Classic and Contemporary Buddhist Works

Scripture, Logic, Language - Introduction

Essays on Dharmakīrti and His Tibetan Successors

INTRODUCTION

The present collection of essays spans a number of years of work on various aspects of the philosophy known as “Buddhist logic” or “Buddhist epistemology.” This philosophy is generally taken to have begun with Dignāga and Dharmakīrti in the sixth and seventh centuries and to have flourished until the end of Buddhism in India in approximately the thirteenth century. It was taken up with great energy in Tibet, especially from the eleventh century on, the time of the “second propagation” (phyi dar) of Buddhism, and has remained an important element of Tibetan Buddhism up to the present day. It is what many people, within or outside the Buddhist community, have considered to be the most philosophical, and even the most critical, form of the Mahāyāna.

Curiously enough, although one speaks of a distinct and influential philosophical school composed of the followers of Dignāga, it was one that remained fundamentally nameless in Sanskrit. In Tibetan traditions, however, the philosophy received the conventional designation, tshad ma, the Tibetan equivalent of the Sanskrit term pramāṇa, a term which in its more ordinary sense means “measure” and which in its technical use means “a means of valid cognition”/“a means of knowledge.” It was in part this Tibetan transformation of the Indian technical term pramāṇa into a name for a philosophy and discipline of study that led modern writers to speak of “Buddhist logic” and “Buddhist epistemology” or pramāṇavāda. Indeed, the transition from the study of “means of valid cognition” to “epistemology” is relatively natural; “logic,” on the other hand, seems to be better based on the term hetuvidyā/gtan tshigs rig pa, the “science of reasons,” which is one of the important subsidiary domains in tshad ma studies. In any case, one should not be misled: these English terms are no more than approximations for a multi-faceted system in which logical theory was a major element, but certainly not the only one. There is no reason to think that this school’s elaborate debates on particulars, universals, mind, matter, idealism and realism were somehow more logical or epistemological than metaphysical, or that the arguments concerning the virtues of the Buddha, his omniscience and compassion were any less religious or scholastic than they would seem to be.

If one looks at the present collection of essays, it is quite apparent that “Buddhist logicians” did much more than what we might call “logic” and “epistemology,” even in loose uses of those terms. Indeed they very actively pursued the doctrinal and religious aspects of Buddhism, so much so that many Indians and Tibetans, and indeed some modern writers too, would depict the religious as the primary aim of this philosophy. How did these Buddhist philosophers see themselves as doing something unified and coherent? Given that inference and perception (the two “means of valid cognition”) would seem to concern rationally decidable matters, how can the apparently non-rational elements belonging to the religious side of Buddhist philosophy be coherently accommodated in this system?

The first section of this collection of essays (i.e., “Scripturally Based Argumentation”) consists of three pieces in which I tried to grapple with the Buddhist logicians’ stance on religion and rationality. The striking feature of the Dharmakīrtian school is that it holds that religious doctrine can be justified and can be argued for, and with extremely restricted tools, i.e., perception and inference. Yet if religious matters can be argued for in this way, did the Dharmakīrtian school adopt the conservative view that religious reasoning is just as objective and certain as reasoning about uncontroversial, non-religious matters (like smoky hills having fires)? These are the concerns of the first two essays, i.e., “Dharmakīrti, Āryadeva and Dharmapāla on Scriptural Authority” and “How Much of a Proof is Scripturally Based Inference?” The third essay in this section is somewhat more historical in orientation. Dharmakīrti recognizes that much religious argumentation demands allegiance to a school and to a body of texts, but nonetheless maintains that the ordinary, or unexceptional, uses of logical argumentation should have complete independence from such doctrinal affiliations. This extremely radical view on scripture has as its consequence that when one is arguing about most empirical or even metaphysical matters, conformity with the propositions found in the scriptures of a school is virtually irrelevant. The problem that “Pre-Dharmakīrti Commentators on the Definition of a Thesis” seeks to solve is “Who first came up with this position?” Was it already in Dignāga? If not, how did Dharmakīrti come to hold it?

