Empty Subject Terms in Buddhist Logic: Digna¯ga and his Chinese Commentators by Zhihua Yao
Abstract; The problem of empty terms is one of the focal issues in analytic philosophy. Russell’s theory of descriptions, a proposal attempting to solve this problem, attracted much attention and is considered a hallmark of the analytic tradition. Scholars of Indian and Buddhist philosophy, e.g., McDermott, Matilal, Shaw, and Perszyk, have studied discussions of empty terms in Indian and Buddhist philosophy.
His approach is subtle and complicated.
(2) by allowing exceptions for non-implicative negation; and
(3) by indicating the propositional attitude of a given proposition.
Among these, the third proved most popular.
(2) by allowing exceptions for non-implicative negation; and
(3) by indicating the propositional attitude of a given proposition.
Among these, the third proved most popular.
For instance, ‘‘no-self’’ (ana¯tman) means ‘‘the self does not exist’’; ‘‘impermanence’’ (anitya) means ‘‘permanent entities do not exist’’; ‘‘emptiness’’ (s´u¯nyata¯) means ‘‘intrinsic nature does not exist’’ (nih: svabha¯vata
For example, some [i.e., the Sa¯m: khyas argue:
While some others [i.e., the Buddhists argue:
Reason Because there is non-apprehension of it.
How do you explain this?
[Answer:] [As for the first inference,] the thesis should be formulated as ‘‘The various individuals certainly possess one and the same cause [i.e., primordial matter,’’ but they do not prove [directly the existence of] primordial matter [i.e., the subject; hence, there is no error [of proving the subject of the thesis with the reason.
[As for the second inference,] when they argue that primordial matter does not exist [because of non-apprehension], ‘‘non-apprehension’’ is a property of the imagined concept [i.e., primordial matter (kalpitasya ¯nupalabdhir dharmah
Here Digna¯ga deals with two types of propositions:
I classify these into four approaches:
(1) the method of paraphrase;
(3) the distinguishing of two types of negation;
The first two approaches have been discussed by Tillemans (1999; pp. 171–185), who suggests that they can be traced back to the above-cited passage and that they were both used by Indian Buddhist scholars such as Dharmakı¯rti and Prajn˜ a¯karagupta.
Although it entails certain difficulties, this approach can be seen in the work of authors 1 Nya¯yamukha, T1628, 1b-c: [問] 若即成立有法為有,或立為無。如有成立‘‘最勝為有,現見別物有 總類故’’; 或立‘‘為無, 不可得故’’, 其義云何?[答] 此中但立‘‘別物定有一因’’ 為宗,不立‘‘最勝’’, 故 無此失。若立‘‘為無’’, 亦假安立‘‘不可得’’ 法, 是故亦無有有法過。
The Method of Paraphrase
For instance, ‘‘the present king of France’’ is the grammatical subject in the sentence ‘‘The present king of France is bald,’’ but cannot be its logical subject; otherwise it will run into the problem of empty subject term because presently there is no king of France.
Its logical structure is revealed when paraphrased as ‘‘There is one and only one entity which has the property of being king of France, and this entity is bald,’’ or in symbolic form as ‘‘$x [(Kx & "y(Ky fi x=y)) & Bx].’’
In this Russellean translation, the subject position is occupied by what is known as a ‘‘bound variable’’ or ‘‘variable of quantification,’’ e.g., words like ‘‘something,’’ ‘‘nothing,’’ or ‘‘everything.’’
If, however, it is paraphrased as ‘‘The various individuals certainly possess one and the same cause,’’ then the logical subject is ‘‘the various individuals’’ rather than ‘‘primordial matter,’’ and the empty subject term is avoided. In his later work, Prama¯n:asamuccaya, Digna¯ga made a similar statement regarding this positive existential proposition:
[Question:] Some [i.e., the Sa¯m: khyas argue:
3 See Matilal 1985; p. 85.
How do you explain this?
[Answer:] They should formulate the thesis as ‘‘The various individuals certainly possess one and the same cause [i.e., primordial matter],’’ and the example is ‘‘just like the pieces of a thing possess one and the same cause.’’4
[Example] Just like the pieces of a thing possess one and the same cause.
