Tibetan Developments in Buddhist Logic

Chapter I: The Reception of Indian Logic in Tibet

1. Introduction

What do people mean by “Tibetan Buddhist logic,” or by the more or less equally common phrase “Tibetan Buddhist epistemology,” and what connection do these widely used designations have with subjects studied traditionally by Tibetan Buddhists? The underlying Tibetan term is tshad ma. It conserves the etymological sense of the Sanskrit original pramāṇa, viz., a “standard” or “measure”; tshad renders the Sanskrit verbal root MĀ, “to measure”, with the Tibetan ma capturing the Sanskrit ana suffix and showing a means, source, or instrument. In philosophical Sanskrit pramāṇa is the technical term for a source of knowledge, a reliable means to a correct new understanding. The Tibetan term tshad ma, of course, has that technical sense, but it also takes on a more general sense of the “theory of sources of knowledge” or, more broadly, a discipline of study and the literature pertaining to it. In what follows, we’ll use the terms “Pramāṇa” and “Tshad ma” (capitalized and without italics) to designate the Indian and Tibetan theoretical disciplines respectively and their literature, even if the use of the term to designate a discipline is admittedly not as clearly present in the Sanskrit as it is in Tibetan.

Modern writers also regularly use the term “Buddhist epistemology” to capture the use of the words tshad ma / pramāṇa in the general sense of a theoretical discipline concerning sources of knowledge. It is, however, perhaps less clear why people speak of “logic.” Part of what looks recognizably like logic is the Indo-Tibetan Buddhist “science of reasons” (hetuvidyā= gtan tshigs rig pa), a so-called “minor Buddhist science,” and the related genre of indigenous Tibetan texts known as rtags rigs “the varieties of reasons” – in them one finds discussions of good and bad reasons, fallacies, implication and consequences. However, Tshad ma certainly is not limited to what we find in hetuvidyā or rtags rigs manuals. It also includes the extensive discussions of philosophy of logic that we find typically in works or chapters on “inference” (rjes su dpag pa = anumāna), one of the two sources of knowledge, along with perception. In short, besides the “science of reasons,” Tshad ma encompasses philosophical accounts of how logical reasoning proceeds and even some ontological issues of what must exist for that reasoning to be grounded in reality.

Perception, metaphysics, and even philosophy of mind were also to be included in the general subject of Tshad ma – with more or less complex connections with epistemology—, just as for Indians they were also regularly taken up in Pramāṇa literature. And so were doctrinal matters of Buddhism. Indeed, many traditional Tibetans and Indians saw Tshad ma as essentially destined for Buddhist religious purposes rather than as a secular discipline of logic, epistemology, or philosophy of logic and language; its raison d’être was thus to provide proofs of Buddhist doctrine, like rebirth, omniscience, the four noble truths, compassion, no-self, etc., the culmination of Pramāṇa being in effect pramāṇasiddhi, the proof of the Buddha’s superiority to other teachers and his being a standard and reliable source in spiritual matters. The demarcation between broadly religious and philosophical approaches to Buddhism has, of course, been an enormous subject of conversation, not only in modern Buddhist Studies but also in the past in Tibet. Suffice it to say here that Tibetan Tshad ma, when viewed religiously, would need a very different treatment from what we are offering, and that a secular orientation to Tshad ma / Pramāṇa is not only legitimate in modern scholarship but was also to quite a degree present in traditional Tibet. A disclaimer is thus in order from the outset: we will largely leave aside the extensively discussed issues of perception, metaphysics and philosophy of mind as well as Tshad ma-inspired approaches to Buddhist religious doctrine and scripture. Tibetan Tshad ma, and indeed Tibetan Buddhist philosophical literature generally, has often been regarded as a prolongation, a supplement, or a kind of fine tuning of India, or even a pedagogical aid to Indian developments. Indeed, one of the finest scholars of both India and Tibet, David Seyfort Ruegg, has rightly maintained that Tibetans were in many respects Indological scholars avant la lettre, making important and necessary contributions to our own historical understanding of Indian Buddhist thought. That said, although one certainly needs to know Indian thought well to understand Tibetan thought, it is odd to focus on Tibet only or principally as a way to understand India. For a wide-ranging scholar like Seyfort Ruegg the interest of ties to India certainly does not detract from the value and interest of ideas that were indigenously Tibetan and that perhaps had few or only obscure sources in India. Unfortunately, however, this type of open position was for quite some time preceded by a more closed orientation that was much less defensible, namely, that Tibetan Buddhist philosophical literature was of interest essentially in so far as it reflected or even copied Indian thought. Such a view was even promoted by quite a number of Tibetans themselves for perhaps understandable reasons of religious authority, India long being considered in Tibet the “Land of the Nobles” ('phags yul= āryadeśa) and the repository of what is authentic in Buddhism. It is somewhat unfortunate, however, that a similar attitude to things Indian was for long a working premise of much modern Buddhist Studies. Arguably, the originality of indigenous developments in areas like logic and epistemology have still, to a large degree, been underestimated and underexplored.

Indeed, when it comes to Tshad ma, in spite of the great respect that we should have for Indian writers like Dharmakīrti (6th or possibly 7th century C.E.?) and the Tibetan exegesis of his philosophy, there were also important Tibetan works that exhibited a high degree of originality and were only tenuously related to India. As we shall try to show, this genre of literature made some important conceptual distinctions concerning logic, significantly moving away from Indian preoccupations with themes in epistemology and metaphysics. By remaining centered on the consequences of various acceptances – be they true or not – these indigenous thinkers increasingly replaced concern with how things actually were in reality with a typical logician’s focus on what followed from what. There are thus two sorts of Tshad ma literature in Tibet that will concern us in this study: (a) Tibetan exegetical works closely based on Indian texts; these are largely commentaries, summaries, or independent analytical treatises whose primary purpose is clarification of Indian texts and argumentation. Examples are the Tibetan commentaries on Dharmakīrti’s Pramāṇavārttika and Pramāṇaviniścaya by various authors, as well as works, like Sa skya Paṇḍita's Tshad ma rigs gter or dGe 'dun grub pa's Tshad ma rigs rgyan, that provide an introduction to and interpretation of Indian Pramāṇa.

(b) Indigenous Tibetan works on epistemology and logic that involve, to a large degree, Tibetan concepts, debate procedures, and argumentation that is unfindable in Indian texts or, in some important cases, even radically counter to Indian positions. The best examples are the so-called “Collected Topics” (bsdus grwa), of which the earliest text is the Ra bstod bsdus grwa of 'Jam dbyangs mChog lha 'od zer (1429-1500). In what follows, we will consecrate a chapter to each of these two sorts of Tibetan literature, in order to bring out the dual character – i.e. the Indian-based and the indigenous— of the Tibetan contribution to Buddhist logic and the philosophy of logic. It should be borne in mind that our emphasis is primarily philosophical: apart from the necessary historical background and a few important historico-philological discussions, many of the complicated questions concerning connections between Tibetan thinkers or the origins of ideas and terms can not be pursued here; the reader is referred elsewhere. On a final apologetic note, let me say that although the scholarly transcription of Tibetan names and terms tends to render them notoriously impenetrable to non-specialists, such transcription is nevertheless necessary – phonetics can be used for a proper name or word here and there, but they are not adequate at all when there is significant reliance upon original sources. There are several approaches that writers adopt in dealing with this difficulty. Ours has been to provide a guide to standard Lhasa Tibetan pronunciation as an appendix. It is better to avoid short-cuts and quick fixes with purely phonetic transcriptions or computerized converters: the reader's investment of time and effort pays off in the long run.

2. Four periods

We begin with a whistle-stop tour of the terrain. Following van der Kuijp 1989 and Hugon 2015, let us speak of four periods in the history of Buddhist logic and epistemology in Tibet, starting with the initial diffusion (snga dar) of Buddhism in Tibet from the 7th century C.E. on and continuing to the present day.

(a) An ancient period, until very early 9th century C.E, or pre-Glang dar ma., during which some smaller Indian pramāṇa works of Dignāga, Dharmakīrti, Vinītadeva, Śubhagupta, Kamalaśīla, Arcaṭa, and Dharmottara were translated.

(b) A pre-classical period from the beginning of the so-called “second diffusion” (phyi dar) of Buddhism in the 10th century up to about the 13th century, during which the emphasis was on the Pramāṇaviniścaya of the pivotal Indian Buddhist thinker Dharmakīrti. The text was translated and was the object of several influential indigenous Tibetan commentaries. The period is marked by the work of Ngog lo tsā ba Blo ldan shes rab (1059–1109), who translated the Pramāṇaviniścaya and wrote commentaries upon it. It also saw the so-called “Summaries of Pramāṇa” (tshad ma bsdus pa) of the school of Phya pa Chos kyi seng ge (1109-1169) of the bKa' gdams pa monastery of gSang phu sne'u thog. These texts, as their name implies, were résumés of Indian thought, but actually seem also to inject a substantial dose of original interpretation, possibly in part because of the relatively incomplete access to Indian material at that time.

(c) The classical period of the 13th and 14th centuries. It begins with Sa skya Paṇḍita Kun dga' rgyal mtshan (1182–1251), the most significant figure in the consolidation of Tibetan and Mongol power in the south of Tibet, and himself a first-rate scholar of Indian texts in Sanskrit. During this period, Dharmakīrti’s largest and most important work, the Pramāṇavārttika, is finally well translated into Tibetan and becomes the focus of indigenous commentaries. A major delegation of Indian monks– led by the Kashmiri scholar Śākyaśrībhadra (?-1225)— visits Tibet and closely collaborates with Sa skya Paṇḍita. This can be said to be the most Indian-oriented period, and probably even the period that was most reliably informed on Indian Pramāṇa literature in Sanskrit.

(d) A post-classical period that begins in the 15th century and is characterized by debate between traditions of the pre-classical and classical periods. In particular, we find competing developments based on the earlier Phya pa and bKa' gdams pa traditions, on the one hand, and the Sa skya schools, on the other, i.e., the so-called Phya-traditions (phya lugs) and Sa-traditions (sa lugs) respectively. The bKa' gdams pa and Phya-traditions evolved to become the dGa' ldan pa or dGe lugs pa, and would count such luminaries as Tsong kha pa Blo bzang grags pa (1357-1419) and his principal disciples, rGyal tshab rje Dar ma rin chen (1364-1432) and mKhas grub rje dGe legs dpal bzang po (1385-1438). Two of the most important figures of the Sa-traditions were Go rams pa bSod nams seng ge (1429-1489) and gSer mdog Paṇchen Śākya mchog lden (1428–1508). We should also mention that it is in this post-classical period that we find the so-called "Collected Topics" (bsdus grwa) literature, which presents a sophisticated Tibetan logic with only rather tenuous connections with India. This indigenous Tibetan logic will be taken up in detail in the second chapter of this study.

3. Indian sources for Tibetan Tshad ma

As we can see from the above periodization, Tibetan theorizing about Indian logic and epistemology began in earnest in the 10th and 11th centuries in the pre-classical period. While the initial diffusion of the Dharma, from the 7th century to the mid 9th, saw first attempts at translating Indian Pramāṇa texts, it was from about the 10th until the 15th century that there was genuine assimilation and competent translation of the major Indian Buddhist works. The Pramāṇaviniścaya, Pramāṇavārttika and other works of Dharmakīrti and his school were well translated and understood by Tibetan writers and formed the main Indian textual basis for Tibetan exegesis on Indian Buddhist logic and epistemology.

By contrast, the works of Dignāga (c. 480 - c. 540 C.E.) never played a role comparable to those of Dharmakīrti. Dignāga’s major opus, the Pramāṇasamuccaya, although certainly said to be the founding text for Tshad ma, was actually of relatively little influence in Tibet. While there were a number of indigenous commentaries over the centuries, from that of bCom ldan rigs pa'i ral gri (1227-1305) to that of Mi pham ‘Jam dbyangs rnam rgyal rgya mtsho (1846-1912), the abysmally low quality of Pramāṇasamuccaya's two Tibetan translations no doubt impeded in depth study and understanding of this text in its own right. Dharmakīrti's interpretation of Dignāga predominated instead. Indeed, Dignāga's logic and epistemology were essentially known via quotations and commentary in other texts, notably in the works of Dharmakīrti and the Dharmakīrtian commentator on Pramāṇa¬samuccaya, Jinendrabuddhi. The specific features in Dignāga's philosophy that set it apart from that of Dharmakīrti were largely obscured. As for Dignāga's Nyāyamukha, it does not seem to have been studied or translated in Tibet. Instead Tibetans studied a related text, the Nyāyapraveśa of Śaṅkarasvāmin and often confused the Nyāyamukha with the Nyāyapraveśa, understandably because the Tibetan title of the Nyāyapraveśa, viz. Rigs sgo, was easily wrongly taken to designate the Nyāyamukha instead.

The main Tibetan orientation in Tshad ma was thus significantly different from that of the indigenous Chinese school of Xuanzang and Kuiji in that the latter did focus on Dignāgan positions in their own right fundamentally untouched by Dharmakīrti, whose works were untranslated in Chinese. For the Tibetans, by contrast, Dharmakīrti was well translated and his influence eclipsed that of the largely inaccessible Dignāgan literature. It is important to note too that although much of the in depth Tibetan assimilation of logic and epistemology dates from the 10th or 11th centuries on, the highly technical later Indian logical literature of that period was not the primary inspiration for Tibet. The Indian sources inspiring Tibetan study were essentially the works of Dharmakīrti and the 7th and 8th century commentators, Devendrabuddhi and Śākyabuddhi, who commented quite closely upon the wording and syntax of Dharmakīrti's works in their Pramāṇavārttikapañjikā and Pramāṇavārttikaṭīkā respectively. Prajñākaragupta (8th century C.E.) was well known, and his voluminous Pramāṇavārttikālaṃkāra was the source of some of the more philosophically sophisticated developments as well as applications of Pramāṇa to Buddhist religious ends. We also find the later Kashmiri Brahmin writer Śaṅkaranandana (ca. 940/50-1020/30) playing a significant role as a commentator on Pramāṇavārttika and as a philosopher of language, perhaps one of the promulgators of a moderate realism about universals. It is telling that in indigenous commentaries on Pramāṇavārttika –for example the rNam ‘grel thar lam gsal byed of rGyal tshab rje and other such commentaries—Tibetan authors quite regularly contrast the positions of Lha dbang blo and Śākya’i blo (Devendrabuddhi and Śākyabuddhi), rGyan mkhan po ( “the author of the [Vārttik]ālaṃkāra”, i.e., Prajñākaragupta), Bram ze chen po (“the big brahmin”, i.e., Śaṅkaranandana) and Chos mchog, i.e., Dharmottara (8th century), who did not write a commentary on Pramāṇavārttika, but instead wrote commentaries on Dharmakīrti’s Pramāṇaviniścaya and Nyāyabindu. The regular contrasts between these four or five positions show that on significant themes the works of Dharmakīrtian commentators and their different interpretative traditions were well understood.

Very important too are the works of Śāntarakṣita and his disciple Kamalaśīla, no doubt because of the presence of these scholars in Tibet in the 8th Century and the founding of the first Tibetan monastery at bSam yas in the Brahmaputra Valley. Indeed, it is difficult to overestimate the influence of Śāntarakṣita and Kamalaśīla on Tibetan Buddhism, be it in Madhyamaka, Buddhist doctrine, or Pramāṇa – Śāntarakṣita's Tattvasaṃgraha and Kamalaśīla's Pañjikā thereupon were thus influential texts in Pramāṇa. By contrast, later Indian logicians of the 10th-12th centuries such as Jñānaśrīmitra (floruit 975-1025), Ratnakīrti and Mokṣākaragupta, who had technically sophisticated debates with the Brahmanical schools of the time, were of negligible influence in Tibet. While the Pramāṇavārttika and Tattvasaṃgraha debates with the Brahmanical schools were studied and understood, important texts of the 10-12th Indian Buddhist literature dealing with the specific later developments on logical problems arising in refuting permanence, God, etc., were often only of marginal influence – many works that had considerable influence in Indian Buddhism were simply never translated into Tibetan. So, although there were some exceptions to this marginalization – bits and pieces of later Indian Pramāṇa positions that somehow came to be assimilated into intra-Tibetan debates --the impact of the later Indian literature was little, one of the reasons probably being that the works of the post-8th century non-Buddhist authors figuring heavily in Buddhist-Brahmanical debates —principally Jain, Nyāya, and Mīmāṃsaka— were not adequately understood in Tibet or even known at all. For example, in texts like Jñānaśrīmitra’s Apohaprakaraṇa, the argumentation is largely directed against Naiyāyikas like Trilocana, Bhāsarvajña and Vācaspatimiśra, who were, as far as I can tell at least, unknown in Tibet. The contextless logico-metaphysical debates on Pramāṇa, if anyone in Tibet ever looked at them in their dense Sanskrit, must have seemed particularly confusing.

In sum, Tibetan debates, innovations, and fine tunings on Indian Pramāṇa philosophy concern essentially the period from Dharmakīrti to the 9th century, with Dignāga’s thought little understood in its own right, and the thought of the very late Indian thinkers playing little role at all. Many of the Tibetan commentarial developments, it should be said, were more or less learning experiences, rather complicated stages in the Tibetan discovery and assimilation of Indian philosophical literature. Others, however, are of genuine philosophical interest. We will look in some detail at the most important of these developments concerning logic. After that, we will move on to Tibetan positions on crucial semantic issues in Dharmakīrti and then finally to Tshad ma-related issues concerning negation operators and parameterization in the wider context of Indian tetralemma argumentation.

4. The triply characterized logical reason (trirūpahetu) in Tibet.

The key concept in the Indian Buddhist “science of reasons” (hetuvidyā) is the notion of a good logical reason (saddhetu), and the criteria for a reason’s being good, viz., the three characteristics. It hardly needs saying that good reasons and their triple characterization (trairūpya) is a subject of major importance in Indian Buddhist Pramāṇa—it figures in in the opening verse of Pramāṇavārttika and in other works of Dharmakīrti and Dignāga. What did Tibetans do with this idea? Did they understand it properly and further develop it in any interesting directions? Let’s begin with presentations of the three characteristics in Dignāga, Dharmakīrti, and in a representative nineteenth century work by Yong 'dzin Phur bu lcog Byams pa tshul khrims rgya mtsho (1825-1901), a dGe lugs pa rTags rigs that was regularly used in Lhasa’s Se ra monastery. A comparison of the three gives a snapshot of how things evolved and what typical Tibetan contributions were.

Here, first, is Dignāga's Pramāṇasamuccaya II, 5:

anumeye 'tha tattulye sadbhāvo nāstitāsati "[a good reason] is present in the inferendum [i.e., in the subject] and in what is similar to it, and is absent in what is not [similar to it]." Dharmakīrti's Nyāyabindu II, 5 then reads:

trairūpyaṃ punar liṅgasyānumeye sattvam eva sapakṣaiva sattvam asapakṣe cāsattvam eva niścitam tshul gsum pa nyid kyi rtags ni / rjes su dpag par bya ba la yod pa nyid dang / mthun pa’i phyogs nyid la yod pa dang / mi mthun pa’i phyogs la med pa nyid du nges pa’o //

"The triple characterization [of a good reason] is as follows. It is ascertained (niścita) that: (1) [the reason] is only present [i.e., and never absent] in the inferendum [i.e., in the subject]; (2) [the reason] is present in only the similar instances (sapakṣa) [i.e., and not in the dissimilar instances too]; (3) [the reason] is only absent [i.e., and never present] in the dissimilar instances (asapakṣa= vipakṣa)."

