what is the logic in budhist

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The history of Indian logic is usually divided into


three periods, Old Nyaaya (circa 50 B.C. ) ,


Buddhist logic (sixth century A.D.) and New Nyaaya.


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The Buddhist logic text, Nyaayaprave`sa


(Introduction to Logical Methods) , had great


influence upon Indian and Chinese Buddhism and also


among the Jains. As a pivotal work, the


Nyaayaprave`sa has received critical attention from


historians of religion, philologists, philosophers,


and logicians. As with all advances in scholarship,


there is controversy over interpretation, but in the


case of Buddhist logic, the controversy cuts to the


very heart of the issue of whether Buddhist logic is


in any recognizable contemporary sense a logic.


The received view holds that Buddhist logic bears


very close similarities to syllogistic forms and


that it can be represented and analyzed by standard


deductive techniques.(1) A much different and


opposing view has been argued by Professor Douglas


Daye in a series of papers. Daye maintains that ...


the descriptive utility of mathematical logic with


early Nyaaya texts has simply been overrated;()


that although the Nyaaya texts contain metalogical


rules for evaluating the legitimacy or


illegitimacy of arguments, the distinction between


validity and invalidity does not apply;() that


Nyaaya models are not inferences but formalistic


explanations; and that ... Buddhist logic is not


deductive, nor can it be formally valid nor is it an


inference.(4)


The cumulative effect of these claims is to


assert that Buddhist logic is not a logic at all,


at least not in any sense which is recognized by


Western philosophers. There is a radical


incompatibility between the Nyaaya methods of logic


and those of the Prior Analytics or Principia


Mathematica. Of course, there will be differences,


possibly very great differences, between any two


traditions so diverse as fourth century (B.C.)


Greece and sixth century (A.D.) India, but are we to


go so far as to say that the Nyaaya does not contain


inferences? The radical incompatibility thesis is, I


maintain, a mistake; moreover, it is a mistake which


can readily be uncovered by examining the typical


Nyaaya inference scheme. Of the notion that a Nyaaya


scheme could be a formalistic explanation


without being an inference, I shall say very little


because I do not see how anything which functions as


an explanation could not involve inferences of some


kind or other. It is important to know whether the


Nyaaya scheme is deductive or not, and if it is,


whether all of its parts are essential to the


deduction. I will demonstrate that there are two


ways of reading the Nyaaya form one which is


straightforwardly deductive and a second which is


best understood by what the American pragmatist,


C.S. Peirce, and later Norwood Hanson,


call retroduction.


To begin with, consider this representative


example from the Nyaaya(5)


1. pak.sa (thesis) Sound is imprrmanrne


. hetu (mark or Reason) - Because of its


property of being produced


P.184


. d.r.s.taanta (Exemplification)--Whatever is


produced, is impermanent


4. sapak.sa (similar case)- As with a pot, and


so forth


5. vipak.sa (dissimilar case)- As (not with the


case) of space, and so forth


Tachikawa proposes the following scheme for what


he calls the three-membered Indian syllogism(6)


6. There is property p in locus L


7. (because) there is property q (in L).


8. Wherever there is property q, there is


property p, as in locus w


Clearly, if this schema is reversed, (8) and (7)


become premises for a valid deductive inference of


(6) as the conclusion. The reverse of our example


becomes an instance of modus ponens.


. d.r.s.taanta - Whatever is created is


impermanent.


10. hetu - Sound is created.


11. pak.sa - Sound is impermanent.


Why is this instance of modus ponens a matter of


dispute? The incompatibilists point out that the


relationship between the thesis (pak.sa) and the


justification (hetu) is always expressed in the


Sanskrit ablative case and that this relationship


cannot be represented or translated as the English


therefore (or ergo). Its best translation is


because. Thus, for the incompatibilist, the


primary objection to identifying the Nyaaya scheme


as a deductive inference is the familiar one of


ordinary language philosophers who resist the


translation of expressions as `q because p into `p


) q on the grounds that the causal or explanatory


meaning of because is lost in the


truth-functional conditional.


