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On translating the term ''d.r.s.taanta'' in early Buddhist formal logic

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By Douglas D. Daye Philosophy East and West Volume 38, number 2 1988 April P.147-156 (C) by University of Hawaii Press


The discussion of problems in the translation of nyaaya/ vaada terms into their possible English target expressions remains relevant for philosophers because to translate such terms is to presuppose some implicit interpretations of formalistic logic.

This, in turn, takes us beyond the confines of traditional Indology to philosophical questions about comparative formal logics.

Since my task is to utilize tests for philosophical ends rather than philological or "Buddhological" ends, the text of the Nyaayaprave`sa is more than adequate for present purposes, for its many formalistic jewels have not yet been brought to the conceptual surface for studies in cross-cultural logics and philosophy.(1)

While my translations of as "thesis" and hetu as "justifier/justification"(2) are not as common as "conclusion" and "reason, " respectively, my translations of "d.r.s.taanta" as either "warrant"or"exemplification" are more controversial and require a more complex justification.

Thus, I shall consider the important Sanskrit logical term "d.r.s.taanta, " a member (avayava) of the paraarthaanumaana, the so-called "inference-for-others."(3)

My translations differ with the tradition of secondary scholarship on Buddhist vaada, where in the whole of "d.r.s.taanta" has usually been translated as "example"; an alternative translation which projects the Anglo-European syllogistic would be "major term/premise."(4)

One of the two functions of the d.r.s.taanta is to make explicit the relation of concomitance (vyaapti) , and although the word "vyaapti" is commonly found throughout Buddhist nyaaya/pramaana vaada texts, it is absent in the Sanskrit text of the Nyaayaprave`sa.

However, this concept is operative in the d.r.s.taanta member which expresses the concomitance of two properties (dharma) and its relationships with the (thesis) and hetu (justifier) members of the paraarthaanumaana (cited hereafter as "PA").


In the text, the whole d.r.s.taanta statement consists of three major components, all three of which are usually referred to as the `d.r.s.taanta'.

Since two of the three components are different in form and in function, an equivocation on the word "d.r.s.taanta" has occurred.

To justify this claim of equivocation, I distinguish two aspects of the "d.r.s.taanta": (1)

The "yatra... tatra" conditional proposition, which expresses the asymmetrical concomitance of two properties, should be distinguished from (2) the two nonpropositional (joint) appendages, which exemplify the presence or absence of concomitance of the two properties described but not illustrated in the conditional proposition, namely, 'the similar exemplification' ( and the 'dissimilar exemplification' (

To distinguish them, I hereby name the conditional expression "d.r.s.taanta" and the two exemplifying appendages "d.r.s.taanta." Quite often in the texts, both the conditional statement "yatra ...tatra" and the and exemplifications are referred to by the word "d.r.s.taanta."

Hence, as with and hetu, equivocations have occurred.(5)

In a correctly constructed paraarthaanumaana, the whole d.r.s.taanta describes an exemplified normative model of (correct) concomitance which, I would hold, constitutes an implicit rule and thus a metalogical warrant.

This warrant, then, must express (in d.r.s.taanta1) and exemplify (in d.r.s.taanta) the concomitance described in the metalogical model/rule of the triruupahetu, the three legitimate forms or patterns of the justifier/hetu property in relation to the thesis and to each of the exemplifications.

Then (and only then) can the total "d.r.s.taanta" satisfy a necessary (but not sufficient) condition for legitimizing the thesis (

Not only do the two exemplifications ( and of d.r.s.taanta serve to satisfy the rule to exemplify the concomitance in a manner commensurate with the threefold components of the triruupahetu model/rule, but they also continue the rhetorical tradition of the early Indian vaada development the historical roots of which may be found in the Nyaaya Suutra.

As a vestige of the earliest vaada arguments by analogy, this rhetorical tradition required explicit "concrete" examples, that is, exemplifications.

Furthermore, the great metalogical attention paid to the d.r.s.taanta2 ( and[[) in the nondeductive manner of earlier nyaaya argumentation leads one to suggest that the requirement of explicitly expressing d.r.s.taanta2 is historically older than the metalogical requirement of explicitly expressing ppd.r.s.taanta[[ and it relationships.


Two initial (and fairly common) responses to a nontraditional translation of ppd.r.s.taanta[[ would be (l) that my translation of "warrant" does not appropriately follow the etymology of the term "ppd.r.s.taanta[[," and/or (2) that my translation is not a "standard" one commensurate with the tradition of scholarship.

