggest sets, the widest applicable properties (like emptiness), the limits of conceivability and expressibility, the limits of thought. Given this exclusively "big picture" in which Ngrjuna would figure with his fellow explorers of the transconsistent, it is hard to see that his paradox and the supposedly resultant dialetheism is going to have much bearing on the basic fabric of his Madhyamaka philosophical system, such as his idea of the two truths, their inseparable connection or the identity of sasra and nirva. We are left a bit in the lurch as to how to interpret his more basic and pervasive doctrines other than the rather isolated totality paradoxes.

In fact, it looks to me that there may be something of a non-sequitur in what Priest and Garfield claim the Ngrjunian inclosure paradoxes show. They claim that the second paradox about emptiness shows the following:

"All phenomena, Ngrjuna argues, are empty, and so ultimately have no nature. But emptiness is, therefore, the ultimate nature of things. So they both have and lack an ultimate nature."9

This conclusion seems to involve a certain leap, in that Priest and Garfield are using the big picture paradoxes to come up with a view on each and every individual thing. I'm not at all sure that this works.

After all, the point about the emptiness paradox is that one very important universal property, emptiness, both is and is not empty, or in other words, lacks an intrinsic nature and does not lack one. This paradox concerns the nature of the totality of empty things and it is that nature that is shown to be both empty and not empty. Indeed, that is the way the emptiness paradox is formulated by Priest and Garfield:

"The limit-contradiction is that the nature of all things ()viz., emptinessboth is and is not empty.

But immediately after this, they then say: Or to repeat Ngrjuna quoting the Prajpramitstra, 'all things have one nature, that is no nature.' "10

Now, whether individual things, like tables and chairs, have the contradictory properties of being both empty and not empty looks like a separate matter from whether emptiness itself has those contradictory properties. Indeed all things, like tables, chairs, etc., having no nature and yet also having as their nature emptiness would yield a paradox of them having and not having a nature, i.e., being empty and not empty. That may perhaps be where Ngrjuna and the author(s) of the Prajpramitstra want to go in saying that all things have one nature, i.e., no nature. But it's not obvious that they get there from the Ngrjunian paradox that Priest and Garfield have formalized; that remains, after all, a "limit-paradox" about emptiness itself and does not clearly show that each table and chair have the same contradictory properties that emptiness itself supposedly does. It doesn't seem to follow that if there was a inclusion paradox about a universal set , or an intrinsic nature of , the things in would themselves exhibit the same paradoxicalness.11

Secondly, historical and textual considerations. It seems to me difficult to account for the spirit and letter of Indian texts and also say that Ngrjuna would advocate true contradictions that he would see as stemming from totality paradoxes. Consider what we do know about the "spirit" of Indian discussions of totalities. Indeed, arguments about inconsistency in the notion of a totality do explicitly

and repeatedly figure in Indian philosophy's arguments about the coherence of the notion of sarva (all, the totality, the universe), but they are certainly not accepted as cases of dialetheism or genuine true contradictions. They are instead used by Naiyyikas, like Uddyotakara in his Nyyavrttika to Nyyastra 2.2.6612, to refute Buddhist doctrines, like the semantic theory of apoha, by reductio ad absurdum. The non-Buddhist Naiyyika argues, for example, that the Buddhist theory of apoha, where the term X signifies non-non-X, is impossible in the case of word like "the totality" "all" (sarva). The reason is that the Buddhist would (absurdly) have to admit that there is something, be it a set or a property or an individual, that is outside the totality of things, because given the principal that any word X signifies non-non-X, "the totality" would express the negation of non-totality (asarvanivtti) the hidden premise is that there always must be something to negate, a real, existing negandum. Of course the problem then is that this something outside the totality would have to be both outside and not outside the totality of things.

Whatever the value of Uddyotakara's attack, the Buddhists, including Madhyamakas like Kamalala in his Madhyamakloka and ntarakita in the apoha chapter of his Tattvasamgraha, repeatedly take great pains to show that these totality paradoxes are not paradoxes at all, and that there is a way to preserve consistency by saying that "something outside the totality" (asarva) is just a conceptual invention: it's not necessary that it actually be real to be the negandum in non-non-totality. In short, the most explicit and frequent discussions about contradictions stemming from totalities are those between non-Buddhists and Buddhists; the Buddhists defend themselves by arguing that acceptance of totalities does not lead to any inconsistencies at all. The Buddhists never, as far as I know, accept any explicitly formulated argument, non-Buddhist or otherwise, to the effect that sarva, the universe, the totality, would be contradictory. It would thus be odd that they would somehow implicitly promote true contradictions involving totalities elsewhere in their philosophy.

