The Logic of Gotama: Monographs of the Society for Asian and Comparative Philosophy no. 5 9780824887223

Citation preview

The Logic of Gotama

The Society for Asian and Comparative philosophy, organized in 1967, aims to serve the professional interests of scholars involved in Asian and Comparative Philosophy, to advance the development of these disciplines in the academic world, and to bring Asian and Western philosophers together for a mutual beneficial exchange of ideas.

With a mem-

bership of over 200 scholars and advanced students, the Society holds annual meetings and sponsors panels and workshops on themes of both scholarly and topical interest. The Society also sponsors a monograph series on specialized topics in Asian and Comparative philosophy.

The monographs are more detailed than

journal articles and more specialized and of shorter length than standard books.

Editorial inquiries

should be sent directly to Eliot Deutsch, SecretaryTreasurer, Department of Philosophy, University of Hawaii, Honolulu, Hawaii 96822.

THE LOGIC OF GOTAMA

Kisor Kumar Chakrabarti

MONOGRAPH NO. 5 OF THE SOCIETY FOR ASIAN AND COMPARATIVE PHILOSOPHY THE UNIVERSITY PRESS OF HAWAII 1977

©

by The University Press of Hawaii 1978

All rights reserved Manufactured in the United States of America

Library of Congress Cataloging in Publication Data Chakrabarti, Kisor Kumar. The Logic of Gotama. (Monographs of the Society for Asian and Comparative Philosophy ; no. 5) Bibliography: p. 1. Nyaya. 2. Gotama, called Aksapada. I. Title. II. Series: Society for Asian and Comparative Philosophy. Monographs of the Society for Asian and Comparative Philosophy ; no. 5. B132.N8C4 160 ISBN 0-8248-0601-8

77-13853

CONTENTS Acknowledgments

vii

Introduction

ix

Abbreviations

xiv

CHAPTER I. II. III.

THE NATURE OF INFERENCE . . . . CLASSIFICATION OF INFERENCE . .

V.

14

PANCAVAYAVANYAYA OR THE REASONING WITH FIVE STEPS

IV.

1

. .

32

HETVABHASA OR PSEUDO PROBANS. .

88

DISJUNCTIVE SYLLOGISM

103

VI. ARTHAPATTI CONCLUSION

123 136

Bibliography

144

ACKNOWLED GMENTS

This monograph is a revised and shortened version of my Ph.D. dissertation, submitted to and accepted by the State University of New York at Buffalo.

I would like to thank Professors

William T. Parry, John T. Kearns, and Kenneth K. Inada of the State University of New York at Buffalo, for their assistance.

I would like to

especially mention that Professor Parry made many valuable suggestions and improvements.

I would

like to express my gratitude also to my teachers of Indian philosophy at Calcutta—Professor Gopinath Bhattacharya, Pts. Pancanana Sastri, Visvabandhu Tarkatirtha, and Madhusudana Nyayacharya—for those many years of help without which I could not acquire the knowledge of Nyaya logic requisite for this study.

Finally, the whole manu-

script was kindly read by Professor Bimal K. Matilal, whose various suggestions and critical comments were of great value.

INTRODUCTION The purpose of this monograph is to give an objective account of the logic of Gotama, the founder of the Nyaya school of philosophy in India. No attempt has been made to cover the entire logic of Gotama.

The discussion is confined almost exclu-

sively to the part which deals directly or indirectly with deductive arguments. Gotama's own work, called the Nyayasutra (literally, aphorisms on logic), consists entirely of a list of aphorisms that are extremely cryptic and almost unintelligible without the help of the commentators.

Hence it has been necessary to refer

constantly to the earliest commentator, Vatsyayana. But I have avoided going beyond Vatsyayana to later logicians, as far as practicable.

On a number of

occasions there is reference to the work of Uddyotakara, who wrote a commentary on the commentary of Vatsyayana, and of Vacaspati Misra, who wrote a further commentary on the commentary of Uddyotakara. These references are solely for the purpose of revealing the views of Gotama and of explicating some difficult passages in Vatsyayana's commentary.

T h e i n t r o d u c t i o n is f o l l o w e d b y six dealing with the following topics: inference,

chapters

(1) n a t u r e

(2) c l a s s i f i c a t i o n o f i n f e r e n c e ,

pancavayavanyaya,

(3)

or the r e a s o n i n g w i t h five

h a v i n g a deductive core,

(4) h e t a v a b h a s a ,

of

steps

or

falla-

cies of the nyaya,

(5) s e s a v a t a n u m a n a , or d i s -

junctive syllogism,

(6) a r t h a p a t t i ,

a reasoning

having only one premise w h i c h may be either gorical or compound.

cate-

In a r r a n g i n g t h e t o p i c s w e

have not followed Gotama's order but have

followed

t h e m o s t l o g i c a l a r r a n g e m e n t for o u r p u r p o s e s .

It

is n a t u r a l t o b e g i n w i t h G o t a m a ' s v i e w of the n a t u r e o f i n f e r e n c e a n d its c l a s s i f i c a t i o n .

Next

w e have discussed the m o s t influential part of G o t a m a ' s l o g i c , n a m e l y , t h e n y a y a a n d its In c h a p t e r s 5 a n d 6 w e h a v e s t u d i e d

fallacies.

reasonings,

t h e v a l i d i t y or i n v a l i d i t y o f w h i c h m a y d e p e n d propositional or term connectives used. 7 contains concluding

Chapter

remarks.

One factor that makes the interpretation G o t a m a ' s l o g i c e x t r e m e l y d i f f i c u l t is t h e style of his writing.

on

of

aphoristic

Gotama did not invent the

aphoristic style of w r i t i n g b u t merely followed a c c e p t e d n o r m of p h i l o s o p h i c a l w r i t i n g o f h i s A sutra or aphorism must fulfill the standard.

It m u s t b e s v a l p S k s a r a ,

the

time.

following

or composed

of

Gotama's influence on Indian logic is vast and pervasive.

The literature on logic of the

Nyáya school, including the Navya-Nyaya or the New Nyáya school, numbers many hundreds of volumes.