The first possible criticism is that "warrant" does not convey the metaphor of exemplification, as indicated in the etymology of ppd.r.s.taanta2[[, -> √ d.r.s.t, to see, to observe visually or to exhibit.

However, to make the normative claim that here one should translate etymologically, that "ppd.r.s.taanta1[[" "means" example, illustration, or exemplification, ignores the equivocation and may be refuted by referring to the counterexample of ""

If etymological translation is to be of first importance in translating nyaaya terms (the apparent proclivity of philologists), then we should translate "" as "wing" and "ppaabhaasa[[" as "semblance."

Of course we should not do so, for the words "" and "ppaabhaasa[[" have acquired technical meanings in vaada and require (and receive) nonetymological translations. Thus a simple claim to translate always with an eye to etymologies illustrates by counterexample the inappropriateness of trying to justify translating "d.r.s.taanta1" solely on etymological grounds rather than on functional and appropriate metalogical grounds.

I turn to the second criticism. Since about 1900, scholars have struggled with many difficult formalized and formalistic translations of the paraarthaanumaana.

To this end, scholars have used a variety of Anglo-European formal logics as target expressions;examples include the uses of syllogistic, modern-term logics, the propositional and predicate calculi plus the logic of relations.(6)

All these, at one time or another, have been projected upon the PA and then, in translation, the PA has been molded within the restrictions of the formalized target expressions.

Thus there is no more a "standard" natural-language translation for nyaaya technical terms than there is a standard, formalized ideal-language logic for the target expressions of the translated PA; unfortunately, "standard" translations are notoriously short-lived, as witnessed by such difficult terms as "vij~naana," "sa.mskaara," and "dharma" as in "dharmavicaya."

Obviously, I am not claiming that all such translations are arbitrary, nor am I claiming that all translations are equally appropriate; I am claiming that if the grounds for my "new" translation are found better, then the observation that my translation is nonstandard becomes irrelevant.

Furthermore. comparisons and variations from the vaada sources, within the possible target logics of formal translation and the interpretation of comparative metalogical considerations, are the theoretical sources of the (metalogical) evidence for selecting a new translation of any nyaaya term.

Thus it is so with "d.r.s.taanta"; it is metalogical function which, I would hold, should lead us to justify a translation.

The third criticism, my own, is that most scholars of the early Buddhist PA have discounted the metalogical function of the d.r.s.taanta1, the conditional, and have emphasized d.r.s.taanta2 the descriptive exemplifications (, of concomitance.

This latter emphasis is quite in accord with the traditional (emic) nyaaya process of justifying the legitimacy of a specific paraarthaanumana.

However, while such scholars so emphasize in d.r.s.taanta2, they usually project other non-nyaaya (non-emic) assumptions onto the paraarthaanumaana, such as formal deductive validity (which it lacks) , which would presuppose a metalogical emphasis upon d.r.s.taanta1 which is generally absent.(7)

The fourth criticism is about the translation "major term/premise," which uses the technical terms from the Anglo-European tradition.

In relation to the third criticism, this translation does focus upon the metalogical aspects rather than on the philological; however, in my opinion, it mistakenly considers the possibility of translating "d.r.s.taanta1" as if the PA actually were an untidy implicit syllogism (which it is not).

I now offer a protoargument to justify this claim, and in part VI of this article I offer an argument (something quite rare in Indology).

The technical term(s) "major term/premise" would remain a viable candidate for translation if (and only if) , in the process of evaluating and justifying the legitimacy of a PA,

(1) the metalogical emphasis was placed upon d.r.s.taanta1 rather than upon d.r.s.taanta2 (which is false) and

(2) quite explicit was the implicit claim that the major premise cum d.r.s.taanta1 is isomorphic with the antecedent of the conditional major premise within the metalogical context of either Modus Ponens or of Modus Tollens, as, for example, in the paraphrases "if P then Q, and P therefore Q," or "if P then Q, and Non-Q therefore Non-P."

However, a textual examination of the metalogical process of evaluating and justifying a PA indicates that the latter assumption of such isomorphism is false.


I now turn to the textual evidence from the Nyaayaprave`sa to justify my translation of d.r.s.taanta1 not as "example, " but rather as "warrant," and my translation of d.r.s.taanta2 as "similar exemplification"for and "dissimilar exemplification" for

Within the Buddhist metalogical tradition (emically), there are two types of d.r.s.taanta2: "concordant" (saadharmya)and"discordant" (vaidharmya).(8)

The text employs d.r.s.taanta2 in only six cases among the ten fallacies: the concordant d.r.s.taanta (saadharmya) ( and the discordant d.r.s.taanta (vaidharmya) ( .