The rTags rigs of Yongs 'dzin Phur bu lcog then gives a fully elaborated version of the three characteristics: de sgrub kyi shes 'dod chos can skyon med kyi steng du 'god tshul dang mthun par yod pa nyid du tshad mas nges pa / de sgrub kyi phyogs chos kyi mtshan nyid "The definition of the pakṣadharma [i.e., the fact that the reason qualifies the subject] for proving P is as follows: [the reason] is ascertained by means of a source of knowledge (pramāṇa) to be only present, in accordance with the appropriate way of stating [the verb yin or yod], in the faultless subject of inquiry when one is proving P."

de sgrub kyi mthun phyogs kho na la 'god tshul dang mthun par yod pa nyid du tshad mas nges pa de / de sgrub kyi rjes khyab kyi mtshan nyid. "The definition of the anvayavyāpti [i.e., the positive pervasion ] for proving P is as follows: [the reason] is ascertained by means of a source of knowledge to be present, in accordance with the appropriate way of stating [the verb yin or yod], in only the similar instances for proving P." de sgrub kyi dngos kyi bsgrub bya'i chos kyi don ldog dang 'brel stobs kyis de sgrub kyi mi mthun phyogs la 'god tshul dang mthun par med pa nyid du tshad mas nges pa / de sgrub kyi ldog khyab kyi mtshan nyid.

"The definition of the vyatirekavyāpti [i.e., the negative pervasion] for proving P is as follows: on account of its necessary connection with the concept that is the actual property being proved, [the reason] is ascertained by means of a source of knowledge to be only absent, in accordance with the appropriate way of stating [the verb yin or yod], in the dissimilar instances for proving P." The first thing one notices is that the definitions obviously become longer and more complicated over time. Dignāga is the most concise, while at the other extreme Yongs 'dzin Phur bu lcog includes so many provisos as to virtually defy English translation. Here are some of the things that catch one's eye in reading a Tibetan like Phur bu lcog in comparison with his Indian predecessors. Some are philosophical innovations; others are essentially dependent on, and account for, linguistic features of the Tibetan language.

de sgrub. We begin with the first words of the definition of the pakṣadharma(tva) in Yongs 'dzin Phur bu lcog, i.e., de sgrub kyi ('for proving P') Although many of Phur bu lcog's definitions, as we shall see, are amplifications of Dharmakīrtian ideas, we see an innovation in his introduction of a propositional variable, literally "that" (de) in Tibetan, which I am rendering by P. This is a difference vis-à-vis Indian Buddhist texts on the trairūpya, where no such variable figures. Indian texts do admittedly use tad (“that”) on occasion in other philosophical contexts more or less like a variable standing for a property or entity (as, for example in a phrase like tatkāryatā “being an effect of that”, “being an effect of x”), but Tibetans seem to recognize that a fully fledged propositional variable is needed in a general theory of reasons.

shes 'dod chos can skyon med. The proviso in Yongs 'dzin Phur bu lcog that the first characteristic must be established on the basis of a "faultless subject of enquiry" (shes 'dod chos can skyon med) is a way of bringing out Dharmakīrti's idea, in the second chapter of the Pramāṇaviniścaya and other texts, that the opponent must have the appropriate "desire to know" (jijñāsā) whether the proposition to be proved is true or not. In the Indian texts we find the term jijñāsitadharmin, literally, “the subject about which one desires to know,” “the subject of enquiry.” However, the idea is much more precisely formulated by Tibetans. Yongs 'dzin Phur bu lcog in his rTags rigs explains that it must be possible for the opponent to know that the reason qualifies the subject and yet still reasonably doubt whether the proposition to be proved is true. This obviously rules out circular proofs along the lines of “A is B because it is B” and various other forms of question begging. As well, it rules out cases where the debate falls flat, because the opponent simply does not have the required doubt at all. More sophisticatedly, in Tibet it leads to debates concerning what could be called problems of “epistemic priority,” e.g., arguments that can be challenged because understanding the fact that the reason qualifies the subject would already somehow presuppose understanding the truth of the proposition to be proved. Tibetans elaborate upon this in considerable detail and in ways that are not present in Dharmakīrti, employing a technical term go dkar sla "[[[relative]]] ease or difficulty of understanding." For example, it is argued that when one invokes a definiendum (mtshon bya = lakṣya) to prove a defining characteristic (mtshan nyid = lakṣaṇa) the former is more difficult to understand (go dkar ba) in that it presupposes the understanding of the latter, and that therefore the subject will not be a faultless subject of enquiry – this in turn means that the first characteristic will fail.

'god tshul dang mthun pa. The proviso “in accordance with the appropriate way of stating [the verb yin or yod]” ('god tshul dang mthun par), which is present in each characteristic's definition, is a somewhat longwinded formula designed to account for the fact that Tibetan (like modern Chinese shi 是 and you 有) distinguishes between a simple copula, yin, and an existential verb, yod. Being “in accordance …” is a way to say that if the verb is yin in the argument, it must remain yin when one is assessing the three characteristics. Similarly for yod. These two verbs, and the resulting possibilities for confusion between them, are not reflected in Sanskrit verbs like asti and bhavati. They are of course important in Sino-Tibetan languages, and hence it became important to provide for them in transposing the Indian trairūpya schema into Tibetan. Thus, for example, where Sanskrit uses a nominative (parvataḥ “mountain”) and a substantive with the mant suffix (“having…”) to express “having fire” (vahnimān) in the stock reasoning parvato vahnimān dhumāt (“The mountain has fire, because of [its] smoke”), the Tibetan has to use an oblique case marker la plus the verb yod (du ldan gyi la la me yod te du ba yod pa'i phyir, literally “On the smokey pass there exists fire because there is smoke”). Equally, where Sanskrit uses the genitive case and the abstraction suffix tva or tā, but no copula (e.g., śabdasyānityatvaṃ kṛtakatvāt “Sound has impermanence because of its being a product”) the Tibetan is obliged to proceed differently with a copula yin. nyid. Tibetan has two ways of expressing the Sanskrit particle eva (“only”) that is so important in the Indian trairūpya. In Tibetan canonical translations we typically find kho na being used for eva, but often, as in the case of the translation of the Nyāyabindu passage (see above), nyid is used instead. In indigenous works too nyid is used widely. The use of nyid here creates some problems, for the particle is ambiguous in Tibetan, often rendering Sanskrit abstraction suffixes tva or tā (as in stong pa nyid = śūnyatā “emptiness” or sngon po nyid = nīlatva “blueness”), but also eva. The rTags rigs definitions under scrutiny compound the difficulties because they use both nyid and kho na: thus yod pa nyid renders Nyāyabindu’s sattvam eva in the first definition, mthun phyogs kho na la renders Nyāyabindu’s sapakṣa eva (mthun phyogs nyid la) in the second, yod pa nyid then renders sattvam in the second, and med pa nyid renders asattvam eva in the third. While the use of nyid in rTags rigs accurately reflects the canonical translation’s use of nyid to render eva in the first and third definitions, it seems, however, that dGe lugs pa rTags rigs texts came to add an additional nyid in the second definition because of the tva in sattva. There was, then, obviously some confusion because of the double sense of nyid. In the anvayavyāpti definition dGe lugs pa authors confusedly use nyid after yod pa, while in the usual Dharmakīrtian second definition sattva is not followed by eva at all, nor is there a nyid here in the canonical translation of the passage. The potential for going astray is relatively serious. If, par malheur, one happened to take this yod pa nyid as expressing sattvam eva, instead of just sattvam, the anvayavyāpti definition would become quite wrong; indeed Dharmakīrtians in India and Tibet explicitly argue against putting eva (nyid, kho na) there after sattva in the second definition.

That said, if this and other indigenous formulations may have sometimes had problems with an ambiguous nyid, the uses of eva in the trairūpya and in Indian grammarians’ analysis of Sanskrit syntax were certainly understood in Tibet. Those uses were taken up by Dharmakīrti in extenso in texts such as Pramāṇavārttika IV, k. 190-192; two of the three are particularly important in the context of the trairūpya. Notably, the “elimination of non-possession” (ayogavyavaccheda = mi ldan rnam gcod) and “elimination of possession of something else” (anyayogavyavaccheda = gzhan ldan rnam gcod) conveyed by different placings of eva (“only”) in the first and second definitions respectively serve as ways to convey different uses of universal quantification. These uses of eva in the trairūpya are regularly discussed in Tibetan literature. They form a kind of recurring “lesson” in indigenous Pramāṇavārttika commentaries and in some rTags rigs texts. Tibetans were, for example, aware of the detailed and rigorous discussion in Dharmottara’s Nyāyamukhaṭīkā ad II, k. 5 of the logical consequences of right and wrong placements of eva in the trairūpya. The understanding of the logical aspects of quantification in the trairūpya, thus, does not differ from that of Dharmakīrti, even if the vacillation between nyid and kho na and the double duty of nyid suggests some nagging philological difficulties in handling the Indian material.

5. The Goodness and Badness of Reasons for Dignāga, Dharmakīrti and Tibetans

So much for specific details and philological issues in the formulations of the three characteristics. What can we say about the more philosophical aspects concerning logical reasons in Dignāga, Dharmakīrti and in Tibetans like Phur bu lcog? Modern writers on Indian and Tibetan logic frequently speak of reasons being “valid” or “invalid,” which unfortunatley tends to lead to a bout of conceptual chaos in rendering the Indian term saddhetu or the equivalent Tibetan terms gtan tshigs yang dag and rtags yang dag. I have regularly argued that the triply characterized reason, a saddhetu, is not to be viewed as a reason that is simply formally valid, as if a reason P being a saddhetu for Q were no than a matter of P⊧Q, viz., that Q was a logical consequence of P, in virtue of the form of the statements and independent of content. Let's instead just speak of a saddhetu as a “good reason” and a hetvābhāsa (gtan tshigs ltar snang, literally “pseudo-reason”) as a “bad reason.” Here are some general comparative observations about what that goodness is for Dignāga, Dharmakīrti and a Tibetan like Phur bu lcog.

First of all, factual content, and not just logical form, matters to a reason's goodness for these three logicians—India and Tibet are no different on that score. If we, for the moment, slightly deform things by taking the three characteristics as showing, inter alia, premises in an argument (rather than criteria for evaluating a reason), then the question of the truth of the premises is crucial, and not just the formal validity of the inference: this is part of what is involved in Dharmakīrti and rTags rigs saying that the three characteristics must be “ascertained” or “ascertained by a pramāṇa” – if a proposition is ascertained by a source of knowledge it is true. Though Dignāga does not state “ascertained,” still for him too reasoning from truths to other truths is essential. To put things in other terms, in India and Tibet soundness (arguments that do have true premises and entail a true conclusion) is much more emphasized than validity (arguments where the premises, if true, would entail a true conclusion).

Second, while the actual truth of the premises as well as the entailment of the conclusion are important, this certainly isn't all there is to goodness. Providing an account of what type of reason is a good one also involves considerations of epistemic priority, the makeup of the opponent’s belief set, the opponent’s receptivity to certain arguments, and his doubts. Thus the triple characterization, with its provisions concerning “ascertainment,” “faultless subjects of enquiry,” “proper opponents” and the like, also takes up essentially epistemic, and even rhetorical, matters: what can one rationally doubt when one believes or knows such and such a proposition to be true? What type of reason will, or should, succeed in changing beliefs and for which kind of person? Indian Pramāṇa specialists treated these matters as largely implicit in their trairūpya definitions; Tibetan Tshad ma makes them quite explicit.

Here is a sample of the type of epistemically oriented discussions that arise. First, as mentioned earlier, for a reason to be a good one, the opponent must have the requisite doubt as to whether the proposition being debated is true. Indeed the fact that a particular opponent already believes or knows the truth of the proposition being debated means that the reason will be categorized as faulty for him given his belief set, even though it may generally be a good one for opponents. Thus reasons are good relative to opponents and their belief set; often the opponent is understood to be the ideal rational individual; sometimes one delves into the belief sets of particular (less than ideal) individuals. Second, as a good reason is one that can rationally persuade opponents to revise their beliefs, it must be couched in terminology and concepts to which the opponent is receptive; if, for example, the reason or subject are not ones that the opponent can acknowledge in his philosophy, then the argument will not be persuasive at all to him and will not change his beliefs. Another requirement: the opponent must still be able to rationally doubt the proposition’s truth even though she has ascertained that the subject is qualified by the reason and has even ascertained that the reason is pervaded by the property. For example, a reason like “being audible” is not a good one for proving that sound is impermanent, because audibility is coextensive with sound: in that case it would be impossible to know that all audible things are impermanent and yet continue to doubt rationally whether sound is impermanent. “Audibility” (mnyan bya (nyid) = śrāvaṇatva) is considered here to be “a reason that is uncertain because of being overly exclusive” (thun mong ma yin pa’i ma nges pa’i gtan tshigs = asādhāraṇānaikāntikahetu): there is an extensive analysis of this type of reason, in epistemic terms, in the dGe lugs pas’ rTags rigs texts and in their commentaries on Pramāṇavārttika.

To represent these epistemic aspects of the triple characterization adequately it seems that we would need to change course significantly from the way modern writers have typically used elementary logic tools to elucidate Buddhist ideas. Instead of simply using first order predicate calculus to elucidate the triple characterization, we may well need to see it as fully involving a type of logic of belief revision. This cannot be attempted here in anything but general themes for reflection. In any case, while determining what follows formally from what or determining which statements are true would be important in revising beliefs, they only represent part of the story. The larger problem being investigated by Indians and Tibetans is the rational process whereby an opponent’s existing belief states --a set of propositions some of which are epistemically entrenched, while others can be more or less doubted— meet new added information (a fact presented as a reason) and then change into new belief states. Up until now, the Indo-Tibetan trairūpya has been studied by and large as a fragment of formal thinking, with epistemic aspects seemingly more or less inessential add-ons. Seeing the trairūpya as a fragment of a logic of belief revision would integrate those epistemic and rhetorical aspects that have hitherto been deemed secondary or have even been selectively disregarded.

Third, there is a significant metaphysical dimension to the Dharmakīrtian and Tibetan idea of a good reason. This is the requirement that there be a “necessary connection” (sambandha, pratibandha), i.e., a naturally existent real connection (svabhāvapratibandha) of either causality (tadupatti) or same nature (tādātmya) between the reason and the property to be proved (sādhyadharma). It is supposedly in virtue of this connection that the debater can be certain that the pervasion holds. Thus the metaphysical requirement is also implicit in the Nyāyabindu's use of the proviso niścita (ascertained). Yongs 'dzin Phur bu lcog is more explicit in that he clearly specifies, in the third definition, that this ascertainment is by means of a source of knowledge (tshad ma = pramāṇa) grounded by a necessary connection ('brel ba = sambandha).

That requirement, i.e., grounding of logical reasoning in necessary connections between terms, comes straight from Dharmakīrti, but is not present in Dignāga’s works. The natures (svabhāva) and their connections– to which a logician is ontologically committed as real facts—are what ensures the second and third characteristics, i.e., the pervasion. It is thus the ontological precondition for certainty (niścaya, niścita) and guarantees, in some sense, that the pervasion must hold, and not that it simply does hold as far as we can see. Another Dharmakīrtian way to put it is that the existence of real facts and the relevant connections between them ensures that the reason “operates due to real entities” (vastubalapravṛtta); reasoning is thus not an arbitrary process of freewheeling thought and language. It is no exaggeration to say that Dharmakīrti’s demands for certainty, necessary connections, and grounding in reality are among his main contributions in the Buddhist philosophy of logic.

6. Certainty, Formal Matters and the dGe lugs – Sa skya Debate on Similar Instances.

Let it be granted that, besides logical or formal considerations, there are many other aspects—rhetorical, epistemic, factual, metaphysical—involved in the goodness of a reason, in both Indian and Tibetan philosophies of logic. Nonetheless, what can be said about the implication of the conclusion from the reason when the triple characteristic is satisfied and the reason is thus good? Is the truth of the conclusion guaranteed by formal considerations when the three characteristics are established (and the premises are thus true), or is it at best fallibly established to be true in, let's say, normal situations? One way of interpreting Dignāga was indeed that the three characteristics were thought to be fallible in this way. We can see that the much-maligned Īśvarasena, who supposedly wrote a commentary on the Pramāṇasamuccaya, was quite aware that satisfaction of the triple characteristic would generally establish truth of the conclusion, but that there were exceptional cases where it would not. Hence he added three supplementary characteristics to rule out such abnormal cases. If we adopt the official Dharmakīrtian line about certainty (niścaya), then fallible truths are not enough; truth of the conclusion should be guaranteed.

Indeed, there are several passages in the Pramāṇavārttika, notably chapter I. 15, that clearly show that Dharmakīrti thought that Dignāga himself used or intended to use the term niścaya / niścita in order to eliminate, inter alia, “deviant reasons” (vyabhicāra), i.e., those that did not guarantee the truth of the conclusion because the pervasion was not rigorously established. The emphasis on certainty is so strong an imperative that Tibetan monastic textbook (yig cha) writers, like e.g. Se ra rje btsun Chos kyi rgyal mtshan (1478-1546), regularly also back-read Dharmakīrti's position onto Dignāga's texts, and argued, that niścaya/niścita was actually present in the passage from the Pramāṇasamuccaya II.5 quoted above. That, however, is just not so: it is not there in the Sanskrit of that verse of Pramāṇasamuccya nor in Dignāga’s Pramāṇa¬samuccayavṛtti; Dharmakīrti added it in a kind of borderline plagiary of that key Pramāṇasamuccaya passage in his Pramāṇaviniścaya so that he could accommodate his own ideas about grounding for logical reasoning, and the certainty ensured by natural connections (svabhāvapratibandha). Ever since the Pramāṇaviniścaya, Dharmakīrtian commentators such as Arcaṭa and Durvekamiśra, and notably Tibetans, have been doing a back-reading of Dignāga to say that it was there all along. In fact, there is no convincing evidence that Dignāga was concerned with grounding and metaphysical foundations of logic. The back-reading thus did not fit him easily at all.

Besides the Tibetan debates on the presence or absence of the “word niścita” (nges pa'i tshig = niścitagrahaṇa), however, there are other considerations that have a bearing on the question of the conclusion's truth being guaranteed. There are formal considerations. If we go back to the passages from Dignāga, Dharmakīrti and Phur bu lcog, truth conservation depends upon how one takes the terms “similar instances” (sapakṣa) and “dissimilar instances” (vipakṣa/asapakṣa). This question is not explicitly discussed in India, but it is the subject of a significant debate between dGe lugs pa (and their gSang phu predecessors, the followers of Phya pa Chos kyi seng ge), on the one hand, and Sa skya pa on the other. Let us now look at the details of that dGe lugs-Sa skya debate. It is a debate which starts in the classical period with Sa skya Paṇḍita’s Tshad ma rigs gter criticizing Phya pa and the gSang phu thinkers; it is then prolonged in the post-classical period in the writings of Go rams pa bSod nams Seng ge and those of dGe lugs pa writers like Se ra rje btsun Chos kyi rgyal mtshan, the former defending Sa skya Paṇḍita and the latter defending his opponents.

If we go back to Dharmakīrti's definitions of the three characteristics as given in Nyāyabindu II.5 (translated above), the subject, or pakṣa, is known to be only present (i.e., never absent) in the reason, the reason is known to be present in only similar instances (sapakṣa), and the reason is known to be wholly absent from dissimilar instances (vipakṣa). Let us, for the sake of convenience, represent a typical argument in Sanskrit or Tibetan as having the general form "A is B because it is C." In that case, to put it very approximatively, the first characteristic ensures that all A's are C's, while the remaining two conditions are designed to ensure that all C's are B's, all three of them enabling us to infer that all A's are B's.