This objection has force, but one must


distinguish between the assertion that


truth-functional connectives preserve or capture the


meaning of `q because p and the claim that


truth-functional connectives can represent a


deductive relationship between propositions within


the Nyaaya scheme. It is the latter which the


received view upholds it is the former which the


incompatibilist vehemently opposes. The issue is not


joined, because surely one can maintain that there


is a deductive inference in the inversion Nyaaya


scheme without maintaining that it captures the


meaning of or even approaches synonymy with the


original. In sum, the issue between the received


view and the incompatibilist pivots on the formers


willingness to invert the Nyaaya form and read it as


a valid deduction and the latters insistence that


the form cannot be so reversed without losing the


special relationship of the hetu. Given the merits


of both views and given the fact that both positions


are not explicit contradictories of one another,


there is a way to understand the Nyaaya scheme which


allows both sides to have their cake and eat it too.


I believe that the three-membered Nyaaya is best


understood as a retroductivc inference. A


retroduction, as it has been described by C. S.


Peirce and


P.185


Norwood Hansonl is a pattern of reasoning which


leads from some phenomenon or perception to an


explanatory hypothesis of that phenomenon. Its form


is not truth-functional nor are the relationships of


that premises completely rulegoverned. Peirce said,


It must be remembered that retroduction, although


hampered very little by logical rules, nevertheless,


is logical inference, asserting its conclusion only


problematically or conjecturally....(7)


Retroduction does have a recognizable pattern,


and indeed it is very close to the three-membered


syllogism of Indian logic. Its form, according to


Peirce, is


1. The surprizing fact Q is observed.


1. But if P were true, Q would be a matter of


course.


14. Hence, there is reason to suspect that P is


true.


As a schema, for retroduction we have


(1) q


(1) q because p


(14)p


which is isomorphic with that of the Nyaaya (that


is, pak.sa, because hetu and d.r.s.taanta; hence


there is evidence for the pak.sa). The similarity


(sapak.sa) and dissimilarity (vipak.sa) cases serve


as further evidence in support of the explanatory


justification.


The philosopher of science, Norwood Hanson,


argued that retroduction was a logic of discovery


which led to deductive-nomological explanations.


Like Peirce, Hanson pointed out that the reversal of


a retroduction was a deductive inference q, q


because p, becomes p, if p, then q, hence q. The


notion of reversal or inverting a retroduction is


not a technique or rule of formal logic, but rather


a simple psychological description of changing the


order of premises.


If the three-membered syllogism is retroduction


and if a retroduction is part of a


retroductive-deductive pair, one should expect to


find internal evidence for the presence or absence


of a deductive fragment. To return to the Nyaaya and


its commentary on this three-membered syllogism, is


there internal evidence to treat it as a


retroduction-cum-deduction? A crucial point of


philological interpretation is the function of the


ablative because and the meaning of hetu


itself. The weakness of the standard view is that it


disregards the special features of the ablative


because and translates the three-membered


syllogism as if it contained conditionals. Following


Daye, I suggest that that move is too hasty, and


that we must regard the ablative because as an


operator connecting the hetu and d.r.s.taanta to the


thesis. Since the Sanskrit ablative expresses a


relation of physical or conceptual removal,


separation, distinction, or origin, it was used to


convey the notion of causal explanation. This fact


gives prima facie evidence for interpreting it in


the sense of a reason for. Such an understanding


is reinforced by the meaning of hetu, which is the


name of the explanatory part of the three-


P.186


membered syllogism. According to Tachikawa, hetu


primarily means reason.(8) This is solid ground


for reading q because p as p is the reason for


q, p is the explanatory hypothesis for q, or even


the Peircean if p were true, q would be a matter of


course.