The remaining four cases of d.r.s.taanta1 (,5 and,5) require that the statement of the conditional d.r.s.taanta1 be explicit and that the conditional expression be in proper order ( and

This completes the distribution of d.r.s.taanta1 and d.r.s.taanta2 within the ten saadharmya and vaidharmya fallacies.

The discordant conditional d.r.s.taanta1 (vaidharmya, as in the last two fallacies (, 5), is repeated as in the concordant section (

Hence, for a paraarthaanumaana d.r.s.taanta to be legitimate, one must state it explicitly in correct conditional form, expressing the proper vyaapti relationship of concomitance between the two properties, one in the hetu (justifier/justification) and one asserted to be in the thesis (


Now we shall turn to the d.r.s.taanta2, the and exemplifications.

In this century, there has been an equivocation on the word "d.r.s.taanta," and when the term "d.r.s.taanta" has been translated as "example," d.r.s.taanta2 has been the presumed referent.

The following passages are metalogical comments about d.r.s.taanta2, where the focus is upon the similar exemplification (, and, on fewer occasions, the dual/mutual absence of the saadhya/saadhana properties at issue) rather than on the conditional d.r.s.taanta1.

"A fallacious warrant is one in which the property (dharma = hetu-as-dharma-property) of the means of proof (saadhana) is not established (asidha)," as in the following.

The property-to-be-proved, permanence, resides in the exemplification, atom, but the property of the means of proof, corporeality, does not exist in the exemplification,atoms, because atomsare corporeal" (3.3.1 (1)).

This illustration of the fallacy of d.r.s.taanta2, the two exemplifications, does not focus on the conditional warrant, but focuses on

(1) the similar exemplification ( as the dual loci (dharmin) of two properties and (this instance focuses upon)

(2) the presence of the concordant property (saadhya-dharma) and the absence of the property to be demonstrated in the thesis (saadhana-dharma) in the two exemplifications.

Mr. Tachikawa notes this,(9) but he fails to recognize the informal fallacy of equivocation which has occurred here with the concordant(saadharmya) "d.r.s.taanta, " the equivocation being between "d.r.s.taanta1" as warrant and "d.r.s.taanta2" as both exemplifications.

The first three fallacies (ppaabhaasa-s[[, are about ppd.r.s.taanta2[[; the last two (,5) are about the conditional statements (yat... tat) ppd.r.s.taanta1[[.

The pattern of these three ppd.r.s.taanta2[[-s is repeated with discordant ppd.r.s.taanta[[ (vaidharmya, and,5).

While d.r.s.taanta1 denotes the conditional warrant and d.r.s.taanta2 denotes the exemplifications as property possessors (dharmins), it is important to remember that to omit d.r.s.taanta1 is to violate a necessary condition of a legitimate PA; that is, it is fallacious to omit d.r.s.taanta1 regardless of what the recipient "understands" about the "understood" concomitance of a particular PA (,5 and,5).


I now offer two translations and comments regarding d.r.s.taanta1 on the basis of which I shall justify my translation of d.r.s.taanta1 as "warrant."

Also I focus on the fallacy named "ananvaya," which denotes the absence of conditional form in a d.r.s.taanta1 statement of (positive) concomitance (3.3.1.(4) ) .(10)

"A fallacious warrant (d.r.s.taanta1) is where a statement of (positive) concomitance(which expresses) the coexistence of both the property-to-be-proved and the property of the means of proof lacks explicit illustration; hence, it is well known that (the properties of) being causally generated and impermanence reside in a pot."

Note that this fallacy (aabhaasa) refers to the absence of the explicit conditional statement of the warrant which would be: "whatever is causally generated, that is impermanent (thing).

" Thus the explicit presence of the conditional warrant is a necessary condition for a legitimate PA; what is not legitimate is the mere statement of the similar exemplification ( or the mere juxtaposition of the asserted properties.

Thus. if the statement of the d.r.s.taanta1 is a necessary condition for a legitimate PA, what, then, is its metalogical function, its logical role?

My conclusion is that it functions as and should be described as an implicit (emic/internal/ traditional Buddhist vaada) rule disguised as a universally quantified law of concomitance to which an appeal of isomorphism is made to justify the legitimacy of a specific PA.