Turning to the letter of the texts, I would argue that not just are totality arguments used differently in Indian philosophy from the way Priest and Garfield would have it, but that it seems rather implausible to say that Ngrjuna himself accepted any true contradictions at all: indeed he seems to give pretty good textual evidence that he does not.

For example, in Madhyamakakrik XXV.14 he gives what looks like a clear prohibition against contradiction:

bhaved abhvo bhva ca nirva ubhaya katham / na tayor ekatrstitvam lokatamasor yath //

"How could both non-being and being pertain to nirvna? Both are not present in one place, just as light and darkness [are not present in one place]" Even more explicit in banning true contradiction is Candrakrti's comment: bhvbhvayor api parasparaviruddhayor ekatra nirve nsti sabhava iti // bhaved abhvo bhva ca nirva ubhaya katham / naiva bhaved ity abhiprya / "For being and non-being too, there is no possibility for the two mutually contradictory things (parasparaviruddha) to be present in one place, i.e., nirva. Thus "how could both non-being and being pertain to nirva?" The point is they could not at all. The argument is situated in the context of the fourfold negation of the tetralemma (catukoi), where an opponent suggests that nirva both is and is not in short the opponent is advocating that a true contradiction would apply. Ngrjuna and Candrakrti reply that such a true contradiction is not possible. Now, there is no indication whatsoever that their reasoning is restricted to some isolated specific case, i.e., nirva. It looks pretty clearly generalizable: no true contradiction in this case, because no true contradictions at all. To suggest otherwise and say that there are some true contradictions in certain specific cases, makes for a circumscribed rejection of the third lemma of the tetralemma that is hard to reconcile with fundamental Madhyamaka texts. Indeed, there is solid evidence (e.g., in the work of Ngrjuna's disciple, ryadeva, in Candrakrti and in others) that the essence of the Madhyamaka method is that the rejection of the four lemmas in the tetralemma is and must be generalizable and is the way a Mdhyamika should always proceed in criticizing philosophical positions. This is the point of the famous verse in ryadeva's Catuataka XIV.22 which advocates negating all four positions:

sad asat sadasac ceti sadasan neti ca krama / ea prayojyo vidvadbhir ekatvdiu nityaa // "Being, non-being, [both] being and non-being, neither being nor non-being: such is the method that the wise should always use with regard to identity and all other [theses]." Again, it would be quite odd if a Buddhist were to allow that, inspite of verses like this, Ngrjunian totality paradoxes nonetheless yielded true contradictions that were "exceptions" to the rejection of the third lemma.

How to read Ngrjuna and the Prajpramit naturally and yet not embrace dialetheism Let me try to make the best case I can for a paraconsistent interpretation of Ngrjuna and the Prajpramitstras. Instead of "totality arguments" suggesting some form of paraconsistency or even dialetheism, as Priest and Garfield have it, I think that it is the whole system that suggests a type of paraconsistency on a natural reading, and in a particular it is the use of the two truths, customary (savtisatya) and ultimate (paramrthasatya). I'll take up the matter of which form of paraconsistency below, but suffice it to stress again that it is not full-fledged dialetheism. Here's a key Indo-Tibetan problem of interpretation when dealing with the two truths in early Madhyamaka and Prajpramit texts. Suppose the Buddhist author(s) says or somehow endorses that is true and also say that not- is also true, as the Mdhyamikas and the author(s) of the Prajpramitstras are wont to do when they say that dharmas, aggregates, Buddha-marks, karma, suffering, etc. exist and also say that they do not exist, i.e., are empty. Are parameters, like the qualifiers "customarily" and "ultimately" implicit, somehow built-in to and not- respectively so that there is only a pseudo-appearance of contradiction?13 Or is it the same statement, without any implicit parameters, whose truth is being endorsed (for one set of reasons) at some points in the text and rejected (for another set of reasons) at other points in the text?

