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Personal Details
Principal Investigator A. Raghuramaraju, Department of
Philosophy, University of
Hyderabad
Paper Coordinator Ranjan Mukhopadhyay
Pradeep Gokhale
Vishva Bharati, Shantiniketan, West Bengal
Central University of Tibetan Studies,
Sarnath, Varanasi.
Content Writer Amita Chatterjee Emeritus Professor, Jadavpur
University
Content Reviewer
Heeraman Tiwari
Professor, Centre for Historical Studies,
Jawaharlal Nehru University
Language Editor
Abha Thapalyal Gandhi Publishing & Editorial Services
Advisor, New
Delhi
Description of Module
Subject name
Philosophy
Paper Name Logic-II
Module Name/Title Indian and Modern Logic
Module Id 7.34
Prerequisites Pramāṇa theories, syllogism, elements of inductive
logic, first order
predicate logic
Objectives To find out how some modern interpreters have
understood Indian
theories of logic
Key words Sādhya, pakṣa, hetu,udāharaṇavyāpti,
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Indian and Modern Logic
1. Logical culture has been prevalent in the classical Indian
theoretical tradition for more than 2000
years. In fact, logic was a part of public and private life,
rural and urban life, scientific and religious forms
of life. All major philosophical systems of India developed
theories of inference in consonance with the
ontology and the epistemology of their respective systems.
However, in course of time, and with the
advent of modernity under the colonial rule, the entire logical
tradition was forgotten till it was discovered
anew by the European scholars. This module aims at giving an
account of how Indian logic is understood
by the modern interpreters of Indian logic.
Indian logic is said to have been discovered by the famous
Orientalist and mathematician H.T.
Colebrooke. He read, under the guidance of the traditional
pundits, Gotama’s Nyāya-sūtra with
commentaries and glosses on it and reported his discovery at a
public meeting of the Royal Asiatic
Society in 18241. Prior to Colebrooke’s declaration, western
scholars were blissfully ignorant about the
scientific and logical pursuits of the ancient Indians, though
they knew and acknowledged the
contribution of Indian scholars to mathematics and astronomy.
Most western scholars and the colonial
scholars had thought that the Indian mind was not logical at
all. So Colebrooke’s discovery is considered
as a landmark in the History of Ideas.
2. What did Colebrooke discover? He found that the Naiyāyikas
used reasoning to provide evidence for
the ontological categories they acknowledged. About Nyāya he
wrote, “The first, as its title implies, is
chiefly occupied with the metaphysics of logic.”2 He showed that
reasoning or inference proper forms
part of the Nyāya theory of Evidence or Proof (pramāṇa). He
meticulously observed the standard form of
the argument and christened this argument ‘syllogism’ following
Aristotle. This view led to a lot of
controversy which I shall discuss later.
Let us look at the following observation of Colebrooke. 'A
regular argument, or complete syllogism,
(nyāya) consists of five members (avayava) or component parts.
1st, the proposition (pratijῆā); 2nd, the
reason (hetu or apadeśa); 3rd, the instance (udāharaṇa or
nidarśana); 4th, the application (upanaya); 5th,
the conclusion (nigamana). Example:
1. The hill is fiery: 2. For it smokes. 3. What smokes is fiery:
as a culinary hearth. 4. Accordingly, the hill is smoking; 5.
Therefore it is fiery.
Some (the followers of the Mimāṃsā) confine the syllogism
(nyāya) to three members; either the
three first, or the three last. In this the latter form it is
quite regular. The recital joined with the instance is
the major; the application is the minor; the conclusion
follows.”3
Colebrooke worked out the similarity between the nyāya argument
and the Aristotelian syllogism in
more detail in footnote no 84 of his essay presented before the
Royal Asiatic Society. So before making
any comment on Colebrooke’s interpretation of Indian logic, I
shall quote at length from this extremely
1Colebrooke’s essay ‘On the Philosophy of the Hindus: On the
Nyāya and Vaiśeṣika systems’ was first
published in the Transactions of the Royal Asiatic Society,
1824, 1: 92-118; reprinted in Indian Logic: A
Reader, ed. Jonardon Ganeri, Curzon Press, UK, 2001, pp. 26-58.