The second section (i.e., “Logic”) is the largest and probably most technical part of this collection, dealing in one way or another with questions of implication, negation, valid reasons and the so-called Buddhist syllogisms—in short, the type of topics that a Westerner would associate, in part at least, with the idea of logic. It should be obvious that no one in the Indian and Tibetan schools could be said to have been doing formal logic. Nevertheless, it is so that these philosophers were aware of questions of logical form, although often inextricably combining questions such as “What is logical implication?” with what might seem to be extra-logical considerations. The first essay in this section, “Parārthānumāna, Theses and Syllogisms,” looks at the so-called “Buddhist syllogism,” and more generally the idea of proof (sādhana). The second, “On Sapakṣa,” examines the notion of a logical reason and the role of examples in argumentation in Dharmakīrtian and Tibetan logics, focusing on the Buddhist position that certain types of seemingly sound arguments are nevertheless to be rejected because examples cannot be given. The next essay, “Formal and Semantic Aspects of Tibetan Buddhist Debate Logic,” investigates the logical structures and semantic notions in Tibetan bsdus grwa, a system which is considered by its exponents to be a faithful continuation of Dharmakīrti, and yet which is also, in many ways, quite remarkably original. “Dharmakīrti and Tibetans on Adṛśyānupalabdhihetu” then takes up Indian and Tibetan ways to argue for nonexistence, while “What is the Svadharmin in Buddhist Logic?” examines the problems that arise when the subject of an argument is itself nonexistent. The section ends with an article translated from French on the general problem as to whether Buddhists somehow reason in a fundamentally different or even incompatible manner from the classical logic that one finds in typical Western works on formal logic.

The third section (i.e., “Philosophy of Language”) takes up aspects of the Buddhist semantic theory known as apoha (“exclusion”), the fundamental idea being that abstract entities such as universals, concepts and meanings can be analyzed away in terms of double negations (supplemented, at least for Dharmakīrti, by a purely causal account as to how we make judgements of similarity). In its Indian forms, apoha yields and reinforces a type of nominalism where the real is the particular. (Note that “nominalism” is used here in the modern sense as found in Nelson Goodman and W.V. Quine, where the essential requirement is that what exists must be particular; nominalism need not be, and indeed is not for the Buddhists, a philosophy where universals are just mere words alone, or flatus vocis.) The peculiarly Buddhist contribution is that abstract entities are not just dismissed, but accounted for as mere absences of difference and are hence unreal, just as are all other absences for Buddhists. The first essay in this section, “On the So-called Difficult Point of the Apoha Theory,” looks at ontological matters and shows that the nominalistic rejection of real universals was considerably modified by certain Tibetan schools who reintroduced a type of realism in the garb of a system as much inspired by bsdus grwa as by Dharmakīrti. The second essay, written with Donald S. Lopez, Jr., consists in a translation of a Tibetan text that applies the theory of apoha to account for what it is one talks about when discussing nonexistent pseudo-entities. The underlying problem which Indian and Tibetan Buddhists took up is not unlike that which inspired the philosophy of language of Meinong and provoked the reaction that one finds in Bertrand Russell’s Theory of Descriptions and later in W.V. Quine’s celebrated essay “On What There Is.”

The papers presented here are intended to be, broadly speaking, historical, though it is obvious that the conceptual tools employed are often those of contemporary Anglo-American analytic philosophy. It is equally obvious that the history I am pursuing is the history of a philosophy, and as such it should not be surprising that what counts most in this aim are texts and philosophical analyses of them. One of the main reasons why the history of logic in the West has become so well developed and interesting is that historico-philological competence in textual studies has been combined with philosophical sensitivity. There is no reason why such a combined approach should not yield results in an Indo-Tibetan context too. Indeed, in order to disentangle what a Dharmakīrtian or a Tibetan text could be saying it is necessary not just to adopt a Principle of Charity, but also to formulate a number of alternatives in terms more precise than the text itself and, if need be, using alien philosophical or logical notions. Being faithful to an historical author does not demand that one keep the possible interpretations couched in the same problematic or obscure language that is the author’s. This type of “faithfulness” is the misguided rationale for translations that read like “Buddhist Hybrid English.” More generally, such a methodology seems to rest on a fallacy of imitative form, i.e., that talk about something obscure, mysterious, funny, boring, etc., should itself have the same stylistic characteristics as what is being talked about. Using philosophical tools is not, however, an attempt at appropriating Dharmakīrti so that he might somehow become relevant to a contemporary Buddhist philosophy. Perhaps a contemporary “Buddhist theology” using selective doses of Dharmakīrti is possible, but, even if it is not, the absence of blueprints for the present doesn’t detract from Dharmakīrti’s importance, just as it doesn’t detract from that of Plato, Leibniz or Spinoza to whose systems virtually no one subscribes now. Indeed, I would think that Dharmakīrti’s system, if better available, would receive a mixed response today; its reductionism, its strict mind-body dualism, and its highly fragmented ontology of partless atoms and instants might well be quite difficult to accept for the many Buddhists who are seeking a more holistic, integrated vision of the world.

