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