2Ganeri, 2001, p. 26. 3Ibid.,p. 47-8.
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relevant footnote too. We must remember that it was this article
which coloured the interpretation and
understanding of subsequent scholars who wrote on Indian logic
up to the latter half of the 20th century.
Colebrooke wrote: 'In the Nyāya the middle term of an
affirmative argument is called hetu "the reason",
sādhana, "the instrument of proof", or linga "the sign"; and the
major term sādhya, "or that which is to be
established". The last term is, however, sometimes used for the
minor…The later school of logic adopted
pakṣa for the minor term (or sometimes vivādapadam or vimatam),
and developed the notion of vyāpti
"pervadedness", or "the being invariably accompanied by some
other thing". Thus the major term of an
affirmative argument became the vyāpaka or "pervader" from its
wider extension, the middle the vyāpya
or "pervaded". The argument, "the mountain has fire because it
has smoke", is true, because smoke is
always accompanied by fire; "the mountain has smoke because it
has fire", is false, because fire is not
thus always accompanied by smoke. The latter is a favorite
instance of the anaikānta or savyabhicāra
fallacy. 'He further writes, 'There is an interesting passage in
the Muktāvalī, p.122 on the induction by
which the vyāpti or universal proposition is arrived at. It is
to be tested by affirmative and negative
induction (anvayavyatirekau), which correspond to the methods of
Agreement and Difference in Mill’s
Logic, Vol. I. p.454, the great object being to discover, if
possible, the relation of cause and effect
between the two phenomena.'
It is evident from the above excerpts that Colebrooke did find a
lot of similarities between logic in the
Greek and Indian traditions. So he drew a parallel between three
terms of an Aristotelian syllogism and
the five-pronged argument of the Nyāya system; he also noted the
fallacies pointed out by the Naiyāyika-
s. Though he was inclined to consider the Nyāya exercise as
deductive, he also noticed inductive elements
in the Nyāya syllogism especially in the process of ascertaining
the relation of universal concomitance
(vyāpti) between the pervader (sādhya, here) and the pervaded
(hetu, here), which he found to be
comparable with Mill’s methods of agreement and of difference.
This reading had a far-reaching effect on
the way Indian logic was understood. It also led to an
understanding of the Indian (the colonized) psyche
vis-à-vis the western (the colonizer’s) psyche. Debates of the
time proceeded mainly along two lines: (a)
If Indians had logic, then where did they get it from and (b)
what was the nature of Indian logic, or more
succinctly, under which framework of western logic could it be
accommodated?
3. The majority of western scholars were of the opinion that
Indians must have learnt logic from the
Greeks. But there were a few who thought that during the Indian
invasion of Alexander of Macedonia,
some Greek scholars who travelled with him must have come into
contact with Brahmin scholars and then
carried back the seeds of logical thought to Greece which was
then developed to its full potential by
Aristotle and the Aristotelians. However, we find that Max
Müller4 opposed both these conjectures and
maintained that these views were based on questionable
assumptions and that therefore it was more
logical to think of Greek and Indian logic as autochthonic,
i.e., these two systems of thought developed in
parallel and independently. He contended that to account for the
similarity of the two systems, it was
sufficient to maintain that ‘in philosophy also there is a
certain amount of truth which forms the common
heirloom of all mankind, and may be discovered by all nations if
they search for it with honesty and
perseverance’5.
In the course of explaining the structure of the five-pronged
syllogism and the nature of pervasion
(vyāpti), Max Müller made an important observation which should
be the guideline for any scholar
pursuing comparative philosophy. He wrote, ‘We might have
clothed Kaṇāda in a Grecian garb, and made
him look almost like Aristotle…But what should we have gained by
this? All that is peculiar to Indian
philosophy would have been eliminated, and the remainder would
have looked like a clumsy imitation of
4‘Indian Logic’, printed as an Appendix to An Outline of the
Necessary Laws of thought, Thomson, W.,
3rd edition, Longmans, London, 1853; reprinted in Ganeri, 2001,
pp.59-74. 5Ganeri, 2001, pp. 60-1
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Aristotle.’6 To find out the differences amongst the systems
compared should be the principal interest of a
comparative philosopher.