In this vast literature Gotama is acknowl-

edged as the undisputed founder of a rich logical tradition.

Even outside the Nyáya school his in-

fluence on the logical writings of other philosophical schools such as the Vaisesika, Bauddha, Jaina, Saitikhya, Yoga, Mimamsa, and so on is unmistakable. Through Buddhist logicians who, though highly critical of his work, were deeply influenced by his theory of the Nyáya and its fallacies, Gotama's influence was carried outside India even to China and Japan, wherever Buddhist logic went.

In this

respect the only other logician whose influence on a long and continuing logical tradition is comparable to that of Gotama's is Aristotle.

In spite

of occupying a position of unique honor and importance in Indian logic, Gotama has been represented, by a host of modern writers in English and other European languages, as an inferior logician whose contribution to logic is insignificant.

We

will respond to this modern account and prove how grossly wrong it is.

a few letters.

It must be asamdigdha, that is,

what it says must be beyond doubt.

It must be

saravat or state the minimum essential matter. It must be visvatomukha or contain diverse information.

The last two characteristics make the

interpretation of a sutra specially difficult. Since the aphorism states the minimum essential matter, it becomes necessary to speculate on how much more is implied.

Also the aphorism is likely

to contain diverse information.

Hence it is nec-

essary to search for alternative explanations. The author of a sutra must also avoid any kind of repetition.

He must avoid "repeating what is ac-

tually said" (sabdapunarukti).

He must also avoid

"repeating what is implied by what is actually said" (arthapunarukti). stringently applied.

These conditions were

Vacaspati Misra has said,

"What can be gathered without being stated from the hint alone should not be stated by the author of a sutra work" (NDBVTV, p. 573).

The author was

expected to provide only the briefest possible hints (sucanad sutram).

He was absolutely pre-

cluded from giving examples or otherwise clarifying what is meant.

This standard of writing is quite

uncommon in Western philosophical tradition.

Hence

it has to be emphasized that Gotama belonged to a

very different cultural background.

Cryptic style

and extreme brevity were required and not blamed in the type of work he set out to write. Owing to the lack of chronological record in India, the dates of early logicians are uncertain and estimates of different scholars vary widely. Since I am concerned with the logical doctrines of Gotama and not with the date of his birth, I do not have to enter into this controversy.

Suffice it

to say that Gotama1s date has been placed by different scholars between sixth century B.C. and second century A.D. and Vatsyayana's date, between second century B.C. and fifth century A.D.

The

dates of Uddyotakara and Vacaspati Misra are placed in the sixth century A.D. and the ninth century A.D., respectively.

The interested reader may con-

sult U. Misra's History of Indian Philosophy, vol. 2, for a discussion of different opinions.

ABBREVIATIONS BL

T. Stcherbatsky, Buddhist Logic, Vol. 1.

HFL

I. M. Bocheriski, A History of Formal Logic.

English translation by Ivo

Thomas. HIL

S. C. Vidyabhusana, A

History of

Indian Logic. I LA

A. B. Keith, Indian Logic and Atomism.

ILES

H. N. Randle, Indian Logic in Early Schools.

Jha

Nyaya-Sutras of Gotama and Vatsyayana's Bhasya.

English translation by M.

G. Jha. Materials

D. H. J. Ingalls, Materials for the Study of Navya Nyaya Logic.

MI IL

S. S. Barlingay, A Modern Introduction to Indian Logic.

NDBVTV

Nyayadarsana with the commentaries of Bhasya, Varttika, and Vrtti.

Vol. 1.

Tatparyatika Eds. Amarendra

Tarkatirtha and Taranatha Tarkatirtha. NDFC

Nyayadarsana with the four commentaries of Bhasya, Varttika, Tatparyatika and Parisuddhi. Thakur.

Vol. 1.

Ed. Anantalal

S. C. Chatterjee, The Nyaya Theory of Knowledge. Padarthadharmasamgraha of Prasastapada with the Nyayakandali of ¿ridhara. Edited with a Hindi translation by Durgadhara Jha. Benson Mates, Stoic Logic. Samkhyatattvakaumud1 of Vacaspati Misra.

English translation by

Ganganatha Jha. B. Faddegon, The Vaisesika System.

CHAPTER 1 The Nature of Inference Both Gotama and VStsyayana (and Indian logicians in general) conceive of inference (anumana literally means anu or after, mana or knowledge, that is, after-knowledge or knowledge that follows) in a broad sense to include both deductive and nondeductive inference.

In this study I am concerned

with Gotama's study of inference as a process of deductive reasoning.

Hence I shall leave out re-

ferences to his study of nondeductive inference, as far as possible. In order to get an understanding of the views of Gotama and Vatsyayana on inference as a process of deductive reasoning, first we will consider Vatsyayana's comment on the aphorism 1.1.3:^" "Perception, inference, analogy and authoritative 2

statement are the sources of knowledge."

-

-

Vatsya-

yana' s comment on inference here consists of a single sentence: "Inference is knowledge of an 3 4 indicated object (or meaning) that follows from the knowledge of the indicator (liftga)."

It is

not clear whether this statement is intended to be a definition of inference in the strict sense. Whether it is to be taken as a definition, it is admittedly vague, and because of this vagueness

2 it is applicable to all of the different kinds of deductive and nondeductive inferences considered by VStsyayana.

Thus in the inference of a cause

from an effect, the cause would be the indicated object and the effect would be the indicator.

In

a pentapod argument the probandum is the indicated object and the probans is the indicator.

In artha-

patti the premise would be the indicator and the proposition deduced would be the indicated meaning.

In this last case, the double meaning of the

word artha becomes specially significant. One important word in the preceding quotation is the word "follows

(pascat). 5

Since VStsy3-

yana's statement is intended to cover both deductive and nondeductive inferences, this word would have at least two radically different meanings, depending on whether it is taken in the context of deductive inference or in the context of nondeductive inference.

As far as deductive in-

ference is concerned, the following statement of VStsySyana, from his comments on aphorism 2.2.2. (which asserts among other things that arthSpatti c is inference), "following":

will throw light on the nature of "Inference is knowledge, through the

given, of the not-given related

[to the given]

. . . . Since arthSpatti is knowledge of something

3

other than what is stated from the precise understanding of the meaning of a sentence related by 7 way of opposition, it is definitely inference." According to this statement, if a proposition is derived from the meaning of a certain other proposition, such derivation should be labeled as a case of inference.

