Master Gangxiao: On the Branches of Buddhist Logic

Gang Xiao

“A bodhisattva seeking the Dharma—where should one look? One should look to the five vidyās.”[1] Still, the outer vidyās[2] are, relative to the inner vidyā, little more than auxiliary tools for spreading the Dharma. That said, hetuvidyā—one of the outer vidyās—achieved considerable success thanks to the reforms introduced by Ācārya Dignāga, rose to prominence, and took root as a major field within Buddhism. Eventually it even solidified into its own distinct discipline called “pramāṇa theory” (量论). Here I’ll focus solely on the question of the branches (支分) of hetuvidyā.

The Five Branches of Old Hetuvidyā

In the era of the Nyāya Sūtra, an inference (论式) always consisted of five component parts: thesis (宗), reason (因), example (喻), application (合), and conclusion (结). As the Nyāya Sūtra puts it: “The thesis is the statement of the conclusion one aims to prove.” The reason comes in two types: positive reason and counter-reason. “The (positive) reason is an argument that shares a common property with the example and proves the establishment of the thesis.” “What contradicts the example is also thus (meaning that what contradicts the example is also a type of reason, called a counter-reason).” The example also has two forms: similar example (同喻) and dissimilar example (异喻). “A (similar) example is an instance that shares a common trait with the thesis and bears its defining characteristic.” “Anything directly opposed to the thesis counts as a dissimilar example.” On the application step, the sūtra explains: “The application of the thesis is the judgment that the conclusion is established on the basis of the example, and is thus—or is not thus.” The conclusion is “the restatement of the thesis after the reason has been stated.”[3] The scholar Yao Weiqun, in his article “The Origins and Main Lines of Development of Buddhist Hetuvidyā,” notes only that the reason is a justification, without distinguishing between positive and counter-reasons. The most commonly used example is as follows:

Thesis: Sound is impermanent. Reason: Because it is produced. Similar example: Whatever is produced is impermanent, such as plates and bowls. Application: Sound is thus—it is produced. Dissimilar example: Whatever is not produced is permanent, such as ātman. Application: Sound is not thus—it does not belong to what is unproduced. Conclusion: Therefore, sound is impermanent.[4]

In early Buddhist hetuvidyā, it is often said that old hetuvidyā masters used the five-member inferential form, but this is a rather loose claim—they also employed three-member forms. For instance, there is a treatise called the Vādavidhi (压服量论), attributed to Ācārya Nāgārjuna. No Sanskrit original of this text survives today, but in the Tibetan bstan 'gyur there is a sub-commentary from 650 CE titled the Vādavidhi Pañjikā (〈压服量论〉论科文注). In his essay “Mādhyamaka and Yogācāra Hetuvidyā Prior to Dignāga,” Xu Dishan writes that the Vādavidhi commentator describes the “branch” (分) entry among the sixteen categories of Nāgārjuna’s logical framework as “what modern logic calls a sorites or syllogism, whose three components are thesis, reason, and example.”[5] He adds:

The three members can serve both affirmative and negative inferences. The hetu corresponds to what logic calls a “reason,” and can be expressed through one of three relations: effect (kārya), inherent nature (svabhāva, identity), and non-perception (anupalabdhi). The example illustrates the relationship between the reason (the middle term) and the major term.[6]

That said, the Vādavidhi Pañjikā was written in 650 CE, long after Nāgārjuna lived. Ācārya Dignāga was born around 400 CE and passed away around 480, and his new hetuvidyā system was already well established by 650. It is therefore quite possible that the commentator was reading Nāgārjuna’s original text through the lens of Dignāga’s new hetuvidyā. For this reason, the argument that three-member inferences existed in early hetuvidyā is not well supported. In the Śūnyatāsaptatiṭīkā (full title: 顺中论义入大般若波罗蜜经初品法门), translated into Chinese during the Northern Wei dynasty by the Brahmin Gautama Prajñāruci (瞿昙般若流支), we find the following passage:

Question: “Superior entities” (胜) exist, because we observe a sequential pattern of perishable features. Just as seeing tree bark lets us know there is heartwood inside a tree. Answer: If that were the case, this would be a private standard of proof specific to your school, and its reasoning would hold. But in reality no such “superior entities” exist: perishable features are observable, but they are like rabbit horns. Rabbit horns are said to exist on the basis of perishable features, just like tree bark and so on.[7]