In the other three fallacies of the "d.r.s.taanta" (, excluding the fifth

fallacy of an (improperly) reversed warrant, the justification of fallaciousness focuses not upon the conditional warrant (d.r.s.taanta1) but upon the presence and/or absence of the justifier properties (hetu) and thesis properties ( = saadhya) in the similar exemplification (

Thus the fallaciousness of the conditional warrant (d.r.s.taanta1) is quite different from the fallaciousness of the first three fallacious uses of the term "d.r.s.taanta2."

In the latter, the emphasis upon the presence or absence of the alleged concomitant properties in the two exemplifications plus the metalogical tendency to deemphasize or ignore the potential role of the d.r.s.taanta1 is a particular feature of the (traditional/emic) metalogical rules-of-the-game in justifying a type of formal argumentation in this early Buddhist text.

Hence, this focus upon the specific exemplification(s) and not on the warrant constitutes more evidence for the nondeductive nature of the PA and its emic metalogical theories and procedures. To illustrate this point and to return to the point I mentioned in part III of this article, I offer a counterargument:

(a) if, in the metalogical process of justifying a PA, there was anemphasison the warrant/d.r.s.taanta1 (which there is not) and

(b) if the canonical form of the PA was always asserted with the thesis last, preceded by the justification/hetu and the warrant in a form of isomorphic with modus ponens (which it is not), and

(c) if there were transformation rules for the rearrangement of the latter two (hetu and d.r.s.taanta1) to approximate mdous ponens (for which there are not), and

(d) if there were explicit deductively valid content-neutral inference rules to which the interpreter could then compare and to which could be matched a PA allegedly isomorphic with modus ponens and against which could be justified the alleged formal (Anglo-European) deductively at issue concerning the PA,

(e) then (and only then) would we be able to make the case for PA deductivity, and (hence) argue that a specific PA is formally deductive and, in specific cases, a sound (deductively valid) formal argument.

(f) However, we do not find a, b, c, or d actually exhibited within the asserted PA and/or within its metalogical theories or in its procedures of justifying PA argumentation.

Therefore, the PA is not formally deductive nor is there sufficient evidence that the d.r.s.taanta1 is the metalogical focus and (thus) should be translated as "major term/premise."


Furthermore, to strengthen my case and pursue these questions a bit more, let us consider the last fallacious warrant, the illicitly reversed expression of concomitance (vipariitaanvaya).

The explanation and example of a fallaciously reversed warrant (3.3.1.(5)) is as follows: "A fallacious warrant (d.r.s.taanta1) which is illicitly reversed is, for example: "whatever is impermanent, that is well known to be causally generated," when what should be said is (vaktarye) "whatever is causally generated, that is well known to be impermanent."

Note that here the preferred warrant is the reverse of the missing warrant of the previous fallacious warrant (3.3.1(4)); the latter fallacious warrant lacked "whatever is impermanent, that is causally generated," which is the fallacious instance quoted in this fifth of the fallacious warrants through concordance (saadharmya).

Thus the implicit PA model here is different from the only other fallacious warrant (d.r.s.taanta1).

It is also clear that in neither "reversed (vipariita) fallacy (3.3.1 (5) or 3.3.2 (5) ) is there any justification or evidence explicitly offered in the Nyaayaprave`sa text as to why the warrant must be explicitly expressed.

The reader is reminded that normative recommendation concerning the correct order of the conditional warrant does not constitute evidence for the issue of why the warrant is needed.

However, while the text then offers no explicit evidence for the answer to this important metalogical question, the reasons are not difficult to supply.

The correct explicit expression of the asymmetrical relation of concomitance (vyaapti) is another necessary condition of a legitimate PA.

Given the textual evidence just cited, we now turn to make the case for the translation of "warrant" for d.r.s.taanta1.

First, there is the implicit but obvious and simple normative rule that one should not utilize fallacious PA expressions; to omit the proper expression of the conditional d.r.s.taanta1 is to commit a fallacy (as in

Thus one should not omit the conditional d.r.s.taanta1 regardless of how deceptively "clear" the PA seems without it.

To do so is to commit an explicit emic fallacy; and merely to mention or simply conjoin the two properties in exposition is also to commit an emic fallacy (

Second, the correct order of the conditional d.r.s.taanta1 can be accurately described as the naming of the justifier (hetu-dharma) as the antecedent of the conditional d.r.s.taanta1 and the property-to-be-justified (the saadhya dharma of the as the consequent.

