INTERNATIONAL CONFERENCE ON
HETUVIDY¼ (BUDDHIST LOGIC)
ASSOCIATION OF THE HISTORY OF CHINESE LOGIC
CHINESE
C O N T E N T S
Introduction
1. The History of Indian Logic
2. eva in DharmakÌrti
3. NËgËrjuna’s catuÛkoÖi
4. Formal Languages of Science
and the Power of Theory
Bibliography
Introduction
There are at least three ways of formalizing a system of logic that is not expressed in a formal or artificial language (such as one of the systems of modern logic), but in a natural language (such as Sanskrit, Chinese or Tibetan). The first may be called the logical method. It is:
not to state the Indian authors’ words into symbols, but express what they meant to say – i.e., what they would have said if they had used precisely the same language as we do (R.S.Y. Chi 1969: 15).
Harbsmeier (1998: 371) quotes this passage and characterizes it by its use of mathematical logic without raising the question which system is referred to by the phrase “precisely the same language as we do.”
I take it that Chi means by “language”: “artificial language” and by “we”: “modern logicians.” Although there is no single logic that can be called “modern,” it is an appropriate phrase. I would use it in the same vague and general sense that we use the phrase “modern science” about which Joseph Needham has written:
To write the history of science we have to take modern science as our yardstick – that is the only thing we can do – but modern science will change, and the end is not yet (Needham 1976: xxix).
We must accept modern logic as our yardstick. But before we apply it we must make sure what the authors we study say.
Harbsmeier himself uses a different method to which he refers as philo-logical. He distinguishes his method from “proto-logical adumbrations of modern logical concepts.” Instead, it offers:
A conceptual scheme in its own right. A conceptual scheme not to be reduced to modern logic, but to be more fully understood by comparison with modern theories (Harbsmeier ibid.).
In the present article I will advocate the use a third method which I shall call formal. I regard it as preparatory to the other two. The reason is that it stays as close as possible to the original form of the logical text we are studying and seeking to clarify. It turns out to be presupposed by both the logical method, which involves a certain amount of translation of that original form, and the philo-logical, which involves not only translations but introduces one or more conceptual schemes.
Before I gave it a name, I practised the formal method in my early studies of Indian Nyâya and Navya-nyâya (Staal 1960, 1961, 1962a, reprinted in 1988). But strangely enough, I did not use that method in dealing with Dharmakîrti (Staal 1962b, also reprinted in 1988). I propose to clarify the matter and in so doing illustrate what I mean by formal. Provisionally I would describe it as follows:
The formal approach to the study of a logical expression formulated in a natural language, such as Sanskrit, Chinese or Tibetan, is to concentrate on the form of the expressions.
My paper consists of five parts. The first provides a brief sketch of the history of Indian Logic to which Buddhist Logic belongs. The second deals with some famous expressions from DharmakÌrti using the particle eva. The third comments on the even more celebrated catuÛkoÖi due to NËgËrjuna and developed in his school. The fourth deals with the role of artificial or formal languages in science, of which logic is or has become a part, and draws some conclusions with regard to theory formation and the future.
1. The History of Indian Logic
Two weeks before participating in the Conference on HetuvidyË, I took part in a series of events on the history of science in Europe and
This had been introduced two centuries earlier in
I shall omit in this paper the history of Jaina logic, not because it is unimportant but in other to arrive at a simple picture. Keeping that simplification in mind, we may describe the history of Indian logic as a sequence of three large steps:
A. Old NyËya
B. Buddhist Logic
C. New NyËya.
Putting it in a more historical perspective we may describe it thus:
A. The
B. The Mediaeval
C. The
That historical perspective was adopted by an early pioneer, Satis Chandra Vidyabhusana, in his History of Indian Logic (Calcutta 1921; reprinted in Delhi). This book is outdated in many respects, but its main strengths are its clear distinction between the three periods and the uses it makes of Tibetan sources and not only of the Sanskrit.