By way of illustration of the two approaches, let us go back to the signature formulae of the Vajracchedikprajpramitstra: X does not exist/is not the case, and thus we say that X does exist/is the case. E.g., the Buddha doesn't have any distinctive marks and that is why one says he does. Now these types of statements can be and have been approached in both above-mentioned ways. We could do what Kamalala did in his Vajracchedikk, and which was a kind of common later Buddhist interpretative strategem, namely, clearly differentiate the perspectives involved: the buddhadharmas, etc. are not buddhadharmas,etc., looked at ultimately, and are buddhadharmas, and so forth looked at from the point of view of customary truth.14 We

could either add explicit qualifiers right into the wording of the respective affirmative and negative statements (as did for example the Tibetan writer Tsong kha pa (1357-1419)) or we could leave the actual wording in the stra unchanged but say that qualifications of perspective had to understood, as did the 8th century Indian Mdhyamika, Kamalala. In any case, for our purposes, the result is more or less the same: appearance of contradiction vanishes. There would be nothing more logically provocative here in endorsing both statements than there would be in endorsing the statements "It is ten o'clock" and "It is not ten o'oclock", when we also know that the first statement concerns Eastern Standard Time and the second concerns Pacific Standard Time.

We could also adopt an approach that leaves the provocation of the signature formulae intact, i.e., say that the same completely unparameterized statement is being affirmed and negated. In short, no explicit parameters nor timezone-like switches of perspective along the lines of Tsong kha pa or Kamalala, but only radically different kinds of supportive reasoning as to why the one statement is true and why its denial is true. Thus, the stra author(s) would have good reasons to say that dharmas or Buddha marks do exist (e.g., to account for truths that must be accepted in the world, or at least amongst worldling Buddhists) and other good reasons to say they don't (e.g., to give an account of their ultimate status, emptiness). Indeed this move might well bring out just how close and inseparable customary and ultimate truths are for early Mahyna Buddhist authors: as Ngrjuna had himself oft repeated, the customary, i.e., sasra, is nothing but (eva) the ultimate, i.e., nirva, and vice versa: put in our terms, the two truths are so close that the very same unparamaterized statements about dharmas, aggregates, suffering, etc., are both asserted and denied.

There is, I think, a good reason to prefer the second style of interpretation and be suspicious about the imposition of hedges and parameters and other attemps at non-literal nuancing of early Madhyamaka. Simply put: If we can read Ngrjuna and the Prajpramit without qualifiers and pretty much literally, let's do it: Ngrjuna is interesting and intelligent as is and charity will not require anything more.

A not infrequent, but significantly less persuasive, argument is that a nuanced and finessed approach is downright wrong, or even a travesty to Madhyamaka, because it would bring in philosophical

theses by the back door and thus fatally weaken the Madhyamaka project.15 Indeed there is a traditional Sa skya pa interpretation of Madhyamaka that goes a considerable distance in fleshing out this argument: I'm thinking of the lTa ba'i shan 'byed of the fifteenth century Tibetan writer, Go rams pa bSod nams Seng ge (1429-1489), probably the most explicit traditional source I know of for a potentially coherent, unparamaterized interpretation of Ngrjuna and the Prajpramit. Go rams pa's target was of course Tsong kha pa, who advocated adding qualifiers like "ultimately" (don dam par), or "truly" (bden par), to all the negative statements in the Madhyamaka: things are not ultimately/truly produced, are not ultimately/truly existent, and so on and so forth for all properties a person might wish to attribute.

Go rams pa's main point, in his refutation of Tsong kha pa, was that if a Mdhyamika commentator adds that kind of ultimate parameter and thus gives a non-literal interpretation of the Ngrjuna's negative statements, he has in effect denatured the whole Ngrjunian dialectic to the degree that it will no longer be able to accomplish its (religious) purpose of quietening philosophical speculation and attachment and irenic quietism, or complete "freedom from proliferations" (spros bral, niprapaca), is for Go rams pa the main point of the negative dialectic of the Madhyamaka. So his alternative is thus to take literally the idea of yod min med min "no existence, no non-existence" and not add any qualifiers like "ultimately"/"truly", the danger being that by negating "ultimately " instead of itself for any statement, the Mdhyamika thinker will arrive at smugness about being free of positions, but will in fact remain as attached to the truth of as any other realist philosopher. Qualifiers and hedges, so the argument can be paraphrased, make everything a little too neat and refute straw men.

