Pranam
Logic in India
PERCEPTION OF Daniel H. H. Ingalls ( ignore the period marked)
1 ORIGINS
The origins of formal logic in India lie in exegesis and debate. By
perhaps the 4th century B.C. the school of exegetes or interpreters of
Vedic texts (mfmarrzsa) began to furnish technical terms and a few basic
concepts that were to be used later in logic. Actual logical operations are
first found in the patterns of debate, called in some schools nyaya, which
crystallize about the 2nd century B.C. The opening argument of the Buddhist
Kathavatthu of this period falls into such a formal pattern. It contains a
refutation that may be summarized thus: If my first statement (a) was true,
then you should consent to my second (b). You are wrong to say that a is
true but b is not true. If b is not true, then a is not true. You are wrong
to say that a is true but b is not true This is certainly an approach to
propositional logic, as Stanislaw Schayer has pointed out. But it is
consistent with the practical nature of such texts that while logical
operations are actually performed no general rules are yet given for their
performance. These patterns of debate were often very lengthy, their form
being chosen for psychological or rhetorical effect.
According to the Jaina author Bhadrabahu (1st century B.C.) the best
pattern is one of ten members, which he lists as follows: (1) general
thesis, (2) particular thesis, (3) general reason, (4) particular reason,
(5) counter-argument, (6) denial of the counter-argument, (7) example, (8)
doubting the Logic in India example, (9) laying the doubt, (10)
conclusion. It is from such a pattern as this that the classical Indian
syllogism, likewise called nyiiya, arises.
2 THE OLD NyAYA (PRACINA-NYAYA)
The major school of Indian logic takes its name from the syllogism.
The oldest writings of the school, the Nyiiyasutras, may go back to the
time of Christ but acquired additions perhaps as late as A.D. 200. The
early period of the school is characterized by intense and beneficial
argument between orthodox (Hindu) and Buddhist logicians. Important
contributions to logic were also made by the physicists (vaise?ika) in the
early period and from the 5th century onward by the Jainas. The classical
Indian syllogism is found in the earliest Nyaya texts. It consists of five
members and shows clearly its origin from a pattern such as Bhadrabahu's
(see above).
It has become a syllogism by the expansion of the "example" to
include a statement of universal concomitance or pervasion (vyiipti). In
the following example the particular argument is directed against the
exegetes, who claimed that the word of the Veda is eternal. 1. Thesis: 2.
Reason: 3. Example: 4. Application: 5. Conclusion: Word (is) non-eternal,
Because (it possesses) the property of being produced. What possess(es} the
property of being produced (is) seen to be non-eternal, as a pot. What
possess(es) the property of not being produced (is) seen to be eternal, as
the soul. It (viz., word) (is) like this (viz., possesses the property of
being produced). Therefore, word (is) non-eternal. The original of the
above contains no finite verb. According to commentators the last three
members only are assertions. In the first two the terms are simply brought
together without anything yet being asserted of the truth or falsity of the
collocation. This syllogism contains three parts (a1?1sa) or terms. (I) The
pak?a (field), viz., the subject of thesis and conclusion. It is called a
field because the other two parts occur (vartate) in it. In the above
example pak?a = word. (2) The hetu (reason proper). In the example hetu =
the property of being produced. (3) The siidhya (that which is to be
proved). The early Nyaya argues about just what the siidhya is, e.g.,
whether in Logic in India the above example it is "the non-eternality of
word" or "word-asnon-eternal" or, what was finally agreed on, simply
"non-eternality." This analysis shows how the classical Indian syllogism
differs both from those of Aristotle, the terms of which are classes, and
from the formulas of propositional logic.