One of the brilliant papers during the Masterclass in
Present day scholarship, dominated by increased specialization because of the increase in knowledge, is split into departments that are no longer in touch with each other. While early pioneers such as Vidyabhusana or Stcherbatsky were still able to control the entire field of Indian logic, Sanskrit and Buddhist Studies have at present almost totally diverged. As a result, there are very few scholars or scientists who are at home in both, let alone have mastered both. Alas! I am not one of them because I don’t know Chinese or Tibetan and have a hard time keeping up with Sanskrit.
I have made a long detour before I come to our HetuvidyË meeting which took place less than two weeks after the
At the HetuvidyË meeting, some participants seemed to believe that Buddhist Logic existed on its own, in a vacuum so to speak, without any connection with the earlier and later NyËya logics and without being part of Indian logic of which, as a matter of historical fact, it is a part.
To summarize. If we omit the Jaina logic, the history of Indian logic may be divided into three periods: the ancient period of the Old NyËya, the medieval period of Buddhist Logic, and the modern period of the New NyËya.
Fortunately logic is a universal discipline because it explains the fortunate fact that humans are in a position to discuss together. That is not an uncontroversial matter – many philosophers have claimed that different civilizations possess different logics. Such a claim is based on ignorance and often combined with the belief that “our logic is best.” Since I happen to have written a book about Universals (Staal 1988), I may be excused for not discussing it any further on the present occasion. However, I should provide at least one illustration to demonstrate that HetuvidyË is part of Indian logic.
The illustration I have in mind is an obvious one: the term hetu itself. It occurs in the same meaning in the NyËyasÍtra (1.1.34) where it is defined as that which “concludes the conclusion” or “infers what is to be inferred” (sËdhya-sËdhanam). The commentator VËtsyËyana illustrates it with the inference: “sound is non-eternal (the sËdhya) because it has the character of being produced (the hetu)” (utpattidharmakatvËd anityaÒ ÚabdaÒ). The use of the term hetu in Buddhist logic is obviously a development from the early logic of the NyËyasÍtra.
Before discussing the formalization of logical expressions, a few facts about the notion of “formal” should be mentioned. Indian logicians never created a fully formal or artificial language such as PËÙini and other Indic grammarians had done (Staal 1995, 2006). But they were concerned, as many philosophers were, about being exact and precise. Many of their expressions may be described as “formal” in that more general sense. It applies in particular to expositions of the two valid means of knowledge (pramËÙa) which all Indic philosophies agreed in accepting: perception (pratyakÛa) and inference (anumËna).
The NyËyasÍtra goes a step further in the sÍtra I just quoted, 1.1.34. It declares there that the hetu concludes the conclusion or infers what is to be inferred “through similarity” (sËdharmyËt) with a (similar) instance. In the next sÍtra (1.1.35) it adds: “through dissimilarity” (vaidharmyËt), that is, dissimilarity with a dissimilar instance.
Similarity and dissimilarity may have something to do with comparison, but they go beyond comparison as Bochenski (1956: 498 sq.) has explained. But he cannot be right when he construes the NyËyasÍtra scheme at the same time as a “rhetorical analogy.” In the NyËyasÍtra, proof is not based on instances or examples, but on similarity and dissimilarity which are general and formal properties. Bochenski’s confusion may be due to the fact that he relies on Walter Ruben’s 1928 translation. The correct translation is found in Ganganatha Jha 1939.
Buddhist Logic recognizes two conditions that seem to correspond to the similarity and dissimilarity properties of the Old NyËya. Somehow they came to be referred to as three conditions. Perhaps it has something to do with the transmission of DignËga’s work which has been largely lost in Sanskrit; for it is he who seems to have introduced these three conditions that came to be known as the TrairÍpya or “Doctrine of Three Conditions.” The threesome occurs in the TarkaÚËstra (Tucci 1929, 1930) as I mentioned in 1962b (634 = 1988: 93, note 1). During the HetuvidyË conference in
Whatever the differences or apparent differences between the early NyËya and Buddhist Logic, there is an important point that should be kept in mind. All parties agreed that it was necessary to adopt the same general notion of logical inference and express it in as exact and precise terms as could be found. Only a universally accepted logic would enable philosophers to effectively argue with and refute each other. Such cases are well attested in the history of Indic philosophies. In the most striking cases, the defeated opponent accepted the philosophy of the victor by whom he had been defeated in a public debate.