This is found in the legitimatePA,where"causal generation" (ppk.rtakatva[[) is the name of the consequent of the conditional.

The antecedent property "causal generation" is the justifier (hetu) , which is purportedly concomitant with the consequent property named in the d.r.s.taanta1; this property of impermanence (anitya) is the thesis property ( , that is, the property-to-be-justified (saadhya).

This asymmetrical relation to causally generated things and impermanent things is expressed in the conditional d.r.s.taanta1, the absence or the improper formulation of which necessitates the legitimate charge of asserting a fallacious PA.

The fifth fallacy ( of the d.r.s.taanta1 with concordance (d.r.s.taantabhaasa saadharmyanena) also illustrates the antecedent/consequent relation of the conditional described in the preceding sentences.

Again. rules of fallaciousness are normative; hence the conditional form of d.r.s.taanta1 is the implicit expression of a normative rule, as was the rule stating its fallacious omission (

Also, the warrant states the concomitance as a generic or universally quantified relation and functions as a metalogical rule.

My translation of "warrant" conveys its normative, rule-like metalogical function; "example" does not convey this normative function of d.r.s.taanta1, nor does the translation "exemplification."

Furthermore, in the last two fallacies of the d.r.s.taanta1 with concordance (, 5) , the two normative characteristics of the last two fallacies are captured in the explicitly normative term "warrant," whereas this normative quality is absent, or, at best, only very vaguely implicit in the translations "example" or "exemplification."

As noted, the latter two candidates for translating "d.r.s.taanta" are primarily descriptive and nonnormative in meaning.

Moreover, it is clear that it is the conveyance of the crucial normative meaning and rule of d.r.s.taanta1 as a universally quantified law used as a rule that provides the crucial evidence of the superior translation of "warrant" over "example" or "exemplification."

The term "exemplification" is exactly right for the and, for both descriptively do exemplify, illustrate, or exhibit the alleged concomitance of the properties, the justifier (hetu), and the thesis (

The roles of the and are illustrative but not primarily normative, whereas the role of the d.r.s.taanta1 is primarily normative.

Therefore, my translations of d.r.s.taanta1 as "warrant" and d.r.s.taanta2 as "similar/dissimilar example(s) " convey the descriptive and normative aspects more explicitly and more accurately than other translations.


Four important points have been established. First, the absence of an explicit statement of either positively or negatively expressed concomitance is fallacious.

Second, it is clear that the mere juxtaposition, however accurately named, of the two properties of the thesis ( and the justifier (hetu) is also fallacious.

Third, the correct warrant (d.r.s.taanta1) must express accurately, in a conditional statement, the legitimate concomitant properties of the thesis (paksa = ppsaadhya[[) as necessary condition, the consequent, and of the justifier (hetu) as sufficient condition of the antecedent.

These relations are to be expressed in an appropriate conditional statement such as "where there is causally generatedness, there is impermanence."

Fourth, the characteristic of the discussion of the ppd.r.s.taanta[[ supports my claim that the PA and its theories are neither deductive nor is validity an appropriate metalogical concept here.

Given my analysis of these two types of metalogical errors (ppaabhaasa[[), the absence of the conditional statement and the illicitly reversed order, I would hold that the implicit, normative, rule-like functions of the ppd.r.s.taanta[[ (both ppsaadharmya[[ and/or vaidharmya) are explicitlyexpressed in "warrant" but are significantly misleading and certainly less explicit in either "example" or "exemplification."

On the truism that one should choose the more accurate translation, I have concluded that my case for translating "ppd.r.s.taanta1[[" as "warrant" and "ppd.r.s.taanta2[[" as "similar/dissimilar example(s)" has been stated and stands justified.


This specific normative function of the rule in d.r.s.taanta1 occurs at the metalogical level; additionally, d.r.s.taanta1 as a metalogical rule instantiates the general tendency in early Buddhist nyaaya (and of course, in Jaina nyaaya, too) to develop greater degrees of such general metalogical qualities as precision, clarity, formalism, freedom from error, and formal explicitness.

These metalogical qualities are repeatedly exhibited in the large corpus of vaada texts in epistemology, ontology, and pragmatics and in the style of demonstration which remains akin to, but certainly not identical with, the various traditions of Anglo-European formal logic.

