INDIAN LOGIC PART 6 KR 20/2/23
INDIAN LOGIC VERSUS WESTERN LOGIC: DIFFERENCES
If one were to ask at the outset, what is the difference between so-called
Indian logic and Western logic, the question would be
almost a non-starter. We may put a counter question: "What is Western
logic?", and thousands of conflicting answers are available
from the text books since the time of Aristotle. There is, however, a "modern"
conception of logic, and we may try to spell out the
difference between Indian conceptions of logic and this. In the broadest
terms, one may note briefly the following differences.
First, certain epistemological uses Are found to be included in the discussion
of what we wish to call "Indian logic”. The reason is
obvious. Indian logic is primarily a study of inference-patterns and
inference is clearly identified as a source of knowledge, a pramana. So
the study includes general questions regarding the nature of the derivation
of knowledge from information supplied by evidence,
which evidence may itself be another piece of knowledge.
Epistemological questions,
however, are deliberately excluded from the domain
of modern logic.
Second, to a superficial observer, discussion of the logical theories in
India would seem to be heavily burdened with psychologistic and
intuitionistic terminology -a feature which, since Frege, logicians in the
West have tried carefully to weed out from modern logical
discussions. Yet the role of psychology, how one mental event causes another
mental event or events and how one is connected with the
other, seems to be dominant in the Indian presentation. The Indians
psychologized logic, but perhaps without totally
committing the blunder into which an emphasis on psychology may often
lead. Thus,
one may claim that they psychologized logic, without
committing the fallacy of psychologism. Alternatively, the claim could be
that this was a different conception of logic, where the study of the
connections between mental events and the justification of
inferentially- acquired
knowledge-episodes not a fault (for a development
of this idea, see Matilal 1986, º4.7).
Third, historically, from the time of the Greeks, the mathematical model
played an important part in the development of logic in the
West. In India, it was grammar, rather than mathematics, that was dominant,
and logical theories were influenced by the study of
grammar. Why this was so is a question that we cannot answer. This point is
to some extent related to the second.
Last but not least, the usual distinction, so well entrenched in the Western
tradition, between deduction and induction was not to be
found in the same way in the Indian tradition. The argument patterns studied
were at best an unconscious mixture of the two processes Yet
it seemed that these mixed patterns were not very far from the way human
beings across cultural boundaries would tend in fact to argue
or rationally derive conclusions from the available data or evidence or
premises.
This last point needs to be emphasized for another reason. Almost all
modern treatments of the character of the argument pattern in
Indian logic has tended to analyze it as a form of deductive reasoning. At
best, this might have contributed to an appreciation that
forms of rationality in classical India, to the extent they are
reflected they’re
in the West. However, it has also undermined certain unique
features of the Indian argument patterns, or at least blocked our
clear understanding
and appreciation of such features. One reason for this confusion of modern
scholars is that the inferred conclusion in the Indian theory was regarded
as a piece of knowledge (derived normally from the observation of
adequate evidence),
and hence it was accorded that certainty which we usually associate with
states of knowledge. Inductive conclusions by contrast are, in today's
terms, only probable, although they may sometimes have a very high degree
of probability. The inductive element of the argument patterns studied by
the Indian philosophers has thus often been lost sight of by modern
scholars who emphasize the alleged certainty of the inferred conclusion,
and then go on to equate the Indian argument patterns invariably with
deductive or syllogistic
forms.
Let me develop this point further. Since the time of Stcherbatsky, Randle,
and others, and even still today, the typical example of the model of
inference in Indian logic is reformulated as follows:
A Wherever there is smoke, there is fire.
There is smoke on the yonder hill.
Therefore, there is fire there.
A is clearly an example of the form that we call Barbara in
traditional Aristotelian
Logic. In modern first order predicate logic, it would be
an example of an inference schema which uses universal instantiation,and
would have the form (see Quine 1961).
[image: image.png]
A is derived from, and hence regarded as transformationally
equivalent to, the following presentation of the argument, which is
the one actually used in the Indian texts:
B The hill is fire-possessing.
Because it is smoke-possessing or because of smoke. For
example, the kitchen. The idea being considered is that whoever
asserts B means
exactly A. The common reconstruction of the Indian argument pattern, B, is in
fact more often presented, not exactly as A, but as
A *: Wherever there's smoke there is fire, as in a kitchen. There is smoke
on the yonder hill Therefore, there is fire there.