Tillemans (1999; pp. 177–180) singled out other instances employing the same method to deal with empty subject terms in Dharmakı¯rti’s Prama¯n:ava¯rttika, Chapter IV, verses 141–142 and 144–145 and their commentaries by Prajn˜ a¯karagupta.
These instances, however, do not closely follow Digna¯ ga’s classical cases.
In Shentai’s commentary on the Nya¯yamukha—the only extant complete commentary on this work—he further explains how Digna¯ ga’s method of paraphrase is not only used to deal with positive existential propositions, but also negative ones.
5 Shentai first of all explains that ‘‘the various individuals’’ refers to the 23 kinds of entities, which, along with the transcendental self (a¯tman) and primordial matter (pradha¯na), constitute the 25 entities in the Sa¯m: khya doctrinal system.
Similar Example: Just like multiple slips of white sandalwood.6 S1 is only slightly different from D1; both exemplify the method of paraphrase used by Buddhist scholars to deal with such positive propositions.
4 Prama¯n:asamuccayavr: tti, Peking 5702, 128b6-8: dper na gtso bo gcig yod pa yin te / khyad par rnams la rjes su ‘gro ba mthong ba’i phyir ro zhes bya ba lta bu’o // de ni khyad par rmans kho na rgyu gcig pa can nyid du bsgrub par bya ba yin te / der yang gyo mo la sogs pa’i rgyu gcig pa nyid dper byed pa yin no //.
Similar Example: Just like the horns of a rabbit.7
On the contrary, since the Madhyamaka doctrine of emptiness and the logical system of Digna¯ga and Dharmakı¯rti were equally important for the dGe lugs pas, the dominant school in Tibetan Buddhism, the handling of empty terms was an urgent matter, since the concept of emptiness is itself usually expressed in a proposition with an empty subject term: ‘‘intrinsic nature does not exist.’’
According to that theory, things like ‘‘roundsquare’’ are nonexistent objects, which means that they are neither existences (Existenz) nor subsistences (Bestand), but their so-being (Sosein) or character can still be referred to or discussed.
Russell instead held to a robust sense of realism by insisting that ‘‘entities should not be multiplied unnecessarily,’’ and his theory of description would not work if it were not based on this sense of realism.
The Buddhist logicians Digna¯ga and Dharmakı¯rti were committed to a nominalist view with regard to ontological issues (though their views had minor differences). They held that the particulars (svalaks:an: a) perceived by
And conceptual constructions are made possible by the theory of excluding others (anya¯poha), according to which, a concept that has no real referent is established through the exclusion of other concepts.
As a result, the so-called empty term ‘‘the horns of a rabbit’’ shares the same ontological status with terms like ‘‘desk’’ in the sense that both are believed to refer to certain verbal objects (s´abda¯rtha).
As mentioned before, in his later work, Prama¯n: asamuccaya,
Katsura (1992; p. 231) and Tillemans (1999; p. 175) suggest that Digna¯ga in his later career simply adopted a more rigid attitude towards this issue and no longer admitting negative existential propositions with empty subject terms.
That they are claimed to be nonexistent in the conclusion is only because they do not have a basis in real existence (bha¯va¯nupa¯da¯ne), and hence cannot be perceived or apprehended (anupalambhana). It is not because they do not exist (abha¯va) as imagined concepts.9
In the view of Russell, however, Dharmakı¯rti has to face the so-called Meinongian paradox: To say that the existent king of France does not exist is self-contradictory, and it is an inevitable weakness in Meinong’s theory.
10 The 8 Prama¯n:ava¯rttika I, 212: s´abda¯rthah:
/ dharmo vastva¯s´raya ¯siddhir asyokto nya¯yava¯dina¯ //.
Chinese commentator Huizhao points out the same difficulty: ‘‘If it is admitted that primordial matter, i.e., a dharmin exists, then it cannot be said to be nonexistent [i.e., having nonexistence as its property (dharma)].
This is selfcontradictory.’’ 11
This is because the subject ‘‘primordial matter’’ is assumed to exist, to be something of which properties can be predicated, and it would be self-contradictory if the predicate happened to be ‘‘nonexistent.’’12
As a matter of fact, some Sarva¯ stiva¯da scholars explicitly classify things like the horns of a rabbit or the hair of a turtle as verbal existence (*s´abdasat or *na¯masat, 名有), one of the five types of existence. 13
Instead, it eliminates the problem by adopting an entirely different philosophical view.
