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

·期刊原文
On translating the term d.r.s.taanta in early Buddhist formal logic

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

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P.147

I. INTRODUCTION

The discussion of problems in the translation of
nyaaya/pramaa.na 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 pak.sa 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 pramaa.na 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 pak.sa (thesis) and hetu
(justifier) members of the paraarthaanumaana (cited
hereafter as "PA").

II. THE D.R.S.TAANTA

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'
(sapak.sa) and the 'dissimilar exemplification'
(vipak.sa).

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To distinguish them, I hereby name the
conditional expression "d.r.s.taanta1" and the two
exemplifying appendages "d.r.s.taanta2." Quite often
in the texts, both the conditional statement "yatra
... tatra" and the sapak.sa and vipak.sa
exemplifications are referred to by the word
"d.r.s.taanta." Hence, as with pak.sa 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.taanta2) 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 (pak.sa).

Not only do the two exemplifications (sapak.sa
and vipak.sa) of d.r.s.taanta2 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 pramaa.na
vaada development the historical roots of which may
be found in the Nyaaya Suutra. As a vestige of the
earliest pramaa.na 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 (sapak.sa and vipak.sa) 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 d.r.s.taanta2 and it relationships.

III. FOUR CRITICISMS

Two initial (and fairly common) responses to a
nontraditional translation of d.r.s.taanta would be
(l) that my translation of "warrant" does not
appropriately follow the etymology of the term
"d.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 d.r.s.taanta2, ->
ЎФ 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
"d.r.s.taanta1" "means" example, illustration, or
exemplification, ignores the equivocation and may be
refuted by referring to the counterexample of
"pak.sa." If etymological translation is to be of
first importance in translating nyaaya terms (the
apparent proclivity of philologists), then we should
translate "pak.sa" as "wing" and "aabhaasa" as
"semblance." Of course we should not do so, for the
words "pak.sa" and "aabhaasa" have acquired
technical meanings in pramaa.na vaada and require
(and receive) nonetymological translations. Thus a
simple claim to translate always

P.149

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 pramaa.na 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 (sapak.sa, vipak.sa) 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

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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.

IV. TEXTUAL EVIDENCE

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 sapak.sa and
"dissimilar exemplification" for vipak.sa.

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) (3.3.3.1.-3)
and the discordant d.r.s.taanta (vaidharmya)
(3.3.2.1-3) . The remaining four cases of
d.r.s.taanta1 (3.3.1.4,5 and 3.3.2.4,5) require that
the statement of the conditional d.r.s.taanta1 be
explicit and that the conditional expression be in
proper order (3.3.1.5 and 3.3.2.5). 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 3.3.2.1-3), as in the last two fallacies
(3.3.2.4, 5), is repeated as in the concordant
section (3.3.1.1-5). Hence, for a paraarthaanumaana
d.r.s.taanta1 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 (pak.sa).

V. DRSTAANTA2

Now we shall turn to the d.r.s.taanta2, the sapak.sa
and vipak.sa 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 (sapak.sa,
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

P.151

exemplification, atoms, because atoms are
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
(sapak.sa) 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 (aabhaasa-s,
3.3.1.1-3) are about d.r.s.taanta2; the last two
(3.3.1.4,5) are about the conditional statements
(yat... tat) d.r.s.taanta1. The pattern of these
three d.r.s.taanta2-s is repeated with discordant
d.r.s.taanta (vaidharmya, 3.3.2.1-3 and 3.3.2.4,5).
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
(3.3.1.4,5 and 3.3.2.4,5).

VI. D.R.S.TAANTA1

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 (sapak.sa) 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 pramaa.na 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" (3.3.1.1-3), excluding the fifth

P.152

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 (pak.sa = saadhya) in
the similar exemplification (sapak.sa).

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 ofjustifying
a PA, there was an emphasis on 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."

VII. THE FALLACY OF A REVERSED WARRANT (VIPARIITANVAYA)

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

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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
3.3.1.4-5). 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 (3.3.1.4).

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
pak.sa) as the consequent. This is found in the
legitimate PA, where "causal generation"
(k.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
(pak.sa) , 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 (3.3.1.5) 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 (3.3.1.4). 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

P.154

does the translation "exemplification." Furthermore,
in the last two fallacies of the d.r.s.taanta1 with
concordance (3.3.1.4, 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 sapak.sa and vipak.sa, for
both descriptively do exemplify, illustrate, or
exhibit the alleged concomitance of the properties,
the justifier (hetu), and the thesis (pak.sa). The
roles of the sapak.sa and vipak.sa 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.

VIII. SUMMARY

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 (pak.sa) 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 = saadhya) 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 d.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
(aabhaasa), the absence of the conditional statement
and the illicitly reversed order, I would hold that
the implicit, normative, rule-like functions of the
d.r.s.taanta (both saadharmya and/or vaidharmya) are
explicitly expressed 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 "d.r.s.taanta1" as "warrant" and
"d.r.s.taanta2" as "similar/dissimilar example(s)"
has been stated and stands justified.

P.155

IX. EXTENDED METALOGICAL COMMENTS

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 pramaa.na 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`se.sa,
anumeya, and prameya; the generalized
property/possessor descriptive relation
(dharma-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
out are the second-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 pramaa.na 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

P.156

between dar`sanas, of which the uses of and
equivocations on the word "d.r.s.taanta" remain
illustrative instances.

NOTES

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 'Pratyak.sa, '" 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. Vidhyaabhuu.sa.na, 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
Procrustean Translation of the Buddhist
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. The translations "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.