This text, the Śūnyatāsaptatiṭīkā (commonly shortened to the Shun Zhong Lun), is traditionally attributed to Bodhisattva Longsheng (龙胜, i.e., Nāgārjuna) with a commentary by Asaṅga. In reality, however, it is essentially Asaṅga laying out his own views in line with the principles of the Mūlamadhyamakakārikā, so it is generally credited to Ācārya Asaṅga. In this exchange, the questioner is a Sāṃkhya thinker, and the respondent is Ācārya Asaṅga himself. This passage can actually be parsed into three distinct inferential forms: first, the one put forward by the Sāṃkhya questioner to affirm the existence of “excellence”; then the two forms Asaṅga uses to refute the Sāṃkhya position. The Sāṃkhya inference is:

Thesis: There is excellence. Reason: Because a sequential pattern of perishable characteristics is observed. Example: Just as seeing tree bark lets us know there is heartwood inside a tree.

Ācārya Asaṅga counters that this is merely a private standard of proof for the Sāṃkhya school, and that no such “excellence” actually exists. We can lay out two inferential forms to show his refutation. The first:

Thesis: There is no excellence. Reason: Perishable characteristics are observed. Example: Like rabbit horns.

The second:

Thesis: Rabbit horns exist. Reason: Perishable characteristics are observed. Example: Like tree bark and similar things.

Seen this way, these are clearly three-member forms, not five-member ones. Of course, in early Buddhist hetuvidyā the five-member form was far more common, and ācāryas always used it for formal doctrinal expositions. For instance, the Mahāyānābhidharmasamuccaya (大乘阿毗达磨集论) defines the five members as follows:

To establish the thesis is to declare to others the proposition one accepts as true, so that they may grasp it. To establish the reason is to set forth the marks of verifiability—such as perceptibility or non-perceptibility—pertaining to the meaning that is to be proven but is not yet evident. To establish the example is to correctly articulate the connection between what is already known and what is not yet known. Application means to set forth the line of reasoning that draws other meanings of the same type into alignment with this dharma. Conclusion refers to the final exposition that brings the argument to its full endpoint.[8]

In addition, the Mahāyānābhidharmasamuccayabhāṣya (大乘阿毗达磨杂集论)[9] provides the following example of an inferential form:

Thesis: All phenomena (dharmas) are without self. Reason: If one posits a self within the aggregates, four logical faults follow. Example: Just as positing the nature of past phenomena based on present ones leads to errors. Application: Having thus refuted the delusion of a self through this reasoning, eternal entities and the like are also negated. Conclusion: (By this line of reasoning,) therefore the five aggregates are all impermanent, and ultimately without self.[10]

The “four faults” referenced here are the errors that arise if one holds that a “self” exists within the five aggregates, or that the five aggregates are themselves a “self”:

If one identifies the self with the characteristics of the aggregates: the aggregates are not autonomous, they arise from many conditions, and they are subject to birth and cessation. If the self is nothing but these same characteristics, it cannot be established as a distinct entity. This is the first fault. If one posits the self within the aggregates: since the supporting aggregates are impermanent, the self that depends on them would also be impermanent. This is the second fault. If one posits the self somewhere apart from the aggregates: the self would have no cause, and would serve no purpose. This is the third fault. If one posits the self as unrelated to the aggregates: the self would have to exist independently, its nature already liberated, which would make any further effort toward liberation pointless. This is the fourth fault.[11]

The phrase “positing the past based on the present” refers to the errors that arise when one tries to determine the nature of past phenomena by extrapolating from the characteristics of present phenomena, and so on—the original text details four such faults. “Permanence and so forth” refers to things like the eternal “self” posited by non-Buddhist schools. The Shun Zhong Lun also includes this example:

Sound is impermanent, for it is conditioned. Its conditions break apart; it arises only after being fashioned, and so on. All conditioned things are impermanent, like a pot. Sound is the same: because it is made, it is impermanent.[12]

This is the common example we use, which can be laid out as:

Thesis: Sound is impermanent. Reason: Because it is conditioned. Example: All conditioned things are impermanent, like a pot. Application: Sound is likewise. Conclusion: It is impermanent because it is made.