However, an important controversy arises concerning the terms sapakṣa and vipakṣa in the second and third characteristics. Looking at Sa skya Paṇḍita's major work Tshad ma rigs gter and the dGe lugs rTags rigs literature, we see that there was a significant divergence on the issue of what Indians meant by “similar” and “dissimilar.” Indeed these texts develop two scenarios, what I have called “the orthodox scenario,” according to which similar and dissimilar instances excluded the subject (dharmin) and thus did not exhaust the whole universe of things about which we might reason, and the “unorthodox scenario,” according to which the subject was included amongst the similar or dissimilar instances respectively, these two exhausting the universe and admitting no third alternative. In brief, the orthodox scenario leads to a tripartite division of the universe into (1) the set of similar instances, {x: Bx & ¬Ax}, i.e., the set of all those things x that have the property B but not A. (2) the set of dissimilar instances, {x: ¬Bx & ¬Ax}, i.e., all those things x that do not have B and do not have A. (3) the set of things which are the subject, i.e. {x: Ax). The unorthodox scenario in effect is an advocacy of bipartition: there is no third alternative apart from the similar and the dissimilar instances; the similar instances are simply {x: Bx} and the dissimilar instances are {x: ¬Bx}.

Now, whereas the orthodox scenario is plausibly ascribed to Dignāga, the unorthodox scenario is especially what we find in later Indian texts of the so-called “intrinsic pervasion” (antarvyāpti) school, such as the Antarvyāptisamarthana of the 10th century thinker, Ratnākaraśānti. The opponents of Sa skya Paṇḍita were characterized in his Tshad ma rigs gter as followers of antarvyāpti (nang gi khyab pa). This seems to have been on the mark, for we can see that the dGe lugs pa and Phya pa Chos kyi seng ge indeed do use Ratnākaraśānti's definitions of similar and dissimilar instances, and that they are exponents of the unorthodox scenario (although they do not endorse the key tenet of Antarvyāptivāda that examples are dispensable when arguing with intelligent people). An interesting question – which alas I cannot take up here, but have discussed elsewhere-- is how we should situate Dharmakīrti. In any case, whether rightly or wrongly, the Sa skya pa interpret him (and Dignāga) as following the orthodox scenario, and the dGe lugs take him (and Dignāga) as following the unorthodox. The problems for the orthodox scenario are formal. Here is what those formal issues look like. Let C be the reason, A the subject property and B the property to be proved. For simplicity, let us simply take the term A as a general term – if we want to take it as a particular that adaptation can be made. The two scenarios can be best differentiated by formulating the second characteristic along the lines of “all C's apart from those that are A are B's” and “all C's are B's” repectively. The difference applies mutatis mutandis to the third characteristic. We represent the universal quantifier “For all x: …” by “(x) (…)” and material implication (“if … then …”) by “→.” Here then are the two scenarios concerning the triple characterization:

(a) Orthodox (x) (Ax→Cx). (x) ((Cx & ¬Ax) →Bx) (x) (¬Bx & ¬Ax) →¬Cx)

(b) Unorthodox (x) (Ax →Cx) (x) (Cx → Bx) (x) (¬Bx → ¬Cx)

It is clear that on scenario (a), the conclusion (x) (Ax →Bx) does not follow from the three statements, whereas on scenario (b) it uncontroversially does. We could say that the three statements in (a), if true, might provide some fallible grounds for thinking that (x) (Ax →Bx) is true, but that there is no guarantee that it is true, because that statement is not formally implied; it cannot be derived from the other three. At most, the move to the conclusion would be a defeasible inference, one which would be tentative and might be retracted once further information became available. In (b), however, the truth of the conclusion would be guaranteed as the statement is formally implied and easily derivable; there is thus no possibility of the inference subsequently being revised because of new information. That difference with regard to defeasibility is also sometimes spoken of as a difference between non-monotonic and monotonic logics, or, less precisely, between inductive and deductive logics.

If we accepted (b) as capturing the trairūpya, there would be no problem in seeing a good reason as guaranteeing truth of the conclusion. And for the dGe lugs there is indeed no problem with this. The Sa skya pa, however, had some major exegetical conundrums. On the one hand, it seems to be so, as the debate shows, that similar instances and dissimilar instances for Dignāga were easily and naturally interpreted along the lines of (a). At least it is demonstrable that some very competent logicians in seventh century India did interpret Dignāga’s logic in this way. When, for example, the Chinese pilgrim Xuanzang used Dignāga’s logic of triply characterized reasons to frame a tortuous proof of idealism, his proof is only intelligible, as Franco 2005 convincingly shows, if we take similar and dissimilar instances in the orthodox fashion, i.e., as excluding the subject. It seems clear that the logic on which the argument was based was not an idiosyncratic invention of Xuanzang himself nor a purely Chinese development; it reflected a going Indian interpretation of Dignāga.

Nonetheless, there are problems in saying that for Dignāga himself, the satisfaction of the triply characterization reason, as in (a), could have provided only a fallible justification for the claiming the conclusion to be true, or that Dignāgan logic is therefore non-monotonic/inductive, while Dharmakīrti’s logic is monotonic/deductive. I now think that unfortunately one cannot be so categorical in this fashion about Dignāga, even if we probably can continue to use those terms to characterize the logic of Dharmakīrti and his successors.

My reluctance is for the following two reasons. First of all, some later Sa skya pa Rigs gter ba writers such as Glo bo mkhan chen Bsod nams lhun grub (1456-1532) were aware of the problem that Dignāga seemed to advocate a tripartite universe, but that it would come with the unacceptable price that a triply characterized reason did not entail its conclusion. They thus made a difference between similar instances taken epistemically, or subjectively (blo ngor gnas pa’i mthun phyogs), and similar instances as they are in reality, or objectively (don la gnas pa’i mthun phyogs). To take the sound-impermanent example, the first is the set of all things that the debaters know to be impermanent. Since they wonder whether sound is in fact impermanent, sound is excluded from those known impermanent entities. The second is what is really so, irrespective of what debaters may think; thus, in this sense, sound is actually included amongst the similar instances because it is an impermanent thing. In short, the orthodox account would focus on epistemology and epistemic processes of how people reason, whereas the unorthodox account would better capture the logical aspects of what follows from what.

Secondly, it is now clear, thanks to the detailed study of Shōryū Katsura 2005 on Dignāga’s use of the terms pakṣa, sapakṣa and asapakṣa / vipakṣa, that Dignāga himself tried to distinguish both the epistemic/subjective and the logical/objective perspectives in his use of the key terms. It seems then that the diagnosis by Glo bo mkhan chen of two senses is on the mark and helpful in understanding Dignāga. As Katsura 2005, 124 hypothesizes, while Dignāga’s subjective interpretation of “similar instances” was captured by the orthodox tripartite division of the Rigs gter ba, the objective bipartite division that he also had may have contributed to the unorthodox bipartite division promulgated by Dharmakīrti, the Antarvyāptivādins, and the dGe lugs pa. In that case, the modern researcher wondering whether Dignāga’s own trairūpya promoted non-monotonic or monotonic logic, or one that was inductive or deductive, etc., would have to content herself with the somewhat unsatisfying (but historically right) answer that the trairūpya for Dignāga was a mixture of both – it all depended on whether you read the terse formulae about similar and dissimilar instances from the logical or epistemic perspectives.

That being said, Sa skya Paṇḍita (Sa paṇ) no doubt emphasized the epistemic perspective and thus the orthodox reading of the Indian trairūpya’s talk about similar and dissimilar instances. That is how he talks in Rigs gter 10 about pakṣa, sapakṣa and vipakṣa and that is how he and the Rigs gter ba were read by their dGe lugs pa adversaries, such as Se ra Chos kyi rgyal mtshan. The problem for the Sa skya pa was, however, that he, like Phya pa and the dGe lugs pa, demanded guaranteed truth of the conclusion – it had to formally follow from true premises. This was the Dharmakīrtian stance and both sides in the Tibetan debate adhered to it. Not surprisingly, then, given that Sa paṇ must have been sensitive to the formal problems of entailment in the tripartite universe, he chose a very different exegetical route to specify the logical and objective aspects of a triply characterized reason more precisely. The Indian trairūpya was drastically revamped and no longer formulated in terms of presence in similar instances and absence in dissimilar instances at all. Instead he and his Sa skya pa followers reformulated the second and third characteristics to be simply that the property to be proved must be implied by the reason and that the reason must be absent when the property is. This is an unconvincing rewrite of the attested canonical formulations of the Indian Buddhist trairūpya – it is part of the “slow death” of the Indian trairūpya in Tibet — but shows, if more evidence were ever needed, just how uneasy the inherited Indian position was for Tibetans. In Sa paṇ’s eyes, the price to be paid to save the trairūpya as a definition of a good reason that entailed the conclusion was that he had to make a clean sweep of the old Indian definition. He had to relegate talk of similar and dissimilar instances to epistemology and then do logic with a new version that simply dispensed with them.

7. Deviant logic? The tetralemma and the law of double negation elimination in Tibetan Madhyamaka

It is frequently wondered whether the formal structures in Indian and Tibetan Buddhism represent a type of radically different logic, or “deviant logic,” one that does not respect fundamental theorems of classical western logic. Whereas the trairūpya, in India and in Tibet, clearly does not suggest any such deviance, the argumentation concerning the tetralemma (catuṣkoṭi) might. The tetralemma is found in numerous texts of the so-called school of the “philosophy of the middle” (madhyamaka = dbu ma), and although it is not used by the major figures in Indian Pramāṇa literature, Tibetans tended to synthesize Madhyamaka and Pramāṇa so that what they held about one tradition affected, in varying degrees, what they held about the other. Here is how the recurring schema of four alternatives, or the tetralemma, is presented in verse 21 of chapter 14 of Āryadeva’s Catuḥśataka: sad asat sad asac ceti sadasan neti ca kramaḥ / eṣa prayojyo vidvadbhir ekatvādiṣu nityaśaḥ / “Existent, nonexistent, both existent and nonexistent, neither existent nor nonexistent, that is the method that the learned should always use with regard to oneness and other such [theses].”

The philosophy of the middle, starting with the 2nd-3rd century C.E. thinkers Nāgārjuna and Āryadeva, regularly uses this schema, or a partial version of it, to dismiss all philosophical theses (pakṣa, pratijñā = phyogs, dam bca’) and thus arrive at a quietist stance of “no more discursive proliferations” (niṣprapañca= spros bral)— a Mādhyamika thinker supposedly negates all four lemmas, and this with regard to any philosophical position presented. In short, we are supposed to negate existence, nonexistence, both and neither, as well as oneness, not-oneness, both, neither, and every other such proposition in its four alternatives. Granted the last two lemmas are left out and one often speaks simply of negating the first two, i.e., “existence” and “nonexistence”, with all other attributes in philosophical debates negated mutatis mutandis. And this twofold negation yields the famous middle way (madhyamā pratipad = dbu ma’i lam). Things do not stop at the first two negations, however. Lest it be thought that “neither existent nor nonexistent” is the final view on how things are in reality, this lemma is negated too. How that path to thesislessness is to be interpreted and practiced is a major theme in Tibetan Buddhism. Now, prima facie at least, the fourfold negation of the lemmas of “existence”, “nonexistence”, “both” and “neither” would seem to result in a very deviant Buddhist logic. To put things in terms of propositional calculus, the four negations would seem to yield the conjunction of the following four statements: (a) ¬P (b) ¬ ¬P (c) ¬(P & ¬P) (d) ¬(¬P & ¬ ¬P)

Notably, the law of non-contradiction seems to be violated if we apply the law of double negation elimination to (b) (i.e., ¬¬P) and then adjoin (a) (i.e., ¬P) to the result of that elimination. We end up simply with ¬P & P, a contradiction. It doesn’t stop there: adjoining (c) to P & ¬P would yield (P & ¬P) & ¬(P & ¬P). And so on it goes. That specter of deviance did not go unnoticed in Tibet, where, as in India (at least from about the 5th century C.E. on), there were strict, explicit prohibitions against contradiction (virodha = ’gal ba). Indo-Tibetan Buddhist logicians spoke of propositions that were “mutually contradictory” (parasparaviruddha = phan tshun spangs ‘gal), and if one asserted such a “mutual contradiction” it was a point of defeat (nigrahasthāna = tshar gcod kyi gnas).

Two moves suggest themselves to enable Buddhists to avoid contradiction in the fourfold Madhyamaka reasoning. First they could reinterpret the negation operator so that the law of double negation elimination would not apply in these discussions. Negation here would be a kind of “mere denial” without any implied positive assertion, so that ¬ ¬P would not imply P; the adjoined negations would remain mere denials and would not yield any positive assertion of P that could be adjoined with ¬P. The second move is to add parameters to the various propositions so that the appearance of contradiction is dissipated. Both these moves were present to varying degrees in Indian Madhyamaka discussions. The first move to interpret tetalemma-style negation as “mere denial” (pratiṣedhamātra = dgag pa tsam) dates from the 6th century Mādhyamika Bhāviveka’s appropriation of two types of negation in Indian logic, viz., implicative (paryudāsa) and non-implicative (prasajya), the latter being a negation that does not imply any positive phenomenon (vidhi). The second move is not given a developed theoretical treatment in India, but figures, at least implicitly, in Indian Madhyamaka uses of qualifiers like svabhāvena (by its intrinsic nature), paramārthatas (ultimately), satyatas (truly, really) and other terms that are synonymous.

Both moves stimulated significant debate and philosophical reflection in Tibet. In particular, we find major figures of the dGe lugs and Sa skya tradition arguing as to how precisely to interpret the “mere denial” sort of negation and whether or not it obeys the law of double negation elimination. For the Sa skya pa it does not obey the law of double negation elimination, whereas for the dGe lugs pa it most certainly does.

We also find debates between these two traditions about whether the statements of the tetralemma should be explicitly parameterized. The dGe lugs pa have a sophisticated position where they maintain that instead of understanding, say, the first lemma as “… exists,” it should be understood as “… exists by its intrinsic nature” (rang bzhin gyis) or “… exists ultimately” (don dam par), “… exists truly (bden par)”, etc., These qualifiers can be represented with a term of art, the operator “REALLY.” Thus, (a) and (b) would become respectively:

(e) ¬ REALLY P

(f) ¬ REALLY ¬P

There would be no contradiction in asserting both (e) and (f) to arrive at a middle way where P may be true but “REALLY P” is not true and “REALLY ¬P” is not true either. Double negation elimination need not be rejected because there is no threat at all that REALLY P will follow from ¬ REALLY ¬P. Indeed, the philosophical upshot of the tetralemma negations would just be that no statement or its negation is ever true when prefixed with the REALLY operator. The dGe lugs pa Madhyamaka-style negation of qualified statements is thus a frontal attack on metaphysical realism and ontology, but it does not exclude accepting and arguing for the truth of unqualified statements. One can, in effect, claim the truth of “The world is round”, “Enlightened people exist”, or “There are no three positive integers a, b, and c that satisfy the equation an + bn = cn for any integer value of n greater than two.” Such truths may sometimes be obvious and sometimes profound, but for those statements to be true one need not, and indeed cannot, claim the truth of “It is REALLY so that the world is round”, “It is REALLY so that there are no three positive integers, etc.” The Sa skya pa, on the other hand, maintains that the statements in the tetralemma should not be parameterized at all. Given that the goal of the Madhyamaka is a completely irenic state where one makes no truth-claims whatsoever, qualification would run counter to that goal, for if the tetralemma’s statements were qualified one could still claim a propositon P to be true and argue strenuously for it – as did the dGe lugs pa—and hence be irremediably lost in “discursive proliferations.”

The key technical term in this dGe lugs pa-Sa skya pa argument is dgag pa gnyis kyis rnal ma go ba, literally “understanding the main [proposition] by means of two negations.” It is not difficult to see that this is indeed a law of double negation elimination. The term is found in early Pramāṇaviniścaya commentaries, such as that of rNgog lo tsā ba Blo ldan shes rab (1059–1109), and also figures regularly in Tsong kha pa’s Madhyamaka texts, such as his commentary on the Mūlamadhyamakakārikā, his Rtsa she ṭīk chen. It is not itself an original Tibetan idea, but can be traced back to Indian Buddhist logic, the Sanskrit original pratiṣedhadvayena prakṛtagamana being found in the third chapter of Dharmakīrti’s Pramāṇaviniścaya. There are also Indian uses of the same or equivalent terms in non-Buddhist texts—like Kumārila’s Ślokavārttika Nirālambanavāda 125, which uses pratiṣedhadvayāt vidhir eva (The positive does indeed come from the double negation) —as well as in Indian Madhyamaka texts such as Candrakīrti’s Prasannapadā to Mūlamadhyamakakārikā 4.5ab and especially Bhāviveka’s Prajñāpradīpa (D. 80a7) and Avalokitavrata’s Prajñāpradīpaṭīkā (D. 180b3). But although double-negation elimination does seem to be invoked on relatively rare occasions in those Indian Madhyamaka commentaries, it is not at all clear whether the Mādhyamika himself endorses it as a universally applicable logical law, or whether he restricts it to implicative negations, or just uses it in certain situations as a rhetorical stratagem that is recognized by the opponent. The interest of the Tibetan debate is that it takes up this issue, one that was philosophically crucially important but was still probably quite unclear in India. In effect, for the Sa skya pa, the rejection of double negation elimination is essential to the Madhyamaka goal of thesislessness; a Mādhyamika supposedly makes “mere denials” but never makes any positive truth claims; parameterization does no work here and is in fact an obstacle. For the dGe lugs pa, by contrast, parameterization is key; the issue of double negation elimination is irrelevant; the logical features of the tetralemma and non-implicative negation are taken to be thoroughly classical. Tibetan positions on these issues thus concern the most basic matters of Madhyamaka quietism.

8. Semantic issues: Indians and Tibetans on referential opacity and intensional entities

As a final subject in our exposé on Tibetan developments of Indian Pramāṇa debates, we turn to an important logico-semantic issue connected with Dignāga and Dharmakīrti’s apoha (exclusion) theory of meaning. This semantic problem, similar to western debates concerning substitution of identicals for identicals in opaque contexts, was regarded as crucial for logic, both in India and Tibet, because it was thought that failure to find an acceptable solution threatened the possibility of logical reasoning across the board. In short, Dharmakīrti and Tibetans characterized the semantic solutions as necessary conditions for the legitimacy of one of the Buddhist sources of knowledge, inference (anumāna). Here are the Indian basics and the Tibetan developments. Buddhist logicians knew well that pervasion (vyāpti = khyab pa) between two terms F and G sometimes hold in only one direction, as in the case of “being a tree” and “being a śiṃśapā tree”—all śiṃśapās are trees, but obviously not all trees are śiṃśapās— and that sometimes pervasion is bidirectional. The former case is analysable as a universally quantified material implication, i.e., a conditional like for all x: if x is a śiṃśapā then x is a tree, while the latter case, termed "equal pervasion" (samavyāpti = khyab mnyam), is, in effect, analysable as a universally quantified biconditional, for all x: x is F if and only if x is G. In India, and in Tibet, semantic problems then arise in cases of a bidirectional pervasion, like that between impermanence (anityatva = mi rtag pa nyid) and being causally produced (kṛtakatva=byas pa nyid), where in effect (adopting the above analysis) we have a true biconditional, for all x: x is impermanent if and only if x is causally produced. Tibetans will then say that given this birdirectional pervasion, the terms are therefore coextensive. Indeed, Tibetans regularly use the technical term don gcig (literally: same objects) for this extensional identity of F and G and speak of "eight types of pervasions" (khyab pa sgo brgyad) holding between F and G when they are the "same objects": (1-2) a bidirectional pervasion using the copula "is" (yin); (3-4) its two contrapositions; (5-6) a bidirectional pervasion using the existential verb yod ("There is..."); (7-8) its two contrapositions.

When there is extensional identity between F and G, a problem of substitutivity then arises. It can be unpacked in the following manner, with the use of a few familiar notions and principles. Although the extension of terms may be the same (e.g., the set of impermanent particulars = the set of causally produced particulars), still in some contexts substitutivity of one term for the other would seem to lead to an invalid inference where the premises are true but the conclusion is not. To bring this out, take the following tempting, but invalid, inference:

(a) Being a product is a good reason for proving that sound is impermanent (b) Being a product is coextensive with being impermanent (i.e., for all x: x is impermanent if and only if x is a causal product) (c) Therefore (by substitutivity of identicals for identicals), being impermanent is a good reason for proving that sound is impermanent.