2. eva in DharmakÌrti
DharmakÌrti’s use of eva in the discussion of inference occurs in the Nyāyabindu (ed. Stcherbatsky 1918, 1970: 18-9; Candrasekhara Sastri 1954: 22-3; Malvania 1955, 1971: II.5):
(1) liÔgasyËnumeye sattvam eva
(2) sapakÛa eva sattvam
(3) asapakÛe cËsattvam eva
DharmakÌrti’s emphasis on sattvam “existence” and his reference to his own work as sattvānumâna, “inference based on existence,” supplements the inference based on non-existence that had been used by other Buddhist thinkers to argue for momentariness.
In my 1962 formalization of DharmakÌrti’s expressions I used a mixture of formal and logical methods. I wrote that I formalized the threesome in a manner “which preserves as far as possible the structure of the Sanskrit expressions”; and I introduced, for that reason, the restricted variables I had used before in the study of Indic expressions (in NyËya as well as Buddhist logic) and that are related to the lambda notation introduced into modern logic by Alonzo Church (1941). Restricted variables are close in form to the Sanskrit expressions. I was successful to some extent, because I gave the reader who is familiar with modern logic an idea of the formal structure of these expressions. But I was not consistent because what I presented was at the same time a logical argument that was intended to show that DharmakÌrti’s expressions (2) and (3) were contrapositives. That was due to the fact that the topic of my paper was Contraposition. My sequences of definitions and expressions suggested, that DharmakÌrti did not or did not always realize that he was dealing with contraposition though it was clear that his commentator Dharmottara did. That difference was not perceived by Stcherbatsky, Bochenski or Frauwallner. The scholar who had come closest to seeing it was Randle (1930: 183).
I shall now attempt to provide a formal analysis of the Sanskrit particle eva and its position in DharmakÌrti’s logic. We must begin with a grammatical or linguistic account. According to Sanskrit usage and its traditional interpretations, eva expresses emphasis or stress: avadhâraÙa. It is generally placed after the expression which it emphasizes and often excludes everything else.
Mere emphasis is used in (4) and probably in (5):
(4) darÚanenaiva bhavatÌnËÑ puraskÎto’smi “the very sight of the ladies honours me” (KËlidËsa’s ÉakuntalË; it is not excluded that their smiles would also honour me);
(5) aham eva kariÛyËmi “I myself will do it” (PaÕcatantra).
Exclusion of everything else is clear in (6) and fully explicit in (7):
(6) prajËpatir hË va idam
(7) tvam eva yantË nËnyo’sti pÎthivyËm “you only are the charioteer, no one else on earth” (MahËbhËrata).
Dharmakîrti himself gives in his PramāÙavārttikā Svopajõavrtti two examples of the use of eva from non-logical Sanskrit. They raise several problems which have been discussed by Kajiyama (1973:162 = 1989:156) and Gillon and Hayes (1991: 31-2; cf.) but need not concern us here.
The particle eva may be translated into English as “only,” “just,” “precisely,” “exclusively,” etc., or by special phrases such as “all by himself,” “myself” or “very.” The generally preceding phrases on which it operates need not precede immediately: prajËpati in (6) is separated from eka eva by four other words.
The preceding or special phrases in our four examples are, respectively:
darÚanena (“by your sight”), aham (“I”), prajËpati and tvam (“you”). All of
these are nouns or Noun Phrases (NP). These are either nouns or larger
expressions that contain nouns and function as nouns. The Noun Phrases “I
myself” functions like the pronoun “I” and the name “PrajËpati” is a
compound Noun Phrase meaning “lord of living beings.” The particle eva
may also occur after a Verb Phrase (VP), under similar conditions, not
exemplified here.
Unfortunately, I cannot judge the Chinese equivalent of Sanskrit eva or English only in similar contexts, but it would be worth to find out whether earlier logicians of the Mohist tradition used that term. I find “only” used in the English translation by A. C. Graham (1978: 337) of the third of four stages in a Mohist theory of a description: “If a man’s blackness is only partial the standard fits him only partially.”