The Tarkaśāstra (如实论) also contains an inferential form of this kind:

Thesis: Sound is impermanent. Reason: It is produced by effort, with no intermediate stage of arising. Example: Like a clay vessel, which is produced by effort and perishes after arising (similar instance). Like space, which is permanent and not produced by effort (dissimilar instance). Application: Sound is likewise (applying the similar instance). Sound is not thus (applying the dissimilar instance). Conclusion: Therefore, sound is impermanent.[13]

In short, early hetuvidyā always used the five-member form for formal doctrinal exposition, but three-member forms occasionally appeared in practical use. (It is not unreasonable to characterize these practical three-member forms as abbreviated versions of the five-member form.)

New Hetuvidyā Is Customarily and Superficially Three-Membered, But Is Essentially Two-Membered

When the Dignāga school’s new hetuvidyā emerged, the inferential form was restructured into three members. The Nyāyapraveśa (因明入正理论) refers to these three members throughout: for instance, “By the multiple statements of thesis, reason, and example, one reveals the meaning not yet grasped by inquirers”; “Only these three constituents are called valid means of proof”… We are still accustomed to talking about hetuvidyā’s three members: thesis, reason, and example. But a habit, repeated long enough, hardens into a fixed assumption—and is this assumption actually correct? It is worth pausing to reflect on this.

In the Chinese hetuvidyā tradition, the core sources for the Dignāga school’s new hetuvidyā are in fact just two texts: the Nyāyapraveśa and the Nyāyamukha (因明正理门论本).[14] The Nyāyamukha is an early work by Ācārya Dignāga, the founder of new hetuvidyā. It lays out the theoretical foundations of the system, but is quite dense and difficult to parse. To make the Nyāyamukha more accessible to a wider audience, Dignāga’s disciple Bodhisattva Śaṅkarasvāmin created an abridged version of it: his Nyāyapraveśa. This Nyāyapraveśa went on to become the foundational canonical text for the Chinese hetuvidyā tradition. Any abridgment inevitably loses some of the original’s subtle nuances. As I note in my Two Treatises of Chinese Hetuvidyā:

When Bodhisattva Śaṅkarasvāmin simplified the Nyāyamukha, he ended up distorting Dignāga’s hetuvidyā: the Nyāyamukha explores the fundamental principles underlying the system, while Śaṅkarasvāmin’s Nyāyapraveśa focuses instead on the operational rules for constructing the three-member inferential form …[15]

Since my Two Treatises of Chinese Hetuvidyā is based on lecture notes, I did not go into detail at the time, but I flagged the core problem.

The Nyāyapraveśa deserves immense credit for spreading hetuvidyā widely. But because it cut out so much of the system’s essential meaning, it also led to a great many misunderstandings about hetuvidyā. The idea that the form has three members is one of the biggest. In Dignāga’s new hetuvidyā system, there are in essence only two members: thesis and reason. The Nyāyamukha records a discussion on this point between Ācārya Dignāga and the early hetuvidyā masters.

In the early masters’ five-member form, thesis, reason, example, application, and conclusion are five distinct, independent parts. Take the “conclusion” member: on the surface, it looks like nothing more than a repetition of the thesis, as if it could be left out without losing anything. But in actual debate, it is far from optional—you have to have been present in the thick of a live debate to understand why. In reality, the “conclusion” member is the moment, after you have finished laying out your proof, when you turn to your opponent and demand: “Do you still deny that sound is impermanent?!” Or even: “How could sound possibly not be impermanent?!” This final member has to be delivered with force—that is what creates the charged atmosphere of a formal debate. Ancient India was a civilization famous for its love of dialectical disputation; its many philosophical schools debated each other constantly. This was not unlike the contention of the Hundred Schools of Thought during China’s Spring and Autumn and Warring States period, only with far more bloodshed than characterized China’s intellectual golden age. The Nyāya Sūtra even lays this out explicitly:

Formal debates [disputation and refutation] are to be carried out with both parties shouting at the top of their lungs.[16] To safeguard the sincere search for truth, one may even use fallacious argument and destructive dialectic, just as one covers tender seeds and seedlings with thorny branches to shield them from harm.[17]

In early hetuvidyā, the independent “reason” and “example” were two separate members. In the new hetuvidyā, by contrast, they effectively merge into a single member. The clearest proof of this is the three characteristics of the reason (因三相). A typical new hetuvidyā inferential form looks like this:

Thesis: Sound is impermanent. Reason: Because it is produced (i.e., of the nature of being made). Example: All produced things are impermanent, like a pot. All permanent things are not produced, like space.