Beyond points of translation, one of the


strongest reasons for seeing the three-membered


syllogism of the Nyaayaprave`sa as a


retroduction-deduction is the existence of the


five-membered syllogism in the earlier Nyaaya


tradition, particularly the Nyaaya Suutra.() The


five-membered syllogism of the Nyaaya Suutra is


perfectly symmetrical between its three initial


retroductive steps and its two culminating deductive


steps


15. Thesis(pratij~naa) for example, there is


fire on the mountain.


16. Reason (hetu)- The mountain smokes.


17. Exemplification (d.r.s.taata) - Wherever


there is smoke. there is fire, as (for


example) on the hearth in the kitchen.


18. Recapitulation of the reason (upanaya) - The


mountain smokes.


1. Conclusion (nigamana) There is fire on the


mountain.


If one were to picture this pattern as an isosceles


triangle, one side would represent the retroduction


from [15] the pratij~naa reasoning through the [16]


hetu to [17] the d.r.s.taanta, and the opposing side


of the triangle would represent the deduction


beginning with [17] the d.r.s.taanta to [18] upanaya


and inferring the nigamana.


The French Indologist Rene Guenon pointed out


that after the appearance of the Nyaaya Suutra,


there were two abridged forms of the five-membered


syllogism, (10) in which either the first three


[15-17] or the last three [17-1] parts appeared


alone. Gutnon also pointed out that the latter


abridgment resembles the syllogism of Aristolle; the


former abridgment, of course, is precisely the one


found in the 6th century Nyaayaprave`sa and indeed


the same smoke-fire example occurs there also. Given


the interpretation I have offered, it is not


surprising that there should be two abridgments of


the five-membered syllogism. One abridgment captures


the retroductive move; the second captures the


deductive move. Deduction and retroduction are


inversions of one another, and they can be separated


by positioning the property-locus statement. One


abridgment reasons from the thesis statement to an


explanatory generalization; the other abridgment


deduces the thesis from the generalization. The


Buddhist logicians Mere quite emphatic about which


abridgment they favored. The Nyaaya quite explicitly


says, We say that these three statements make the


members of the syllogism and no more! (11)


Tachikwas gloss on this statement indicates that it


is an assertion that only three statements are


necessary for an inference.


We may conclude that what inference primarily


meant to the Buddhist logicians was reasoning to an


explanatory causal hypothesis; however, it would be


wrong to further conclude that they had no


appreciation of the


P.187


deductive abridgment. To them logic was a means of


bringing others to a recognition of particular


statements; it was an upaaya, a heuristic teaching


device. The retroductive abridgment of the


five-membered syllogism clearly teaches in the sence


that it brings the hearer to an awareness of a causal


or conceptual connection. The deductive abridgment


does not teach in this sense because like all


deductions its conclusion does not contain


information nor already found in the premises, Thus,


from the standpoint of an upaaya the retroductive


inference is enough, or, as the author of the


Nyaayaprave`sa put it, ...these three members make


the [retroductive] syllogism and no more.


A further point in favour of reading the Nyaaya


inference schema as a retroduction is that it makes


the remainder of the manual on logical methods,


especially the detailed sections on kinds of


fallacies, more intelligible and enljghtening. More


than two thirds of the text covers identification


and classification of fallacies, but none bear any


resemblance to the formal fallacies of deduction


such as affirming the consequent or denying the


antecedent, nor does the system resemble Western


notions of an informal fallacy. Fallacies of


irrelevance such as the ad hominem or post hoc


propter hoc call attention to the lack of support


between premises and putative conclusion. In


Buddhist logic the classification of fallacies does


not attempt to circumscribe the ways premises can be


irrelevant; on the contrary it fives criteria for


grading the strength or weakness of the explanatory


hypotheses. This is precisely what is required for


retroductive accuracy. Weak hypotheses emerge in


three circumstances (1) the hetu is unrecognized by


proponent or opponent, () the hetu is inconclusive,


or () it is contradicted. Inconclusive hetus are


those which are not supported by further evidence


from the similarity and dissimilarity cases;