A feature of these papers is that they regularly zigzag between Indian and Tibetan contexts. Almost needless to say, this does not mean that we take as given that Tibetan Buddhist traditions are identical with their Indian counterparts. Tibet as being the faithful prolongation or even duplication of India has been a seductive idea, even one which motivated people to do valuable work on Tibet, but it is one whose time is now definitely past. The course that we have taken between Tibet and Dharmakīrti may often be different from that of Tibetans themselves, as is our sense of what is the Indian debate and what is a Tibetan development. But then there is no easy recipe for pursuing an Indo-Tibetan approach, nor are there any shortcuts enabling us to avoid reading both languages and both sets of texts. What makes the effort worthwhile is that history may perhaps be seen in a binocular fashion, in stereo vision, thus lending further depth to our understanding of these texts.

Publishing a collection of this sort allows me to nuance a few things and speculate on some future directions to be pursued. One particularly interesting area for reflection is the question of pragmatism in Dharmakīrti, and more generally the theories of truth and justification implicit in his system. Another is the problem of vyāpti (the implication between the reason and what is to be proved), what it is for Indians and what it is for Tibetans. Finally, the question of whether Buddhists ever use a logic different from the usual classical variety is not easily put aside. As it was practically impossible to incorporate these discussions into the articles themselves, let me use the remainder of this introduction to sketch out some of the broad outlines of how these philosophical themes appear to me now.

Pragmatism
First of all, it has sometimes been suggested that Dharmakīrti has some type of a pragmatic theory of truth, especially because the reliability (avisaṃvādakatva) of a means of valid cognition (pramāṇa) consists in there being “confirmation of practical efficacy” (arthakriyāsthiti). To take one of the most common versions of a pragmatic theory of truth, as found in William James, a belief is true for people if and only if it is in the long run most useful for them to accept it. Now, irrespective of how we translate the term arthakriyā, i.e., “efficacious action,” “practical efficacy,” “goal accomplishment,” etc., there is no reason to believe that Jamesian pragmatism or anything much like it is Dharmakīrti’s theory of truth, certainly not when it comes to the usual examples of pramāṇas, i.e., direct perception (pratyakṣa) of things like vases, and inference (anumāna) such as that there is fire on a hill because there is smoke. The point for Dharmakīrti, following Devendrabuddhi and Śākyabuddhi, is that an awareness can be asserted to be a pramāṇa because of a confirmation—this “confirmation” (sthiti) is glossed by Śākyabuddhi as being an “understanding” (rtogs pa)—which in typical cases is subsequent to the initial awareness. In other words, we can rationally say that we genuinely saw a vase, and not some vase-like illusion, because after the initial perception we came to perceptually confirm that this seeming vase really does permit us to carry water as we expected and wished. Equally, although initially we might have suspected that what we saw was not actually fire, subsequently we were able to infer that it was indeed fire, because there was smoke. While most initial sights and other sense perceptions are to be confirmed by subsequent perceptions or inferences, an inference itself is something of an exception: it is said to be confirmed simultaneously and needs no subsequent understanding—the point turns on the idea of inference having svataḥ prāmāṇyam or “intrinsically being a means of valid cognition.” Be that as it may, what is important for us to note in the present discussion is that one understanding is being confirmed by another or in certain special cases by itself. There is nothing at all here in Dharmakīrti, Devendrabuddhi or Śākyabuddhi which suggests a Jamesian account along the lines of “the understanding/belief/statement that there is a vase/fire over there is true for us because it is in the long run most useful for us to believe that there is a vase/fire over there.”

Nor for that matter is there very much which would suggest a “pragmaticist” theory like that of C.S. Peirce, who held that “the opinion which is fated to be ultimately agreed to by all who investigate is what we mean by truth.” The major similarity between these two philosophers is, as far as I can see, their common commitment to the importance of results and to there being an objectively right version of what there is. However, the idea of truth as an ideal rational assertibility is neither asserted nor rejected by Dharmakīrti: what we regularly find for him is that existent things are those that are actually established by a means of valid cognition (pramāṇasiddha). Peirce’s theory is not that truths consist of opinions that are now established, but that they are the limits to which people’s informed opinions will or should converge, i.e., the destined upshot of inquiry. Indeed, his theory defines truth in terms of a consensus which may well never actually be realized (as Peirce himself recognized); this all-important reference to an ideal consensus that may even be just a regulative principle is what is absent in Dharmakīrti. In any case, in what follows I will mean by “pragmatism” and “pragmatic theories” essentially the Jamesian version.