As Vâtsyâyana says the deri-

vation takes places "from the precise understanding of the meaning of a sentence."

In other words

the conclusion is derived by analyzing the meaning of the proposition that occurs as the premise. Hence as far as deductive inferences are concerned, "following" may be taken to mean "following from an analysis of the meaning."

In this connection

one may also consider the import of the term nigamana (outcome) given to the last step of the pentapod argument.

The term suggests that the last

step is what is extracted or deduced from the previous steps and may suggest that it is obtained from an analysis of their meanings. Vâtsyâyana writes in the passage immediately preceding the one from which the last quotation was taken that, "where from a proposition stated another proposition (meaning, artha) follows necq essarily,

that is arthapatti."

Though this state-

ment is a definition of arthapatti, we can use it

4

to get a reasonably good account of what is meant by deductive reasoning, namely, that, in a (valid) deductive reasoning from something being stated, something other than what is stated follows as a necessary consequence.

This account of deductive

reasoning is essentially the same as Aristotle's account of what reasoning is:

"Now reasoning is

an argument in which, certain things being laid down, something other than these necessarily comes about through them" (Topics 100 a 25).

Reasoning

here naturally has to be taken to mean deductive reasoning and not inductive reasoning.

Aristotle's

definition of syllogism in the Prior Analytics (24^ 18) is also basically the same:

"A syllogism is

discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so."

Aristotle's definition

of syllogism is applicable to deductive reasoning in general and not merely to the specific kind of reasoning called syllogism by Aristotle.

Similar-

ly, Vatsyayana's definition of arthapatti applies to deductive reasoning in general and not only to what is specifically construed as arthapatti. I have thus far been considering the significance of Vatsyayana's statement that "Inference is knowledge of an indicated object (or meaning)

5 that follows from knowledge of the indicator,"

in

the light of his further remarks about inference as a process of deductive reasoning.

In translating

the original sentence in this w a y I have taken the words linga

(indicator) and l i n g ! (indicated) in

their ordinary literal sense.

However, in the In-

dian philosophical literature these terms are also widely used in a narrower, technical sense which must now be stated.

In the narrower,

technical

sense the term liflga signifies the pervaded and lingi the pervader concept of pervasion a later chapter.

(vyapaka).

(vyapya)

The important

(vyapti) will be explained

For the time being it will

in

suf-

fice to say that an object A may be said to pervade another object B if and only if A is present wherever B is present and B is absent wherever A is absent.

If taken in this technical sense, what VSt-

syayana's statement would amount to is: is knowledge of the pervader that follows knowledge of the pervaded."

"inference from

Then, of course, the

statement would not apply to all the different kinds of inference considered b y Vatsyayana but would apply primarily to nyaya,

(discussed in chap-

ter 3) which, of all the different kinds of inference, certainly occupied the foremost attention of Gotama and VStsy5yana and Indian logicians in

6 general.

Thus the same statement, when interpreted

in a literal way, would give us a somewhat vague account of inference in general, and, when interpreted in a technical sense, would give us an account of inference specially applicable to a very common and important kind of inference, the study of which dominated the history of Indian logic.

It

would be extremely difficult, if not impossible, to decide that only one of them is the correct interpretation, to the exclusion of the other.

Our guess

is that Vatsyayana was alive to the possibility of both interpretations and deliberately wanted to give an account of both inference in general and inference of a specially important kind through the same statement. There is the same kind of double significance in Vatsyayana1s comment on the aphorism 1.1.5 that "Inference which is based on (or is preceded by or follows from) those, is of three kinds. . . . "

He

explains that the word "those" "refers to seeing the indicator (linga) and seeing the connection between the indicator and the indicated (ling!)." This gives us the following definition of inference: "inference is knowledge which is based on seeing the indicator and seeing the connection between the indicator and the indicated."

Here also the terms

liftga and lingi may be taken once in the literal

7

sense of the indicator and the indicated, thus yielding a definition of inference in general, and then in the technical sense of the pervaded and the pervader, thus yielding a definition that is primarily applicable to the nyaya.

The word used for

seeing, namely, darsana, is frequently used in the sense of knowing and would include discerning the connection in meaning between two propositions. A question that must be faced now is what evidence is there to show that the technical sense of liftqa and liftgi was known to Vatsyayana?

This is

important because modern interpreters (Keith, Stcherbatsky, Randle, and so forth) have held that the concept of pervasion (vyapti) was not known to either Gotama or Vatsyayana.

The question cannot

be fully answered until the views of Gotama and Vatsyayana on nyaya are discussed in the third chapter.

There are, however, a few things that

may be mentioned now.

First of all, though vatsya-

yana has nowhere said that linga and ling! mean the pervaded (vyapya)

and the pervader (vygpaka),

the word vyapti, its several cognates as well as its synonyms—for example, avinabhavasambandha, necessary or inseparable or invariable (avinabhava) relation (sambandha), appear in his writing (such as in comments on 1.2.5, 2.2.1, 2.2.2., and so on).

8 This lends support to my view that the concept of vyapti or pervasion was known to Vatsyayana.

Se-

cond, Gotama has used the word linga in a semitechnical sense, in the aphorism 1.1.10 (and others) when he said that "Desire, aversion, volition, pleasure, pain and knowledge are the indicators (linga = reasons for inferring) of the soul."

Tech-

nical use of the word lirtga is also found in the Vaisesika Aphorisms of Kanada, such as aphorism 9. 2.1, 9.2.4, and so on.

Third, as we shall see in

the third chapter on the pentapod argument, both Gotama and Vatsyayana use the terms hetu (probans) and sadhya (probandum), which are virtually synonymous with linga and lingi, to mean the pervaded and the pervader.

Finally, ancient writers such as the

Buddhist Dihnaga and have profusely

the Vaisesika PrasastapSda

used the terms liftga and liftgi in

the technical sense of the pervaded and the pervader.

