What is the "logic" in Buddhist logic? By R. Lance Factor

The history of Indian logic is usually divided into
        three periods, Old Nyaaya (circa 250 B.C. ) ,
        Buddhist logic (sixth century A.D.) and New Nyaaya.
        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";(2)
        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;(3) 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

            2. hetu (mark or Reason) - Because of its
               property of being produced

                                P.184


            3. 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.

            9. 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 former's
        willingness to invert the Nyaaya form and read it as
        a valid deduction and the latter's 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:

            12. The surprizing fact Q is observed.

            13. 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:

            (12') q
            (13') 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.(9) 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.

            19. 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 [17-19] 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)
        Tachikwa's 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, (2) the hetu is inconclusive,
        or (3) 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.

                                P.188

        NOTES

            1. Daniel H. H. Ingalls, Material for the Study
        of Navya-Nyaya Logic, Harvard Oriental Series, vol.
        40 (Cambridge: Harvard University Press, 1951);
        Hajime Nakamura, "Buddhist Logic Expounded by Means
        of Symbolic Logic," Indogku Bukkyogaku Kenkyu 7
        (1958) : 375-395; 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, 1958; H. Kitagawa, "A Note on the
        Methodology in the Study of Indian Logic," Indogaku
        Bukkyogaku Kenkyu 8 (1960) : 380-390; S. S.
        Barlingay, A Modern Introduction to Indian Logic
        (Delhi: National Publishing House, 1965) : A.
        Charlene S. McDermott, An Eleventh-Century Buddhist
        Logic of "Exists, " Foundations of Language,
        Supplementary Series, vol. 2 (Dordrecht, Holland: D.
        Reidel, 1970); B. K. Matilal, The Navya-Nyaaya
        Doctrine of Negation, Harvard Oriental Series, vol.
        46 (Cambridge: Harvard University Press. 1968): and
        particularly Epistemology, Logic and Grammar in
        Indian Philosophical Analysis, Janua Linguarum,
        Series Minor, 111 (Mouton: The Hague, 1971).

            2. Douglas Daye, "Metalogical Incompatibilities
        In the Formal Description of Buddhist Logic
        (Nyaaya)," Notre Dame Journal of Logic 28, no. 2
        (1977): 231.

            3. Douglas Daye, "Empirical Falsifiability and
        the Frequence of Dar`sana Relevance in the Sixth
        Century Buddhist Logic of Sankaravamin," Logique et
        Analyse 86 (June 1979): 221.

            4. Douglas Daye, Comparative Issues in Buddhist
        and Angle-European Formal Logics (unpublished
        manuscript), p. 121.

            5. Musashi Tachikawa, trans., "A Sixth Century
        Manual of Indian Logic (the Nyaayaprave`sa) ,"
        Journal of Indian Philosophy 1, no. 2 (1971): 114.

            6. Ibid., p. 115, Norwood R. Hanson, Patterns of
        Discovery (Cambridge: Cambridge University Press,
        1958), pp. 93-105.

            "Is There A Logic of Discovery," Current Issues
        in Philosophy of Science, edited by H. Fergland and
        G. Maxwell (New York: Holt-Rinehart & Winston,
        1961), pp. 20-35. Also Aristotle, Prior Analytics II,
        25.

            7. C. S. Peirce, Collected Works (Cambridge:
        Harvard University Press, 1933), vol. 1, p. 188.
        Also vol. 6, pp. 522-28.

            8. Tachikawa, p. 116.

            9. A. B. Keith, Indian Logic and Atomism
        (Oxford: 1921), p. 21. The author dates the Nyaaya
        Suutra at 200-450 A.D.

            10. Rene Guenon, Introduction generale a l'etude
        des doctrines hindous(Paris: 1930), pp. 226-227.

            11. Tachikawa, p. 122.

Source

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