In fact we can go further on the question of truth and arthakriyā: arthakriyāsthiti does not, I think, set forth a theory of truth at all. Let us speak of a truth theory as one which gives a definition of truth, i.e., the necessary and sufficient conditions for statements or understandings to be true, while a justification theory will provide us with the properties that allow us to reasonably determine that a statement or understanding is true and satisfies the definition. Looked at in that light, arthakriyāsthiti, especially as it is explained by Devendrabuddhi and Śākyabuddhi, is best taken as part of Dharmakīrti’s justification theory. Dharmakīrti is giving a procedure for truth testing, typically a kind of verification principle along commonsense lines: “Look and see or analyze logically whether the object actually behaves as you think it does, and if it does, you can be confident that you were right in your initial understanding.” In short, he is telling us when and how we can be confident that our understandings are true, but not what truth is.

What then is Dharmakīrti’s theory of truth and is there any role to be found for pragmatism in his system? It is not clear to me that Dharmakīrti explicitly gives a generalized theory of truth anywhere, although if we cobble one together in keeping with his system it is probably best viewed as turning on stronger and weaker forms of a correspondence theory. To see this better let us briefly look at how Shōryū Katsura depicted truth for Dharmakīrti. Katsura cited what he termed “the timehonored definition of error in India”, i.e., “that which grasps x as non-x,” as evidence that Dharmakīrti “believes in some kind of real ‘correspondence’ between perception and its object, namely, resemblance of the image.” He then remarked that this definition of error is used by Dharmakīrti to classify inference as erroneous:

In other words, inference takes a universal as its immediate object and possesses a partial and generalized picture of the object rather than the true representation of it. There is no real correspondence between inference and its real object [i.e., the real particular in the world], but merely an indirect causal relationship. In short, inference grasps the object through its universal characteristic. Therefore, Dharmakīrti considers inference to be erroneous.

On Katsura’s interpretation of Dharmakīrti, while inference is erroneous (bhrānta) in that it does not correspond to reality, it is nonetheless true “from a pragmatic point of view,” in that it “can lead to the fulfillment of a human purpose.”

What Katsura has rightly focussed upon in speaking of perception as being “non-erroneous” (abhrānta) and corresponding to its object is the well known principle in Buddhist logic that perception has a certain resemblance with its objects, because it sees only particulars, undifferentiated into substances, qualities, actions, etc., and in reality it is only the undifferentiated particular (svalakṣaṇa) entity which exists. The other side of the coin for the Buddhist is that these fundamental distinctions between separate substances, universals, etc., are only invented by the conceptual mind and hence are not mirrored by the facts. There is therefore, in an important sense, no resemblance between how things are conceived by inferential cognition and how they are. While it is thus undoubtedly right to say that for Dharmakīrti inference is bhrānta in a way in which perception is not, I don’t think that it follows that the implicit truth theory in Dharmakīrti’s account of inferential understanding must be a type of pragmatism, rather than correspondence. We can untangle this problem by distinguishing two senses of correspondence, and when they are distinguished there will be no need to introduce a pragmatic theory of truth.

A contemporary analytic philosophy textbook surveying truth theories distinguishes between two varieties of correspondence: “correspondence as congruence” and “correspondence as correlation.” Both types are correspondence theories in that a certain fact must exist if the relevant proposition, statement or belief is to be true. The first type, congruence, involves an added condition, viz., that there be a structural isomorphism, a type of mirroring relation between the truth-bearer and a fact. (Thus, for example, subject-predicate structures in thought and language might or might not be congruent—depending upon one’s metaphysics—with facts composed of real substances and universals.) The second type, i.e., correlation, is a weaker type of correspondence, where there is no such isomorphism, but where it suffices that the fact exist for the statement or understanding to be true. Now, if we accept that for Dharmakīrti there is correspondence involved in perception, as I think we should, then it is the strong kind, congruence, i.e., the undifferentiated perception is congruent with the undifferentiated particulars. For inferences, however, although there is no structural mirroring, there is a causal relation that does link the understanding, or truthbearer, to a fact, or more exactly to the particular real entities. When we come to understand a subject-attribute proposition like “sound is impermanent,” there is, for Dharmakīrti, no separate substance, sound, in which the universal, impermanence, inheres. There are, however, impermanent sounds, which are the real particulars to which the understanding is linked and which must exist if the latter is to be true. Granted, impermanent sounds, hills on which there is smoke, etc., are not in themselves strictly speaking what we might term facts or states of affairs, but the transition to facts like “sound’s being impermanent” or the “hill’s having smoke” is relatively easily made. For inference and conceptual thought, then, we still have a weak form of a correspondence theory, like in many respects the correspondence theory that was advocated by J.L. Austin in the 1950’s or, interestingly enough, like the theory of the great English idealist, J.M.E. McTaggart, who specifically rejected a “copy theory of truth” but nonetheless maintained correspondence.