If I were to try to provide a general description in linguistic terms of eva, only and the Mohist equivalent in these cases and in many others we might say that it is used in connection with a Noun Phrase (NP) or Verb Phrase (VP):
(8) NP/VP-eva.
In English it often means:
(9) “only NP/VP” or “only NP/VP and nothing else.”
I shall now try to formalize DharmakÌrti’s expressions (1) – (3) adopting the formal approach. First of all, we need some letter variables to refer to the basic terminology. The term liÔga or “sign” refers to the hetu or “reason” which I shall call h. It is explicitly mentioned only in (1), but understood in (2) and (3). The term anumeya, “conclusion” or “thing-to-be-inferred” is more often called sËdhya and I shall refer to is as s. The term pakÛa is basically simple although it has been obscured by ambiguities (Staal 1973; other difficulties are alluded to by Matilal 1968, p.531, note 1). It may be translated as “instance” or “locus.” We should avoid “subject” which introduces an Aristotelian category that is as misleading in the study of Indian logic as is the expression “syllogism.” I refer to the locus as p, and to sapakÛa, “similar instance” or “similar locus,” as p*. Sattvam means “existence” and I shall express it as a relational predicate A. It always presupposes a locus: A(h, p) means “h is existent in p” or “h is present in p.” I shall use “~” as a symbol for negation or, when it precedes a term, for dissimilarity, e.g.,: “~ p*” means “dissimilar instance” or “dissimilar locus.” I refer to eva as µ. (1) – (3) may now be formalized as:
(10) A(h, p) µ
(11) A(h, p* µ)
(12) ~ A(h, ~p*) µ.
What do these three expressions mean and what does the symbol µ contribute to that meaning?
(10). I believe that eva is used in (1) simply for emphasis and not “to exclude everything else.” It means, therefore, A(h,p) “h is present in p.” If it meant “h is present in p only and nowhere else”, it would contradict the next expression, (11), which asserts that h is present in p* , another instance. The µ should therefore be omitted and (10) should simply be replaced by:
(13) A(h, p).
At this point we should recall our discussion of the early NyËya and Buddhist Logic at the end of the previous section. We took note of a
difference or apparent difference between the two: the latter refers to three conditions, of which the second and third correspond to the former’s two. Did Buddhist logicians imagine three where there were only two? If that were so, it might be explained by the “emptiness” of (10): it is not a condition, it states the problem. But did the famous TrairÍpya or “Doctrine of Three Necessary Conditions” not come from DignËga? Whether it did or not, he had original views on it. He considered nine possibilities but accepted only two as valid and these two correspond to (11) and (12). The name TrairÍpya, which seems to illuminate much of the landscape of HetuvidyË, and seems to have passed on as “three” to PraÚastapËda and thereby the schools of the Old NyËya and VaiÚeÛika, is therefore confusing. I must leave it to others to disentangle its much discussed history.
In (11), no confusion is possible. The µ occurs after p*, that is, after similar instances as it does in (2). It means therefore: “A is present in p* and only in p*” or” “A is present in p* and nowhere else.” (11), therefore, is correct as is. It includes A(h, p) because p is similar to p* .
(12) is more subtle because µ occurs after the entire expression as does eva in the Sanskrit of (3). It means therefore: “A is not present in ~p* and only not present in ~p*” or: “A is not present in ~p* and not not-present anywhere else” which is generally taken to mean: “A is not present in ~p* and present everywhere else.” That is correct because A is present in p and p* both. (12), therefore, is correct as is.
What have we gained by this? We have used µ formalization to illustrate the use of eva to express what in modern logic would, in general, be expressed by quantification. Without formalization, it was put in clear terms, perhaps for the first time, by Yuiji Kajiyama : “DharmakÌrti demonstrates a kind of quantification theory of the affirmative proposition” (Kajiyama 1973:162 = 1989:156).
