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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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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.