What is seductive is to take Dharmakīrti’s contrast between bhrānta and abhrānta as also being his explicit formulation of a theory of truth, or his theory of “truth from an epistemological point of view,” and to somehow identify this and this alone with correspondence. The problem then arises, however, as to how to classify inferential understanding, which is bhrānta and thus would not seem to be true in the sense of correspondence. Hence, we are stuck with an equivocal Dharmakīrtian theory of truth: correspondence for perception and pragmatism for inference. I think that the root of the problem lies in looking for a pan-Indian, and hence Dharmakīrtian, theory of truth in the pair of terms bhrānta-abhrānta: for Buddhist logic, at least, we would come up with a more elegant, univocal result by analyzing the notion of truth implicit in the concept of prāmāṇya, “being a means of valid cognition.” In short, we might do better to try to find a unified idea of truth which allows Dharmakīrti to say univocally that both inference and perception are pramāṇa. That minimalist single notion of truth which Dharmakīrti actually seems to apply in common to both inference and perception is as likely to be correspondence as correlation.

The reason a Jamesian “pragmatic truth” theory should be ruled out as applying to Dharmakīrtian inferences is that it does not require that a certain fact or certain objects must obtain for an understanding/statement in question to be true: on a pragmatic theory, no matter how much we talk about “long term utility,” it remains logically possible that a belief be useful, but that there is no such fact. Now contrast this with Dharmakīrti’s system. It is a cardinal element in Dharmakīrti’s account of how the usual type of smoke-fire inference works that the particular entities to which it is causally related must exist: if there wasn’t actually any fire on the hill, the inferential understanding would not make us obtain (prāpaka) the object in question and hence could not be a pramāṇa. The upshot is that inference does satisfy the condition for the weaker version of the correspondence theory, correlation, because the entities in question must exist for the understanding to be true.

Alas, the terms, bhrānta and abhrānta, are not naturally translated as “incongruent” and “congruent,” but rather as “erroneous” and “non-erroneous.” Still, if we are looking for notions close to congruence, these are the likely candidates. In “On the So-called Difficult Point of the Apoha Theory,” I opted for the usual translation and hence had to put up with the usual infelicities of expression. If we see the bhrānta-abhrānta contrast as pertaining to congruence, however, it becomes possible to say, in keeping with Dharmakīrti, that certain understandings, like inferences, are incongruent, i.e., bhrānta, but are nonetheless true (because they are pramāṇas). The gain in clarity is substantial. I’m afraid that the alternative where one says that inference is erroneous but also true is, for the uninitiated at least, bordering on incomprehensibility. At any rate, it makes Dharmakīrti look quite exotic, whereas if the point is one of incongruence being compatible with truth, Dharmakīrti ends up holding a subtle and defendable position.