On the second question too Müller had a very original answer
which, we shall see soon, is altogether
different from the views of other scholars of Indian Logic. He
clearly points out, 'Nevertheless, it would
be wrong to call the Nyāya, Logic, in our sense of the word. The
Nyāya, as well as the other systems, has
for its highest object the solution of the problem of existence,
and only as a means towards accomplishing
this object, does it devote particular attention to the
instruments of knowledge – and, as one of them, to
syllogistic reasoning.”7 But after a few paragraphs, he
observes, 'Even terms as conclusion or syllogism
are inconvenient here, because they have with us an historical
colouring, and throw a false light on the
subject.'8 However, most of the scholars remained confined to
the framework of syllogistic reasoning and
its extensions. In sum, H. T. Colebrook (1824), S.C.
Vidyabhusana (1921) and Stcherbatsky (1930)
thought that the Nyāya and the Buddhist theory of inference were
versions of Aristotelian syllogism. Max
Müller (1853) disagreed with them but he interpreted the Nyāya
inference as a rule-based deductive
inference.
Roer9, on the other hand, maintained that since Nyāya inference
always depends on a vyāptivākya, a
generalization based on observations, Indian logic was
inductive. Almost one hundred years after
Colebrooke, B. N Seal gave a syncretic view and upheld that
‘Hindu inference is … a combined Formal-
Material Deductive-Inductive process.’10 S.C. Chatterjee, D.M.
Datta, S. Radhakrishnan and M.
Hiriyanna all endorsed this view.
4. One unfortunate outcome of treating the Nyāya argument as a
kind of syllogism is that in comparison
to the structure of Aristotelian syllogism the five-step Nyāya
argument appeared logically weak. The
major objections that were raised against a standard Nyāya
argument were as follows. (i) Two of the steps
of a five-step argument are ‘manifestly superfluous’11. The last
three steps are an example of a complete
syllogism, viz., whatever has smoke also has fire, the hill has
smoke, and therefore, the hill has fire. Why
should then the argument contain the first two steps (the
proposition and the reason) at all? Now we all
know the answer to this objection. The first step resembles the
conclusion. However, the first step only
floats a thesis which is to be proved but the conclusion is
established on the basis of evidence and hence
eligible for being asserted as QED. The second step mentions the
ground of the argument but the same-
looking fourth step is an application of the general rule
mentioned in the context of the given inference.
So, none of the steps is superfluous. (ii) The second weakness
as pointed out by Ritter is that the
introduction of an example in the third step vitiates the
universality of the conclusion. This also led to a
general criticism of Indian Logic that unlike western logic it
wasnot formal in nature. According to A. B.
Keith12, the example makes it evident that Indian logicians were
arguing from particular to particular as is
done in an argument by analogy. On the other hand, those who
laid emphasis on the third premise where
the general rule has been established on the basis of particular
observation, took the Nyāya argument to be
inductive in nature. Ganeri13, however, rightly points out that
J.S. Mill maintained that in a syllogism
6Ibid., pp. 67-8 7Ibid., p. 61 8Ibid., p. 68. 9 Division of
Categories of the Nyāya Philosophy (Bhāṣāpariccheda), ed. and
trans. by E. Roer, Baptist
Mission Press, Calcutta, 1850. 10Positive Sciences of the
Ancient Hindus, Motilal Banarasidass, New Delhi, 1985, p.252.
11Ritter, A. H., ‘Oriental Philosophy and its influence on the
Grecian’, in The History of Ancient
Philosophy, trans. A. J. Morrison, Oxford, 1846. 12Indian Logic
and Atomism, Clarendon Press, Oxford, 1924. 13Ganeri, 2001,
p.12.
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inference is from particular to particular and the major premise
is a ‘memorandum’ of previously
observed instances. In that case,why should one blame the Nyāya
argument as a weak and impoverished
version of Aristotle’s syllogism because it is an argument from
particular to particular? (iii) The third
criticism was raised by H. N. Randle14. The Naiyāyikas often
mentioned two examples one positive and
one negative in the third step and then developed two arguments
leading to the same conclusion. When
spelt out, this argument can be split into two separate
syllogisms, one having the form BARBARA and
another CESARE as follows.