This is the most complete form of a new hetuvidyā inference. In this structure, the first characteristic of the reason—“pervasion as a property of the thesis subject” (遍是宗法性)—is conveyed by the phrase “it is produced.” The second characteristic—“certain presence in similar instances” (同品定有性)—is conveyed by “all produced things are impermanent, like a pot.” The third characteristic—“complete absence in dissimilar instances” (异品遍无性)—is conveyed by “all permanent things are not produced, like space.” This makes clear that both “it is produced” and the two example statements are, in fact, part of the reason member. If we were to treat “it is produced” as the reason and the two example statements as a separate example member, we would end up with “one characteristic of the reason” and “two characteristics of the example”—but this is not how the Dignāga school’s new hetuvidyā system is structured. Dharma Master Kuiji makes this clear in his Commentary on the Nyāyapraveśa (因明入正理论疏):

Speaking of the three characteristics of the reason includes the two examples within it. The two examples are themselves part of the reason, for both exist to demonstrate the thesis.[18]

In other words, the two examples are integral parts of the reason member and cannot be separated from it. In essence, they make up a single, unified member. This is a radical departure from early hetuvidyā. Ācārya Dignāga takes up this very point in his own Nyāyamukha, in a discussion with the early hetuvidyā masters:

"If so, the statement of the example shouldn't be a separate limb, since it reveals the meaning of the reason." "That may be true in fact, but the statement of the reason only clarifies its nature as a property of the subject — not whether it is present in similar instances and absent in dissimilar ones. That's why similar and dissimilar examples need to be stated separately." "If only the meaning expressed by the statement of the reason is called the reason, what's wrong with that?" "What's the benefit?" "Speaking of the example as a separate limb — that's the benefit." "It would then be like the expedients of worldly non-Buddhists, entirely disconnected from the meaning of the reason." "If so, what's the flaw?" "Such a statement merely parallels the thesis by analogy. It has no real function and cannot establish the thesis. Because it only speaks of the analogous property of 'being produced' without explaining the meaning that actually establishes the thesis. Furthermore, with reason and example kept separate, having similar and dissimilar examples for the thesis ultimately fails to demonstrate the inseparability between the reason and what is to be established. So it merely parallels the thesis by analogy but lacks any real function." "Why does it lack function?" "Because in a similar example, the property of the subject and the meaning of the thesis need not be analogous; and since it is established by still other analogies, it would lead to an infinite regress." [19]

In the old Hetuvidyā, the reason and the example were two separate limbs. Master Dignāga merged them into one, making reason and example a complete, organic whole. The old Hetuvidyā masters objected: "If that's the case, why do you still include both a reason and an example when constructing an inference?" Dignāga replied that the example limb in an inference is simply a necessity of verbal expression. In other words, while the example is an organic component of the reason, presenting it as a separate example limb only serves as an auxiliary to the reason. The old Hetuvidyā masters pressed further: "Since you've listed both reason and example, why not just keep them separate?" Dignāga asked: "What's the benefit of separating them?" The old masters replied: "Speaking of the example as a separate limb — that's the benefit," meaning they simply felt more comfortable keeping them apart. Dignāga responded: "This is exactly what the worldly non-Buddhists do — the Vaiśeṣikas, for instance. If it were like that, wouldn't you end up with one characteristic for the reason and two for the example?" The old masters asked again: "So what's the flaw in separating them?" Dignāga said: "If reason and example are separated, an inference like 'Sound is impermanent, because it is produced, like a pot' becomes a mere analogy. Because a pot has the property of being produced, you say it's analogous to sound. But since it's an analogy, couldn't you just as well say that sound can be burned? This fails to show the universal relationship between the reason and the property to be established — it fails to demonstrate the inseparability of reason and thesis. Viewed this way, it merely offers an analogous property without any real power to prove the thesis." The old masters asked: "Why does it lack the power to prove the thesis?" Dignāga said: "Your analogies would spiral into an infinite regress, endlessly." Master Kuiji elaborated on this point at considerable length in his Commentary on the Nyāyapraveśa. [20]