contradicted hetus are those which prove the


opposite of the pak.sa. Such a contradiction is


established by deducing the opposite property-locus


assertion. A hetu can fail to be recognized, that


is, it can fail as a teaching device by not making


the auditor (or speaker) aware of the connection


between the assertion statement and its warranting


hetu. Thus, when hypotheses fail to be understood,


they engender fallacies of recognition, but when they


fail in evidential support they engender fallacies


of contradiction or inconclusivity. On the whole,


this classification of fallacies reflects a


sophisticated, but also a commonsensical, means of


evaluating hypotheses. It is open textured as


retroductive reasoning must be, and more importantly


it does not attempt (as the Western notion of fallac


does) to classify fallacious reasoning as a kind of


deductive argument gone awry.


In this paper I have attempted to enlarge the


dialogue about the nature of Buddhist logic by


arguing that it is essentially retroductive. As


philosophers and psychologists continue to


investigate the conceptual and factual aspects of


hypothesis formation, the study of Buddhist logic


will increase in importance because, unlike other


logical treatises, the Nyaayaprave`sa is an


historyically significant document about ways of


reasoning and misreasoning to an explanatory


hypothesis.


1. Daniel H. H. Ingalls, Material for the Study


of Navya-Nyaya Logic, Harvard Oriental Series, vol.


40 (Cambridge Harvard University Press, 151);


Hajime Nakamura, Buddhist Logic Expounded by Means


of Symbolic Logic, Indogku Bukkyogaku Kenkyu 7


(158) 75-5; J. F. Staal, Means of


Formalization of Indian and Western Thought, Logic,


Metlzodology and Philosophy of Science, Proceedings


of the XIIth International Congress of Philosophy,


Venice, 158; H. Kitagawa, A Note on the


Methodology in the Study of Indian Logic, Indogaku


Bukkyogaku Kenkyu 8 (160) 80-0; S. S.


Barlingay, A Modern Introduction to Indian Logic


(Delhi National Publishing House, 165) A.


Charlene S. McDermott, An Eleventh-Century Buddhist


Logic of Exists, Foundations of Language,


Supplementary Series, vol. (Dordrecht, Holland D.


Reidel, 170); B. K. Matilal, The Navya-Nyaaya


Doctrine of Negation, Harvard Oriental Series, vol.


46 (Cambridge Harvard University Press. 168) and


particularly Epistemology, Logic and Grammar in


Indian Philosophical Analysis, Janua Linguarum,


Series Minor, 111 (Mouton The Hague, 171).


. Douglas Daye, Metalogical Incompatibilities


In the Formal Description of Buddhist Logic


(Nyaaya), Notre Dame Journal of Logic 8, no.


(177) 1.


. Douglas Daye, Empirical Falsifiability and


the Frequence of Dar`sana Relevance in the Sixth


Century Buddhist Logic of Sankaravamin, Logique et


Analyse 86 (June 17) 1.


4. Douglas Daye, Comparative Issues in Buddhist


and Angle-European Formal Logics (unpublished


manuscript), p. 11.


5. Musashi Tachikawa, trans., A Sixth Century


Manual of Indian Logic (the Nyaayaprave`sa) ,


Journal of Indian Philosophy 1, no. (171) 114.


6. Ibid., p. 115, Norwood R. Hanson, Patterns of


Discovery (Cambridge Cambridge University Press,


158), pp. -105.


Is There A Logic of Discovery, Current Issues


in Philosophy of Science, edited by H. Fergland and


G. Maxwell (New York Holt-Rinehart & Winston,


161), pp. 0-5. Also Aristotle, Prior Analytics II,


5.


7. C. S. Peirce, Collected Works (Cambridge


Harvard University Press, 1), vol. 1, p. 188.


Also vol. 6, pp. 5-8.


8. Tachikawa, p. 116.


. A. B. Keith, Indian Logic and Atomism


(Oxford 11), p. 1. The author dates the Nyaaya


Suutra at 00-450 A.D.


10. Rene Guenon, Introduction generale a letude


des doctrines hindous(Paris 10), pp. 6-7.


11. Tachikawa, p. 1.


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