All that is smoky is fiery as in a kitchen stove
This hill hassmoke
Therefore, this hill is fiery.
And
Nothing that is not-fiery is smokey as in the lake
This hill is smokey
Therefore, it is not non-fiery, i.e., it is fiery.
So Randle was convinced that one of these syllogisms is
unnecessary and two examples are superfluous.
Besides, there are others who objected that in Aristotelian
syllogism we have different argument
forms but in Indian logic all arguments can be represented
either as BARBARA or CESARE and that
suffices to bring out that poverty of Indian logic.
5. Some Indologists came forward to defend the Nyāya argument in
various different ways. The
representative of one line of argument was J. R. Ballantyne15
who realized that the Nyāya argument
should not be construed as an impoverished syllogism. According
to Ballantyne, ‘the five-membered
exposition is not the Hindu syllogism at all, but the Hindu
rhetorical exposition.’ So this is a form of
debate and can be understood better if each of the five steps
are construed as a response to a silent
interlocutor. This view has also been endorsed by B.K. Matilal
when he points out that the Nyāya
arguments originated within the vāda (debating) tradition and
then were developed within the pramāṇa
(epistemic) tradition. In support of introducing an example in
the third premise Ballantyne maintained
that the example helped to convince one’s opponent in a debate
situation of the truth of the general rule.
Müller, however, affirmed that the mention of an example
wasnecessary because it indicated the nature of
the general rule.16Roer gave a different reason and maintained
that an example provided the inductive
confirmation of the general premise and that the soundness of
the inference depended on the truth of the
general premise. This feature brings out a unique property of
Indian logic — a syllogism can be valid
without being sound but in Indian logic soundness and validity
of an argument go hand in hand.
6. With the development of mathematical logic by Russell,
Lukasiewicz, and others some new
interpretations of the Nyāya argument came into vogue. Stanislaw
Schayer was not ready to force Indian
inference onto the Procrustean bed of the authentic Aristotelian
syllogism under any circumstances. He
pointed out for the first time that the Nyāya argument should
rather be interpreted within the frame of the
First Order Predicate Logic. He symbolized the five-step
argument as follows.
14‘A Note on Indian Syllogism’, Mind, Vol. 33, 1924, pp.
398-414; reprinted in Ganeri, 2001. 15‘Concerning Criticism on
Oriental Matters in general and the Nyāya in particular’, Benares
Magazine,
Vol.1, 1849. 16The Naiyāyika-s admit three kinds of the general
rule (vyāpti-vākya): all-pervasive or those whose
antecedent holds over the whole domain (kevalānvayī) , e.g.,
‘Whatever is nameable is knowable’; those
whose antecedent holds over only part of the domain
(anvaya-vyatirekī), e.g., ‘Whatever has smoke has
fire’; and those whose antecedent holds over none of the domain
(kevala-vyatirekī), e.g., ‘Anything
except earth which is different from the elements other than
earth has odour ‘.
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1. Thesis Fa There is fire on a (= on this mountain). 2. Reason
Ga There is smoke on a. 3. Statement of (x) (Gx →Fx) For every
locus x: if there is smoke in x then there is fire
pervasion in x.
4. Application Ga →FaThis rule also applies for x = a. 5.
Conclusion Fa Because the rule applies to x = a and the statement
Ga is
True, the statement Fa is true.
Schayer here applies two rules of inference. On step 3 he has
applied ‘substitution’, or what we
call now Universal Instantiation following Copi, to obtain 4 and
the rule of ‘separation’ on 4 and 2 to get
5 which is nothing but the rule Modus Ponens. Schayer identifies
the ‘Indian syllogism’ with a proof in a
natural deduction system as follows.
Thesis: Fa because Ga
Proof: (1) Ga Premise
(2) (x) (Gx →Fx) Premise
(3) Ga →Fa 2, by universal quantifier elimination
(4) Fa 1 & 3, by → elimination, QED.