We would seem to go from two true premises to a false conclusion, for Buddhists are explicit on the point that the conclusion is false. (Indeed, arguing that something is so because it is simply so is not giving a good reason, neither for Buddhists nor for most people in the world!) Buddhists, however, as we saw in discussing the definitions of the triple characteristic, would phrase the problem in terms of the jijñāsā / shes 'dod "desire to know" becoming impossible: it is impossible to know that sound is impermanent and still want to know whether sound is impermanent; the pakṣadharmatva would thus fail because once one understood the reason as qualifying the subject, that subject would not be a jijñāsitadharmin / shes 'dod chos can, one about which one wishes to know whether it is qualified by the property to be proved. And yet we would also seem to be using an acceptable principle of substitutivity of identicals for identicals salva veritate. What went wrong? Is Leibniz’s famous law of substitutivity of identicals salva veritate not recognized? Or, if it is—and in fact it is recognized by Buddhists, as far as we can see—then why does it not apply here? Dharmakīrti, in Pramāṇavārttika I verse 40 et sq. and his own commentary (svavṛtti) di agnosed the problem as one of bidirectional pervasions (i.e., coextensive concepts) seeming to force us to accept pratijñārthaikakadeśahetu "reasons that are one part of the thesis proposition" (e.g., when one says "sound is impermanent because it is impermanent," then the reason "being impermanent" is also a part of what is being proved). He saw this undesirable consequence as one of the main challenges to logical thought being a source of knowledge (pramāṇa), for unless one can somehow rule out the problematic substitutions in what I have called the "tempting inference," we would seem to have to accept as good a huge number of singularly uninformative circular reasons.

The issue is indeed a recognizably familiar one in formal semantics and in philosophy of logic and language: substitutivity in referentially opaque contexts, such as propositional attitudes and modal contexts (see Tillemans 1986). One might know who Kim Philby was but not know who was the leader of the infamous Cambridge Five spies (or perhaps one might be convinced that the leader was none other than W.V. Quine’s famous sleuth Bernard J. Ortcutt). Though it is so objectively that Kim Philby = the leader of the Cambridge Five spies the reference of the two terms is opaque in typical belief contexts, in that using “the leader of the Cambridge Five spies” instead of “Kim Philby”, or vice versa, may well yield a false sentence. Likewise, talk of good reasons being ones where the debater has a desire to know P but not an equivalent P’ which is different from P only in substituting a new term for identical entities, is indeed an opaque context. To analyze what goes wrong in the tempting inference, Dharmakīrti, in effect, made a usual move by distinguishing between types of identities: "being impermanent" and "being produced" are extensionally identical, but somehow not intensionally so. He speaks of the expressions making us understand differences and individualities; the concepts— more literally, in his apohavāda jargon, the "exclusions" or "isolates" (vyāvṛtti = ldog pa)— are different. The point is that, in the opaque context, substitution could only be made between terms for identical concepts and not between terms that just happen to refer to the same entities in the world.

In fact, though, it could well be objected that the usual idea of an intensional identity (one that is understood to hold between properties F and G when the biconditional for all x: x is F if and only if x is G is true in all possible worlds) will not get us very far out of the woods, as being impermanent and being produced are arguably identical in that way. And it would thus seem that if that is what conceptual identity is about for a Buddhist Epistemologist it should be possible to make the substitution in the opaque contexts under discussion. Dharmakīrti's idea of concepts F and G being identical thus demands a much stronger criterion than the necessary truth of the biconditional for all x: x is F if and only if x is G. If that latter necessary truth is the criterion for identity between F and G, when taken as intensions, then we would seem to be forced to accept "ultra-intensional" entities where the identity criterion would have to be even stronger.

In dGe lugs pa commentaries to verse 40 and in the Tibetan Collected Topics (bsdus grwa) literature, probably indebted to the Phya-tradition, we find the makings of an idea of "conceptual identity/difference" (ldog pa gcig/tha dad) such that to each meaningful subject or predicate term in a language there is a different concept— synonyms (ming gi rnam grangs), for example, will still express different concepts (ldog pa tha dad). Thus, for example, we find a telling passage from Yongs ‘dzin Phur bu lcog which I will translate in full:

“An opponent says that real entity, impermanent, product, and composite, as they are simply a group of synonyms, are all identical (gcig). Analogously, knowable thing (shes bya), existent (yod pa), established basis (gzhi grub) and discriminable entity (gzhal bya) are also identical. Just as, for example, the Incomparable Son of Śuddhodana, the Omniscient One of Solar Line, and the Omniscient Sugar Cane One [are identical]. [We reply:] This is incorrect because the Son of Śuddhodana, the One of Solar Line and Sugar Cane One are all different (tha dad). If [you say that the reason is] not established, we affirm that it does follow [that the Son of Śuddhodana, etc. are different] because it is possible that one might ascertain, with a source of knowledge, to which basis one applies the words “One of Solar Line” and “Sugar Cane One”, even though one does not acertain, with a source of knowledge, to what one applies the words “Son of Śuddhodana.” Therefore, although the basis [i.e., the actual person] for applying the names “Son of Śuddhodana,” “One of Solar Line” and “Sugar Cane One” is identical, they [i.e. the Son of Śuddhodana, etc.] are not identical; if they were identical, they would have to be identical both in name and meaning.”

There are use-mention problems here but the idea is still understandable: the fact that the names differ for the same actual person, i.e., Buddha Śākyamuni, allows us to say that Son of Śuddhodana, One of Solar Line, etc. are themselves different (tha dad). The same type of difference holds between being impermanent and being produced. In short, following the dGe lugs pa text cited above, the substitution in the problematic inference would be blocked by saying that being impermanent and being produced are not actually identical after all, but are somehow different.

Now, it will be said that it is quite counterintuitive that synonyms would nonetheless express different concepts. As Stoltz 2008 points out, there were also some Tibetans, including even Phya pa himself, who said that terms like shing and ljon pa (two words translatable as “tree”) expressed the same concept (ldog pa gcig). In that sense, there was no complete unanimity amongst Tibetans and some seemed to have adopted a more common-sensical position that two different words could express one concept. But, oddly enough, that seemingly common sense truism that two words sometimes express one concept would probably go astray as a close reading of Dharmakīrti’s own text. Although the precise terminology of ldog pa gcig/tha dad may be new, the idea of one difference (bheda), or one meaning (artha), being expressed by one and only one word is certainly present in Dharmakīrti’s Svavṛtti to verse 40-42:

“So, though there is no difference in their intrinsic natures, still the individuality (viśeṣa), the difference (bheda), which is understood through its respective specification, i.e., a name, cannot be made understood through another. Thus, all the words do not have the same meaning (artha). And therefore it is not so that the reason is a part of the thesis proposition (pratijñārthaikadeśa).”

Indeed, Dharmakīrti’s proposed solution to the problem of substitutivity in opaque contexts would not work at all if the two expressions like “being impermanent” and “being produced” had the same meaning. It’s disturbing but true: the extreme position in dGe lugs pa Tshad ma textbooks got Dharmakīrti essentially right about a principle of “one word one meaning.”

But where would this talk of conceptual identity and difference leave us philosophically? It might well seem to lead to far too many strange entities, a new separate entity for each word. The Sa skya pas were indeed loath to tolerate any such mysteriously subsistent entities and considered the Phya pa position concerning concepts as an aberration. For the Sa skya pas, concepts, universals and the like were not objects (yul = viṣaya) at all. The only objects for them, were impermanent causally efficacious entities, the particulars (rang mtshan = svalakṣaṇa) of Dharmakīrti – the rest, be they perceptual illusions or concepts, were just cases of mistaken cognition (‘khrul shes). Thus, Sa skya Paṇḍita (in the first chapter of his Tshad ma rigs gter) emphasized that concepts were only façons de parler for different states of mind. States of mind are fully existent and could be individuated so that a thought (i.e., the mental state or episode) that A is F would not be the same as a thought that A is G, even if the predicate terms F and G were synonymous. Precisely how those thoughts would be individuated does, however, remain to be seen. Indeed, whether Sa paṇ’s approach would offer a satisfactory way out of Dharmakīrti's conundrum with referential opacity, or whether ultra-intensions will come in again via the back door to explain how thoughts do in fact differ, has to remain open here.

9. A Theme for Further Investigation: Meinong in Tibet?

In the final analysis, the debate on the logico-semantic problem of substitutivity in opaque contexts seems to turn on one’s commitment to ontology and metaphysics, and notably one’s adherence to the strongly nominalistic orientation of Dharmakīrti. The dGe lugs pa-Phya pa traditions, as their adversaries rightly depicted them, did indeed claim that the entities in question, the ldog pa or "concepts," weren't actually real entities (dngos po = bhāva, vastu) at all, but just objects created by thought and language, or in other words, customarily existent things (kun rdzob bden pa = saṃvṛtisatya). Indeed for them, objects (yul = viṣaya) could be really existent particulars or merely customarily existent universals, permanent things and concepts. And the later dGe lugs pa would even flirt with completely nonexistent things (like rabbit’s horns) as being a type of quasi-object, although not an object (yul) properly speaking. The upshot of tolerating everything as an object is a position that might win favor with someone like the 19th century Austrian philosopher Alexius Meinong (1852-1920), who accepted objects that existed really as well as those that were nonexistent but merely subsisted. Ontologists naturally balk at such a seemingly baroque account of what there is, as they attach importance to parsimony, thus avoiding unnecessary entities, as well as to the abjuration of double talk – i.e., talk "which would repudiate an ontology while simultaneously enjoying its benefits." (Quine 1960, 242). I think the Sa skya pas, like Dharmakīrti, accepted that principle of parsimony, distrusting dGe lugs-Phya lugs profligacy and their seeming double talk about things that didn’t fully exist but were objects nonetheless. The Sa skya pas, in short, reasoned in a predictable fashion, as the ontologists they were, and followed the nominalism of Dharmakīrti, allowing as objects only those things to which they were univocally committed in a pared down ontology.

On the other hand, the dGe lugs pa and Phya lugs were not unlike Meinong in that they maintained that every mental state had an object, but not necessarily a fully really one – mental states are intentional and directed to things that may or may not be real, be they particulars, concepts, or even completely nonexistent things like barren women’s children. The question then arises whether the dGe lugs pa-Phya pa followers, or Meinong for that matter, were guilty of multiplying entities unnecessarily, as their critics suggest. As Dreyfus 1997 shows, it is clear that the dGe lugs pa were far less nominalistically inclined than their Sa skya pa counterparts: they allowed real universals as well as commonsense objects extended both in space and in time, thus radically reinterpreting the Dharmakīrtian insistence on momentary extensionless particulars; as we shall see in the next chapter, they had no compunctions about taking pervasion (and hence quantification) as ranging over all really existent, conventionally existent, or completely nonexistent things. Here is my own take on this debate: the dGe lugs pa were simply not much bothered by ontological scruples in their talk of objects, but were up to something else. They remained closer to description instead of radical revision. Now, undeniably, we do think of things that are unreal and predicate properties of them, and so it is relatively easy to think that a phenomenological description of ordinary thought and language should simply allow for such intentional objects and not try to explain them away. Meinong sought that type of phenomenological account and so did the dGe lugs pa. Of course, an ontologist would retort that an account in which unreal things are objects is only phenomenology and that a metaphysically acceptable account would have to analyse them otherwise. But it looks like the dGe lugs pa followers were not bitten by that bug. They saw little of the imperative to paraphrase or analyse surface level phenomenological description away in favor of some radically revisionist deeper metaphysical position. The lesson seems to be that lightweight (non-metaphysical) talk of objects is harmless; intentional objects are harmless, have little to do with ontology, and hence need no Quinean or Sa skya pa overkill.

Chapter II. Indigenous Tibetan Logic: Collected Topics and the Logic of Consequences

1. Introduction, History and Texts

As we had mentioned in section 1 of the previous chapter, the post-classical period in Tibetan Buddhist epistemology and logic includes a notable development of an indigenous Tibetan logic, one that is considerably less of a copy or even interpretation of India than are the theory of good reasons and the related discussions in Tibetan commentaries on Pramāṇavārttika and Pramāṇaviniścaya. This logic figures especially in bsdus grwa texts, what we have been calling “Collected Topics.” In fact, the Tibetan term bsdus grwa is not an easy one to translate. Shunzō Onoda gives what may be the most thorough explanation, taking it as probably bsdus pa slob pa'i sde tshan gyi grwa "the schools or classes in which [primary students] learn bsdus pa or summarized topics [of logic or dialectics];" he then quotes a later etymological explanation according to which the word bsdus grwa meant "the class where many arguments are summarized together" (rigs pa'i rnam grangs du ma phyog gcig tu bsdus pa'i grwa). In short, while the term grwa clearly refers to the first classes in the monastic curriculum, it is less clear what bsdus pa refers to, especially because it might well suggest the tshad ma’i bsdus pa of Phya Chos kyi Seng ge, the so-called “Epistemological Summaries” of the pre-classical period. A translation of the term bsdus pa as “Collected Topics” or "The Class (grwa) of Collected Topics (bsdus pa)", however, emphasizes the fact that bsdus grwa is a collection of various topics ranging from colours, ontology, concepts and causality to consequences (prasaṅga) and the “exclusion theory of semantics” (apohavāda).

While there was no doubt a connection between Collected Topics and the Summaries (bsdus pa), either of Phya pa or of other writers connected with gSang phu sne’u thog monastery, the exact details and degree of influence still needs more investigation. In the 18th century, Klong rdol bla ma (1719-1794), in his Tshad ma rnam ‘grel sogs gtan tshigs rig pa las byung ba’i ming gi rnam grangs, spoke of eighteen "lessons" (rnam bzhag) by Phya pa, most of which have the same titles as those of Collected Topics, thus reinforcing the speculation that bsdus grwa derived from Phya pa's tshad ma'i bsdus pa, or Epistemological Summaries. However, the details of the debt of bsdus grwa to Phya pa’s Summaries are still to be fully investigated. And there are other writers, like rGya dmar ba Byang chub grags (11th century), a student of rNgog lo tsā ba, who supposedly wrote one or more Tshad ma’i bsdus pa, as did a figure like Chu mig pa (13th century), texts which are unavailable at this time.

Up until the late 1990’s the works of Phya pa were also unavailable, both to Tibetan and western scholarship. They were already classified as "rare" (dkon po) in a 19th century Tibetan catalogue. Fragments were cited and claims were made by Tibetan authors—in the case of Sa-tradition authors this was generally for polemical purposes. Now that we are finally gaining access to a number of Phya pa's own texts it turns out that they have less in common with Collected Topics than some of us, myself included (and perhaps many Tibetans), had imagined.

Significantly, it is now not clear that the thal-phyir logic of consequences that Stcherbatsky had attributed to Phya pa as its probable inventor, did actually come from Phya pa himself. Its precise origins are still obscure. Hugon 2008a shows how important argumentation by analogy was in Phya pa—if the opponent affirms P, then Q should be true too, because they are similar (mtshungs pa). The debate would increase in complexity when it is replied that they are not similar (mi mtshungs) and that some other proposition R would be similar, etc. etc. This relentless tit for tat style of argumentation seems to have been a preferred tactic of Phya pa in debate, seemingly more so than the bsdus grwa style thal-phyir reasoning.

The earliest Collected Topics is the Rwa bstod bsdus grwa of the gSang phu abbot 'Jam dbyangs mChog lha 'od zer (1429-1500). Several other authors subsequently took up the genre. 'Jam dbyangs bzhad pa (1648-1722), of Bla brang monastery, wrote a small Collected Topics in verse, and four other works concerned, in one way or another, with subjects in bsdus grwa. There are works of varying size and affiliated with different dGe lugs pa monastic colleges – e.g., the Collected Topics of bSe Ngag dbang bkra shis (1678-1738), representing the tradition of Bla brang, or those of Yongs 'dzin Phur bu lcog Byams pa tshul khrims rgya mtsho, representing especially Se ra. Although the Sa skya tradition is known to have engaged in very vigorous polemics against the Summaries of the Phya-tradition, there also may have been, curiously enough, a type of Sa skya pa Summary, the bsDus pa rigs sgrub of ‘U yug pa Rigs pa’i seng ge (?-1253), who was the major student of Sa skya Paṇḍita, and there even seems to be a seventeenth century Sa skya pa bsdus grwa, the Chos rnam rgyal gi bsdus grwa.

Collected Topics continue to be studied and even composed in the Tibetan cultural community, both in the Tibetan Autonomous Region and the diaspora. Indeed, debate is still widely practiced as a study technique in the dGe lugs curriculum. One of the most extraordinary recent records of actual Tibetan debates and sophisms is the "Mnemonic Notes on the Collected Topics " (bsdus grwa brjed tho) composed in Tibetan by the 20th century Mongolian abbot of sGo mang college of Drepung monastery, the late dGe bshes Ngag dbang nyi ma. Collected Topics is regularly studied in Dharamsala in the dGe lugs pa “Philosophy School” (mtshan nyid slob grwa) and in Sarnath at the Central University for Tibetan Studies, as well as in some modern Sa skya pa institutions. In short, Collected Topics and its logic are alive and well in communities both within and outside Tibet. The examples I give below of reasonings from Collected Topics come essentially from Yongs 'dzin bsdus grwa, bSe bsdus grwa, Ra stod bsdus grwa, and bsDus grwa brjed tho, but are also often considerably simplified. Finally, what does it mean to say that Collected Topics are "indigenously Tibetan," "original" or even "un-Indian?" The matter is somewhat complicated by the fact that the dGe lugs pa / dGa' ldan pa regularly back-read the positions of Collected Topics onto Indian Pramāṇa texts; the originality of the dGe lugs/Phya ideas is thus often disguised or downplayed. Nonetheless, Collected Topics offers interesting and important developments that, as we shall see, are not found in India and need to be seen in their own rights. These indigenous developments often depend upon features of the Tibetan language that are significantly different from those of Sanskrit. They also reflect a different direction in logic, one that is much less oriented towards metaphysical and epistemological issues than is its Indian counterpart.

2. The Rules of the Game

Let us take up the recurring feature and probably major contribution of Collected Topics: the logic of consequences, or what Stcherbatsky called the “logic of sequence and reason.” As we have seen, the triple characterization – the key structure Indian Buddhist logic—was fraught with problems of interpretation. Indeed in 14th-15th century dGe lugs pa philosophical texts, and certainly in the logic of the Collected Topics, the triple characterization became marginalized and figured relatively little in the working logic used in discussions of philosophical issues. That logic consists in so-called “consequences” (thal 'gyur= prasaṅga). A consequence is simply defined in Collected Topics as thal ngag su bkod pa “what is presented as a statement that something follows [from something else]”, or to put it conditionally, that “something would follow [from something else] (thal ngag).” The consequence, in short, need only state what would follow from what the opponent accepts, or would have to accept given his or her position.

Generally, the form common to all consequences in this indigenous Tibetan debate logic is: “Take A as the subject (chos can); it follows (thal) that it is B, because it is C.”

Such was the style of reasoning that was, and still is, used in the context of dGe lugs pa (and some Sa skya pa) monastic debates in Tibetan Buddhism, both in actual oral debates and in written records of them. It is the staple fare of Collected Topics and is then applied to the five major Indian texts (poṭi lnga) of the dGe lugs curriculum and the commentaries and monastic textbooks (yig cha) upon them.

The contrast with the triply characterized reason is striking. While the latter, requires, inter alia, that A actually be qualified by C, and that all C's be B's – this is the requirement that the characteristics be “established/ascertained by pramāṇas” – a consequence's goodness (thal 'gyur yang dag) need not turn on key statements actually being true, but only on them being accepted by the opponent. Goodness is largely dependent on what is “established by positions” (khas len pas grub pa=*abhyupagamasiddha) rather than on “establishment by pramāṇas (tshad mas grub pa),” as in the case of triply characterized reasons. More specifically, the consequence is a good one if the opponent cannot consistently maintain what she accepts and still reply (lan 'debs mi nus pa) in one of the three permitted manners.