I think this was because of the involvement of Ma¯dhyamika scholars. In that tradition, propositions with empty subject terms are not incidental cases; rather they effect its foundational doctrine of emptiness, and their problematic nature must be resolved.
The Madhyamaka nominalist or even nihilist position and Digna¯ga’s more technical theory of exclusion made the principle of conceptual subjects so influential in India and Tibet that the general attitude of Buddhists towards empty terms has been characterized as pan-fictionalism.
12 See the next section for further discussion on this issue.
13 Maha¯vibha¯s:a¯, T1545, 42a. The other four types of existence are real (*dravyasat, 實有), conventional (*prajn˜ aptisat or *sam: vr: tisat, 假有), composite (*sam: gha¯tasat or *sa¯magrı¯sat, 和合有), and reciprocal existences (*anyonyasat or *apeks:a¯sat, 相待有). For further sources on the Sarvastivada notions of existence, see Dhammajoti 2007; pp. 76–86. 14 See Matilal 1985; p. 96.
Funayama (1991) suggests that this position was associated with Jn˜ a¯nas´rı¯mitra and Ratnakı¯rti, but as we have discussed, it can actually be traced back to Dharmakı¯rti or even Digna¯ga himself. Z. Yao
Distinguishing Two Types of Negation
In the Buddhist tradition, the issue of empty terms primarily involves the subjects of negative existential propositions, so the most effective solution has entailed distinguishing two different types of negation.
Tillemans (1999; pp. 173–174) has elided this distinction and the principle of conceptual subjects, though in fact, distinguishing between types of negation is a more technically logical method that may stand independent of the principle of conceptual subjects.
We will see this in operation in the case of Huizhao, to be discussed below.
The distinction at issue is between implicative negation (paryuda¯sa, ma yin dgag) and simple or non-implicative negation (prasajya-pratis:edha, med dgag), and it can be traced back to the Grammarians, Digna¯ga and Dharmakı¯rti.
The Ma¯dhayamika scholar Bha¯vaviveka also discussed this distinction.16 Later scholars such as Prajn˜ a¯karagupta, Kamalas´ı¯la, Tsong kha pa, lCan skya ro pa’i rdo rje, A lag sha ngag dbang bstan dar, and S ´ a¯kya mchog ldan applied the distinction to solve numerous cases of empty subject terms.17
According to a definition given by the Grammarians, implicative negation ‘‘is a paryuda¯sa where the negative particle is construed [directly] with a following [substantive] word; in it affirmation is predominant and negation is subordinate.’’
19 It implicitly affirms a property while negating another, e.g., ‘‘John is unhappy’’ and ‘‘The bottle is not-red.’’
He treated this issue in his gCig du bral gyi rnam bzhag, a Madhyamaka work on various problem centered around the Sva¯tantrika Madhyamaka’s use of the ‘‘neither one nor many reason’’ (eka¯nekaviyogahetu) for emptiness.
16 See Kajiyama 1973. 17 See Tillemans 1999; p. 173. 18 Nyayamukha, T1628, 2c: 前是遮詮, 後唯止濫. It corresponds to the Prama¯n: asamuccayavr: tti,
See Kitagawa 1965; p. 242, n.498 and Katsura 1981; p. 63. 19 pradha¯natvam: vidher yatra pratis:edhe ‘pradha¯nata¯ / paryuda¯sah: sa vijn˜eyo yatrottarapadena nan˜
According to Edgerton 1986; p. 167, n.219, this verse and the verse in the following note are quoted from the Va¯kyapadı¯ya of Bhartr: hari, but they are not found in its received version. See Matilal 1968; p. 157 for his translation and discussion. Empty Subject Terms
Here, a negative predicate term (‘‘unhappy’’ or ‘‘not-red’’) is affirmed of a subject. In contrast, non-implicative negation ‘‘is prasajya-pratis:edha where the negative is construed [directly] with the verbal phrase; in it affirmation is subordinate and negation predominant.’’20 It is a simple negation that does not imply any affirmation, e.g.,
‘‘The horns of a rabbit do not exist,’’ or ‘‘The bottle is not red.’’ This type of negation corresponds to the predicate denial in Aristotelian logic, and it is the strict sense of negation in which the operation of negation takes scope over the entire predication.