Like Colebrooke, Schayer too offered a path-breaking
interpretation which influenced the views of later
scholars. Both D. Ingalls17 and I. M. Bochenski18 gave qualified
acceptance to this view. Ingalls found
some problems with the representation of the third step and
feels that Schayer’s representation of this step
has somewhat distorted the spirit of the argument. For, '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.'19 Besides, he pointed out another distinctive feature
of the Indian argument, and that is, while the
major, middle and minor terms in the Aristotelian syllogism are
classes, inthe Indian scheme there occur
two properties, the property that serves as a reason (hetu) and
the property that is to be inferred (sādhya)
in a single individual (pakṣa). The salience of this point was
understood by Staal, Sibajiban
Bhattacharyya and B.K. Matilal and they developed their
interpretations along this line.
But before expounding on this point let us see how Bochenski
evaluated the Nyāya argument. In
Bochenski’s words, '(1) The Indian syllogism is not a thesis,
but a rule, like the Stoic and Scholastic
syllogisms. (2) Structurally, it is Ockhamist rather than
Aristotelian, since the "reason" always
corresponds to a singular proposition. (3) Yet the formulation
rather suggests a formula of modern
mathematical logic, than an Ockhamist syllogism, viz.: for all
x, if x is A, then x is B; but a is A;
Therefore a is B. (4) The Indian formula also contains an
express justification of the major premise. In
this respect there seems to be a difference between the classic
Nyāya logicians and the Tarkasaṃgraha.
The latter, and later, text fairly evidently envisages an
inductive proof, while the earlier thinkers intuit the
connection of two essences in an individual. (5) It should be
evident that we are still in a logic of terms.
Modest as these results may seem to a western logician, the text
undoubtedly attains to the level of
genuine formal logic, though it is very far from being
formalistic.'20 [Emphasis supplied.]
17‘Logic in India’, entry in the Encyclopedia Britannica, 14th
edition, Vol.8, 1955; reprinted in Ganeri
2001, pp. 110-6. 18 ‘The Indian Variety of Logic’ in his A
History of Formal Logic, Freiburg, 1956, trans. I. Thomas,
Notre
Dame University, Notre dame Press, 1961, pp. 416-47; reprinted
in Ganeri, 2001, pp. 117-150. 19Ganeri, 2001, p. 112 20Ganeri,
2001, pp. 142-3.
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7. J. F. Staal21 was astute enough to understand that terms in
an Aristotelian syllogism are related by one
single relation, i.e., the relation of belonging to, but in the
so-called Indian syllogism three terms (pakṣa,
hetu and sādhya) are related by two relations. The relation
between reason (hetu) and the thing to be
inferred (sādhya) is that of pervasion while the relation of
both these terms with the locus of the
argument is that of occurrence. As Staal put it, 'Since such a
relation relates x to y, it is a two-place
relation, which may therefore be written as A (x, y)'22 which
can be read either as x occurs in y or y is the
locus of x. So a sentence, "if (the hetu) smoke occurs on a
mountain (pakṣa), then fire (the sādhya) occurs
on that mountain (pakṣa)" is to be symbolized by A (h, p) → A
(s, p). Though Sibajiban Bhattacharyya23
and B. K. Matilal agreed more or less with Staal, they offered
refined interpretation of their own.
Following the texts of the New School of Nyāya, Sibajiban
Bhattacharyya has laid bare the structure of a
Nyāya argument vis-a-vis Aristotelian syllogism. Let us
therefore look at Bhattacharyya’s analysis.
To compare the standard Nyāya argument with Aristotle’s
syllogism, Bhattacharyya takes the last three
steps and gives exact English rendering of the Sanskrit form.
Let us look at the examples he has given.
N.N.1. (The) hill (is) fire-possessing/ because of smoke.
N.N.2. This (is) fire/ because of heat.