(a) 'dod (= *iṣṭaḥ). I agree that A is B. (b) rtags ma grub (= *liṅgam asiddham). The reason is not established. That is to say, in effect, I maintain that A is not C.

(c) khyab pa ma byung/ma khyab (=*na vyāptiḥ). The pervasion does not hold. That is to say, I maintain that it is not so that all C's are B's. Note that the latter two replies do not allow for an opponent being simply skeptical or in want of some further persuasive argumentation. If the opponent says that the reason is not established, this is interpreted to mean that she has the belief that the reason actually does not qualify the subject. It is similar for the pervasion. In short, the replies rtags ma grub and khyab pa ma byung allow the proponent to infer that her opponent believes the opposite proposition, and then argue accordingly against that belief by presenting further consequences.

Also, an opponent's inability to reply (within a quite short time!) is not accepted as just slowness or prudence; it is, de facto, an admission that the consequence tells against one of the positions she holds, and it thus allows the proponent to reiterate the argument to probe which position the opponent will agree to abandon. If the opponent simply remains mute, she loses the debate. On the other hand, if the opponent does reply in one of the three permissible ways, then the debate will continue, and the proponent will have to argue to show that those replies lead to other consequences. This process continues until the opponent can not consistently reply and, on probing, will have to give up something: this is then a partial victory for the proponent who can then “backtrack” using that concession to bring about other consequences further undermining the opponent's position. Typically, the concession will become the reason in the new consequences. The debate will then proceed in this fashion until the opponent is forced to give up her “root position” (rtsa ba'i dam bca' = *mūlapratijñā), i.e., the fundamental proposition which started the debate. At this point, of course, the proponent can claim complete victory and the debate ends.

So much for the moves found abundantly in the texts. There are also moves and strategies that rarely figure in the texts but are often used in actual Collected Topics debates. One of them is to say chos can skyon can (Faulty subject!) when the subject term involves some double entendre or other trick. When a pervasion might normally hold but is taken in a deliberately ambiguous way or involves a patently sophistical special case, the reply can be 'dir ma khyab “There would be no pervasion in this case!”

A reply that is particularly ingenious – and worth exploring in some detail, as it seems to be largely unknown to western Tibetologists— goes by the exotic name “Knowable thing and crushed garlic!” (shes bya sgog rdzog). It does figure once in Yongs 'dzin bsdus grwa chung, but without any explanation, as it is the kind of orally learned reply competent debaters know and use as a kind of shorthand for a claiming that an argument commits a particular type of fallacy. The reply shes bya sgog rdzog meant that one thought an opponent's reasoning committed the same fallacy as in the following faulty argument:

shes bya chos can; khyod rdzog pa [or rdzog rgyu] yin par thal; sgog pa khyod yin pa gang zhig sgog pa rdzog pa [or rdzog rgyu] yin pa'i phyir.

"Take as the subject knowable thing. It follows [absurdly] that it is crushed [or crushable] because garlic is one and garlic is crushed [i.e., crushable]." Or a little less exactly:

"Take as the topic, knowable thing; it follows that it is crushable, because garlic is a knowable thing and garlic is crushable."

The debater knows that the reply to this reasoning must be: "There is no pervasion" (khyab pa ma byung), for obviously it is not so that when garlic is an instance of x and garlic is crushable then x itself must be crushable. If there were such an implication, you would have to agree that knowable thing itself is crushable. Here, then, is the structure of the fallacious arguments that shes bya sgog rdzog supposedly encapsulates: A is B because an instance of A is B. This is, of course, an understandable and genuine fallacy, something people commit quite frequently. E.g.,

"Humankind is evil, because Son of Sam is human and Son of Sam is evil." Indeed, to put it another way, shes bya sgog rdzog is a common Tibetan way to claim that the opponent is pursuing bad inductive reasoning. True, the debate can continue to determine whether the opponent's reasoning really is a case of bad inductive reasoning, as alleged. But what is striking for our purposes is that the usual Dharmakīrtian metaphysical and epistemological arguments about natural connections (svabhāvapratibandha) existing in the real world and the illegitimacy of establishing a generalization by merely not seeing a counterexample (adarśanamātra) will play no role whatsoever. In effect, metaphysics and epistemology are replaced by a set of rule-guided moves in a game. Occasionally, there are set pieces, as when one claims shes bya sgog rdzog. But questions about grounding for pervasions in reality are not germane, as that they would in effect make a debater step back and appeal to what is so outside the debate, instead of following the rules where they take her. What there really is outside, or underlying, the rule guided activity of debate seems to be largely irrelevant: Tibetan debate logic is a kind of formalism.

3. Two Sorts of Consequences

Consequences, in Collected Topics, are sometimes, but certainly not always, recognizable Indo-Tibetan forms of reductio ad absurdum, in which the consequence B follows from the reason C that the opponent accepts, but is in contradiction with the other positions of the opponent. Sometimes, but not always, the truth of the opposite proposition is then derived by an application of contraposition.

Thus, for example, suppose that a non-Buddhist Mīmāṃsaka, or someone like him, holds that sound/a word (śabda = sgra) is permanent, that it is produced from causes and conditions, but also accepts that whatever is produced is impermanent. To this individual, the Buddhist can give the following consequence: (1) sgra chos can / ma byas pa yin par thal / rtag pa yin pa'i phyir

"Sound, the subject; it would follow that it is unproduced [from causes and conditions]; because it is permanent." The Mīmāṃsaka opponent is then faced with a situation where each permitted reply entails abandoning a statement in which he himself believes, and so he cannot reply leaving all his Mīmāṃsaka philosophy intact. In that sense (1) is a “good consequence” for him. In Tibet, as in India, one also speaks of a so-called “contraposition of the consequence” (thal bzlog = prasaṅgaviparyaya). The contraposition of the consequence in (1) provides a “proof” (sgrub byed = sādhana) as follows:

(2) sgra chos can mi rtag pa yin te byas pa yin pa'i phyir "Sound, the subject, it is impermanent, because it is produced [from causes and conditions]." The reason of the consequence in (1) is negated and becomes the property to be proved in (2); the property in (1) is negated and becomes the reason in (2). Crucially, in (2) the reason is indeed supposed to satisfy the three characteristics, so that the goodness of that reason is not just a matter of acceptance but of establishment via pramāṇas. That is why (2) is considered to be a proof and not just itself another consequence.

The type of consequences as exemplified by (1) are said to be “consequences that imply a proof” (sgrub byed ‘phen pa’i thal ‘gyur). What does “imply” (‘phen pa =*kṣipta) mean here? This is clearly not just simple prediction that actual opponents will, as a matter of fact, come to understand and accept a proof after hearing a consequence showing a contradiction in their positions. In fact, in (1) we seem to be dealing with a type of ideal rational individual, a “proper opponent” (phyi rgol yang dag), who knows with a pramāṇa that sound is produced (or to put it more traditionally, he has a pramāṇa that refutes that sound is not produced) and knows that all products are impermanent; yet he still mistakenly believes that sound is permanent. In that case, this opponent will arrive at (2). In short, to say that a proof is “implied” presupposes that certain statements are not just accepted but are in fact known to be true, i.e., “established by pramāṇas” (tshad mas grub pa). Of course, the ideal individual who would know all these truths and still have the required mistaken belief is no doubt rare, but arguably that is not the point. The explanations in Indo-Tibetan Pramāṇa texts about consequences that imply proofs are best seen as normative discourse about what follows from what and about what moves rational people should make; it is not simply anthropology or sociology about how some or most people actually do think.

In India, many significant thinkers such as Dharmakīrti and Bhāviveka, insisted that prasaṅga by itself is incomplete to establish truth and that there must be an implied proof, sometimes termed a svatantrahetu (rang brgyud kyi gtan tshigs) or “autonomous logical reason”, i.e., one that, as in the above example, satisfies the triple characteristic and is thus duly established by pramāṇas. It seems unclear to what degree this was a purely theoretical requirement, i.e., that the proof can be derived by a rational individual, and to what degree Indian debaters actually did make the contrapositions and arrive at proofs. In any case, in Tibetan Collected Topics, consequences are in fact rarely contraposed to yield proofs.

Some consequences could, of course, be contraposed by an ideal debater to yield a proof and triply characterized reason, although they simply were not. Others, however, could not be contraposed even ideally. Sometimes these are known as simply “refuting consequences” (sun ‘byin pa’i thal ‘gyur = *dūṣaṇaprasaṅga), where a contradiction is derived from an ensemble of propositions, but where there can be no use of contraposition to arrive at a proof like in (2). For example,

(3) sgra chos can / rtag pa yin par thal / mig shes kyi gzung bya yin pa’i phyir “Take sound as the subject; it follows that it would be permanent, because it is apprehended by visual consciousness.” If (3) were contraposed, we would get the following bad reasoning: (4) sgra chos can / mig shes kyi gzung bya ma yin te / mi rtag pa yin pa’i phyir. “Take sound as the subject; it is not apprehended by the visual consciousness, because it is impermanent.”

This is obviously not a triply characterized reason, because the pervasion does not hold. On the other hand, (3) does serve to discredit the debater’s position by deriving a proposition in contradiction with the ensemble of his beliefs and thus placing him in a position where he cannot consistently reply in one of the three manners. In that sense, he is refuted. Nonetheless, if he arrives at (4) he clearly has not ascertained the truth on the basis of a good reason where the various characteristics were ascertained. At most, he was just lucky to arrive at a truth by means of a bad reason.

The “refuting consequence” is thus one type of consequence that does not imply a proof (sgrub byed mi ‘phen pa’i thal ‘gyur). It is not a proof of a specific statement by reductio ad absurdum, as in (1) and (2) or in famous western uses of reductio, like the indirect proof of the irrationality of the square root of two. Although it does derive a consequence that is absurd for the opponent and proponent, it is being used as a sort of demolition of the adversary’s whole position: if it proves anything at all, at most, it proves that the conjunction of the propositions accepted by an opponent is not true. A natural interpretation of the logic of Candrakīrti was that he used such a type of reductio ab absurdum to refute the opponent’s position--.he merely demonstrated that the ensemble of the opponent’s propositions was false, by its own internal inconsistency, but did not himself claim any individual propositions to be true or false and did not accept any derivation of prasaṅgaviparyaya. This style of consequence was known by Phya pa, rNog lo tsā ba and other early writers on Pramāṇa. It is, however, of relatively little importance in Collected Topics. Moreover, the dGe lugs pa do not characterize Candrakīrti’s logic in this way either. While the dGe lugs pa recognize that some other Indo-Tibetan Mādhyamikas interpreted Candrakīrti as making no truth claims and only refuting opponents’ views, their own exegesis of his Prāsaṅgika philosophy is much more complicated and does allow that Candrakīrti made specific truth claims on many issues. In fact, in bsdus grwa logic the vast majority of consequences that do not imply proofs are not like (3) at all. Moreover, they seem to be distinctively unlike what we find in any Indian uses of prasaṅga. They are not an indirect proof by reductio ad absurdum as in (1) nor are they a type of reductio ad absurdum qua demolition as in (3). Rather, the implied statement preceding thal will typically be thought to be true by Buddhists, even established by a pramāṇa, and thus not an absurdity at all from the point of view of the Buddhist proponent.

Here is the stock example. (Again the opponent is a Mīmāṃsaka-like thinker who believes that sound is produced, that all products are impermanent, but who does not accept that sound is impermanent):

(5) sgra chos can / mi rtag pa yin par thal / byas pa yin pa'i phyir. "Sound, the subject; it follows that it is impermanent; because it is produced."

Our first reaction is probably going to be that this looks suspiciously like the stock example of a triply characterized reason. Of course, if we compare the second type of consequences with triply characterized reasons, the acceptance that the reason is established (i.e., that (x) (Ax→Cx)) corresponds roughly to the pakṣadharmatva of the triply characterized reason. Similarly, the acceptance of the pervasion (i.e., (x) (Cx→Bx)) corresponds to the second and third characteristics (i.e., anvayavyāpti and vyatirekavyāpti). However, a main difference is that the reason statement and pervasion statement need not be known to be true, only accepted or thought to be so by the opponent. The reason in this prasaṅga is thus not assessed by the same criteria of goodness as for a triply characterized reason. The consequence is, as usual, good if the opponent cannot make one of the three permissible replies while remaining consistent with his other acceptances. Truth, and reality, pramāṇas, and so forth are, strictly speaking, not crucial.

4. Why Use Consequences Rather Than Triply Characterized Reasons? The Problem of Non-existent Subject Terms and Āśrayāsiddha

What difference would it make for Tibetan debaters to use a consequence like (5) rather than a corresponding triply characterized reason? First and foremost, and contrary to what the first characteristic of the trairūpya demands, the subject in a “consequence that does not imply a proof” need not exist at all, as it need not be established by a pramāṇa – we find numerous good consequences in Collected Topics that have as their subject a rabbit’s horn or a barren woman’s child. In Indian logic, by and large, it is a requirement that knowledge and good reasons be about existent things. And, not surprisingly, this is a requirement too in the context of triply characterized reasons. When subject terms do not exist, the reason incurs the fallacy of a “non-established locus” (gzhi ma grub pa = āśrayāsiddha) – the problem led to numerous philosophical debates between Indian Buddhists and Naiyāyikas. We will not, however, go into these issues in India nor into their extremely elaborate Tibetan developments; they have been taken up in some detail elsewhere.

Of course, the underlying intuition behind the Indian fallacy of āśrayāsiddha— viz., that an argument typically goes wrong when there is subject failure—is quite sound and is amply recognized East and West. One can make relevant comparisons with Western debates on Russell’s theory of descriptions, and on the question whether a non-existent subject leads to the falsity of the statement, or a presupposition failure, such as when a debate on Santa Claus' would-be North Pole citizenship becomes moot when it is understood that there is no Santa Claus at all. In Indian Buddhist logic, the emphasis is undoubtedly on presupposition failure: arguments generally cease when the subject is shown to be non-existent. A reason’s possession of the triple characterization presupposes that the subject be “commonly recognized by both parties” (ubhayaprasiddha); this requirement figures prominently in the works of Dignāga, Dharmakīrti and those of their Svātantrika Mādhyamika followers, such as Bhāviveka, Śāntarakṣita, Kamalaśīla et alii. As Dharmakīrti expresses it, if there is a debate about such and such a property, then ipso facto it is understood that the subject is commonly recognized.

Interesting Indian examples of the problem of subject failure were the debates about the existence of pseudo-entities such as God (īśvara) or the Sāṃkhyas' Primordial Nature (prakṛti). The obvious conundrum is that such a debate would seem to be "short circuited" by the fallacy of āśrayāsiddha if it actually succeeded in proving the subject’s nonexistence. Dignāga, Dharmakīrti and others devoted great efforts to avoiding such self-refutation. They would argue that the real subject was not God, but the concept of God; or they would argue that non-existence, being a non-implicative negation (prasajyapratiṣedha), a mere denial of entityhood, does not presuppose any existent real entity as subject. But while there is considerable ingenuity here, it has to be said that such debates are not easily pursued within the framework of the triply characterized reason. The later Indian scholastic writers, and Tibetans too, thus had to do some of their most subtle apoha philosophy of language to preserve the requirement that the subject exist.

Consequences show much greater flexibility than the triply characterized reason in that their goodness usually only demands that the opponent thinks that the subject exists. Thus, a proponent's personal conviction that the subject is not actually established by a pramāṇa may well have no impact on the debate: there is no strict need for mutual consensus, nor for establishment by a pramāṇa. The advantage that consequences have over triply characterized reasons, then, is that they allow debates about properties that have no existence-implication and thus can be predicated of non-existent subjects. It becomes unproblematic, for example, for Buddhists to argue that a creator God does not exist: no talk of subsistent concepts, the theory of apoha, or purely non-implicative negation is needed. There is no need to worry that debates become moot when the presupposition of the subject’s existence fails.

In many cases, neither the opponent nor the proponent thinks that the subject exists, but nonetheless it is quite possible to argue about its properties via a consequence. In the Tibetan Collected Topics we see that, in effect, some properties imply that the subject exists, but others do not. Let's borrow a term from Nino Cocchiarella 1968, and call these existence implying properties "E-attributes" for short. For example, if one is arguing about a rabbit's horn being sharp, then sharpness, being an E-attribute, would necessitate that the rabbit's horn exists; a property like “being something expressed by the words that mention it” (rang zhes brjod pa’i sgra’i brjod bya), however, does not necessitate existence. In the case of E-attributes, statements are considered to be false when such an attribute is asserted of subjects that are nonexistent. However, Collected Topics has numerous reasonings concerning properties that are not E-attributes, and in those cases the statements may well be accepted to be true, in spite of the commonly recognized nonexistence of the subject. Thus for example, if we have an argument about whether every item, existent or non-existent, is expressed by words, then all existent and nonexistent things—including non-existent but possible things, like a rabbit's horn, and even impossible items like a barren woman's child— can be the subjects without any danger of āśrayāsiddha or the debate rhetorically collapsing. None of this is easily handled with a triply characterized reason.

5. Pervasion in the Tibetan Debate Logic and in Dharmakīrti

As we saw earlier, the pervasion (all C's are B's) in Dharmakīrtian logic had to be grounded by a necessary connection, i.e., a so-called natural relation (svabhāvapratibandha) between the terms C and B. Ontology is at the heart of the triply characterized reason. The Tibetan bsdus grwa logic of consequences, on the other hand, had a much simpler account of pervasion, that of a debate logic in which ontology played little role. Indeed, that debate logic probably would have made Dharmakīrti wince, as it comes uncomfortably close to Īśvarasena's accursed adarśanamātra (merely not seeing a counterexample) method of establishing pervasion. Here are the details.

One of the rules of this debate logic is that if an opponent challenges a pervasion, by saying khyab pa ma byung the pervasion doesn't hold, the proponent can say, Give me a counterexample! (ma khyab pa'i mu zhog), and if that counterexample is not forthcoming in a reasonable time, the proponent has the right to say that the pervasion does in fact hold. Necessary connections and ontological considerations play little role. What counts is not so much whether there are in fact or could be counterexamples, but what one can show in a relatively limited time. This might seem to unpack as close to the accursed adarśanamātra method of asserting pervasion so long as one hasn't (speedily) come up with a counterexample. But it could also be argued in defence of the Tibetans, that Dharmakīrti, in introducing grounding, raised the bar far too high and unnecessarily complicated a rather clear and easy matter of logic. Collected Topics elaborated the truth conditions for a universally quantified material implication, viz., that there is no x such that Cx and not Bx, but without the Dharmakīrtian epistemology and metaphysics that tended to obscure a purely logical account.

In short, Tibetan debate logic seems to have made a separation between the logical question of what pervasion is (viz., absence of counterexamples) and the ontological question of what in reality grounds it (viz., natural connections), and the epistemological issue of what we need to know (viz., an example which instantiates both the reason and the property to be proved) if we are to be able to understand that there is a pervasion. These three issues need to be separated by clear thinkers and it is arguably no mean achievement to do so in the context of Buddhist logic.

6. Other Formal Aspects of the Logic of Consequences: quantification and variables

While consequences function in a context of debate with various permitted moves, there are clearly also significant formal features that can be extracted. In effect, the establishment of the reason and the pervasion means that the opponent accepts (x) (Ax→Cx) as well as (x) (Cx→Bx). The step to having to accept (x)(Ax → Bx) is uncontroversial: an opponent would be considered irrational and disqualified from the debate if he persisted in rejecting that uncontroversial formal implication.