Based on Dignāga's words here, we can put it this way: the inference actually consists of two limbs — the thesis and the reason. The reason itself has two parts, a primary reason and an auxiliary reason. By convention, though, we call the primary reason the "reason," and the auxiliary reason the "example." The example is further divided into the similar method and the dissimilar method. Drawn as a chart:

• Inference
  • Thesis
  • Reason
    • Primary Reason (conventionally called "Reason")
    • Auxiliary Reason (conventionally called "Example")
      • Similar Method
      • Dissimilar Method

The names "primary reason" and "auxiliary reason" in this chart come from Master Kuiji's Commentary on the Nyāyapraveśa. When explaining Dignāga's phrase, "It would then be like the expedients of worldly non-Buddhists, entirely disconnected from the meaning of the reason," Kuiji wrote:

Like worldly non-Buddhists, who also say there are two examples separate from the reason, you too speak of examples outside the reason. Since pervading the property of the subject is itself the primary reason, the two examples spoken of are not the primary reason — they are merely expedients that help form the meaning of the reason. Because this expedient of the example is separate from the reason, it is entirely disconnected from the meaning of the reason. [21]

Here, "expedient" means "worldly skillfulness" — in plain terms, going along with worldly habits and conventional speech. [22] Regarding this compliance with conventional speech, Dignāga said in his Pramāṇasamuccaya:

...Therefore, we, regarding those with causal conditions and those broadly preaching, follow worldly conventions, not seeking absolute truth. We should be understood just as the world understands... [23]

What Dignāga means is that when we teach the Dharma, the words we use follow worldly conventions. We don't chase down the ultimate truth behind every single term — we use language that people can actually understand. So although the New Hetuvidyā inference is essentially two-limbed, it's still presented as three limbs to match people's habitual expectations.

The Significance of the Two Limbs in New Hetuvidyā

Whether Dignāga's reformed New Hetuvidyā system has three limbs or two is actually a major issue that goes to the heart of what New Hetuvidyā is. Only when we recognize that Dignāga's system is essentially two-limbed can we see that Hetuvidyā has always been an integral part of Buddhism — not something imported from non-Buddhist traditions. When reading Buddhist scriptures, one thing stands out: in the Āgamas, there are countless instances where someone asks the Buddha a question, the Buddha simply draws an analogy, and the questioner gets it immediately. But in later texts, the use of analogy drops off noticeably, replaced by more explicit argumentation. The later the text, the more pronounced this shift becomes. If we follow the three-limb theory, the Buddha's analogies in the Āgamas would correspond to the example limb. Dignāga said, "...and it is not strictly necessary for all categories to exist..." [24] That is, an analogy only takes what's usable — for instance, using a pot as an analogy takes only the pot's property of being produced and its impermanence, leaving aside its flammability, its visibility, and so on. Later on, just hearing an analogy wasn't enough — people couldn't tell which aspects of the Buddha's analogies were relevant and which weren't. So the scriptures began explicitly laying out the comparable dimensions between the thesis (thesis limb) and the analogy (example limb). That's the reason limb. In reality, the Buddha's analogy should have been understood as the reason itself — it's just that as soon as the Buddha drew an analogy, his disciples got the point without needing the comparable dimensions spelled out. Only by treating the analogy as the reason does it conform to the theory of the three characteristics of the reason (hetu-trirūpa) — except the other characteristics, the ones the disciples could already grasp, were simply left unsaid. If you treat the analogy as the example limb, though, it can only manifest one characteristic: a similar example shows the reason's presence in similar cases, while a dissimilar example shows its absence in dissimilar cases. With only one characteristic, there's nothing to omit — which doesn't fit the theory of the three characteristics. Of course, if the example is considered an integral part of the reason, then it works — but treating the example as part of the reason essentially means the system has two limbs. It was only later, for less sharp disciples, that the scriptures explicitly required spelling out the comparable dimensions, thereby fully manifesting all three characteristics. Understanding the divisions of Hetuvidyā as two limbs is what connects it to early Buddhism — that's how Hetuvidyā truly becomes part of Buddhism. Otherwise it doesn't work. By the time of Master Dharmakīrti, he explicitly proposed the methods of similar and dissimilar examples, stating: "The 'example' among the three limbs can be merged into the 'reason,' because the meaning or function of the 'example principle' can be contained by the 'reason.' In this way, the 'example basis' actually has no need to stand alone as a separate limb." This is a clear assertion that the divisions of Hetuvidyā are two limbs. Only in practice does Dharmakīrti "not require removing the example limb." [25] Dharmakīrti's Hetuvidyā places more emphasis on practical application than Dignāga's. Another clear example of this is his elimination of the category of conflicting reasons known as viruddhāvyabhicārin. Regarding integrating Hetuvidyā into the Buddhist system, "Dignāga had long intended to do this, but his writings don't yet show this structure. Dharmakīrti, however, realized Dignāga's ideal in this chapter (the Pramāṇasiddhi)." [26] Though Lü Cheng's observation has merit, it's still not the whole picture. This way, we can see that the concept of "Hetuvidyā" in the Buddha's time was consistent with that of Dignāga and Dharmakīrti. We can also understand Kuiji's words: "The treatises of Hetuvidyā originate solely from the Buddha's teachings; though the texts are vast and the meanings scattered, they are fully present in the various sutras." [27] And we can understand why Buddhism cannot be described using the rhetoric of "development."