The pak?a is normally a single individual; hetu and siidhya are
regularly properties, expressible in Sanskrit by an abstract noun. The
translation of the third member as{ "F(x) ::Jx G(x)"} may refer to the same
facts in a given instance as the Indian original, but the facts are not
arranged in the Indian way. The letter F refers by an indissoluble
expression to two notions which are quite distinct to the Indian logician:
the hetu and the relation by which the hetu occurs. In the later
development of Nyaya either of these notions may be qualified independently
of the other. The Buddhist Vasubandhu (4th century A.D.) distinguishes
between inference for others (pariirthiinumiina, i.e., formal debate),
which requires the presence of all five members, and inference for oneself
(sviirthiinumiina), which requires only the first three. The syllogisms of
later textbooks are regularly given in the three[1]membered form.
Prasastapada the physicist and the Buddhist Diimaga (both c. A.D. 400)
give systematic lists of fallacies. Diimaga is the first to give a "wheel
of reasons" (hetucakra), that is, a systematic list of possible hetus. His
list is based on the distribution of the hetu with respect to the sapak?a
(objects other than the pak?a but like it in being loci of the siidhya) and
the vipak?a (objects other than the pak?a and unlike it in not being loci
of the siidhya). There are nine possible distributions, as the hetu may
occur in all, part of, or none of either of these areas. This wheel of
reasons is vastly increased by Uddyotakara (c. A.D. 600) of the orthodox
Nyaya, who gives 176 possible hetus. The increase is occasioned in the
first instance by the addition of cases where sapak?a, vipak?a, or both
simply do not exist. Thus as an example of the third type: "Everything is
eternal, because it (is) an object of knowledge." Other refinements of
Uddyotakara are to distinguish cases where the hetu occurs in all, part, or
none of the pak?a itself, where the hetu is complex, e.g., "Word (is)
non-eternal, because while it (is) nameable it (is) an object of
knowledge," etc.
The Buddhist Dharmaklrti (7th century) propounds a further division {
Many sringeris hang to this buddists who is supposed to have defeated ADI
SANKARA MANY TIMES AND HENCE Adi Sankara belongs to AD and Nopt BCE} of
hetus into: (1) Those which possess a common nature with the siidhya, e.g.,
"This is a tree, because it is a simsapii (tree)." (2) Those which are an
effect of the siidhya, e.g., "This hill possesses fire because it possesses
smoke." (3) Those which are cases of Logic in India nonperception, e.g.,
"There are no simsapas here, because we perceive no trees." It is of this
third class, which includes inferences from negative premisses and
inferences leading to negative results, that Dharmaklrti's analysis is most
elaborate. He lists 11 varieties. The Old Nyaya is summed up from an
orthodox standpoint by Vacaspati Misra, who wrote his Nyayasucinibandha in
A.D. 976. The date A.D. 841, given in many books, is due to an error in
identifying the era.
3 THE NEW NyAYA (NAVYA-NYAYA)
Udayana (11th century) and others were instrumental in altering the
Nyaya to the form which it assumes in the hands of Gailgesa (14th century
according to the evidence adduced by Dinescandra Bhattacaryya). Gailgesa
for the first time expressly refers to his school as the New Nyaya. In the
centuries which followed, other schools also contributed to logic, notably
the pluralistic Vedanta of south India (e.g., Jayanrtha and Vyasatlrtha),
the neogrammarians (e.g., Nagesa Bhatra), and the Jainas. The following
account is limited to the New Nyaya since its contributions appear to be
the most important.
The chief innovations of the New Nyaya are three: a new method of
universalization, rendered possible by the concept of limitation
(avacchedakata); the discovery of a number of laws similar to the theorems
of propositional logic; a new interest in the definition of relations and
the use of these relations in operations of considerable complexity. The
method of universalization springs from a dissatisfaction which had always
been felt with quantifiers. "All things which possess smoke possess fire"
had troubled even the old logicians and for more reasons than one. There
was the formal difficulty of binders. Mountain fire does not occur in a
kitchen nor kitchen fire on a mountain. Deeper than this was a problem of
knowledge. Even if interpreted without cross-connection, such statements
refer to facts which the Naiyayikas claim are impossible to be known except
by inference. And inference cannot serve as the basis for inference.
