P.183

        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.