Notes: [1] Master Kuiji states in the first volume of his Commentary on the Introduction to the Logic of Valid Cognition (Yinming Ruzhenglun Shu): “Thus the Bodhisattva Ground Practice Sutra says, ‘When a bodhisattva seeks the Dharma, where should they seek it? They should seek it in all five fields of knowledge.’” This is not, in fact, a verbatim quotation from the original scriptures; similar statements appear in texts such as the Bodhisattva Ground Practice Sutra and the Yogacara Ground Treatise (Yogacarabhumi Shastra) (Buddhist dictionaries uniformly note that the Bodhisattva Ground Practice Sutra is an abridged translation of the Bodhisattva Ground section of the Yogacara Ground Treatise). This phrasing is still commonly used by contemporary scholars: for example, Master Yinshun writes in his Notes on the Sutra of Queen Srimala: “The Yoga Treatise states, ‘When a bodhisattva seeks the Dharma, where should they seek it? They should seek it in the five fields of knowledge.’”; Guo Yuanxing writes in his On the Transformation of Consciousness into Wisdom in Yogacara and the Attainment of Buddhahood in This Very Body in Vajrayana: “The Bodhisattva Ground Treatise says, ‘When a bodhisattva seeks the Dharma, where should they seek it? They should seek it in the five fields of knowledge.’” But as Mr. Ma Xun of Huafan University writes in his essay Confucianism and Buddhism in Dialogue: On the Education of Enlightenment, “The Avatamsaka Sutra states, ‘When a bodhisattva enters the world, they should seek in the five fields of knowledge.’” No such passage exists in the Avatamsaka Sutra at all. [2] These are the four branches of the five fields of knowledge (vidyas) other than inner knowledge (neiming): logic (yinming), arts and crafts (gongqiaoming), medicine (yifangming), and linguistics (shengming). [3] The essay quoted here is translated by Liu Jinliang; see my A Brief Explanation of the Nyaya Sutra, p. 268 (Dharma Light Publishing House, 1st edition, November 2003). [4] See Vacaspati Mishra, Commentary on the Nyaya Sutra 1.1.33–39, cited in Yao Weiqun, “The Emergence and Main Development Trajectory of Buddhist Logic (Yinming) Doctrine,” Philosophy Gate 1 (2003). I don’t have Vacaspati Mishra’s original text on hand, but standard convention for syllogisms holds that only one example is given for the “example” (yuyi) component; this formulation’s use of “plates, dishes, etc.” deviates from that norm. [5] See Xu Dishan, Taoism, Logic (Yinming), and Other Topics, p. 59 (China Social Sciences Press, 1st edition, June 1994). [6] Same as above. The “Affirmatiu and negatiu” in the text is likely a printing error; it should read “Affirmative and negative”. [7] See Taisho Tripitaka, Vol. 30, p. 41, lower column. [8] See Taisho Tripitaka, Vol. 31, p. 693, lower column. [9] The Compendium of Mahayana Abhidharma (Dasheng Abidamo Jilun) was composed by the Bodhisattva Asanga. Later, his disciple Jue Shizi wrote a commentary on the treatise, and Master Sthiramati ultimately combined Asanga’s original text with Jue Shizi’s commentary to produce the Compiled Compendium of Mahayana Abhidharma (Dasheng Abidamo Zajilun). [10] This is a synthesized summary of the original passage, which appears in the Taisho Tripitaka, Vol. 31, pp. 771 (lower column) to 772 (upper column): “First, the text states that all dharmas are without self; this is the thesis. Next, the text states that if one posits a self within the aggregates, four logical faults can be identified; this is the reason……Next, the text states that just as the past is posited in relation to the present, this is the example……Next, the text states that after refuting the delusion of a self in this