Let's suppose we adopted an unqualified reading either because simplicity and naturalness are (all other things being equal) better than artifice, or perhaps because of Go rams pa-style quasi-religious arguments. Where does this unhedged interpretation of Ngrjuna and the Prajpramit take us in terms of logic? I would say the following: it leads to a type of paraconsistent logic according to which Ngrjuna will in certain discussions admit that is true (for worldly, doctrinal or even Abhidharmic reasons) and in other contexts that is true (for reasons involving emptiness of intrinsic nature); however, Ngrjuna will recognize no good reasons at all to ever admit the truth

of the conjunction, &. There will be no such reasons, because Ngrjuna, as I had argued earlier, is deeply respectful of the third negation in the tetralemma, a negation which he generalizes to apply to every statement. In short, we might end up a type of paraconsistency, but not dialetheism if the Madhyamaka is not to run afoul of its own prohibitions. For Ngrjuna, there is no , such that & is true.

Now endorsing and endorsing , but refusing the move to &, does seem to involve a type of paraconsistency, indeed a recognizable one, arguably significantly similar to what Nicholas Rescher and Robert Brandom developed in their joint book, the Logic of Inconsistency. 16 A number of years ago, in a note liminaire to a Felicitation volume for Jacques May who was indeed an uncomprising advocate of a Madhyamaka with no qualifiers or hedges whatsoever I had mentioned that Rescher and Brandom's (weak) inconsistency might allow us to rationally reconstruct aspects of a May-style Madhyamaka. In fact, I later discovered that the approach was not unique to Rescher and Brandom: it was, as Koji Tanaka pointed out in his taxonomy of contemporary theories of paraconsistency, initially developed by the Polish logician, Jakowski, and certain other writers, including some of my Canadian compatriots. Tanaka classified these theories as non-adjunctive approaches to paraconsistency, i.e., ones that prohibit the move from individual premises, , , to their adjunction & 17 In other words, it enables one to affirm that at least in some cases is true and to affirm that is true a weak inconsistency without, however, ever admitting the truth of the statement, & this latter statement would be a strong contradiction that could not be accepted as true in the Rescher-Brandom system if dastardly consequences like explosion were to be avoided.

Finally, following this scenario the logic of Ngrjuna would have a quite remarkable split-level construction. Non-adjunctive paraconsistency would apply to discussions of emptiness, like in the tetralemma where Buddhists endorse , , but do not endorse the adjunction &. It would also, as we have arguing, apply in a general manner to the so-called six logical works (rigs tshogs drug) of Ngrjuna, which sometimes treat of things worldly and then deny those same things elsewhere in discussions of nyavda. Paraconsistency would, not however, be supposed in more ordinary discussions of customary matters, like the usual and banal reasonings

about fires on smoky hills, sound being impermanent, fire being hot and other such non-ultimate considerations. Nor would it be applicable in the numerous reductio ad absurdum (prasaga) arguments where Ngrjuna seeks to show inconsistencies in his opponents' positions. These reductio usually proceed by deriving at some point and at anotheradjunction of the two gives the needed contradiction. In sum, we probably could say that so long as Ngrjuna discusses only such customary things as dharmas, aggegrates and so forth, or when he demolishes others' philosophical views, his logic does stay quite classical. The non-adjunctive paraconsistency would come in in two places (a) when Ngrjuna discusses the ultimate status of things in tetralemma-like terms. (b) When we seek to characterize Ngrjuna's own stance by putting together the different unqualified statements in different chapters of his works: the trick would be to keep all those statements unhedged, but to avoid strong contradiction by blocking their adjunction. I think that dialetheism, however, would probably not apply at all. Final caveats and conclusions