What about the use of variables and quantification? The language used in Tibetan debate is a technical form of Tibetan, in which we find an extensive use of pronouns in a manner that is analogous to the use of variables in an artificial language. The parallel between pronouns and variables is to be seen, for example, in the Tibetan debate idiom's use of khyod, which ordinarily means “you,” but is used technically here to stand for all types of items: anything from inanimate things, to animals and other sentient beings to even nonexistent things. It is used much like English would use a third person pronoun, except that such English pronouns are gendered. In fact, khyod khyod dang gcig yin “you are identical with you,” is best rendered as simply “x is identical with x.” Another variable-like word is chos de “that phenomenon,” typically used when khyod is already present and a second variable is needed, as in khyod chos de'i rgyu yin, literally, “you are the cause of that phenomenon,” but more accurately (though less literally), “x is the cause of y.” When only one variable is at stake, khyod is optional and is often omitted. It is not optional when two variables are needed to express, say, a dyadic relation.

For example, one can say:

(6) sgra chos can, khyod mi rtag pa yin par thal… "Sound, the subject, it follows that you (khyod) are impermanent …"

Or simply: (7) sgra chos can, mi rtag pa yin par thal… "Sound, the subject, it follows that it is impermanent…"

What work does specifying “the subject” (chos can = dharmin) do in the Tibetan logic of consequences? In other words, why use the rather longwinded “sound, the subject, it follows that you are impermanent,” thus setting the subject apart, rather than just simply saying “It follows that sound is impermanent”? It is, I would argue, a special type of quantification, what we can term, following J.A. Faris, “singular quantification.” To see this more clearly, let us take an example of a reasoning with khyod being used as a variable.

(8) bum pa chos can khyod khyod dang gcig yin par thal khyod yod pa'i phyir "The vase, the subject, it follows that you are identical to yourself, because you exist." Or: "The vase, the subject, it follows that x is identical to x, because x exists." Note that if the opponent replies, “there is no pervasion” (khyab pa ma byung), the pervasion in question can be expressed as: (9) khyod yod pa yin na khyod khyod dang gcig yin pas khyab. "If you exist then you are pervaded by being identical with yourself." Or:

"If x exists then x is pervaded by being identical with x." We can express (8) as a universally quantified material implication with x (khyod) functioning in a straightforward way as a variable bound by a universal quantifier that ranges over all items, existent or non-existent. The quantification, in short, is without existential import so that “for all x” means “for all existent or nonexistent items” and “for some x” means “for some existent or nonexistent item.” “Exists” will then be taken as a predicate and represented by “E!”. As we see in (9), existence of x implies identity of x with itself. Thus, (9) is easily rendered in symbols where pervasion is a universal quantifier “for all x” (without existential import) binding the variable x; existence (yod pa) is simply treated as a predicate: (x) (if E!x then x = x) “Subject” (chos can) also shows a type of quantifier binding the variable x (khyod). To see this, let's back up and progressively reformulate a few English sentences:

Ollie loves Nicaragua. Ollie is such that he loves Nicaragua. Ollie, he is such that he loves Nicaragua.

We can see that the pronoun “he” in the last statement also works as a variable and that “Ollie,” in indicating the pronoun's antecedent, is in effect binding that variable. Following Faris 1968, the singular quantification in this statement could be formalized as: (Ollie x) (x loves Nicaragua).

Read: “Of Ollie as x, it is so that x loves Nicaragua.” This type of quantifier for singular statements can be integrated, as Faris shows, into the fabric of first order logic without any special problems. Granted, for the writers of a usual basic Western logic textbook, it might well be considered cumbersome and arguably wouldn't do much that individual constants don't already do. However, if we now turn to the Tibetan Collected Topics, it does have a significant role there. Sentence (8) becomes: (the vase x) (x=x because E!x)

Or: (the vase x) (if E!x then x=x) Read: "Of the vase as x, if x exists then x is identical to x."

Clearly the khyod or x in the statements (9) and in (8) are variables: what changes is only the quantifier; it changes from a universal quantifier to a singular quantifier. "Pervasion" (khyab pa) translates as a universal quantifier that binds the variable khyod or x; "the subject" (chos can) translates as a singular quantifier binding the same variable.

8. The logic of consequences used like a logic of propositions

Interestingly, the correctness of paraphrasing or translating sentences in Collected Topics with singular or universal quantifiers is further corroborated by the fact that this quantification can also be redundant and fail to bind variables. Redundant quantification is a possibility in first order predicate calculus—one could have a well-formed formula like:

(x)(if Mickey loves Minnie, then Donald loves Melania). But redundant quantification is usually of practically little interest. Not so in Tibet. Consider the following:

(10) sgra mi rtag pa yin na sgra byas pa yin pas khyab "If sound is impermanent, then sound is pervaded by being a product." Or: (x)(if sound is impermanent, then sound is a product)

And: (11) shes bya chos can, sgra mi rtag pa yin par thal sgra byas pa yin pa'i phyir "Take knowable thing as the subject; it follows that sound is impermanent because sound is a product." Or, in the singular quantification idiom: (knowable thing x) (sound is impermanent because sound is a product) Or, in other words:

(knowable thing x) (if sound is a product, sound is impermanent) In all of these statements, the quantification is redundant simply because there are no pronouns, i.e.,variables, for it to bind. Tibetan debaters express this idea of a redundant subject/singular quantifier as a chos can nus med, a powerless subject; an ineffectual subject. What these powerless subjects enable Tibetans to do is keep the form and wording of a typical consequence, but do something more like propositional logic than predicate calculus. In fact, they had no separate means to reason about propositions, but adapted the trappings of their logic of consequences to this purpose. We saw earlier that a pervasion such as (x)(Cx→Bx) was true if and only if there is no x such that Cx and not Bx. Now, imagine a pervasion like (x)(P→Q) with a redundant universal quantifier. Here again the pervasion will be true if and only if there is no x such that P and not Q. The basic move, in debate terms, remains the same in both cases: the proponent says ma khyab pa'i mu zhog, “Give me a counterexample!”' And when that counterexample is not forthcoming in a reasonable time, it is presumed to be non-existent and the statement is thus accepted as true, at least for the purposes of the debate. If, as in (10), both P and Q are true propositions with no pronouns/variabes, then clearly no genuine counterexample can be given. In this fashion, Tibetan Collected Topics, in effect, allows for implications, negation, contraposition and the like between complete propositions.

This somewhat roundabout logic of propositions is what Tibetan commentators will use in reformulating many reasonings in Indian texts, often using shes bya chos can “knowable thing x” as a powerless subject familiar to those who are versed in debate. A typical example of such a text is the dGe lugs pa word-commentary (tshig ‘grel) written by dGe ‘dun grub pa (1391-1474) on Madhyamakāvatāra, where Candrakīrti’s first five chapters, concerning Buddhist ethics and religion, are paraphrased in the form of reasonings having shes bya chos can followed by two complete propositions. This type of paraphrase was partly for mnemonic and pedagogical purposes. It also, no doubt, provided some seeming argumentative rigor to what were largely faith-based assertions of the Buddhist religion.

11. Several Types of Pervasions and their Interrelationships Collected Topics elaborate logical relationships between propositions by introducing several different sorts of pervasion and then showing that a consequence in which a pervasion of, say, sort S holds must also be a consequence of which, say, sort T holds. The rjes 'gro ldog khyab lesson, in which these relationships are investigated, is, in spite of its name, significantly different from the usual Indian discussions of anvayavyāpti and vyatirkevyāpti and may well stem from Phya pa himself. Thus, for example, in the usual sound-impermanent-product consequence in (5), the “main pervasion by co-presence” (rjes khyab rnal ma) is the familiar:

(x) (if x is a product then x is impermanent) The main pervasion by co-absence (ldog khyab rnal ma) is: (x) (if x is not impermanent then x is not a product)

The first type pervasion is recognized to hold if and only if the second type of pervasion holds, whatever be the terms for the antecedent or the consequent. There are other pervasions too, most seemingly unknown in the Indian literature. For example, bsdus grwa speaks of the "downward pervasion" (thur khyab), where the property to be proved is pervaded by the reason, and the "opposite pervasion" ('gal khyab), where the reason is pervaded by the negation of the property to be proved. Indeed there are usually said to be eight such pervasions, four main (khyab pa rnal ma bzhi) and four negated (khyab pa phyin ci log bzhi); the former are those where the terms are taken as they are and not negated; the latter are those where the antecedent is left as is but the consequent is negated. If we again take C as the reason and B as the property to be proved in the consequence, then the usual “eight doors of pervasion of a consequence” (thal ‘gyur khyab pa sgo brgyad), as explained in Yongs ‘dzin bsdus grwa or bSe bsdus grwa , can be represented as follows:

The main pervasion by co-presence (rjes khyab rnal ma): (x)(Cx → Bx) The main pervasion by co-absence (ldog khyab rnal ma): (x)(¬Bx → ¬Cx) The main downward pervasion (thur khyab rnal ma): (x)(Bx → Cx) The main opposite pervasion (‘gal khyab rnal ma): (x)(Cx → ¬Bx)

The negated pervasion by co-presence (rjes khyab phyin ci log): (x)(Cx → ¬Bx) The negated pervasion by co-absence (ldog khyab phyin ci log): (x)(¬Bx → ¬ ¬Cx) The negated downward pervasion (thur khyab phyin ci log): (x)(Bx → ¬Cx) The negated opposite pervasion (‘gal khyab phyin ci log): (x)(Cx →¬ ¬Bx)

As Onoda 1992, 99-100 points out, ‘Jam dbyangs bzhad pa (1648-1772) added a third group to these two, with the somewhat mysterious name kha bub or kha sbub “face down,” “upended”, “upside down,” which we could perhaps render as “inverted.” If we take the usual four pervasions, their inverted versions negate both the antecedent and the consequent in the corresponding main pervasions.

Thus:

The inverted pervasion by co-presence (rjes khyab kha bub): (x)(¬Cx → ¬Bx) The inverted pervasion by co-absence (ldog khyab kha bub): (x)(¬ ¬Bx → ¬ ¬Cx) The inverted downward pervasion (thur khyab kha bub): (x)(¬Bx → ¬Cx) The inverted opposite pervasion (‘gal khyab kha bub) : (x)(¬Cx → ¬ ¬Bx)

A recurrent exercise in bsdus grwa is to see which ones are equivalent and which ones are exclusive. This is formulated in terms of debates about consequences that satisfy various numbers of pervasions. Thus it can be argued, for example, that any consequence in which the main pervasion by co-presence is satisfied is one where the negated opposite pervasion will be satisfied. (N.B. the law of double negation elimination is recognized!) Or it can be debated whether there are consequences which satisfy such and such a number of pervasions. For our purposes, we cannot enter into the details here. Suffice it to say that these are fairly sophisticated 12th century exercises in formal relations between propositions – the relations hold completely independently of the propositional content. Nothing along the line of these twelve pervasions seems to be found in Indian Pramāṇa. The only formal discussion in Indian Pramāṇa that might be comparable would be the nine types of reasons in Dignāga’s Hetucakra.

12. Ex falso sequitur quodlibet

A crucial feature of classical material implication, like “If P then Q”, is that the truth conditions are specified so that the whole implication is false only if P is true and Q is false – on any other assignment of truth-values to P and to Q, the material implication is true. The result is, of course, that the falsity of P guarantees the truth of “If P then Q.” In other words, the falsity of the antecedent is a sufficient condition for the truth of the whole conditional, i.e., the material implication. Collected Topics explicitly recognizes that when the so-called khyab bya (=vyāpya, i.e. property that is pervaded) has no instances then the whole pervasion (khyab pa = vyāpti) will be established – in less literal terms, the falsity of the antecedent in the implication will imply the truth of the whole conditional.

Moreover, Collected Topics lucidly and explicitly recognizes that when the antecedent (i.e., the pervaded, khyab bya = vyāpya ) is false, or more exactly instanceless, the pervasion will hold whatever the consequent (i.e. the pervader, khyab byed = vyāpaka) may be. This is a logical principle that mirrors the Medieval logician’s maxim that ex falso sequitur quodlibet (whatever you wish follows from a falsity). It is even slightly eerie how well the Latin sequitur quodlibet (whatever you wish follows) corresponds to the Tibetan phrase used in these contexts, viz., gang dren dren yin pas khyab ("x is pervaded by whatever you might think of"). Thus, for example: (12) ri bong rwa yin na gang dren dren yin pas khyab "If something is a rabbit's horn it is pervaded by whatever you might think of." Thus, e.g., it is true that: (13) ri bong rwa yin na ru bal skra yin pas khyab "If something is a rabbit's horn then it is pervaded by being the hairs of a turtle." Or: (x) (if x is a rabbit's horn, then x is the hair of a turtle). Once again, in debate terms, if the truth of (13) is challenged, then the command is always ma khyab pa'i mu zhog, “Give me counterexample!” That counterexample will not be forthcoming simply because there is no rabbit's horn, or in other words because the property that is pervaded (khyab bya) has no instances. The fact that the pervaded (khyab bya = vyāpya) is always instanceless ensures that the pervasion will be established whatever the pervader (khyab byed = vyāpaka) might be.

To my knowledge, there is no recognition of ex falso sequitur quodlibet in Indian Buddhist logic, probably because, in philosophies like that of Dharmakīrti, the pervasion needed existent terms that would bear a natural connection (svabhāvapratibandha) in reality. A pervasion also need examples (dṛṣṭānta), on the basis of which it could be understood to hold through a source of knowledge – the metaphysical and epistemological orientation is preponderant. In Tibetan debate logic texts, by contrast, talk of ex falso sequitur quodlibet occurs quite frequently, probably because these Tibetans dealt essentially with the logical features of material implication and left the rest of the Dharmakīrtian baggage aside.

13. Modal logic? No thank you.

A question naturally comes up when someone is first confronted with statements like (12) and (13), viz., is there any awareness of modal distinctions in bsdus grwa, or, for that matter, in Tshad ma or Indian Buddhist Pramāṇa? The confusion is probably exacerbated by the fact that it is very frequent, in modern Buddhist Studies discussions of Indian and Tibetan thinkers, to speak of “necessity”, “necessary connections,” etc., especially when discussing the natural connections (svabhāvapratibandha) underlying pervasion in Dharmakīrti’s logic. The temptation is, thus, great to think that pervasion between C and B would unpack in terms of modal logic’s necessity operator, i.e., N (x)(Cx → Bx) “Necessarily, for all x, if x is C then x is B.” Ex falso sequitur quodlibet is differentiated, in Medieval logic, between cases of contingent and necessary falsity. And indeed, the falsity of the antecedent in (12) and (13) is not a necessary falsity (i.e., in all possible worlds) – a modal logician would be quick to point out that many exotic possible worlds are populated by horned rabbits, hairy turtles and the like. Here then is a more precise formulation of the issue at hand: would a modal logician’s difference between possibility and necessity concern Indo-Tibetan logicians?

Let’s look at how contingent nonexistence and necessary nonexistence are handled. First, of course, nothing actually stops a Tibetan from changing a statement like (12) about horned rabbits to a statement in which the pervaded term (khyab bya) is not just instanceless but contradictory:

(14) mo gsham gyi bu yin na gang dren dren yin pas khyab.

"If someone were a barren woman's son, he would be pervaded by being anything one can think of." Indeed, there are several Indo-Tibetan stock examples of nonexistent things, of which we would say that some happen to be nonexistent and others must necessarily be nonexistent – we would say that the rabbit’s horn (śaśaviṣāṇa = ri bong rwa) is a case of the former and the barren woman’s son (vandhyāputra = mo gsham gyi bu) is a case of the latter. Strikingly, however, that difference between contingent and necessary nonexistence, so important to a modal logician, does not seem to have been considered significant at all and, in any case, is not explicitly discussed in Collected Topics and Tshad ma generally. There simply seems to be no interest in, or even awareness of, modal logical distinctions in Tibetan Collected Topics, or in other Tibetan Tshad ma literature. And, to be slightly more provocative, it looks like there is no Indian Buddhist modal logic either. While Indo-Tibetan Buddhists would, if pushed, I suppose, recognize that the rabbit's horn could somehow have existed, or could be a feature of a fantastic imaginary world, that possibility is hardly germane in their logic: truth and falsity, existence and nonexistence are of this world.

It might perhaps be thought that the rabbit’s horn we imagine would nonetheless be said by Tibetans to be a rabbit’s horn and that some of those horns might even be sharp in the appropriate possible worlds! If that were so, then the modern writer on a quest for modal logic in Tshad ma could claim that predication and truth are not just of this world for bsdus grwa adepts. But no: being a horn, whether of a rabbit or of a deer, and being sharp are existence implying properties, E-attributes. Thus, an imagined horn is not a horn at all, nor is it sharp, because it does not exist. The point, of course, is that it does not exist in this world, the only world with which bsdus grwa logicians have any truck.

Turning to Indian Pramāṇa, even when terms C and B have a so-called natural connection (svabhāvapratibandha) of causality or “same nature,” that is best interpreted to mean that C and B are instantiated in this world and that one can be sure that in this world there are no C’s that are not B’s. It does not seem to be the modal version that there are no C’s that are not B’s in any possible world. As we saw earlier in discussing consequences and āśrayāsiddha, Tibetan bsdus grwa logicians certainly had very little problems in reasoning about nonexistent things – much fewer problems than their Indian Buddhist counterparts – but that does not mean that they were at ease with modal notions or existence in possible worlds. On this both Indian and Tibetan Pramāṇa specialists would agree: when things are existent or nonexistent, they are so in the real world. The real world is certainly strange, with its trichiliocosms of universe systems, but existence or nonexistence anywhere “else” would be seen as incomprehensible.

13. Semantic Problems: Count Nouns, Mass Nouns, and Translatability

I close on a larger matter for reflection: what are the prospects for engagement with Tibetan thinking about logic? What are the prospects for engagement with Tibetans on philosophical issues of common interest when their discussions of the issues are couched in the concepts and formal structures of bsdus grwa? Formal structures in bsdus grwa logic are quite clear and can be readily explained; they can be, as we have tried to show, translated into philosophical English, and analyzed, sometimes with the aid of symbolic logic. There is, if one is careful, little risk that one is creating distortions or misunderstandings by using western notions to explain them or translating relevant passages into a western language.

Semantical issues, by contrast, are often obscure. Discussions of them in Tibetan resist translation and engagement with Tibetan philosophy is not easy when these semantical issues come to the fore. I would argue strongly that the problem is not due to an inherent incommensurability of Tibetan with English or European languages or some sort of generalized thesis of linguistic relativism, à la Benjamin Lee Whorf. It is, rather, the intelligibility of many Tibetan philosophical debates when sophisticated and clear-headed Tibetan thinkers exploit possibilities offered by their language that are hardly offered by most European languages. More precisely, the difficulty is in the philosophical uses of Tibetan count and mass nouns, and the odd questions of interpretation that arise. Those difficulties are acute in indigenous Tibetan Buddhist texts on Tshad ma, especially those of the dGe lugs school, and in the many other sorts of Tibetan philosophical texts that in one way or another rely on them.

We begin with some general considerations.The difference between count nouns and mass nouns is usually first approached as a difference in word classes recognizable in terms of syntax: the former are words like table that can take numerals, vary in singular and plural, be qualified by adjectives like many, and have other such morphosyntactic tags, while the latter are words like water that don't take numerals, don't vary in grammatical number, take adjectives like much, etc. , etc. Some of us might like to think that there is a semantic and even corresponding ontological distinction. It might be thought that words that refer to things have clear boundaries of individuation while those that refer to stuffs don't have such boundaries – this too is supposedly captured by count-mass noun distinctions.