The only general historian of logic (as opposed to historian of Indian or Buddhist logic), who understood DharmakÌrti’s logical use of eva, was I.M. Bochenski (1956: 505-6). He did not see that the eva in DharmakÌrti’s first statement was empty, but he had already written a book on Greek logic (Bochenski 1951) and was the first to make Indian logic part of the general history of logic. (He did not include Chinese logic, which had been included in a philosophical encyclopedia by A.C.Graham in 1967, long before he devoted a monograph to Mohist logic: Graham 1978.)
Bochenski was an excellent “modern” logician in his own right, a Dominican priest as indicated by the letters “O.P.” (Tymieniecka 1965), Rector of the
3. NËgËrjuna’s catuÛkoÖi
There exists a vast scientific literature about the catuÛkoÖi formulated by
NËgËrjuna long before DharmakÌrti. Ruegg provided in 1977 a magisterial survey but it should be updated because during the last quarter century there has been a great deal of research – not only repetitive but also new. There are good illustrations of my formal method in some of these works. I shall confine my discussion to some widely accepted facts and make specific use of only one more recent work: Tillemans 1999.
As for NËgËrjuna’s own expressions, they are so well-known I need hardly quote them – but here they are:
sarvam tathyaÑ na vË tathyaÑ
tathyaÑ cËtathyam eva ca
naivËtathyaÑ naiva tathyam
etad buddhËnuÚËsanam
“All is just so, or not just so,
both just so and not just so,
neither just so nor not just so:
this is the graded teaching of the Buddhas”
(transl. Ruegg, p.6, who added “graded” to
anuÚËsanam, “teaching”).
NËgËrjuna’s disciple ¼ryadeva formulated the catuÛkoÖi as follows:
sad asat sadasac ceti
sadasan neti ca kramaÒ
eÛa prayojyo vidvadbhir
ekatvËdiÛu nityaÚaÒ
“Being, non-being, [both] being and non-being,
neither being [nor] non-being:
such is the method that the wise
should always use with regard to identity
and all other [theses].” (transl. Tillemans, p.189).
Note that ¼ryadeva’s krama, “order” or “grade,” not translated by Tillemans, may be taken to justify Ruegg’s addition of “graded.”
Tillemans begins his interpretation as follows: “Clearly, the conjunction of these four negations would make a Western logician dizzy, since, at first glance, the MËdhyamaka offers us the following four statements:
(13) ~P
~~P
~(P & ~P)
~(~P & ~~P). ”
I quote these four statements because they happen to illustrate almost precisely what I mean by formal method: they confine themselves to what the expressions show “at first glance.” I say “almost” because what we read at first glance really is:
(14) P
~P
P & ~P
~(P & ~P).
After ten pages of discussion, Tillemans offers what he regards as “a translation into formal logic,” that is, what would seem to be the result of applying the logical method:
(15) ~(Ex)Fx
~(Ex)~Fx
~(Ex)(Fx & ~Fx)
~(Ex)(~Fx & ~~Fx).
Tillemans has greatly contributed to our understanding of Buddhist logic and it is not my purpose to discuss whether (15) is or is not a result of applying the logical method. I use it as an example of an interpretation in terms of concepts (such as the existential quantifier E and the concept of predicate or function F) that do not occur in (14). Unlike (14), it makes NËgËrjuna mean something that is very different from what he says.
To mean something different from what one says is not uncommon in philosophy but hardly acceptable in logic – any logic. It is part of the concept of “logic” that a logician tries to say as clearly as he can what he means. In logic, as in philosophy, clarity is not enough; but lack of clarity is fatal. If NËgËrjuna means something that is different from what he says, it may not detract from his status as a philosopher, but it affects the question whether he belongs to the Indic tradition of logic. As for DharmakÌrti, he tries to say as clearly as he can what he means to say. He is a logician in the constitutive meaning of the term; and in addition, original and brilliant.
There might be a way out for NËgËrjuna and his school: it may adopt what has been called “an alternative logic.” In order to explain it, let us look at the context of Tillemans’ discussion which is entitled: “Is Buddhist Logic Non-Classical or Deviant?” I am not concerned with the difference between these two types of logic, but they are alternative logics. They are characterized by the fact that they possess a particular “field of application” from which they derive their justification (as Tillemans acknowledges: p. 191). If NË