In both the arguments identifying the hetu and the pakṣa is
simple. The term which is suffixed by
the fifth case-ending in Sanskrit or prefixed by ‘because of’ in
English is the ground/reason/hetu of the
argument. The locus of the hetu is the pakṣa but identifying the
sādhya is tricky. In N. N.1. fire (not the
word ‘fire’) is the sādhya, though in N.N.2 it is the property
of being fire or fire-ness (neither fire, nor the
word ‘fire-ness’). The Navya-Naiyāyika-s have given us a thumb
rule for identifying the sādhya of any
argument. The rule is in two parts, to be applied depending on
the case at hand. (i) Drop the suffix ‘-
possessing’ when it occurs in the second term of the conclusion
(Check N.N.1 now); (ii) add the suffix
‘ness’ to it when the suffix ‘- possessing does not occur (Check
this part against N.N.2).
By applying this rule N.N.1 and N.N.2 may be fleshed out as
follows.
N.N.1.: Whatever is smoke-possessing is also fire-possessing
The hill is smoke-possessing
Therefore, the hill is fire-possessing.
Of course, the argument can be more elegantly paraphrased in
English as
Whatever possesses smoke possesses fire
The hill possesses smoke
Therefore, the hill possesses fire.
N.N.2.: Whatever is heat-possessing is fireness-possessing
This is heat-possessing
This is fireness- possessing.
Or,
Whatever possesses heat possesses fire-ness
This possesses heat
Therefore, this possesses fireness.
21‘The Concept of Pakṣa in Indian Logic’, Journal of Indian
Philosophy 2, 1973, pp. 156-66; reprinted in
Ganeri 2001, pp. 151- 161. 22Ganeri, 2001, p. 152. 23‘Some
Aspects of the Navya-Nyāya Theory of Inference’, Doubt, Belief and
Knowledge, Indian Council
of Philosophical Research, Delhi,1987, pp. 245-267; reprinted in
Ganeri, 2001, pp. 162-82.
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According to Navya-Naiyāyikas, ‘ness’ is an abstraction operator
and ‘-possessing’ is a
concretization operator. There is an interesting relation
between these two operators. The Navya-
Naiyāyikas expresses this relation by the following equation:
a-possessing-ness = a-ness-possessing = a.
(dhūma- vat-tva = dhūma-tva-vat = dhūma).
The aapplication of this rule makes the difference between the
Nyāya argument and a syllogism
palpable.
N.N.1*. syllogism
Whatever possesses humanity possesses mortality All men are
mortal
Socrates possesses humanity Socrates is a man
Socrates possesses mortality Socrates is mortal
It is therefore evident that three terms in the Navya Nyāya
argument are: humanity, mortality and
Socrates, while in the syllogism three terms are: man, mortal
and Socrates.
The rule of identifying the sādhya of an argument can be used
more widely for determining the
predicate of any sentence. Consider, for example, the sentence,
‘Socrates is wise’. According to Navya-
Nyāya, it should be wise-ness or wisdom by the second part of
the rule, since it does not contain ‘-
possessing’. Bur this sentence can also be transformed into
‘Socrates is wisdom-possessing’. And in the
latter case we are supposed to drop ‘–possessing’ and we have
once again wisdom as the predicate of this
sentence.
Another important difference between the Nyāya argument and a
syllogism lies in the fact that
while in a syllogism the major and the minor premise together
necessarily implies the conclusion, in a
Nyāya argument a third premise is required as a necessary
condition to arrive at the conclusion. So the
Navya-Naiyāyikas maintain that the fully fleshed out inferential
form is as follows:
(1) Smoke is pervaded by fire. (‘whatever possesses smoke
possesses fire’ reformulated in terms of pervasion)
(2) The hill possesses smoke (3) The hill possesses smoke
pervaded by fire (4) Therefore, the hill possesses fire.
Against the Mīmāṃsakas the Naiyāyikas point out that (3) is not
a conjunction of (1) and (2). (3) is
weaker because the conjunction of (1) and (2) implies (3) but
(3) does not imply this conjunction. The
necessity of introducing (3) becomes obvious if we look at the
generalized form of the premises.
1*. Something is pervaded by fire
2*. The hill possesses something
3*. Therefore, the hill possesses fire.