It is not unlikely that they got their clue

from Gotama and VStsySyana, with whose work they were thoroughly acquainted. We have seen that inference has been defined as the knowledge that is based on seeing (knowing) the indicator as well as seeing (knowing) the relation between the indicator and the indicated. Since this statement is somewhat vague, more may

9 be revealed on the subject b y studying h o w

in-

ference has been distinguished from analogy

(upama-

n a ) ^ w i t h w h i c h , of all o t h e r s o u r c e s o f k n o w l edge,

i n f e r e n c e is m o s t l i k e l y t o b e

confused.

G o t a m a ' s d e f i n i t i o n of a n a l o g y is as

follows:

" A n a l o g y is p r o v i n g w h a t is t o b e p r o v e d similarity to a well-known object"

(1.1.6).

the aphorism 2.1.47, Gotama takes up the t h a t a n a l o g y is i n d i s t i n g u i s h a b l e

through

from

In

objection

inference.

T h e a p h o r i s m i t s e l f is " B e c a u s e it c o n s i s t s i n the k n o w l e d g e o f w h a t is n o t g i v e n t h r o u g h w h a t given."

The words

" a n a l o g y is n o t h i n g b u t

e n c e " m u s t b e r e g a r d e d as u n d e r s t o o d .

is infer-

Commenting

on this Vatsyayana writes:

J u s t as t h e c o g n i t i o n o f f i r e w h i c h is n o t g i v e n , b y m e a n s o f s m o k e w h i c h is g i v e n , is i n f e r e n t i a l — s o t h e c o g n i t i o n o f t h e u n perceived gavaya

(a k i n d of w i l d cow) b y 12 m e a n s of t h e p e r c e i v e d c o w should be inferential—so does

that analogical

cognition

n o t in a n y w a y d i f f e r f r o m t h e

in-

ferential. T h e o b j e c t i o n , t h e n , is:

since analogy like

in-

f e r e n c e y i e l d s k n o w l e d g e o f w h a t is n o t

perceived

t h r o u g h k n o w l e d g e of w h a t is p e r c e i v e d ,

it

should

b e r e g a r d e d as a s p e c i e s o f i n f e r e n c e a n d n o t as a distinct source of knowledge.

10 In o r d e r t o m e e t t h i s o b j e c t i o n G o t a m a a n d VStsySyana have pointed out several

distinctive

features of analogical knowledge of w h i c h o n e n e e d c o n c e r n u s at t h e m o m e n t . Gotama's own statement:

lar) ' , [it can] n o t [from i n f e r e n c e ] " that:

W e first

"Since analogy

place through the judgment that

(simi-

nondifferent

VStsyayana

"Analogical knowledge, but not

comments

inferential

k n o w l e d g e , t a k e s p l a c e t h r o u g h the j u d g m e n t is so 1

r e f e r r i n g to t h e c o m m o n f e a t u r e s .

so c o n s t i t u t e s t h e i r d i f f e r e n c e . "

note

takes

'it is so

[be r e g a r d e d as]

(2.1.48).

only

'it

This

al-

In other words,

t h e d i s t i n c t i v e f e a t u r e of a n a l o g i c a l k n o w l e d g e t h a t it is b a s e d o n t h e j u d g m e n t of w h i l e i n f e r e n c e is not.

is

similarity,

O n t h e s t r e n g t h of t h i s

w e can say that w h e n Vatsyayana speaks of

inference

being b a s e d on seeing the connection b e t w e e n

the

indicator and the indicated, this connection

can-

n o t b e t h a t of m e r e s i m i l a r i t y .

This result will

b e i m p o r t a n t w h e n w e c o n s i d e r t h e v i e w of m o d e r n i n t e r p r e t e r s t h a t n y g y a , as c o n c e i v e d b y

Gotama

and VStsySyana, was nothing more than an

analogical

argument. W e would observe that though not

explicitly

s t a t e d in t h e d e f i n i t i o n of i n f e r e n c e ,

it is a b u n -

dantly clear that the connection b e t w e e n

the

11 indicator and the indicated is intended to be a universal or invariable connection.

This may be

gathered first from the technical sense of linga and ling! signifying the pervaded and the pervader. The relation between the pervaded and pervader is a necessary relation.

Second, inference has been

declared to be a source of knowledge in the stricter and narrower sense of knowledge that is certain and true.

It is carefully distinguished from apra-

mSna or sources that yield only probabilistic or false belief.

This claim certainly cannot be sus-

tained, unless the connection between the indicator and the indicated is conceived to be a necessary connection.

The definition of inference that is

obtained after a careful analysis of Vatsyayana's statement is:

inference is knowledge that is based

on seeing the indicator and seeing the

(necessary)

connection between the indicator and the indicated.

12

NOTES 1. The aphorism 1.1.3 is the aphorism 3 in the first section (ghnika) of the first chapter (adhyaya). I follow the convention of referring to Gotama's aphorisms by first mentioning the chapter number, then the section number, and the number of the aphorism. 2. These are sources of knowledge in the strict sense of knowledge that is true and certain among other things. 3. The word "indicated" (liftgî) is not found in some manuscripts. 4. The word artha is ambiguous and stands for both object and meaning. 5. The word pascSt ordinarily signifies following in a temporal sense. 6. The word pratyaksa, which has been translated as 'given', could also be translated as 'perceived'. In that case 'perception' should be taken in a wide sense to include both external perception and internal perception and also such acts as apprehending a proposition. In the case of arthapatti, for example, what is pratyaksa is a certain proposition that occurs as the premise from which another proposition which is apratyaksa, is derived. 7. For further comments on this quotation see the chapter on arthapatti. 8. We have translated artha as 'proposition', because in the present context it stands for 'the meaning of a sentence'. VatsySyana himself later speaks of vêCkySrtha or 'the meaning of a sentence'.

13 9.

P r a s a j y a t e h a s b e e n t r a n s l a t e d as

necessarily'

a n d n o t as

'follows'.