A lag sha ngag dbang bstan dar referred to a popular view attributed to Tsong kha ba and his followers that uses the distinction of these types of negation to solve the problem of empty subject terms. According to this view, even if the subject of thesis is a nonexistent entity (e.g., primordial matter), the fallacy of an unestablished basis of reason can be avoided, ‘‘so long as one presents simple negations (med dgag; prasajyapratis:edha) as both the reason and property to be proved (bsgrub bya’i chos; sa¯dhyadharma); but should one present a positive phenomenon (sgrub pa; vidhi) or an implicative negation (ma yin dgag; paryuda¯sa), it will then be an unestablished reason.’’21
[In contrast], its reason expressed with a negation that implies no affirmation is a reason with nonexistent basis, because it is taking the nonexistent subject as its basis, so it is not the case that [the reason has an unestablished basis or a fallacy with regard to the subject.’’22
This solution is coincident to a general principle with regard to empty terms in Aristotelian logic, that is, ‘‘affirmation, with either positive or negative predicate terms, entail the existence of their subjects, while negations (predicate denials) do not.’’23
In contrast, statements with implicative negation such as ‘‘the horn of a rabbit is not-sharp,’’ which implies the 20 apra¯dha¯nyam: vidher yatra pratis:edhe pradha¯nata¯ / prasajya-pratis:edho ‘yam: kriyaya¯ saha yatra nan˜ // Matilal 1968; p. 157 reads ‘yam: as ‘sau. 21 A lag sha ngag dbang bstan dar, gCig du bral gyi rnam bzhag, Sect. 2, English translation from Tillemans 1999; p. 250.
The same phrase ‘‘a negation that implies no affirmation’’ (dan zhe fei biao 但遮非表) was discussed by Kuiji who explained it with the example ‘‘the self does not exist’’ (T1840, 135b). 23 Horn 1989; p. 103.
affirmation of its bluntness, are fallacious.
This approach, however, has its limitations.
In the West, there are on-going debates over whether and how the distinction between the internal or implicative negation and the external or non-implicative negation can tackle the presupposition of the existence of subject terms in semantic, classical logic, and multivalued logic.24 On the Buddhist side,
At this point, it should be emphasized that, unlike Western formal logic, Buddhist and Indian logic was both a product and a means of the debating practice among various religious and philosophical groups in ancient India.
For the Sa¯m: khyas, however, it is the most real thing.
Although the differences between various philosophical views may be apprehended through logical debates, these debates are in turn restricted by the respective philosophical positions of the specific disputants.
Some terms, e.g., ‘‘sound’’ (s´abda), may seem more real.
24 See Horn 1989; pp. 97–153.
He composed numerous commentaries on the works translated by his master.
For his view on this point, see Shen 2002; 147ff.
But it is precisely in this situation that the key to the problem lies, namely, we have to acknowledge them. Acknowledging empty terms does not entail multiplying entities as Meinong or the Sarva¯ stiva¯dins did; rather it means to acknowledge the advocator of the subject term under discussion.
Self-establishing statements are indicated by phrases such as ‘‘we accept,’’ ‘‘we admit,’’ ‘‘we,’’ and ‘‘as we said’’; while the other-refuting statements are marked by phrases such as ‘‘you accept,’’ ‘‘you believe,’’ ‘‘you,’’ and ‘‘holding.’’
Statements that follow the rule of common establishment (ubhayasiddhatva), which states that the subject of an inferential statement (paks:a-dharmin) must be established for both the proponent and the opponent in a debate, are called common inferences (gong biliang 共比量), and these are indicated by phrases like ‘‘commonly admitted.’’
They seem to fall in between the two types of intentional operators identified by Priest (2005; pp. 6–8).
According to Priest, intentional verbs with non-phrase complements are called ‘‘intentional predicates,’’ e.g., ‘‘
I believe in primordial matter
To a certain extent, this makes the issue more complicated, because it not only involves the truth or falsity, the meaningfulness or meaninglessness, of the propositions themselves, but also the intentional state of their advocators.