To have a sound and valid inference it is necessary that
‘something’ in (1) and (2) stand for the same
object, (1) and (2) must be combined to form one complex
judgement, to represent ‘consideration’
(parāmarśa) (3), ‘The hill possesses something pervaded by
fire’. Otherwise, one could have the
following argument:
Smoke is pervaded by fire.
The hill possesses light.
Therefore, the hill possesses fire.
According to the Naiyāyika (3) is both necessary and sufficient
for deriving the conclusion because then
we need not even look at the substitution instance of
something.
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8. It is therefore evident that the Nyāya argument should not be
interpreted either as a syllogism or as an
argument of modern predicate logic. Jonardon Ganeri has summed
up the entire project of interpreting the
Nyāya argument in terms of western logic very aptly.
…any comparative project is liable to catch the Indian theory in
a double-bind: either
Indian logic is not recognized as logic in the western sense at
all; or if it is, then it inevitably
appears impoverished and underdeveloped by western standards.The
only way to escape this
dilemma is to reclaim for Indian logic its own distinctive
domain of problems and applications, to
see how it asks questions not clearly formulated elsewhere, and
in what way it seeks to solve the
problems it sets for itself.24
We shall therefore conclude this lesson by summing up in what
sense then Indian logic can be construed
as logic and what its distinctive features following B. K.
Matilal25 are:
(i) No Indian philosophical system, unlike western logic, takes
a purely formal approach to inference or inferential knowledge. Yet
we consider these theories of inference as logic
insofar as these are theories of human reasoning and tell us how
to distinguish good
arguments from bad arguments, acceptable arguments from
unacceptable ones.
(ii) While mainstream western logic primarily developed as a
deduction-centric discipline and revolved around ‘the consequence
relation’, logic in India has been mainly pervasion
(vyāpti)-centric. Here, syntax always remains hyphenated with
semantics. For inference
as an accredited source of knowing the world, validity is not
enough; soundness and
epistemic progress also need to be guaranteed.
(iii) In Indian theories of inference we find elaborate
discussions on how inference results from a number of cognitive
states, and what conditions give rise to cognitive certainty.
Here the relation between premise and conclusion is viewed not
as an abstract logical
relation but as a psycho-cognitive relation of causal sequence.
This stance may make
Indian logic vulnerable to the charge of psychologism, which
both Frege and Husserl
wanted to avoid. However, here psychologism never led to
subjectivism because Indian
logicians were dealing with psycho-causal conditions that apply
to all cognitive agents.
Besides, unraveling the psycho-causal conditions underlying an
inferential process help
us build a viable model of mental reasoning.
(iv) All Indian logicians adopted a grammar-based model of
logical analysis, while in Western logic the
geometrico-mathematical model is in use. But interestingly,
this
grammar-based model has led Indian theorists to some of the
insights of mathematical
logicians regarding logical connectives. It is true that the
Naiyāyikas did not always stick
to the Grammarian’s insights when they developed their formal
language. While defining
a language of properties and relations they scratched beneath
the grammatical surface
expressed through ordinary language and arrived at logical
correlates of their
metaphysical categories.
(v) Western formal logic is extensional; Indian logic, it has
been said, is basically logic of properties and hence intentional.
Two properties having the same extension are found to
possess different senses and would fail the subjectivity
condition, e.g., potness (ghaṭatva)
24Ganeri. 2001, p. 21. 25‘Introducing Indian Logic’, Chapter 1
of The Character of Logic in India, eds. Jonardon Ganeri and
Heeraman Tiwari, Suny Press, New York, 1998; reprinted in
Ganeri, 2001, pp. 183-215.
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10
and the property of having a conch-like neck
(kambu-grīvādimattva) are extensionally the
same but differ in sense. However, we must remember what Indian
logicians mean by
‘property’ is somewhat different from its meaning in English.
The term ‘property’ here
signifies any located object, be it an abstract property or a
concrete object, which resides
in a locus. The basic combination in Indian logic is not a
straightforward subject-
predicate proposition but a Sanskrit sentence of the
locus-locatee model, e.g., ‘a has f-
ness’.
Keeping these features in mind, modern interpreters of Indian
logic are trying to understand the
Nyāya, Bauddha and Jaina arguments in various different ways
going beyond the frame of first
order logic.