Though

'follows VatsyS-

y a n a c o u l d h a v e u s e d s o m e o t h e r p r e f i x l i k e a n u or 8, h e h a s u s e d t h e p r e f i x p r a a n d k e p t u s i n g t h r o u g h t h e d i s c u s s i o n of a r t h S p a t t i

it

(confer,

d i s t i n c t i o n b e t w e e n m i y a t e and p r a m i y a t e ) .

the

If one

t a k e s n o t e of t h e s i g n i f i c a n c e of p r a , o n e w o u l d s e e t h a t t h e t r a n s l a t i o n is j u s t i f i e d b y t h e al m e a n i n g of p r a s a j y a t e 10.

liter-

itself.

T h e s e a r c h for d o u b l e or t r i p l e

meaning

of a statement m a y seem strange to a W e s t e r n

read-

er, b u t is v e r y c o m m o n a n d i n e v i t a b l e in t h e

In-

dian philosophical

rigid

tradition.

The extremely

d e m a n d for b r e v i t y a n d c o m p a c t n e s s f o r c e d a w r i t e r t o d e v i s e w a y s of e x p r e s s i n g m o r e t h a n o n e by the same 11.

statement.

W e t r a n s l a t e u p a m a n a as a n a l o g y f o r t h e

lack o f a b e t t e r w o r d .

T h e t r a n s l a t i o n is all

r i g h t as far as G o t a m a ' s d e f i n i t i o n o f is c o n c e r n e d .

upamana

B u t it is c l e a r f r o m t h e

of V a t s y S y a n a t h a t b y u p a m S n a is m e a n t

comments identifying

t h e d e n o t a t i o n o f a w o r d o n t h e b a s i s of 12.

thought

similarity.

It h a s a l r e a d y b e e n e x p l a i n e d b y

VStsySya-

n a in h i s c o m m e n t s o n t h e a p h o r i s m 1.1.6 t h a t

this

t a k e s p l a c e t h r o u g h t h e k n o w l e d g e t h a t "a g a v a y a is s i m i l a r t o a c o w . "

W h a t is y i e l d e d b y t h e

logical process, according to VStsySyana, e d g e of t h e d e n o t a t i o n o f t h e w o r d

gavaya.

ana-

is k n o w l -

CHAPTER 2 Classification of Inference Gotama's classification of inference is contained in the aphorism 1.1.5:

"Next inference which is

knowledge based on those, is of three kinds: vat, sesavat, and samSnyatodrsta."

pürva-

We have already

seen in the previous chapter how VátsySyana has explained what is meant by "those."

It is now time to

explain what the threefold classification stands for. Since Gotama had not explained what each kind of inference is, we have to rely mostly on VStsySyana for an account of this classification.

He gives two al-

ternative explanations of the threefold classification:

1

PCTrvavat:

where the effect is inferred from

the cause, for example, from the rising clouds that it will rain.

áesavat is that where the

cause is inferred from the effect:

on seeing

the water of the river and the swiftness of the current as different from what it was and the fullness of the river, it is inferred that there was rain.

SamSnyatodrsta: the

perception of an object at a place different from where it was perceived before is due to its movement; so it is with the sun; therefore, though imperceptible, the sun has movement.

15

Alternatively, pürvavat is [inference] where of two [things] perceived as before, from one of the two that is perceived the other of the two that is not perceived is inferred, for example, fire from smoke. áesavat is 'reasoning through elimination1 (parisesa); and that is ascertainment of what remains after cancellation of certain alternatives when there is no other alternative. . . . S3manyatodrsta is but [inference] when the relation between the indicator and the indicated being inaccessible through perception, the indicated which is imperceptible, is proved through some 'generic character' (sSmgnya) of the indicator, for example, [inference of] the soul from desire and so forth; desire and so forth are qualia (guna), and qualia are supported by a substance, that which is their support is [by cancellation of all other alternatives] the soul (Comment on 1.1.5).

Speaking of the different cases it is obvious that pürvavat and sesavat in the first explanation are nondeductive inferences based on causal connection.

The literal meaning of these words throws

light on the nature of these two kinds of inference Pürvavat may be literally taken to mean "that which has the antecedent" and thus signify the inference from cause to effect.

Similarly, the word sesavat

may be literally taken to mean "that which has the

16 consequent" and thus signify the inference from the effect to the cause. Next comes sam5nyatodrsta which is more problematical in nature.

The complication has been in-

creased by the absence of a general description of this kind of inference such as is found in the two previous cases.

The most natural analysis of the

example given seems to be as follows : 1.

Whatever object is perceived at a place different from where it was perceived before has movement.

2.

The sun is perceived at a place different from where it was perceived before.

3.

Therefore, the sun has movement.

In itself this specimen differs hardly from the second kind of inference mentioned above, that is, inference from effect to the cause (as is correctly pointed out by Uddyotakara, NDFC, p. 295).

The dis-

tinguishing feature, however, can be gathered from the remark that what is being inferred is the sun's movement which is imperceptible.

In the alternative

explanation of this kind VStsySyana also states that it is concerned with the inference of something imperceptible, for example, the soul.

The differ-

entiating feature of the third kind of inference then seems to be that while in the first two kinds inference is confined to the realm of the perceptible, in this case we are concerned with the

17

inference of something imperceptible on the basis of a general connection already established.

The

literal meaning of samSnyatodrsta also throws some light on the nature of the case.

It may be con-

strued as seen (known or proved, drsta) through 2

the universal (sSmSnya),

thus referring to the

crucial role played by the universal connection as 3 the basis of the inference of the imperceptible. The view that samanyatodrsta stands for the inference of something imperceptible is also accepted by ancient writers of other schools.

Tsvara-

krsana writes in the Saitikhyakarika that "suprasensibles are known through the samSnyatodrsta inference" (karika 6).

This view is also shared by

áabara, the earliest commentator on the Mim&tisg Aphorism of Jaímini.

Similar corrobation is found

in the Vaisesika Aphorism of Kanada (aphorisms 2.2.15, 2.1.16 and so on).

The agreement of so

many ancient writers on this point is not surprising,

They all believed in .the existence of super-

sensible objects and hence were interested in a legitimate method of proving their existence. Whether an object is perceptible or imperceptible is in itself of no importance to deductive logic.