way, by this same reasoning, permanence and other such inherent essences also do not exist; this is the application. Finally, the text states that by this reasoning, therefore all five aggregates are impermanent, and ultimately without self; this is the conclusion.” [11] See Taisho Tripitaka, Vol. 31, p. 771, lower column. [12] See Taisho Tripitaka, Vol. 30, p. 42, upper column. [13] The original text in the Taisho Tripitaka, Vol. 32, p. 30, lower column reads as follows: “Sound is impermanent. It is produced by causal effort, with no intermediate production. For example, a clay vessel is produced by causal effort, and after being produced, it breaks and perishes. Sound is the same. Therefore sound is impermanent. This meaning is already established……Furthermore, sound is impermanent. It is produced by causal effort, with no intermediate production. If a thing is permanent, it is not produced by causal effort; for example, space is permanent and not produced by causal effort. Sound is not like this. Therefore sound is impermanent. This meaning is already established.” [14] This treatise exists in two translations: one by Master Xuanzang, titled Treatise on the Gate of Valid Cognition (Yinming Zhenglimen Lun Ben), and a second by Master Yijing, titled Treatise on the Gate of Valid Cognition (Yinming Zhenglimen Lun). A modern collated edition of Master Xuanzang’s text, the Collated Text of the Treatise on the Gate of Valid Cognition (Yinming Zhenglimen Lun Ben), was compiled by Lü Cheng and Yin Cang. The relationship between Master Xuanzang’s and Master Yijing’s translations is as follows: the original treatise included a commentary, but Master Xuanzang translated only the main text and omitted the commentary. Master Yijing set out to translate the commentary, but only completed the opening section before abandoning the work, leaving the rest untranslated. As a result, the surviving Yijing translation consists of Master Xuanzang’s work, apart from that short opening section. [15] See Huiming Publishing Group, June 2002 edition, p. 1. I don’t have the mainland Chinese edition on hand, so this note is drawn from the Taiwan edition. [16] See Mr. Shen Jianying’s translation [IV-2-51], cited in my A Brief Explanation of the Nyaya Sutra, p. 259. [17] See Mr. Liu Jinliang’s translation 4.2.50, cited in my A Brief Explanation of the Nyaya Sutra, p. 293. [18] See Taisho Tripitaka, Vol. 44, p. 109, lower column. [19] See Taisho Tripitaka, Vol. 32, p. 3, upper column. [20] The Taisho Tripitaka, Vol. 44, p. 110, contains nearly a full page of material relevant to this point. [21] See Taisho Tripitaka, Vol. 44, p. 110, upper column. [22] The Mahayana Sutra of the Earth Store Bodhisattva’s Ten Wheels (Dasheng Da Ji Dizang Shilun Jing), Vol. 10, lists two types of skillful means (upaya): worldly and transcendent. The Bodhisattva Ground Practice Sutra lists six types: compliance, making vows, distinguishing characteristics, coercion, repaying kindness, and purity. Per the Ten Wheels Sutra, this reference can be read as pointing to worldly skillful means; per the Bodhisattva Ground Practice Sutra, it can be read as pointing to compliant skillful means. [23] See A Brief Explanation of the Collection of Valid Cognition (Jiliang Lun Liejie), p. 128 (China Social Sciences Press, 1st edition, March 1982). [24] See Taisho Tripitaka, Vol. 32, p. 3, upper column. [25] See Yao Weiqun, “The Emergence and Main Development Trajectory of Buddhist Logic (Yinming) Doctrine,” Philosophy Gate, Issue 1, 2003. [26] See Selected Buddhist Philosophical Works of Lü Cheng, Vol. 4, p. 2369 (Qilu Publishing House edition). [27] See Taisho Tripitaka, Vol. 44, p. 91, lower column.