Other instances of these necessary conditions and/or rules in the metalogical theories of the Buddhist PA are found in the development of the explicit metalogical and content-free "wheel of the justifier property" (hetucakra) ; the explicit metalogical rule of the three characteristics of the justifier (triruupahetu); the generation of explicit PA models;

a series of second order "metalogical cliches"(11) such as saadhya, saadhana, vi`, anumeya,and prameya; the generalized property/possess or descriptive relation (ppdharma-dharmin[[)  ;

and the whole variegated metalogical theory of error, the fallacies (aabhaasa).

The latter theory of error is clearly normative and constitutes a rich fund of implicit metalogical rules and illustrations, not all of which have been explicit in the few explicit metalogical rules such as the three forms or patterns of the justifier (triruupahetu) or in the few nonfallacious PA models.

On reflection, the paucity of nonfallacious models in the texts and the variegated complexities of the fallacies (aabhaasa) are quite understandable and necessary in a basic teaching text, for while it is easy to offer a model example of how a legitimate PA should be, the (nearly) infinite string of possible PAs that could be generated is impossible to anticipate and list.

Thus the most efficient device for helping one evaluate a series of possible PAs is to offer a few models and to codify and illustrate an inclusive range of possible errors in the construction, defense, and justification of PAs.

Also, among the many conceptual instruments by which these relationships and presumptions were pointed outarethesecond-order, content-neutral metalogical cliches (or protovariables) of which the d.r.s.taanta2 are an instance.

Thus these PA models, metalogically explicit rules, other vaada presumptions, and the theory and illustrations of errors constitute the components of the developing foundations of PA evaluation.

As is well known, the earlier stages of protoformalism, from 200 to 1350 A.D., evolved into the mature formalistic schemas of Navya-Nyaaya (New Logic) embedded within amazing Sanskrit compounds and an extremely complex set of metalogical theories.

But what may be of great interest to contemporary philosophers/taarkikas is the declining degree to which these nonformal relations remained operative within the metalogical debates and the philosophical developments between dar`sanas, of which the uses of and equivocations on the word "d.r.s.taanta" remain illustrative instances.


1. M. Tachikawa, "A Sixth-Century Manual of Indian Logic, " Journal of Indian Philosophy 1 (1971): 111-145. All Sanskrit textual references are to Tachikawa's edition of the Nyaayaprave`sa.

2. D. D. Daye, "Remarks On Early Buddhist Proto-Formalism (Logic) and Mr.Tachikawa's Translation of the Nyaayaprave`sa, " Journal of Indian Philosophy 3 (1975): 383-398.

3. D. D. Daye, "Some Epistemologically Misleading Expressions: 'Inference' and `Anumaana,' 'Perception' and ', '" in Studies in Analytical Philosophy: In a Comparative Perspective, B. K. Matilal and J. L. Shaw, eds. Synthese Series (Reidel Publishing Co., 1985), pp. 231-252.

4. For example, S. H., A History of Indian Logic (New Delhi: Motilal Banarsidass, 1971; reprint of the 1920 edition), pp. 289-298.

5. D. D. Daye, "Remarks," pp. 383-384.

6. J. F. Staal, "Formal Structures in Indian Logic," Synthese 12 (1960): 279-286.

7. D. D. Daye, "Metalogical Remarks on the ProcrusteanTranslation oftheBuddhist Paraarthaanumaana into the Anglo-European Predicate Calculus," in Buddhist Logic and Epistemology, B. K. Matilal and R. D. Evans, eds. (The Hague, Netherlands: Reidel Publishing Co., 1986) , pp. 117-131.

8.Thetranslations"concordant"and "discordant" were kindly suggested to me on April 15, 1980, by Dr. Alex Wayman, Professor of Sanskrit, Columbia University, in a conversation with him while I was visiting at the University of California at Berkeley.

9. Tachikawa: "A Sixth-Century Manual," pp. 125, 138, n. 49; also relevant are the remarks of R. S. Y. Chi, Buddhist Formal Logic (London: Luzac and Co., 1969), p. 105.

10. S. Sanghavi, Advanced Studies in Indian Logic and Metaphysics. Indian Studies: Past and Present (Calcutta, 1961) , p. 109; Viniitadeva's Nyaayabindu Tiikaa, trans. M. Gangopadyaya. Indian Studies: Past and Present (Calcutta, 1971), pp. 227, 233-234.

11.D. D.Daye, "Metalogical Cliches (Proto-Variables) and Their Restricted Substitution in Sixth Century Buddhist Logic," Notre Dame Journal of Formal Logic 20, no. 3 (July 1979): 549-558.