I think this is about as far as I can go in making a case for paraconsistency in early Madhyamaka and the Prajpramit. In any case, later Madhyamaka in India or Tibet, or in other words Ngrjuna's philosophy as viewed by commentators from about the sixth century C.E. on, is another story and is much more inclined to paramaterization. It is also much more conservative about consistency. There are more explicit prohibitions against virodha/viruddha (contradiction), a fact which makes it more difficult to read the later Mdhyamika scholastics as tolerating or advocating any paraconsistency, be it weak or strong contradictions. Significant too is that the later Mdhyamika is, with one or two exceptions, under the spell of Dignga and Dharmakrti's logic so that there is an attempt to harmonize Madhyamaka with a logic for realists. I'll give a few examples in an appendix to illustrate how this is done with parameterization, diambiguation and other relatively predictable moves but suffice it to stress for the moment that true (strong or weak) contradictions are anathema for the logicians of the Dignga-Dharmakrti school and there is every reason to think that they are too

for later Mdhyamikas, like Kamalala, ntarakita and many others, who see themselves as under the same constraints as their logician coreligionnists. There was a significant change in orientation between Ngrjuna and later commentators (especially those of the majority Svtantrika persuasion), and that change is largely due to the overwhelming influence of the Dignga-Dharmakrti school on Indian Buddhist thought.18

Would this evolution mean that later Indian or Tibetan Madhyamaka is inauthentic or without philosophical value as a development of Madhyamaka thought? Of course not, unless authenticity demanded no evolution, a kind of pure doctrinal deepfreeze. I think that we can and should defend Tsong kha pa and others from Go rams pa's critique of grotesquely denaturing Madhyamaka thought and yet we can also grant that Go rams pa was quite right at least in saying that what Tsong kha pa did in massively adding qualifiers to early Indian texts and in adopting Dharmakrti's logic did not accord well with the logical structure of early Madhyamaka thought.

We can advance the following historical claim: not only did the philosophical debates and doctrines evolve over time with Buddhist scholastic thinkers, but very possibly the logic evolved away from its rather complex split-level architecture to one of increasing homogeneity and classicalness. Logical simplification also happened elsewhere in Indian thought. A number of us have looked at, for example, the logicians' problems in explaining a theory of valid reasons: with time the formal aspects became ever simpler, even though the philosophical analyses often became increasingly subtle. Something interestingly similar may well have happened with the Madhyamaka.

Appendix: Textual sources illustrating later Indo-Tibetan approaches to inconsistencies. I would argue that the typical later Madhyamaka approaches to (seeming) inconsistencies (strong or weak) are quite recognizable ones that are common to East and West: add parameters, diagnose equivocations and ambiguities and in so doing the "inconsistency" is defused.

An example. There is a provocative canonical statement in the rya Dharmasagti that has led to considerable exegetical manoeuvers on the part of later Mdhyamikas:

"Not seeing any dharmas, this is genuine seeing."19 The statement sometimes has an even starker formulation, as we find it Atia's Satyadvayvatra verse 7: "Non-seeing is seeing."20

As history goes on we find commentators making increasingly explicit and precise attempts to satisfactorily respond to seeming inconsistencies in such canonical statements. Thus the eighth century Indian commentator, Kamalala, in the Madhyamakloka, gives a rather involved dogmatic explanation to show that the non-seeing of any intrinsic natures is not just a mere absence of seeinga so-called "non-implicative negation" (prasajyapratiedha)but implies a type of seeing, i.e., seeing the emptiness or ultimate truth about things.21 In short, non-seeing in this context implies seeing something else. The term adaranam in the stra quotation, especially the negative particle a, is thus disambiguated to mean non-seeing understood in a special way, much in the same way as the word "not" in a statement like "my coat is not blue" can be interpreted so that it is implied that my coat has some other color. In Buddhist logical jargon, the word adaranam is said to express here an implicative negation (paryudsa) in that it also implies a positive fact, i.e., seeing. In this commentator's view, then, the problem turns on there being two types of negation; if a seeming paradox arises it is because of a systematic ambiguity in the negative particle in Sanskrit.

Not surprisingly perhaps, for Tsong kha pa the opposition between "seeing" and "non-seeing" is easily defused by pointing out a type of parameterisation. We can reconstruct his argument as follows. The property, seeing, may appear to be a monadic property (i.e, such and such a person sees), but actually in the stra context it is dyadic (i.e., such and such a person sees such and such an object). The opposition is defused when we can show that non-seeing pertains to one thing and seeing to another.