The last thing to say on this score is that scriptural inference is undeniably something of a special case. In “How Much of a Proof is Scripturally Based Inference?” I argued that this type of (quasi-)inference is the only sort where some forms of pragmatism do seem to be involved, precisely because it bears upon facts to which we have no access other than testimony in scripture. (Indeed, because it is not connected with facts for us, Dharmakīrti explicitly denies that it is a real full-fledged inference.) Is this where we would find a pragmatic theory of truth? No, I don’t think so. A pragmatic theory of truth is an instrumentalist truth theory, i.e., it allows as possible that statements and beliefs may be true just because they are maximally useful, but without any fact or real entities corresponding to them. There is no evidence to me that Dharmakīrti would want to say that the existence of the supersensible facts spoken about in scripture is somehow not needed, or that it is irrelevant to the truth of the scriptural proposition, or that what constitutes the truth of beliefs on such matters is just long term maximal utility. What is more likely is that we have here a pragmatic theory of justification, showing how people of limited understanding can and should determine when it is appropriate for them to believe in things like the details of the law of karma, things which they fundamentally cannot understand on their own and without scripture. In other words, if we wish to pursue spiritual “goals of man” (puruṣārtha), we have no other criterion for testing scriptural statements on supersensible matters and justifying our belief in them apart from the vital beneficial consequences that believing in such things will have for our spiritual progress. This is part of what is involved in Dharmakīrti’s well-known formula that we rely on scripture “because there is no other way” (agatyā): our limited understanding cannot have access directly or inferentially to the facts. Nonetheless, nothing in that discussion implies that there is no fact to the matter or need not be any fact for scriptural statements to be true. Someone like the Buddha or a yogin with perception of the supersensible would not be in our benighted situation and would not be condemned to the pragmatic justification and the fallible, approximative understanding that is our lot in these matters.

Vyāpti
Turning now to vyāpti, the question as to how one formulates this implication between terms has provoked considerable debate in current work on Buddhist logic, as has the question of how we are to understand the so-called “natural relation” (svabhāvapratibandha) underlying vyāpti. I think that what happened historically in the indigenous Tibetan literature is instructive: that is, the system changes when we make a clear separation between the question of what vyāpti is and the question of when we have grounds enabling us to say reasonably that it is present. The two problems, as I tried to show in “Formal and Semantic Aspects of Tibetan Buddhist Debate Logic” are indeed by and large separated by Tibetan writers, who have a consistently applied account as to what vyāpti is (i.e., absence of a counterexample or ma khyab pa’i mu) and another account as to when we can be confident that vyāpti is there (i.e., when we understand, on the basis of an example, that there is a relation between the reason and the property being proved.) This constitutes a significant difference in approach from Dharmakīrti and the post-Dharmakīrti Indian schools in that the purely logical problem of saying what vyāpti is is separated from the very difficult epistemological enterprise of providing a procedure to ascertain that there is a relation guaranteeing the absence of a counterexample.

Some writers, such as Bimal Krishna Matilal, have argued that it is a distinctive feature of Indian logic not to separate logical, epistemological and psychological issues. That is, I now think, true. Let us briefly look at some of the details of Matilal’s position, in particular the indispensable role of the example. Matilal argues that a multi-faceted approach combining logic with extra-logical matters is evident in the Indian position that vyāpti be not just a universally quantified statement but one which is exemplified, as in:

(1) Whatever is produced is impermanent, like a vase.

Although the first part of the statement of the vyāpti is, according to Matilal, translatable into first order logic as a statement of the form “For all x: if x is F then x is G,” the example serves to guarantee that we are not arguing about uninstantiated empty statements and that vyāpti will always have existential commitment. And that is one of the major reasons why, for Matilal, Indian logic is not like a formal logic: a universal premise in a syllogism-like formal structure would have no need for an example at all.

I think that Matilal was indeed onto something here about the Indian context and that it is important to get clear what is right about this characterization to be able to see what happened when we get to Tibet, where this characterization does not apply. Now, first of all, it is not fully accurate to say that a genuine example (dṛṣṭānta) different from the subject (dharmin, pakṣa) is always necessary: as is well known, the “advocates of intrinsic implication” (antarvyāptivādin) did not think examples were necessary for “the intelligent,” and in fact there is an intriguing passage in Dharmakīrti’s Pramāṇavārttika which indicates that he himself held a type of proto-Antarvyāptivāda. Nonetheless, even for an Antarvyāptivādin, the vyāpti will not be uninstantiated, as it will be instantiated by the subject of the reasoning. More seriously, there are real problems in saying that the first part of the vyāpti statement is translatable into a quantified conditional of the usual sort that one finds in first order logic. In first order logic the “for all x” will range only over existent things, whereas it can be rather quickly shown that if we are to introduce quantification to account for the vyāpti statements in certain Indian Buddhist discussions, the quantifier “for all x” must range over both existent and nonexistent things. We see quite clearly in the Buddhist logicians’ use of inferences like the so-called bādhakapramāṇa (based on Dharmakīrti’s Vādanyāya) that the example can be a nonexistent thing, like a rabbit’s horn or a flower in the sky, and that the scope of the vyāpti must therefore range over nonexistents as well as existents. Nor is it particularly infrequent or revolutionary for Buddhists to give such nonexistent items as examples—Bhāvaviveka, who was well before Dharmakīrti, used the example of the sky-flower in Madhyamakahṛdaya and Tarkajvālā too and even Dignāga used the example “space” (ākāśa) in his Hetucakra, an example which is not actually existent for a Buddhist. If we wish to formalize vyāpti statements into first order logic, we probably need quantifiers which range over actual and non-actual items, such as in the logic developed in Richard Routley’s (i.e., Richard Sylvan’s) article entitled “Some Things do not Exist.” And in that case, it cannot be maintained that the use of the example is to guarantee genuine existential commitment, for in many cases the example itself is not something real at all.