But the view that the scope of inference

is not restricted to what is perceptible and the

18 conception of a legitimate method of inferring the imperceptible is important for philosophy and scientific thought in general.

Moreover, the pre-

ceding account is necessary to refute the view of some modern writers.

Keith writes:

Inference samanyato drsta is illustrated by such a case, differing from the previous as that in which from observing the different positions assumed in the course of the day by the sun we conclude by the analogy of ordinary motion that it moves, although such motion is not open to our perception (ILA, p. 89).

Keith writes further:

" . . . the precise sense of

sSmSnyatodrsta must remain obscure, perhaps denoting similarity as a basis of inference" (ILA, p. 90).

Thus according to Keith, sSmSnyatodrsta is

probably a specimen of inference from analogy.

We,

however, do not agree that sSmSnyatodrsta is a specimen of reasoning by analogy.

As we have seen

in the previous chapter, both Gotama and Vatsyayana have distinguished inference as a source of knowledge from analogy (upamana), on the ground that the latter is based on knowledge of similarity, while the former is not.

Hence no specific kind of in-

ference mentioned by Gotama or VStsySyana should

19 be interpreted as basically analogical, unless it is absolutely necessary to do so.

Keith's inter-

pretation is probably derived from the fact that the term samanya may mean 'similarity'.

With this

meaning samgnyatodrsta literally means 'seen (known) through similarity1.

However, the term sSmSnya al-

so means a universal and it has been very widely used in this sense by the philosophical schools from very early times.

(In the Nyiya-Vaisesika view

the universal is a real entity, different from and independent of the particulars to which it may be related.)

The meaning of the term samSnya as uni-

versal naturally fits into the present context and that is how it has to be taken.

Though VatsySyana

has not given a general account of what sSmSnyatojSrsta is in the first explanation, in the example provided by him, the first premise is clearly a general proposition asserting the universal connection between being perceived at two different places and having movement.

We have also seen that the

example provided may properly be restated in the form of a syllogistic argument.

Our analysis of

VStsySyana's alternative account of samgnyatodrsta will also show that it would be very unnatural to interpret it as an analogical argument.

For all

these reasons the interpretation of sgmanyatodrsta 4 as an analogical argument is wrong. Similar

20 comments apply to the view of Chatterjee:

Here the inference depends not on a causal connection, but on certain observed points of similarity between different objects of experience. So it is more akin to an analogical argument than to syllogistic infer5 ence (NTK, 267).

Before going any further we note that Uddyotakara, the commentator on Vatsyayana, has given a completely different account of samanyatodrsta under the first explanation.

We have seen that

purvavat and sesavat have been explained as inference from cause and effect respectively.

Consis-

tently with that and taking advantage of the absence of a general description from VatsySyana (under the first explanation), Uddyotakara holds that it should be construed as. any inference based on a necessary (inseparable) connection other than that 6 of causation.

His own words are:

"Where the

characterized (visesyamano dharmi) is proved through a character (visesana) necessarily (inseparably) connected, though not by 7 way of cause or effect, that is samgnyatodrsta"

(NDFC, p. 295).

There is

ample evidence that Uddyotakara conceived of sSmgnyatodrsta as a very large class of inference,

21

including both deductive inferences and noncausal inductive inferences.

Thus later on when asked to

which class of inference should arthâpatti and sambhava belong (which have been declared to be inferences by Gotama), Uddyotakara replied that they should be classified under sSmgnyatodrsta (NDBVTV, p. 578) .

Under this new interpretation

the threefold classification of inference becomes exhaustive.® We may take this opportunity to rebut a very serious misconception about Indian logic advanced by Bocheriski.

He writes:

Evidently no formal logic was possible without the notion of universally valid laws.

From

this point of view the importance of Plato for the history of logic can best be seen when we consider the development of the science in India, that is, in a culture which had to create logic without a Plato. One can see in the history of Indian logic that it took hundreds of years to accomplish what was done in Greece in a generation thanks to the élan of Plato's genius. . . . (HFL, p. 33).

He writes further: One point already emerges from the Nyâya satra and VStsySyana, that we should not look for any universal premises. . . there is nothing of the kind in the Nygya Vartika

22

of Uddyotakara. Later history also shows how difficult the Indian logicians found it to grasp the universal (HFL, p. 450).

A similar comparison between Plato and Indian logicians is also found on page 431 of the same book. This kind of glorification of Western logicians at the expense of Indian logicians can be done only by one who exclusively relies on secondhand or even thirdhand sources of information about Indian logic. The specific reference to Uddyotakara by name is very unfortunate.

We have already seen that sjSmSn-

yatodrsta, according to him, is any inference based on the necessary (inseparable) connection between two or more properties other than that of causation. It should be clear from this that inference, according to Uddyotakara, is reasoning based on a necessary (inseparable) connection between two or more properties (or two or more statements).

This fact

alone is sufficient to refute Bochenski's sweepingly general statement about the deficiency of early Indian logicians.

With regard to Gotama and Vats-

yayana, Bochenski says that we should not look for any universal premise.

But we have already seen

that VStsySyana has used a universal premise in illustrating the samSnyatodrsta inference.

(One

does not have to use such expressions as "all,"

23

"every," and so on to have a universal premise.) We shall come across more such occasions later and find that Gotama and VStsySyana distinguished several valid and invalid varieties of inference. Moreover, the very conception of sSmgnyatodrsta as an inference (of something imperceptible) based on a universal connection refutes Bocheriski's statement that early Indian logicians did not have a conception of universally valid laws as did Plato. In fact if we take the four earliest NySya and Vaisesika philosophers, namely, Gotama and VStsyayana and Kanada and PrastapSda, we find that all of them believed in the existence of real universáis distinct from and independent of the particulars as Plato did (without subscribing to many peculiarities of Plato's theory).

The ignorance

revealed in Bochenski's statement could be made apparent also by numerous references to hosts of early writers belonging to the other schools, namely, Bauddhá, Jaina, Saitikhya, Mimaitisa and so forth. We now proceed to give an account of Vatsyayana's alternative explanation of the threefold classification of inference.

With regard to pürvavat it

is now said that "pürvavat is [inference] where of two things perceived as before, from the one of the

24 two that is perceived the other which is not perceived is inferred, for example [inference of] fire from smoke."