"As for the meaning of 'not seeing is the supreme seeing,' we don't accept that seeing nothing at all is seeing, but instead, as we had explained earlier, we establish that not seeing conceptual proliferations (spros pa= prapaca) is the seeing of what lacks conceptual proliferation. Thus we do not apply seeing and not seeing to the same basis."22

In no way do we see and not see one and the same thing. Examples of other sorts of disambiguation of seemingly paradoxical canonical statements can be provided, but this will have to suffice. 1 For the technical details on what an inclosure is, see fn. 7. In G. Priest and J. Garfield (2002). 2 See T. Tillemans (1999), p. 12. 3 The phrase "signature formula" I owe to Paul Harrison in his introduction to his forthcoming new translation of the Vajracchedik. 4 Priest (2002), p. 251. 5 It's worth mentioning, however, that later Tibetan commentators would hedge this statement to make a distinction between ultimate truth and what is ultimately established (don dam par grub pa) so that we end up with the tamer principle that the ultimate truth is the ultimate truth, but, like any other dharma, it is not ultimately established. 6 See Prasannapad (ed. L. de la Valle Poussin), 264.12-265.2: atha keya dharm dharmat? dharm svabhva. ko 'yam svabhva? prakti. k ceya prakti? yeya nyat. keya nyat? naisvbhvyam. kim ida naisvabhvyam? tathat. keya tathat? tathbhvo 'vikritva sadiva sthpit.

sarvadnutpda eva hy agnydn paranirapekatvd aktrimatvt svabhva ity ucyate. Note that in this vein there is also an important passage from the Aashasrikprajpramitstra quoted in the autocommentary to Ngrjuna's Vigrahavyvartan. See Priest (2002), p. 266. On the senses of svabhva, see also de Jong (1972). 7 Here briefly is how it goes. The key formal notion that they introduce is that of an "inclosure ": a totality set is an inclosure if (1) its members have a property and have a certain property ; and (2) there is a "diagonalising" function that assigns to each subset x of whose members have a new object that is not in the subset x but is still in . Applying that function to itself we get an object that both is and is not a member of . Symbolically, here are Priest's conditions for an inclosure: ={y:(y)} exists, and () For all x such that x is a subset of and (x), (x) is not a member of x (x) is a member of See Priest (2002), p.134 for the inclosure schema. In the Ngrjunian inclosure paradox, is the set of all empty things, i.e., things without intrinsic nature; these things have the property , i.e., having a common intrinsic nature. The diagonalising function assigns to the subset x the nature of the things in x. Since (x) is a member of , it does not have an intrinsic nature. x however has the property and thus consists of things which do have a common intrinsic nature. Therefore (x) is not a member of x. Applying to itself we have the result that () is a member of and () is not a member of . The nature that assigns to is emptiness. Thus emptiness is empty of intrinsic nature and is not empty of intrinsic nature. 8 On the distinction between logical and rhetorical paradoxes, see p. 4 in N. Rescher (2001). See Tillemans (1999), p. 195-196 on some examples of the stylistic tendency in Indian philosophy to use seemingly paradoxical modes of expression. Often, it is quite clear (e.g. by looking at auto-commentaries) that these are only rhetorical paradoxes. 9 Priest (2002), p. 268. The first paradox, conveyed by the statement "the ultimate truth is that there is no ultimate truth" is spelled out as follows (ibid p. 269): "the claim that there are no ultimate truths, both is and is not an ultimate truth" Here too the move to each and every individual thing both having and not having some property would not be obvious. 10 Priest (2002), p. 268. 11Perhaps the underlying idea in Priest and Garfield is that emptiness is the nature of things and is both empty and not empty, and thus all the things, whose nature it is, should be empty and not empty too. But this seems to involve some non-obvious

steps. Interestingly enough, Priest seems himself aware that he has not proved (and indeed he does not want to prove) that tables, chairs, stars and so forth are contradictory:

"I claim that reality is, in a certain sense, contradictory. I do not, of course mean that the objects that constitute reality, like chairs and stars, are contradictory. That would simply be a category mistake. What I mean is that there are certain contradictory statements (propositions, sentencestake your pick) about limits, that are true." (Priest 2002, p. 295)