None of these criteria, even in their more sophisticated elaborations, seem to be watertight across languages. Precision falters for many reasons. Some Asian languages, like Chinese and Tibetan, arguably, have count-mass distinctions but without many of the usual morphosyntactic tags. As for the thing-stuff distinction, it even becomes problematic with common English mass nouns like furniture, where obviously each piece of furniture is a thing and not an amorphous stuff like water. And crucially the idea of neat word classes in one language or across languages fails. In many languages there are uses of nouns as count or mass in different contexts (Waiter, three coffees please!, Coffee spilt all over her new carpet. She heard several loud sounds. Sound is everywhere.). In some languages, like Chinese, any noun can be used as a mass noun (see Robins 2000), while in other languages specific nouns may not exhibit that same variability of use at all. Finally, what is count in one language may be mass in another (the French count noun bagage has a corresponding English mass noun luggage), so that clear classes across languages prove to be impossible. Probably the most adequate approach for our purposes is a semantic one turning on uses and functions rather than word classes: nouns are used as count nouns in a specific language when they divide their reference into distinguishable and countable objects; they are used as mass nouns when they do not.

Are mass and count noun distinctions in source languages important when one translates Buddhist texts into English? Let me begin with a commonly cited position that I think is not an answer to that question for translators of Sino-Tibetan languages. This is the view that there simply is no distinction at all between mass and count nouns in these Asian languages, and that there are hence only the impositions of translators – the formulation is that of the philosopher W.V. Quine 1968 in his work on indeterminacy of translation and ontological relativity. Indeed Quine had famously suggested that Chinese and Japanese were arbitrary in precisely this way. He made much of the fact that classifiers (= Chin. liang ci 量詞 ) are used with all common nouns and that it is therefor impossible to decide whether a phrase like yi tou niu 一頭牛should be translated as one cow or one head of cattle (cf. Quine 1968, 191-193). As he said bluntly: Between the two accounts of Japanese [scilicet: Chinese] classifiers there is no question of right and wrong. (Quine 1968, 193). This is hard to defend as a description of actual language usage. Sinologists muster ample textual data that show that there are mass and count nouns in Chinese.

They may have differences on how that mass-count distinction unpacks in particular periods, whether it needs to be supplemented, whether mass nouns predominate, etc., but the very applicability of a mass versus count noun distinction to Chinese or Japanese is not in question. The obscurity of some classifiers is not generalizable to all uses of nouns. First, classifiers are often not used in classical Chinese; yi niu 一牛 (one cow) seems, uncontroversially, a count noun usage. Moreover, in modern Chinese, there is evidence that children learn the difference between sortal and mensural classifiers, and that this difference in types of classifiers more or less mirrors the count-mass distinction. In short, taking a straightforward linguistic perspective, one would say that you niu 有牛 (literally, There exists cow) is a mass noun usage of cow and yi niu 一牛 (one cow) is a count noun. Such a version of mass and count noun usage is not just restricted to Chinese. It is largely mirrored in Tibetan. Although Tibetan does not use classifiers, neither in the modern nor in the clasical language, it is certainly fair to say that ba lang yod (Cow exists, There exists cow.) is a mass noun usage and ba lang gcig (one cow) is a count noun usage, and so on in general for common nouns in Tibetan, be it rta (horse), khang pa (house), mi (people), mo ṭa (car), and so forth. We will return to parallels between Tibetan and Chinese in more detail later.

Interestingly enough, however, Quine probably didn't adopt a straightforward linguistic perspective about usage of nouns in Asian languages. Instead he seductively combined the linguistic/philological problems in describing usage of nouns in particular languages with the philosophical issues that arise in interpreting reference in any language. His real point was that we cannot determine the sorts of entities people talk about (in Chinese or any other language) among equivalent possibilities, be it individual oxen versus heads of cattle, particular instances of properties versus distributions of a stuff or fusion (horses versus discontinuous distributions of horsey stuff or the fusion of all horses) or even mathematical expressions versus their corresponding Gödel numbers. The type of entities referred to, or in other terms the inherent ontology of the language is inscrutable. Now, this is a different issue from the question as to whether a given language just simply has mass and count nouns. One could very well say that there are determinate answers about the existence of mass and count nouns in many languages and that yi niu, ba lang gcig, and the like are naturally translated as one cow, but also say that the sort of entities the mass or count nouns refer to remain indeterminate and inscrutable. Indeed, that is a point of view one can defend using an argument from Donald Davidson, not just with regard to Asian languages like Chinese and Tibetan, but across the board.

Let us grant that there are count nouns and mass nouns in Sino-Tibetan languages and that reading a Tibetan or Chinese sentence as having mass or count nouns is not just an arbitrary imposition of the European translator. Let us also grant that Sino-Tibetan languages use mass nouns much much more frequently than European languages do, but that European translators are generally unfazed and adopt strategies of reformulation. (We'll see the details of these strategies below.) That much should be a non-issue. What is, however, a genuine issue for translators and philosophers is whether there are, at least sometimes, uses of mass nouns in the Asian source languages that preclude any adequate translation or reformulation in a European language. Are there such uses that are more than quirks and that a translator of Buddhist texts fundamentally cannot translate, reformulate, nor perhaps even satisfactorily paraphrase? In what follows, I'll frame the problems largely in terms of translation into English, but one can no doubt make the same arguments for other European languages.

Nowhere, in my opinion, is that issue of translatability more urgent than in the indigenous Tibetan Buddhist literature of bsdus grwa (Collected Topics). In what follows, we will look at the details and the antecedents in Tsong kha pa and rGyal tshab rje for the translational problems found in bsdus grwa. And bsdus grwa semantic problems don't just remain in bsdus grwa texts: as argued in Tillemans 1999, they spread to indigenous commentaries on Pramāṇa, Abhidharma, and Madhyamaka that use bsdus grwa notions, and they make various philosophical debates notoriously hard to translate into acceptable English. The issue of intelligibility is a larger one: it is not just the issue of understanding and engaging with the corpus of books that bear the title bsdus grwa. What are these seemingly intractable semantic issues? Puns and equivocations in Tibetan – and Collected Topics is certainly rich with them— are not intractable issues, nor are the many syntactic tricks in Collected Topics that involve plays on Tibetan grammatical cases, such as the genitive used in relative clauses. Unpacking puns and exposing syntactic sleight of hand may be more or less laborious, but in the end there is nothing that cannot be rendered adequately. The problems that interest us turn on a peculiar use of mass nouns. These semantic issues will be my focus here as they pose problems for which we have no solution now nor in the easily foreseeable future. They are very different from the many bsdus grwa brainteasers that turn on double entendre and devious syntax. The problem is the following. Subject terms (chos can) in Tibetan Collected Topics arguments, like vase (bum pa), tree (shing), knowable thing (shes bya), non-red (dmar po ma yin pa), good reason (rtags yang dag) and many others are often not translatable by the count nouns they would seem to require in a Western target language – a vase, some/all vases, this vase, some/all/a/the good reason, “some/all/a/one/the knowable thing, some/all/a/one non-red thing, and so on. Such count noun translations would not preserve truth. Two examples will have to suffice. Here and in what follows I've put the grammatically problematic English terms in italics:

(15) "Non-red (dmar po ma yin pa) is permanent, because there are common bases between permanent and it (khyod dang rtag pa'i gzhi mthun yod pa'i phyir) Comment: The same example can be constructed with knowable thing, good reason, and many other entities; the reason is a usual one in bsdus grwa to prove that something is permanent. The point of Y having a common basis with X is that there are cases of Y which are also cases of X. There are non-red things that are permanent, such as, for example, space (nam mkha' = ākāśa).

(16) "Defining characteristic (mtshan nyid = lakṣaṇa) [of anything] is not a defining characteristic (mtshan nyid mtshan nyid ma yin), because it has a defining characteristic and is thus a definiendum (mtshon bya = lakṣya)." Comment: Defining characteristic itself is defined as what satisfies the three criteria for a substantial property (rdzas yod chos gsum tshang ba) and is thus itself something that can be defined, i.e., a mtshon bya.

Here, in more detail, is the problem in translating (15) and (16) if we use available English renderings involving all, some, a, the/this. Sentences like (15) will be false in the philosophy of Collected Topics when dmar po ma yin pa or shes bya are rendered as all non-red things or all knowable things',' just as (16) is also false if one renders mtshan nyid as all defining characteristics. A sentence like (15) becomes trivially true if we render dmar po ma yin pa or shes bya as some non-red things", "some knowable things, a non-red/knowable thing, and it is perhaps true when rendered as the or this non-red/knowable thing. In fact, in Collected Topics, (15) is not a trivial truth or just a possible truth: it is held to be true, but non-obvious and needing justification – hence the reason about common bases.

What is more dramatic for translation than (15) is (16): it becomes false if mtshan nyid is taken as some or all defining characteristics or even a/the/this defining characteristic. These renderings would all be false because Collected Topics holds that every defining characteristic is indeed a defining characteristic: to say that some, all, or the/a, defining characteristics are not defining characteristics would lead to howls of derision – it would be said to be absurd (ha cang thal = atiprasaṅga) because of being a flat-out contradiction. If we use a generic "the" we get no further, as "the defining characteristic is not a defining characteristic" remains false, and indeed it is not at all clear that the generic knowable thing would be permanent for an adept of bsdus grwa.

Finally, one cannot say that subject terms in Tibetan are actually veiled uses of an abstract term, as if we should simply translate bum pa by vaseness and shes bya by knowable thingness much as if it were the Tibetan bum pa nyid and shes bya nyid (= the Sanskrit ghaṭatva and jñeyatva). It is a cliché in Tibetan philosophical texts to say "Vase is bulbous, splay-bottomed and able to perform the function of carrying water" (bum pa lto ldir zhabs zhum chu skyor kyi don byed nus pa yin): vaseness, as an abstract entity or a property, is obviously not able to carry water, and is thus not what is being talked about. One can come up with many other such examples to show that terms do not designate such abstract entities.

What is left as a plausible English translation? The problem in (15) and (16) and in other such cases is that they seem to need some sort of a mass noun rendering, along the lines of knowable thing, defining characteristic, vase, good reason, etc., if our translation of the Tibetan argument is both to preserve truth and not fall into triviality. But, of course, vase, good reason, knowable thing and the like are not used as mass nouns in English, French, Dutch, etc., i.e., they don't behave like snow, water, and the like. Vase does divide its reference into readily distinguishable and countable objects. It would usually be considered a solecism in English to speak of vase (or French cruche, Dutch vaas, etc.) or knowable thing as being found here, here and here—one naturally understands the sentence Vases are found in the museum, but not Vase is found the museum—, and it makes no sense to speak of a collection of vase or a set of knowable thing, although a collection of vases and a set of knowable things are, of course, perfectly fine. The result: we are, so it seems, forced to translate many philosophical passages in a way we fundamentally don't understand in our own languages, and there is no easy unpacking in English that would preserve the rationality, and hence comprehensibility, of the Tibetan philosophical discussion.

Tibetans themselves were aware that the meaning of bum pa (vase) was not the same as the meaning of bum pa 'ga' zhig (some vases), bum pa thams cad (all vases), bum pa 'di (this 'vase), bum pa zhig (a vase) etc. – they saw that difference as applying mutatis mutandis to good reason (rtags yang dag) versus a/some/all good reasons and numerous other terms, and thought that it was an important difference with philosophical consequences. Indeed it was emphasized by a figure no less than Tsong kha pa (1357-1419) himself, in his Tshad ma'i brjed byang chen mo, that although something may be true of X itself, e.g., reason, positive phenomenon, universal etc., it need not be true of all x's (all reasons, universals, etc.). Tsong kha pa says that when we get this subtlety wrong, it is a major obstacle (gegs) due to which the rest of our thinking goes astray – he applies his diagnosis across the board to metaphysics, philosophy of logic, and philosophy of language. The problem supposedly arises when we fail to reconcile two key propositions in Buddhist nominalism: [The obstacle] is precisely to grasp as contradictory the pair [of propositions] that object of thought (rtog pa'i yul) is not a particular and that particulars are [nonetheless] objects of thought.

lCang skya Rol pa'i rdo rje (1717-1786) elaborates upon Tsong kha pa's solution:

“Now, the reason behind this is that there would be no contradiction [in the fact] that the property per se (rang ldog, Skt. *svavyāvṛtti) actual object of thought is not a particular, but that particulars are actual objects of thought."

On Tsong kha pa's diagnosis, then, people supposedly fail to understand the nominalist perspective because they cannot see the compatibility between the fact that object of thought itself is a fictional creation and hence not a real particular (rang mtshan = svalakṣaṇa) and the fact that there are objects of thought that are particulars (e.g., vases, tables, chairs, etc. are real particulars and also objects of thought simply in that we do think about them.) His solution is that we need to be able to properly differentiate object of thought per se (i.e., X itself ) and objects of thought (i.e., the individual x's) – while the former is a fictional universal, the latter need not be fictions at all.

His disciple rGyal tshab rje (1364-1432), in one of the most commonly used dGe lugs pa Pramāṇavārttika commentaries, rNam 'grel thar lam gsal byed, called this X versus x's differentiation, somewhat bombastically, the supreme main point that is difficult to understand in this philosophical tradition [i.e. Buddhist logic] (gzhung lugs 'di'i rtogs dka' ba'i gnad gyi gtso bo dam pa), in short, the hard point in the Buddhist's philosophy of language and logic. It becomes a recurring dGe lugs pa position, one which is regularly invoked in key arguments by textbook writers such as Paṇchen bSod nams grags pa (1478-1554), Se ra rje btsun Chos kyi rgyal mtshan (1469-1546), lCang skya Rol pa'i rdo rje and others, and is known as the main point that is difficult to understand in the anyāpoha [[[Wikipedia:theory|theory]] of language] (gzhan sel gyi rtogs dkar ba'i gnad kyi gtso bo). It is also what lies behind the bsdus grwa arguments that we see represented by (15) and (16). In other terms, (15) and (16) are the tip of an iceberg. Underneath the surface of bsdus grwa eristics lies a great deal of Tibetan philosophy of language.

Where does this difficult point leave us as translators? The supposed difference between talking of X itself (vase, reason, object of thought, etc.) and talk of x's (vases, reasons, objects of thought, etc.) was no minor matter for these thinkers. Like it or not, it is, for a dGe lugs pa, essential to understanding their philosophy. If Tsong kha pa and rGyal tshab rje are right and we do have to talk of X itself as opposed to x's, or if we simply want to translate their theories, we would have to translate solecistically to render their philosophical thinking in English.

Now, at this point, it might well be replied that this philosophical thinking and writing in Tibetan about X itself versus x's is indeed unintelligible to us; the conclusion to draw is not that it is interesting, but that it is just better confined to the scrap-heap of bad philosophy. Tibetan writers' uses of terms in the sense of X itself, so it might be argued, are confused and would regularly need disambiguation to be explained away. If we are to avoid unintelligibility in English, a term like bum pa (vase) or shes bya (knowable thing) would sometimes have to be interpreted to refer to some or all individual things, sometimes to an abstract universal property, like vaseness, or knowable thinghood, or perhaps even the generic vase, but never to the mysterious vase itself or knowable thing itself.

However, that proposed disambiguation of troublesome contexts would be extremely inelegant and complex, necessitating ad hoc decisions for many arguments: it is generally simpler, and hence desirable, to find a univocal semantics where possible, even if that is not the semantics of a Western language. Worse, it is a type of uncharity to maintain that because such and such a semantics in a language leads to problems when translating up into a prestigious language it must be wrong and hence demand complex disambiguation, as if it were simply a muddle. It is remarkable that many very intelligent Tibetan traditional scholars do not feel that talk of X itself is problematic at all. In explaining Collected Topics, they will often insist that the subject terms (chos can) in most debates refer to "vase itself" (bum pa kho rang), "knowable thing itself" (shes bya kho rang), or "defining characteristic itself" (mtshan nyid kho rang), or equivalently they will use the terms bum pa rang ldog, shes bya rang ldog, mtshan nyid rang ldog ("vase, the property per se", etc.). What is striking is that for many Tibetans, bum kho rang/rang ldog, etc. are felt to be univocal and perfectly clear, needing no disambiguation in terms of vaseness and vases. In my vivid personal experience of learning Collected Topics, my teachers felt frequent puzzlement and even exasperation that something so obvious would be so inexplicably difficult to their foreign student. It may well be their linguistic intuitions deserved greater weight than my nagging feeling that something was going wrong in Tibetan and hence needed the disambiguation that a European could supposedly provide.

Would a parallel with Chinese be of help in understanding the problematic Tibetan uses of mass nouns? The specific Tibetan debates in Collected Topics are not, as far as I can see, of Chinese ancestry, with the quite possible exception of a Tibetan version of the white horse argument (see Appendix). Could one perhaps get some support from common syntactic and semantic features of the Sino-Tibetan family of languages? In Tibetan, as in Chinese, mass and count are not rigid word classes but more like functions of words. There is no clear inherent or essential feature of the Tibetan language that fixes nouns as mass nouns by word class; there are uses of nouns as mass nouns and uses as count nouns – one says sgra mi rtag pa yin pa (Sound is impermanent""), but also sgra gnyis thos pa (She heard two sounds). Moreover, Tibetan is like Chinese in that all nouns, including "horse" (Tib. rta, Chin. ma 馬 ), "person" (Tib. mi, Chin. ren 人) and the like, can be used as mass nouns and even are so used frequently. To take an unphilosophical and very simple example, just as in modern Chinese, it is normal in colloquial Tibetan to say, literally, "In Lhasa, car exists. In Lhasa car is many' (lha sa la mo ṭa yod. lha sa la mo ṭa mang po ('dug/yod) = Chin. zai la sa you che 在拉薩有車; zai la sa che duo 在拉薩車多). It is thus not surprising that the possibilities of using Tibetan nouns as mass nouns are much greater than in English, French, and other European languages and that nouns like bum pa can easily be mass nouns while the English noun vase, French cruche or Dutch vaas are not.

Is that all there is to the translational issues in Tibetan philosophical writing turning on uses of mass nouns, i.e., the so-called "difficult point"? No. The translational problems in the "difficult point go beyond the fact that Tibetan, like Chinese, regularly uses mass nouns that we would not countenance as mass nouns in an English translation. Reformulation of those Tibetan or Chinese mass nouns as English count nouns is usually banal, and yields English sentences salva veritate, i.e., with no change in truth value – Tibetan mo ṭa mang po and Chinese che duo 車多 (Car [is] many) are rendered as There are many cars routinely and unproblematically. I would see this as support for a position with regard to Tibetan like that of Chris Fraser 2007 with regard to Chinese, viz., that usage of mass nouns or count nouns has no implications about what kind of entities people are speaking about. Indeed, one could well deflate much Tibetan similarly. Most uses of mass nouns – e.g., in colloquial speech, in history texts, in opera and epics, in Marxist or Buddhist tracts, cookbooks, what have you – would not have any implications for whether one is speaking of particulars, manifestations of universals, distributions of fusions and other such ontologies. There would be no semantic and metaphysical issues at stake in such cases, only verbal usage. To supplement Fraser a bit, we could say that there certainly are mass and count nouns, but that their reference to metaphysical types of entities like particulars, instantiations of universals, distributions of fusion entities, etc. remains inscrutable. The would-be “inherent ontology” of the language in question is not only unknowable but immaterial to its statements being true or false.

The argument is that of Donald Davidson. Here is how it goes. Inscrutability of reference comes down to an important point in formal semantics that there is always a permutation function Φ that maps one reference scheme for a language onto another scheme, so that when, on the first scheme, a name refers to an object x, then on the second it refers to Φ(x) and when a predicate F refers to the x's of which it is true that x is F, then on the second scheme F will refer to the x's of which it is true that Φ(x) is F. If we grant, as I think we surely must, that every particular rabbit is an instance of rabbitness and is a distribution of the rabbit fusion entity, and that the converse implications all hold so that every distribution is an instance and an individual, etc., etc, then there is a permutation function allowing us to go unproblematically between the three interpretations of rabbit-talk. It is not only easily shown that a is a rabbit is true if and only if a is a rabbit, but that a is a rabbit is true if and only if a is an instance of rabbitness. And so on for rabbit fusions. The truth conditions become equivalent and there is only one fact of the matter needed for the sentences to be true. Whether that fact is a's being an instance of rabbitness, a distribution of the rabbit fusion, or being a particular individual rabbit, is inscrutable and immaterial to truth. The same holds, mutatis mutandis, for tables, people, buddhas, and so on.