While we cannot maintain that vyāpti statements in Indian Buddhist logic must actually have existential import or commitment, we can agree with Matilal in maintaining that the antecedent and consequent terms in vyāpti—i.e., the vyāpya (“pervaded”) and the vyāpaka (“pervader”)— do have to be instantiated. But this instantiation or exemplification can even be by utterly nonexistent items. Take the so-called sādhyaviparyaye bādhakānumāna, or the “inference which invalidates [the presence of the reason] in the opposite of the [property] to be proved” to which we alluded above: “The permanent/non-momentary does not exist, because it does not have any efficacy successively or all at once, like a rabbit’s horn or flower in the sky.” This inference is usually given in something like the following way:

     (2) Whatever does not have a successive or simultaneous [production of effects], is not capable of effective action [i.e., does not exist], like a rabbit’s horn. That which is non-momentary does not have a successive or simultaneous [production of effects].

This bādhaka-inference is thus used to establish that existence is absent amongst non-momentary things, or in other words that whatever is non-momentary/permanent does not exist, which is clearly the contraposition of the fundamental principle that whatever exists is momentary. The vyāpti statement here is:

     (3) Whatever does not have a successive or simultaneous [production of effects], is not capable of effective action [i.e., does not exist], like a rabbit’s horn.

Putting the first part of (3), without the example, into its formal paraphrase yields:

     (4) For all x, if x does not produce effects successively or simultaneously, then x does not exist.

The quantification in this conditional must range over existent as well as nonexistent things. To complete the paraphrase, a statement that the rabbit’s horn does not produce effects and does not exist would have to be conjoined to (4). This example statement would then imply:

     (5) For some (existent or nonexistent) x, x does not produce effects successively or simultaneously and x does not exist.

In short, the example statement, “like a rabbit’s horn,” has the effect of showing that both the antecedent and consequent terms in (4) are not empty. It is not guaranteeing genuine existential commitment, but it is guaranteeing that the vyāpya and vyāpaka must have instances.

Now, what seems to have happened in the case of Tibetan bsdus grwa logic is that the Indian requirement that the vyāpya and vyāpaka be somehow instantiated (either by an example or at least by the subject) was simply dropped. True, the example is cited on occasion, by and large out of deference to the fact that the reasoning in question has been borrowed from an Indian text. Equally, the theoretical discussion about examples being needed is there in the Tibetan texts, perhaps essentially because it is there in their Indian ancestors. However, in the vast majority of statements of vyāpti in bsdus grwa logic texts or in the numerous texts which use bsdus grwa logic, no example is given at all. If an example is presented and discussed, it is generally in order to answer the epistemological question as to how a particular controversial vyāpti is to be established on the basis of an example (dpe’i steng du grub pa). That the statement of vyāpti itself generally does not include an example suggests fairly clearly that, de facto at least, this Tibetan vyāpti is different from its Indian homologue, in that it is just a universal implication, and not a universal implication which also has an instance. But one can go further: bsdus grwa logicians clearly and explicitly recognize that there are vyāpti where in principle no instantiation whatsoever is possible. In these vyāpti not just are there no examples of existent or nonexistent things having the property of the vyāpya, even the subject doesn’t possess the vyāpya. In effect, Tibetan bsdus grwa logicians recognized the fact that the falsity of the antecedent was a sufficient condition for the truth of the whole conditional—one finds this in the curious statements of vyāpti where the antecedent is clearly impossible, as for example when people are arguing about all barren women’s children having such and such properties. The principle is known as gang dran dran yin pas khyab (“whatever one might think of will be implied”) and is similar to the Medievals’ ex falso sequitur quodlibet: because the antecedent is (necessarily) false, the whole conditional is true, whatever might be given as the consequent. As far as I can see, there is no evidence that Dharmakīrtians in India countenanced any analogue to the idea of ex falso sequitur quodlibet. Quite possibly it would have seemed as absurd to them as it has to many in the West, who feel that if that is what material implication in formal logic permits, we had better explain our ordinary notions of entailment in some other way, perhaps along the lines of relevance logic or strict implication. In one way or another, people do demand that there be instantiation and a connection between terms for an entailment to hold—falsity or impossibility of the antecedent does not seem enough.