But in the debate practice of Buddhist logic, this propositional attitude can indicate clearly the advocator of the thesis under discussion, and, more importantly, whether the 27 The classical source for the discussion of this method is found in Kuiji’s commentary on the Nya¯yapraves´aka (T1840).
For contemporary studies, see Shen 2002; pp. 166–196, Harbsmeier 1998; pp. 392–396, and Frankenhauser 1996; pp. 88–90. Z. Yao
Example: Just like the horns of a rabbit.28
As compared to Digna¯ga’s original statement ‘‘primordial matter does not exist, because there is non-apprehension of it,’’ S3 emends the example ‘‘just like the horns of a rabbit,’’ and the phrase ‘‘that you believe in,’’ indicating the propositional attitude.
Their opponents, the Buddhists, can also talk about ‘‘the primordial matter that you believe in’’ as an indirect quotation from the Sa¯m: khyas without worrying about difficulties introduced by empty terms.
In Kuiji’s works, many inferences are marked with phrases such as ‘‘we accept’’ and ‘‘you believe.’’
But we do know that Digna¯ga attempted to develop the concept of own-subject (svadharmin) in his later work, Prama¯n:asamuccaya III.2, and that Dharmakı¯rti further contrasted it with the concept of unrelated subject (kevaladharmin) in his Prama¯n:ava¯rttika IV.136–148.
According to Tillemans, the unrelated subject ‘‘assures that the refutation presents the subject as the opponent conceives it, while the latter [i.e., svadharmin] is the proponent’s actual subject that will serve as the basis upon which will be assessed the three characteristics of the logical reason.’’29
Hence the unrelated subject was understood more in the sense of a nominal subject, and there was a tendency to combine the notions of own-subject and conceptual subjects.30 In other words, even the proponent’s own intended subject is taken to be a conceptual 28 Limenlun shuji, T1839, 82a: 宗: 汝所計最勝是無因: 不可得故喻: 猶如兔角. 29 Tillemans 1999; p. 281, n.32.
30 This probably started with Kamalas´ı¯la’s Madhayamaka¯loka. See Tillemans 1999; pp. 271–272, n.13.
thought rather than an entity accepted as real to the proponent himself. As a result, the distinction between the propositional attitude of a proponent and that of an opponent did not play an important role in dealing with the problem of empty subject terms.
According to Kuiji’s records, Xuanzang’s most important academic achievement in India was emending the ‘‘Maha¯ya¯na’’ inference of his teacher Prasenajit and establishing his own ‘‘mind-only’’ inference.
This principle of propositional attitude may have been a method popularly used by scholars at Na¯landa¯ University in the seventh century, or even earlier, since we have scattered sources that suggest Dharmapa¯ la was familiar with this method.32
But as a matter of fact, saying ‘‘‘sound is impermanent’ is true because sound is impermanent’’ is no more convincing than saying ‘‘‘sound is permanent’ is true because I believe sound is permanent.’’
Buddhist logicians were concerned with communication and commensurability between different parties involved in the debate from the very beginning, and they should be able to offer insights on the issue of incommensurability, but that must be the topic for another paper.
For the most recent study of Xuanzang’s ‘‘mind-only’’ inference, see Franco (2004), who explained this inference with great clarity, but did not treat the phrase ‘‘we accept.’’ 32 See Dharmapa¯ la’s commentary on A¯ ryadeva’s Catuh: s´ataka (T1571, 215a): ‘‘Therefore the past and the future that are accepted by both you and me do not exist independent of the present, because it is included in the [three] times that is accepted by me, like the present.’’ (由此去來共所許 法, 非離現在別有實體, 自宗所許世所攝故, 猶如現在。) Z. Yao
The techniques that the Buddhist logicians adopted, especially the distinction between two types of negation and the principle of propositional attitude, may provide their Western colleagues with even more options.
gCig du bral gyi rnam bzhag of A lag sha ngag dbang bstan dar. The Tibetan text in Tillemans 1999; pp. 258–265; The English translation by Tillemans and Lopez in Tillemans 1999; pp. 249–258. Limenlun shuji 理門論述記of Shentai, T1839.
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