Davidsonian arguments about inscrutability of reference, if right, put paid to a myriad of modern views about inherent metaphysics of languages and ways of thinking supposedly peculiar to their speakers alone. That said, the specific problem of understanding bsdus grwa and the "difficult point" is very different from the usual grand scale discussion about inherent semantics. It is certainly not resolved by simply saying that statements about facts that we understand are interpretable indifferently, salva veritate, in terms of several sorts of entities, so that we could, for example, just as well be talking about distributions of the rabbit fusion (or instantiations of an abstract entity rabbithood) being furry instead of individual rabbits being furry. Rather, the point in bringing up (15) and (16), as we saw, is that we don't understand why these particular kinds of Tibetan statements and their English translations are supposedly true; we don't adequately understand the facts the Tibetan theoreticians are talking about at all when they talk about vase itself or knowable thing itself nor the reasons why they assert what they do of them.

Usual translational strategies to come up with reformulations in English salva veritate are thus simply not available here. More specifically, we are confronted with a dilemma. On the one hand, when the reformulations of (15) and (16) are in proper, clear, English, they do not conserve truth value, but, on the other hand, if we seek to conserve truth value, we are forced into using a badly obscure English, so odd that certain terms are in italics and scare-quotes, suggesting unintelligibility. This is a problem of the philosophical implications of the Tibetan difficult point. They leave (15) and (16) with specific problems of intelligibility and translatability that more ordinary Tibetan does not have.

This dGe lugs theoretical position on Tibetan subject terms was important in Tibetan theorizing about language, but not surprisingly it was also contested by many non-dGe lugs thinkers. Sa skya pa thinkers like Kun dga' rgyal mtshan (1182-1251), Go rams pa bSod nams seng ge (1429-1489), and gSer mdog Paṇchen Śākya mchog ldan (1428-1507) were oriented more towards a more Indian Buddhist semantics where words either had to refer to real individual things, i.e., particulars (rang mtshan = svalakṣaṇa), or to fictional universals (spyi mtshan = sāmānyalakṣaṇa), with no middle ground of a universal that would also be a real thing (spyi dngos po ba). They were thus often very skeptical about interpretations of their own language in accordance with the difficult point. Talk of X itself along the lines of the difficult point theorists would, so they thought, lead to a kind of realism about universal properties. Vase, tree and the like would be fully fledged universals present in several particulars, but also fully real as they would possess the ability to perform functions (don byed nus pa = arthakriyāsamartha). That intra-Tibetan debate took on major importance in contrasting dGe lugs pa/gSang phu versus Sa skya pa Tibetan approaches to the problem of universals and philosophy of language. Go rams pa polemically insisted that talk of "mere tree" (shing tsam) as being a real universal (spyi dngos po ba) present in particulars was just "verbal obfuscation" (tshig gi sgrib g.yog) and an invention of the snowy Tibetans (bod gangs can pa). The main motivation of these Sa skya thinkers was not so much the mere usage of terms like tree (shing)– they used those terms too— but the un-Indian aspect of accepting tree or tree itself as a real universal somehow to be contrasted with trees.

Were Go rams pa and others fair to the dGe lugs? They thought, probably rightly in many respects, that the dGe lugs-Phya pa semantic theories and especially the resultant metaphysics were out of step with mainstream Indian Buddhist nominalist positions such as those that one would find in Dignāga and Dharmakīrti, and they cited Pramāṇavārttika commentators like Śākyabuddhi to show that Buddhists should never accept universals. Georges Dreyfus and I, in a number of separate publications, have taken up the theories of spyi dngos po ba (real universals) in Tibetan thought and the slim Indian antecedents for this theory that might be found in 10th - 12th century Kashmiri philosophers like Śaṅkaranandana and perhaps Bhavyarāja (= sKal ldan rgyal po). It is certainly arguable that the spyi dngos po ba that the dGe lugs pa accepted was not simply the universal of non-Buddhist schools, and that it would thus be unfair to accuse them of wholesale betrayal of Buddhist nominalism. Instead vase is a concrete real entity able to perform functions like carrying water, and it is of the same substance (rdzas gcig= ekadravya) as the particulars; it is not a universal vaseness (ghaṭatva) that is separate from particulars and inherent (samaveta) in them, along the lines of the non-Buddhist Nyāya-Vaiśeṣika school or, for that matter, Platonism.

So far, perhaps, so good. Some might wish to say that although Tibetan in fact has no inherent semantics (for Davidsonian reasons), what these Tibetan dGe lugs pa writers are doing is reading their language as if it had a semantics of discontinuously distributed fusions, i.e., entities composed by adding all the world's snow to make a sum, and (why not?) adding the world's rabbits or horses, what have you, to make their respective sums. dGe lugs pa would, in sum, be theorizing about their own language as involving distributed stuff rather than individual things.

Would such a stuff-semantics, after all, help explain and rationalize the difficult point distinctions that are promoted by dGe lugs pa philosophers? As we argued earlier, there is no reason to think that it is somehow inherent to Tibetan language generally or that the mere extensive use of mass nouns makes it necessary. But nor would reading the dGe lugs pa ideas about Tibetan in this way help much to rationalize what we find in the texts. While stuff-semantics may seem possible for horses, rabbits and vases, it becomes increasingly weird for knowable things and good reasons. Even if we could learn to live with reason-stuffs or reason-fusions distributed here, here and here, the big problem remains: we would still somehow have to learn to argue convincingly in English why the non-red fusion itself and knowable thing fusion itself and finally, the good reason fusion itself, would supposedly have properties that they do and that their distributions quite often don't. It is hard to see that saying the dGe lugs pa (rightly or wrongly) apply a stuff-semantics to Tibetan would make that any clearer at all. The difficult point remains.

Let me conclude on a nuanced note, taking some distance from the usual discussions about translation and translatability that one finds in analytic philosophy post W.V. Quine and Donald Davidson. As should be clear, I subscribe to much of the Quine-Davidson position on the inscrutability of reference. I am thus certainly not advocating a strong thesis, along the lines of Benjamin Lee Whorf, to the effect that a language has its own inherent ontology and is incommensurable with some or all other languages. I do not think that Sino-Tibetan languages have an inherent ontology because of such languages’ extensive use of mass nouns. However, I do think that philosophical Tibetan as used and interpreted by many indigenous authors presents important problems of translatability because of their understandings of Tibetan mass nouns. The authors I am speaking of represent the school of Buddhism that has been dominant in Tibet since the fifteenth century. When they think the difficult point is key to understanding philosophy of language, that is, in a sense, the official Tibetan line. There is a significant problem in translating their writings and the Tshad ma-based philosophy of their school; there is hence a problem in translating some quite influential Tibetan philosophy tout court.

Some might well say that large scale untranslatability is an incoherent notion. And indeed it is often repeated, since Donald Davidson's article On the Very Idea of a Conceptual Scheme, that a culture that did not share with us a common endorsement of a very large number of truths would be thoroughly unintelligible to us – even its difference and foreignness, and for that matter, whether it has a language, would be obscure. However, a Davidsonian a priori argument against untranslatability would be overkill in the case at hand. It is clear we do share a very great number of truths with Tibetans and that understanding Tibetan culture is not the type of (supposedly) radically foreign encounter Davidson criticizes as unintelligible. We may not understand all the whys and wherefores of utterances in difficult point debates but we easily know that they are utterances, and indeed know quite a lot about them, just as we do about Tibetan medical and pharmacological terms that are often untranslatable in the present state of our scientific terminology. The Davidsonian arguments are best seen as directed against a strong thesis: untranslatability in principle, due to inherent features in languages that imply a conceptual scheme incommensurable with that of the translator. It is this necessary, essential or inherent untranslatability of languages and the resultant relativity of truth to a language's inherent conceptual scheme that inspired Whorf and repelled Davidson. Essential untranslatability may well fall under the Davidsonian critique. It is, however, not the untranslatability I am claiming for the difficult point.

Nor is the untranslatability in philosophical Tibetan a practical matter, so that meaningfully translating the difficult point distinctions would be a problem cleared up with new discoveries and supplementary information. No doubt there is often de facto, or practical, untranslatability given a current state of knowledge –the language of the Indus Valley civilization, the Minoan Linear A, and Egyptian hieroglyphics before J.F. Champollion come to mind. We can well imagine what further information we would need to have to be able to translate. What we can say in the case at hand, however, is that we see no way out of the translational problems of the difficult point given the current requirements of English. I suspect that “Tibet hands” who study bsdus grwa and related dGe lugs pa thinking in depth will continue to develop a somewhat divided mind, learn how to reason about certain subjects in Tibetan persuasively to Tibetans, be able to explain that reasoning in a relatively sophisticated manner in Tibetan, but be unable to translate and explain it satisfactorily in English.

More generally, we seem to have to recognize that what is a typically debatable philosophical question in one language, with elaborate answers, and often commonly recognized rational decision procedures to determine whether those answers are good or bad, may be hardly discussable in the other. That does not entail that truth differs between Tibetan and English or varies between the Himalayas, Switzerland, and the west coast of Canada. More reasonable is the following more sober conclusion: the truths and implications of “difficult point” philosophy are not evidence for the relativity of truth, they show rather that some promising, rigorous, philosophy is— and will remain—obscure in translation. Some highly developed Tibetan philosophy won’t translate well enough for the truth or falsity of its statements to be meaningfully debated in English. That is enough untranslatability to be significant.

If that is right, then there are consequences for comparative philosophy and logic, in that there are at least some important areas where, as far as we can see, we cannot cross borders of language and cultures with impunity and philosophize together with clear mutual understanding. In sum, a philosopher who wants to cross borders needs to know where they are and how serious they are. They aren’t much like Whorf imagined them and don’t concern the metaphysics of whole languages, grand scale views on the relativity of truth, nor do they concern whole cultures as remaining exotically inaccessible and alien. (Exaggerating the importance of borders is, unfortunately, the all too frequent stuff of professional Asianists and popular conceptions alike. ) These two chapters, if successful, should show that much of Tibetan philosophical culture is in fact quite accessible to cross-cultural philosophy and not exotic at all. But they should also show that we can legitimately talk about borders concerning a sizable chunk of the intellectual production of a specific culture. We need to look at borders with a very focused vision and case by case. They can be quite serious indeed.

Appendix I: Chinese influence?

Might the debates in Collected Topics have Chinese origins? While at least one Indian Pramāṇa text was translated into Tibetan from Chinese – e.g., the Nyāyapraveśa from the translation of Xuanzang — there are no logic commentaries that I know of by Chinese authors that made there way into Tibetan and influenced Tshad ma. We do find an important commentary on the Saṃdhinirmocanasūtra by a student of Xuanzang, Yuan ce 圓測. It was translated into Tibetan and had a significant influence in Tibet, often being discussed by writers like Tsong kha pa. However, this is not a work on logic and Tshad ma: it is a work on hermeneutics and the interpretation of the three cycles of Buddhist teaching.

There is, however, a white horse argument found in the Tibetan Collected Topics literature that seems like the strongest candidate for Chinese influence and origins. The debate is very well known amongst people educated in the dGe lugs pa curriculum, for whom it is typically taken as showing an important Buddhist point, the unfindability of entities under analysis, the impossibility that any macroscopic entity can be localized or identified with one or more of its constituent dharmas/tropes. Here is a representative version as found in Yongs 'dzin bsdus grwa:

"A certain [debater] might say: A white conch, the subject; it follows that it would be a color, because it is white. If [his opponent says that the reason] is not established [i.e., that a white conch is not white] [then the debater could argue to him as follows:] Take that [white conch as] subject; it follows that it is [white], because it is a white conch. If [this debater] says that, then [one should force upon him the opposing pervasion ('gal khyab) [i.e., that if something is a white conch, it is pervaded by not being white] as follows: Well then, for him, take a white horse, the subject; it follows that it would be white, because it is a white horse. The pervasion would be the same [i.e., in the first case the debater had argued that all white conches are pervaded by being white and in the second case he similarly should argue that all white horses are pervaded by being white]. But [actually] he cannot agree [that a white horse is white], because it is [in fact] not matter (bem po = jaḍa). Why? Because it is a living personality (gang zag = pudgala). Why? Because it is a horse." ¨ How would this compare with famous debate of Gong Sun long 公孫龍 (325-250 B.C.E.) that concludes bai ma fei ma ke 白馬非馬可 (One can say that white horse is not [a] horse)? The differences are considerable. The first and most obvious thing to note is that the conclusions are not the same: Collected Topics seeks to show that white horse is not white and not that white horse is not a horse! Second, while the debate does not figure in Indian Buddhist sources, as far as I can see, the underlying reasoning relies on Abhidharma metaphysics rather than indigenous non-Buddhist Chinese ideas. The point of the white horse not being white is that the white horse cannot be identified with one of the many tropes that constitute it. Indo-Tibetan Abhidharma maintains that a macroscopic entity is always a composite of dharmas, i.e., what would nowadays be termed quality-particulars or tropes. In short, a horse, or any other living being, cannot be identified with its shape, its colour, its weight, its mental features, or any other material or mental trope. On the other hand, the debate in the Gong sun long zi 公孫龍子, if I understand it, does not turn on Abhidharmic trope metaphysics and the resultant impossibility to identify an entity with one of its constituent tropes, but rather, to take Chad Hansen's analysis, on issues of interpretation of Chinese compound terms like white horse (bai ma 白馬), i.e., either as a sum of all white and horse entities, or as a product, the entity which is both a horse and white. The white horse not being a horse is assertable if (for philosophical reasons about language) we say that white horse is to be taken along the lines of ox horse'" (niu ma 牛馬), i.e., as a sum, rather than along the lines of a product like hard white (jian bai 堅白). However, the Confucian semantical principle, the Rectification of Names, precludes that one and the same thing should be referred to by two different words, and hence rules out the product reading of white horse.

The white horse argument is not findable, as far as I can see, in Indian discussions – it is not an Abhidharma debate in India. I would tentatively submit that what may have happened is that the white horse debate in Collected Topics is derived from the Chinese, but that in any case, if it is so derived, it changed significantly, philosophically speaking, in its use in Tibet. Note that there are other discussions in Collected Topics that are thoroughly un-Indian and somewhat suggestive of Chinese views on language. For example, Collected Topics has a whole lesson (rnam bzhag) concerning X being or not being an instance of X, and there are also discussions about products (impermanent sound) and sums (pillar vase) that do and don't respectively admit instances (yin pa srid pa/yin pa mi srid pa). The contents of these discussions do not seem to be due to Indian sources (although some terms have Indian antecedents), so that one might look to Chinese sources for their origins, or one might well say that these are original Tibetan developments. A minimalist hypothesis: there is no smoking gun clearly establishing specific Chinese origins of debates in Collected Topics.

Appendix II. A Pronunciation Guide to Standard Tibetan

In what follows, we provide a guide with English equivalents, so that the non-linguist can arrive at an acceptable pronounciation of Standard Tibetan (bod kyi spyi skad), the language spoken around Lhasa. For a more exact phonetic description of Standard Tibetan, see Tournadre and Dorje 2003, 32-41. Those seeking only to get a very rough idea of the pronunciation of an isolated word or phrase can use the Tibetan-phonetics convertor on the internet sie of the Tibetan and Himalayan Library: http://www.thlib.org/reference/transliteration/phconverter.php. The system of Tibetan transliteration that we have adopted is that of T.V. Wylie 1959.

§1. The vowels, a, e, i, o, u, when they are not followed by consonants are short and pronounced as follows: a: similar to a in English father; e: similar to e in set; i: similar to ee in free, o: similar to o is so. u: similar to u in sue.

§2. When they are followed by the consonants d, n, l, or s, the vowels a, o and u are pronounced like counterparts with umlauts, respectively ä, ö, ü. The consonant d leaves the preceding vowel short and is itself silent; l and s lengthen the vowel and are themselves silent; n is pronounced.

§3. Tibetan consonants are generally pronounced as follows: k: completely unaspirated, similar to the English k in skip

kh: aspirated, similar to a strongly pronounced c, as when one exclaims that something is utter claptrap. g: similar to Tibetan k, but with a low tone vowel. When preceded by other consonants it is voiced, like g in gone, ng: similar to the first ng in singalong. c: completely unaspirated, similar to the ch in speech. ch: aspirated, similar to a strongly pronounced ch in cheese.

j: similar to Tibetan c, but with a low tone vowel. When preceded by other consonants it is voiced, like j in jab. ny: similar to n in newspaper as pronounced in British English. t: completely unaspirated, similar to the t in stag. th: aspirated, similar to a strongly pronounced t in tap. d: similar to Tibetan t, but with a low tone vowel. When preceded by other consonants it is voiced, like d in dab. n: similar to n in not.

p: completely unaspirated, similar to p in spin. ph: aspirated, similar to a strongly pronounced p in pan. b: similar to Tibetan p, but with a low tone vowel. When preceded by other consonants it is voiced, like b in ball. m: similar to m in English, e.g. man. ts: completely unaspirated, similar to ts in treats. tsh: aspirated, similar to a strongly pronounced ts in tsar.

dz: similar to Tibetan ts, but with a low tone vowel. When preceded by other consonants it is voiced, like ds in lads. wa: similar to w in want. zh: similar to sh in shop, but with a low tone vowel. z: similar to s in same, but with a low tone vowel. ‘: not pronounced. y: similar to y in yet

r: similar to r in read, slightly rolled. l: similar to l in led. sh: similar to sh in shop, but with a high tone vowel. s: similar to s in same, but with a high tone vowel. h: similar to h in hard. §4. g, d, b, m, ‘, r, l, s, br, and bs, when they precede another consonant, are not pronounced. Thus, for example, Tibetan sgo and mgo are homonyms and are pronounced like English go.

§5. kl, gl, bl, rl, sl, brl, and bsl are all pronounced like Tibetan l. Thus, for example, blo and glo are homonyms and are pronounced like English lo. The combination zl, however, is the exception: it is pronounced d. §6. kr, skr, bskr, tr, pr, dpr, and spr are all pronounced like an unaspirated retroflex t, like the retroflex ṭ in Sanskrit. Thus, for example, skra is pronounced like Sanskrit ṭa. §7. khr, ‘khr, mkhr, phr, and ‘phr are all pronounced like an aspirated retroflex t, i.e., like the retroflex ṭh in Sanskrit. Thus, ‘phro is pronounced like Sanskrit ṭho. §8. gr, dr, and br, unpreceded by other consonants, are pronounced like a low-toned ṭ, while dgr, bgr, mgr, ‘gr, sgr, bsgr, ‘dr, dbr, ‘br, and sbr are pronounced like the retroflex ḍ in Sanskrit. The combinations sr and mr are the exceptions: sr is simply pronounced like s and mr is pronounced like m. §9. py, dpy, spy, by are unaspirated and pronounced like c. ‘by and sby are voiced and pronounced like j. phy and ‘phy are aspirated and pronounced like ch. §10. In the combinations ky, khy and gy, both letters are pronounced distinctly and normally. However, in dgy, bgy, brgy, mgy and ‘gy the g is voiced and low tone. The combinations my, smy, and dmy are exceptional and are all pronounced like ny. §11. The ten consonants g, ng, d, n, b, m, ‘, r, l, s and the combinations gs, ngs, bs, and ms occur at the end of syllables;.the s in gs is not pronounced but has the effect of lengthening the vowel. g is hardly pronounced but shortens the vowel. d, l, s are themselves silent. Vocalic changes a → ä, o → ö, u → ü and lengthening of vowels occur as described in §2. Sandhi occurs but need not be described here, nor need we master the use of the three tones of Lhasa Tibetan.

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