Subsequently, he grants that (under the inspiration of Ngrjuna) he is also taking an ontological turn, and that he is concerned not just with statements, but with the nature of reality, with what is: that nature is what he takes to be contradictory. However, formulating the problem in this way, the move from the contradictoriness of that nature to the contradictoriness of each individual thing will still be problematic. 12 See Nyyadaranam (ed. Taranatha Nyayatarkatirtha, Amarendramohan Tarkatirtha, Calcutta 1936), p. 687. Transl. on p. 1056-7 in Ganganatha Jha, The Nyya-stras of Gautama with the Bhya of Vtsyyana and the Vrtika of Uddyotakara, Delhi: Motilal Banarsidass, 19??. 13 Here is how Priest describes parameterisation: "The stratagem is to the effect that when one meets an (at least prima facie) contradiction of the form P(a)!, one tries to find some ambiguity in P, or some different respects, r1 and r2, in which something may be P, and then to argue that a is P in one respect, P(r1,a), but not in the other, -P(r2,a). For example, when faced with the apparent contradiction that it is both 2 PM and 10 PM, I disambiguate with respect to place, and resolve the contradiction by noting that it is 2 PM in Cambridge and 10 PM in Brisbane." (Priest 2002, p. 151) 14 See for example Kamalala's discussion on the stra's formula concerning "heaps of merit", i.e., bsod nams kyi phung po, in ryaprajpramitvajracchedikk (ed. Central Institute of Higher Tibetan Studies, Sarnath, 1994) p. 296-297. 15 Cf. Tillemans (1992), p. 11 on Jacques May's Madhyamaka philosophy: "Autre lment clef: le bouddhiste Madhyamaka n'a pas, lui-mme, de position philosophique. May est formel sur ce point et rejette les nuances ou les affaiblissements de ce principe dans la littrature scolastique ultrieure. ... Le Madhyamaka ne peut pas avoir de position philosophique, car toute position s'annule." 16 I.e., Rescher and Brandom (1980). See Tillemans (1992). 17 See p. 29-30 in Tanaka (2003)

18 I have taken up the subject of the Svtantrika-Madhyamaka debt to the logicians in "Metaphyics for Mdhyamikas." See Tillemans (2003). 19 P. 74b: bcom ldan 'das chos thams cad mi mthong ba ni yang dag par mthong ba'o. Cf. the Sanskrit cited in ntideva's iksamuccaya p. 264, 1-2: adaranam bhagavan sarvadharmn darana samyagdaranam iti. The passage has been studied in detail in the third chapter of Keira (2004). 20 ma mthong ba nyid de mthong bar // shin tu zab pa'i mdo las gsungs. "The extremely profound stra says that it is precisely non-seeing that is seeing." Text on p. 194 of Lindtner (1981). 21 Here's a relevant passage from the Madhyamakloka (the translation is that of Keira 2004, p. ???): "However, great yogins who correctly meditate on all dharmas as being like mirages and echoes obtain the concentration (samdhi) which arises from the ultimate limit of meditation upon the true state of affairs (bhtrtha), and therefore they have inconceivable supreme powers.Thus this type of wisdom (ye shes de lta bu), which clearly realizes (mngon sum du byed pa) the thusness of all dharmas being selfless, arises in these yogins, so that (yena) the yogins understand completely directly (mngon sum kho nar) that all dharmas are selfless. It is precisely this that is termed nonseeing (adarana) [in the stra], but [the negation in nonseeing] does not have the form of a non-implicative negation (prasajyapratiedha). Madhyamakloka D. 168b-169a: on kyang rnal byor pa chen po chos thams cad smig rgyu dang sgra brnyan lta bur ji lta ba bzhin du sgom par byed pa rnams kyis / yang dag pai don bsgoms pai rab kyi mtha las byung bai ting nge dzin thob pai phyir mthu phul du byung ba bsam gyis mi khyab pa dang ldan pas rnal byor pa de dag la gang gis na rnal byor pa rnams kyis mngon sum kho nar chos ma lus pa bdag med pa rtogs par gyur pa chos ma lus pa bdag med pai de kho na nyid gsal rab tu mngon sum du byed pai ye shes de lta bu nye bar skye ste / de nyid mthong ba med ces byai / med par dgag pai ngo bo ni ma yin no //. 22 Tsong kha pa, dBu ma dgongs pa rab gsal (Sarnath edition) p. 202: mthong ba med pa ni mthong ba dam pa'o zhes gsungs pa'i don yang / ci yang mi mthong ba mthong bar mi bzhed kyi / sngar bshad pa ltar spros pa ma mthong ba ni spros bral mthong bar 'jog pas / mthong ma mthong gzhi gcig la byed pa min no /.