The argument pattern A undergoes, however, an often unnoticed but important
metamorphosis when it is presented as A *. The citation of
the example," kitchen" underscores first of all the fact that unlike the first
proposition in A (or Aristotle's universal premise) the premise here is
unambiguous For the schema" )" [image: image.png] in A represents any
universal proposition with or without existential presupposition
(For the problems related to the existential import of the subject term of
universal propositions in Aristotle, such as "All S is P" or "All Fs are
Gs", one may consult P. F. Strawson, 1952). However, the citation of an
example in the first proposition of A * shows that it is a universal
proposition along with existential import. In other words, the subject term
now is definitely non-empty. In the above A *, and in B, the insistence on
the presence of an example should thus not be lightly dismissed as an
inessential detail. For it brings to the fore the inductive nature of the
first premise, and Thereby exposes the "weakness “of the entire argument
pattern from a purely deductive point of view. The Indian philosopher of
logic did not generally think of this feature as an indicator of the
weakness of their theory of inference (although the sceptics, as well as
the Charvaka or the Lokayata, who were opponents of the idea that inference
is a source of knowledge, severely attacked the theory just on this
ground). To counter this attack, the Indian logicians sought some way to
accord the conclusion of this type of argument almost the same
degree of certainty that is given to the conclusion of a normal deductive
argument. However, the point remains that the importance
attached to the citation of an example in the Indian schema, B, highlights
the fact that it cannot be reconstructed as a purely
deductive argument, along the lines of A.
It is a commonplace in modern logic to distinguish between truth and
validity. Roughly, validity has to do with the rules of inference in a
given theory. The conclusion may be validly derived from the premises, if
and only if the rules of inference are not violated, while
it may still be a false judgement. The soundness of the conclusion in deduction
depends also upon the adequacy or the truth of the
premises. It is now-a-days claimed that a logician's concern is with
the validity
of inference, not with its soundness wHich may depend upon
extra-logical factors (the truth of the premises). This is the ideal in formal
logic. In India, however, this distinction was not often made,
for the philosophers wanted their "logically" derived inferences or their
conclusions also to be pieces of knowledge. Thus, validity must
be combined with truth. It was allowed that some wild guesses or "invalidly"
derived inferences might happen to be true. Such "invalid"
derivation, however, would not be a proper route to knowledge. The point
just made is that Indian logic is not formal logic. This
does not imply, however, that by introducing some aspects of formal logic
in order to interpret the Indian theories we cannot gain any sort
of deeper understanding of Indian logic. In fact, we can. Hence, reductions
to Aristotelian syllogistic inference along the above lines,
and even modified use of Venn diagrams (for example, Chi 1969), have very
often been fruitful in our attempt to understand, analyze
and explain the Indian theories, as long as they are taken in context. Let
me develop this point a little further. Since Lukasiewicz, it has
been fairly well-known in the West that Aristotle's syllogistic need not be
interpreted as resting on an ontology of individuals and the
mechanism of quantification. It can be seen instead as involving four operators
"A" "E" "I" and "0", treated as primitives, holding upon
variables "u" and "v" which range over non-empty terms (which stand for
properties or sorts). This dispenses with the standard logical
subject-predicate analysis of sentences in which the subject identifies an
object and the predicate sorts (is true of) that object. Modern logic
in the Fregean tradition, on the other hand, requires, in its semantics, a
domain of individuals, to which are attached properties and
relations. Likewise, by subjecting the inference-patterns formulated and
studied in the logical texts of India to various different reductions
and translations, we might get closer to the nature of Indian logical theories,
provided we remain cautious and sensitive to the peculiarities
and differences. Venn diagrams, rules of propositional and first order
predicate
logic, some issues from the logic of classes and relations- all
these can be used in our study, if only to underline the differences
and uniqueness
of Indian logic.
As far as the inductive character of the Indian argument pattern is concerned,
it is reminiscent of J. S. Mill's theory of inference and
induction. Presently we will see how the general premise is supposed to be
supported by a positive as well as a negative example, called
the homologue (sapaksha) and heterologous (vipaksjha). This invite comparison
with Mill's Joint Method of Agreement and Difference,
which is regarded as stronger, in its power to generate certainty or high
probability, than either the Method of Agreement or that of
Difference, when employed independently. Mill, however, obtains certainty
by implicitly basing his theory upon a presumed relation of
strict and necessary causation between the observed and inferred properties,
thereby ruling out accidentally true generalizations Indian
argument patterns too were initially based upon a number of ontological
relations, causation, part-and-whole, essential identity
and so on, and this feature justified the so-called assumption of certainty
or knowledge hood of the inferred conclusions. However, the
history of inference unfolded differently in India, for there it took the form
of a search for a logical, that, inference-warranting relation,
which was called vyapti - "pervasion" or "concomitance," between the
evidence and the conclusion.
We may conclude this section with a quotation of H. N. Randle, who,
incidentally, wrote a paper on Indian logic long ago in the
journal Mind (Randle, 1924; this volume, Essay 3). In his book, Indian
Logic in the Early Schools, published by Oxford University
Press in 1930, he said: Indian formalism in fact seems to break off
abruptly at the point at which western formalism begins, perhaps by a
fortunate
instinct. (1930: 233, fn. 3) He was obviously no lover of formal logic, and
perhaps would have been surprised by today's development in the area of
formal logic in the West. However, he continued: But if formal logic is
admitted to have a certain methodological value -I think it is as good a
mental discipline to turn [Dinnaga's] wheel of the reasons as to plough the
sands of Barbara and Clearent. The study of either logic is almost a
necessary introduction to the philosophical literature of either civilization.
(ibid.) The world of philosophy and scholarship has moved a long way since the
days of Randle. Still, what he said in the concluding sentence of the above
passage is very true even today. KR IRS 20223
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