The preceding discussion has some summarizable results. First of all, in “Formal and Semantic Aspects of Tibetan Buddhist Debate Logic” I had thought that “epistemological and logical aspects were perhaps inadequately distinguished” in Dharmakīrti’s thought, that “pervasion itself in Dharmakīrti translates into the same universally quantified formula as in Tibetan logic,” and that “the Tibetans’ separation of the formal notion of pervasion from its Dharmakīrtian epistemological baggage does, perhaps, represent a certain progress.” It should be clear that I would no longer go to that extreme. Secondly, if we agree with Matilal that one of the main features differentiating Indian logic from Western formal counterparts is the insistence upon the implication being instantiated, then bsdus grwa logic’s notion of implication is not only rather un-Indian, but it shares the major features of the formal notion. And thirdly, it is clear that there were important formal discoveries in bsdus grwa, influenced by the revised understanding of vyāpti. As we mentioned, a logical notion of vyāpti stripped of requirements about examples and relations between terms led the Tibetans to discover and accept formal principles similar to ex falso sequitur quodlibet. Another striking development which this purely logical notion of vyāpti permitted was the bsdus grwa logicians’ discovery that there could be several types of vyāpti (i.e., the so-called khyab pa sgo brgyad or “eight types of pervasion”) by changing the order of the implication and adding negation operators, and that these pervasions would have elaborate formal relations between them. Indeed, ’Jam dbyangs bzhad pa (1648–1721) went very far in this direction, distinguishing twelve pervasions rather than the usual eight; his elaborate calculation of iterated multiples of formal equivalences between these pervasions, abstracted of all content and needing no instances, deserves to be regarded as genuine progress in the formal knowledge of his time.

Deviant Logic
Finally, a word on the perennial question as to whether and to what degree the logic which Buddhists use and advocate is in accord with key theorems of Western logic. Is their logic a more or less classical logic, with perhaps an odd twist or two concerning quantification and existential import, but nothing deviant like a rejection of contradiction or excluded middle? That is essentially what I argued in the essay “Is Buddhist Logic a Non-classical or Deviant Logic?” I would continue to stand by that position in the case of Dharmakīrti and his successors, Indian or Tibetan, and indeed for most of the Indo-Tibetan Madhyamaka too. It can be reiterated that “If there is any deviance, it can only be highly local.” I would, however, be prepared to grant that the logic underlying the Prajñāpāramitāsūtras and, to a lesser degree, the early Madhyamaka, may after all be something of the exception, more prone to paradox or paraconsistency, indeed that it could perhaps be close to the kind of depiction that scholars like Edward Conze and Jacques May gave it. The result would be that on this scenario Buddhist thought would have a history of going from the very provocative logic of certain Mahāyāna sūtras, and perhaps even Nāgārjuna, to the tamer logic of the scholastic. The later Indo-Tibetan scholastic, not surprisingly perhaps, would turn out to have an increasingly conservative reaction to the original writings of their tradition, arguing that the paradoxical or provocative aspects just cannot be taken at face value, but must be explained away with qualifiers and hedges. Indeed, interestingly enough, when it comes to logical deviance, a writer like Tsong kha pa would argue very much in the way that people like J.F. Staal have argued: the thought behind the texts cannot be like that, if it is not to be irrational. This is undoubtedly a powerful interpretative intuition. But with inconsistent or paraconsistent logics becoming ever more sophisticated and respectable, it becomes increasingly difficult to see that all types of contradictions are equally irrational. Furthermore, notions like the Hegelian Aufhebung, which Jacques May relied upon in his interpretations, cannot be dismissed in the cavalier fashion that they were by logical positivists and their successors. I don’t now know how to exclude that the Prajñāpāramitāsūtras are most simply and naturally read as having more or less the contradictions they appear to have. Indeed that Conze-May scenario fascinates me more and more.

Tom J.F. Tillemans
Lausanne, May 1999

 

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