This account is based on a sec-

ond possible analysis of the literal meaning of purvavat which may be analyzed to mean "as before." Vatsyayana's account, however, leaves many things unclarified.

First of all, though he spoke of

things perceived as before, it is not meant that this kind of inference is restricted to only perceptible objects.

Perception has been used only

illustratively to refer to any other accepted source of knowledge as well. this out by saying:

Vacaspati Misra has pointed "Perception refers to any

source of valid knowledge whatsoever"

(NDFC, p.

319) .

Second, the significance of "as before" has to be carefully analyzed.

VStsyayana certainly does

not mean that the inference will be based on the perception (knowledge) of the togetherness of two things in some instances.

That would yield only

a probabilistic result and would be inconsistent with the conception of inference as a source of knowledge in the strict sense of knowledge that is true and certain.

Hence "as before" has to be

construed as referring to the universal relationship between two things as already known.

In the example

cited, inference of fire from smoke, the connection between smoke and fire is not accidental but necessary, being based on causality.

The two things

of which Vatsyayana speaks are obviously the indicator and the indicated.

The indicator is given

and is known already to be universally connected with the indicated.

On this basis the indicated,

which is not given, is inferred. Third, though VStsySyana has mentioned only two terms, there is a third term involved in this kind of inference.

When fire is inferred from

smoke, the inference is always with respect to a specified locus, such as the hill.

The third term

called the subject (dharmx or paksa) is sometimes left understood when it is well known what is intended as the subject.

It seems, therefore, that

in the second explanation purvavat stands for the deductive core of the pentapod reasoning discussed in the third chapter.

Vatsyayana1s account here

is unusually brief, because he discusses it more fully later while commenting on the pentapod reasoning.

Thus the two things mentioned by him, referred

to earlier as the indicator and the indicated, are nothing other than the probans (hetu, liftga or sSdhana) and the probandum (sSdhya) respectively. This is also how VScaspati Misra has interpreted

26 the nature of purvavat:

"...

inference of the

other of the two, that is of the character which is the probandum

(sadhyadharma), from the knowl-

edge of the one of the two characters, that is of the character which is the probans subject

(sadhyadharmi)"

(sadhana) in the

(NDFC, p. 319).

VStsySyana

has said that "from the one of the two that is perceived is inferred the other which is not perceived." Vacaspati Misra has identified the one that is perceived or given with the probans and the other that is not perceived but is inferred, with the probandum.

The inference also involves a third term,

namely, the subject, wherein the character chosen as the probandum is inferred to belong.

The same

inference is set out with five steps as a pentapod reasoning when meant to be a demonstration for others, particularly philosophical opponents. In the second version sesavat is presented as a disjunctive syllogism, the nature of which will be fully discussed in the fifth chapter. The second version of sSmgnyatodrsta is as follows:

samanyatodrsta is but [inference] when, the relation between the indicator and the indicated being inaccessible through perception, the indicated, which is imperceptible, is proved through some [literally, some object

27 which is the] generic character of the indicator, e.g., [the inference of] the soul from desire, etc.; desire, etc. are qualia and qualia are supported by a substance, that which is their support is [by cancellation of all other alternatives] the soul.

Thus what is to be proved in a sSmgnyatodrsta inference is something imperceptible.

In the example

also, what is to be proved is the soul, which is imperceptible.

Vatsyayana has pointed out that in

such a case the relation between the indicator and the indicated is inaccessible through perception. The implication is that the indicated cannot be proved by a straightforward ny5ya for the validity of which the statement of pervasion between the probans and the probandum is indispensable.

The truth

of the statement of pervasion must ultimately be based on perceptual evidence.

But if the probandum

(indicated) is imperceptible, the relationship (=pervasion) with any probans

(indicator) whatsoever

cannot be established by perception. VStsyayana points out that in such a case the indicated has to be proved through some generic character of the indicator.

Since the relationship

between the indicated and any indicator whatsoever

28 cannot be established directly, it must be established indirectly.

The example shows how.

Inter-

nal states like desire, cognition, and so on have been proposed by Gotama as the indicators or marks for inferring the soul (aphorism 1.1.10).

Since

the soul is imperceptible, the universal connection between the soul and desire, and so on cannot be directly established through perception; but desire, etc. are qualia. by a substance.

Every quale is supported

(Here is one more specimen of a

universal premise used by Vatsyayana—a fact not properly noticed by many modern writers.)

Hence de-

sire and so on must be supported by a substance. That substance is nothing other than the soul, because other substances have to be eliminated for various reasons.

Vatsyayana has not mentioned the

elimination of other substances because he has mentioned it elsewhere.

He writes while commenting

on 3.2.40:

That cognition is the quale of the soul is the context. . . . With the cancellation of the physical elements, the external senses and the inner sense, no other substance

is possible; the soul is left and

thus it becomes proved that cognition is its quale.

29

There is no doubt at all that the second half of the reasoning in Vatsyayana's example of sSmSnyatodrsta is a proof by elimination. Though a full exposition of sSmanyatodrsta requires further discussion, we will conclude by noting the interesting logical structure of the example of VStsySyana.

The reasoning is a joint

product of a categorical syllogism and a disjunctive syllogism.

1. 2. 3. 4.

5.

6.

It may be reconstructed as follows:

All qualia are supported by a substance. Desire, cognition, and so on are qualia. Therefore, desire, cognition, and so on are supported by a substance. Desire, cognition, and so on are qualia of either the physical elements or the external senses or the inner sense or the soul. Desire, cognition, and so on are not qualia of the physical elements, the external senses, or the inner sense. Therefore, desire, cognition, and so on are qualia of the soul.

The extreme demand for brevity and compactness has prevented VatsySyana from setting out the argument as elaborately as above. about the reconstruction. significant.

But there can be no doubt The example is highly

The use of the categorical syllogism

and the disjunctive syllogism within the same reasoning enhances the scope of ancient Nyaya logic.

30

NOTES 1.

The alternative explanations are probably

based on two different analyses of the meaning of such terms as pürvavat. 2.