What we perceive, say the Naiyayikas, are the generic principles
(jati or vibhajakopadhi) that reside in the individual manifestations with
which the senses come in contact. If a universal statement is to serve as
the basis of inference, it should be phrased in accordance with the facts
presented by perception. The New Nyaya method of so phrasing Logic in
India statements appears clumsy in English translation and can best be
shown by a graduated example. For" All that possessesmoke possesses fire"
let us first substitute the equivalent expression "No case of smoke occurs
in what is not a locus of fire." And for this let us substitute again: "The
absence of smoke which occurs in the locus of a generic absence of fire is
a generic absence." The terms to be universalized are now (a) generic
absence of fire and (b) generic absence (of smoke). Absence a is said to be
such that its counterpositiveness (pratiyogita, the nature of the thing
which it denies) is limited (avacchinna) by fireness
(vahnitva[1]vacchinna-pratiyogitanirupitabhava).
That is to say, we are denying not this or that case of fire but any case
you choose of an entity inhered in by fireness. Absence b is said to be an
absence whose counterpositiveness islimited by smokeness. Notice that in
these substitutions, which sound so clumsy in English, the Sanskrit
expression is a single compound word. The literal rendering of
vahnitvavacchinna-pratiyogitanirupitabhava would be
fireness-limited-counterpositiveness-described-absence. It is this
syntactical peculiarity which allows the New Nyaya to operate with such
terms somewhat as the modern logician operates with the symbols p and q or
F and G where these symbols stand for whole propositions or functions.
Accordingly, we find in the New Nyaya definitions of conjunction,
disjunction, and implication which cover the facts referred to by sentence
connectives as well as class connectives. One must bear in mind, however,
that a translation of these definitions into logistic notation is never an
exact one.
The New Nyaya units are never precisely propositions or classes; they
are the referenda of abstract nouns. New Nyaya techniques are parallel in
many respects to those of modern logic: thus, where the western
mathematician or logician speaks of class of classes the Naiyayika speaks
of the abstract of an abstract; but parallel lines do not actually meet.
This New Nyaya method of universalizing by abstraction offers a quite
satisfactory substitute for quantification so long as the number of terms
and length of operations is not too great. Limits are imposed by human
memory and corporeal breath but these limits are fairly wide. In formal
debate Naiyayikas of the present day will use words that run to 300-400
syllables and take more than a minute each to pronounce. As
counterpositiveness is limited by an abstract determining the nature of the
entity denied, so are causeness, effectness, etc., limited by abstracts
which determine or show the precise selection of things caused or effected.
A further step is taken by the technique of relational limitors. The
counterpositiveness of absence limited by fireness is said to be limited
also by the relation contact when we deny the presence of fire in a locus
such as hearth, by a relation objectivity if we deny that fire is an object
of knowledge, by identity if we deny that fire is water, etc. In this way
the New Nyaya comes to investigate the relations between entities, and by
simplifying all complex relations into chains of relations of two terms
each, it is able to analyze situations of considerable complexity.
The New Nyaya reaches its height of analytical power with Raghunatha
SiromaI:1i (c. 1475 - c. 1550). This philosopher is as famous for the
innovations he introduced in metaphysics, where he overthrew Nyaya
tradition for a system much closer to Vedanta as he is for his logic.
Raghunatha constructs definitions of concomitance and pervasion (vyapti)
that will fit cases of compound and complex hetu and sadhya. In his
analysis of relations he comes on a discovery of the true nature of number.
It is typical of his school that he does not distinguish abstracts or
classes (e.g. pairs, triples) from the corre[1]sponding cardinal numbers
(e.g., 2, 3). He distinguishes the relation by which twoness is connected
with the components of pairs (the relation of inherence) from the relation
by which twoness is connected with the pairs as abstracts. The latter
relation, called paryapti (which may be translated literally by coining the
phrase "circumtaining relation"), corresponds to what Frege in 19th-century
Europe expressed by saying that a number belongs to a concept; it
represents in another form Frege's insight that, e.g., the number 2 should
be attached to the concept, satellite of Mars, rather than to the concrete
physical objects, Deimos and Phobos
KR IRS 5822
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