SSmSnyatodrsta may also be construed as

samanyata eva drsta, that is, as through the universal

(known) only

(connection)', which is true

in the case of imperceptible 3.

'seen

objects.

The same example of sSmSnyatodrsta is

found in the Upgyahrdaya

(an ancient pre-DiftnSga Bud-

dhist work on logic, the author of which is unknown) without once again a general account of what it is. The passage is:

"Somebody reaches a different place

through movement.

In the sky also the sun and the

moon rise in the east and set in the west.

Though

their activity is imperceptible, their movement is inferred.

This is s5m5nyatodrsta"

(Upgyahrdaya in

G. Tucci's Pre-Difinaga Buddhist Texts on Logic from Chinese Sources, p. 14).

It also gives the three-

fold classification of inference but gives a different account of pürvavat and 4.

sesavat.

Keith admits that later the word

applied

to some abstract form of reasoning in which perception could not directly be applied.

But as our

references to KanSda, áabara, and so forth show, this is how the word was understood from the early times, even outside the Nygya 5.

school.

Chatterjee has added that

involves " . . .

sSmgnyatodrsta

the vygpti or universal

between the middle and major terms.

. ."

relation (NTK, p.

267). This is inconsistent with his other statement quoted by us.

31 6.

Uddyotakara has not rejected the possibility

of inference of the 7.

imperceptible.

This is not a good translation, but the

words visesya and visesana are difficult to translate. 8.

Uddyotakara gave other

alternative

explanations of the threefold classification of inference.

CHAPTER 3 PaftcgvayavanySya, Or The Reasoning With Five Steps 1.

Introduction.

The paftcSvayavanygya, or the reasoning with five steps (avayava, literally, member), from the historical point of view, is the most important logical contribution of Gotama.

By far the greatest

part of Indian logic has been devoted to the critical analysis and exposition of the nygya.

The nygya de-

notes a complex process of reasoning and demonstration with both deductive and nondeductive aspects. Its nondeductive aspect includes an inductive generalization as well as an argument based on analogy. In its deductive aspect it is basically a reasoning through a middle term that is analogous to the Aristotelian syllogism.

Taking the deductive and

the nondeductive aspects together, the nygya, when stated with all the 'five steps' (paficgvayava), was regarded as the method of demonstration par excellence (paramo nyaya) and most useful in proving or disproving philosophical positions in a debate.

It

is then obvious that the customary translation of the nygya as 'syllogism' is misleading.

But at the same

time it is extremely difficult to find a suitable

33 translation, simply because the nygya diverse reasoning processes within it.

comprises For want of

anything better we translate it as the 'pentapod reasoning1

("pentapod" for short).

The literature on the pentapod in English and other European languages is extensive.

The preva-

lent opinion, supported by scholars like Keith, Stcherbatsky, Randle, Bocheriski, Potter, and so forth, is that in Gotama's original formulation of the pentapod as well as in its exposition by VatsySyana, the pentapod did not contain a valid deductive argument within it.

Many of these scholars

have held that the pentapod was basically an analogical argument from particular to a particular without the use of a universal premise.

It may be useful at

this point to quote a few of them.

Keith says:

"The

fact that reasoning can only be by means of a general proposition had thus not yet been appreciated in the school, for this reasoning still was from particular to particular by analogy . . . "

(ILA, p. 87).

Ac-

cording to Randle, " . . . both the Sutra and the Bhgsya formulate inference as based on the likeness of the case under investigation to example (Fragments from DiftnSga, p. 75). what different vein writes:

..."

Potter in a some-

"The situation is rather

that one giving an argument is conceived to be citing

34

examples in order to suggest the plausibility of his hypothesis"

("DiftnSga and the Development of Indian

Logic" in Chi's Buddhist Formal Logic, p. xliv-xlv). These scholars hold that the addition of the deductive aspect to the pentapod containing a valid argument took place much later, through the effort of logicians like DifinSga, Uddyotakara, Dharmakfrti and others.

We shall prove that this current opinion is

wrong and is due to a gross misrepresentation of the positions of Gotama and VatsySyana regarding the pentapod.

We will show that the pentapod contained a

valid argument in its original formulation by Gotama and that Vatsyayana's exposition bears this out. Since a lot has been written on the nondeductive aspect of the nySya, we shall confine our analysis mostly to the deductive aspect. 2.

Gotama's statement of the Pentapod.

Gotama's account of the pentapod is contained in the aphorisms 1.1.32-1.1.39.

Since the text is

short, we quote it in full:

The components [of the pentapod reasoning] are the Thesis, Reason, Exemplification, Application and Outcome. *1.

The Thesis (pratijfig) is the state-

ment of what is to be proved. *The numbers are not part of the text.

35 2A.

The Reason (hetu) is [that from which

we get] what proves the probandum by virtue of the [universal] concomitance

(s5d-

harmya) [stated] in the Exemplification. 2B.

Likewise [is that from which we get

what proves the probandum] by virtue of the [universal] exclusion tance).

(or nonconcomi-

(Vaidharmya) [stated in the Exem-

plification] 3A.

The Exemplification

(udaharana) is

[that from which is obtained] an instance where the character(=the probandum) is present in accordance with the concomitance

[universal]

[of the probans] with the

probandum. 3B.

Or the opposite in the reverse of that.

Vatsy5yana:+ The Exemplification is [that from which is obtained] an instance where the character

(=the probandum) is absent

in accordance with the [universal] exclusion [of the probans] along with the probandum.

4(A,B).

The Application

(upanaya)

is the characterisation of the subject as so or not so depending on [the nature of] the Exemplification. 5.

The Outcome (nigamana) is the repeti-

tion of the Thesis as qualified by the probans.

Since the preceding text is all that Gotama has directly written to describe the structure of the +Since this aphorism is unusually cryptic, we have tagged on to it the translation of the aphorism as restored by Vatsyayana,

36 pentapod, it is useful to briefly state at this point one of the examples of the pentapod supplied by VatsySyana:

Thesis:

Sound is non-eternal,

Reason:

Because of being originated,

Exemplification:

What is originated is non-

eternal like a plate, Application: Outcome:

Sound is so originated,

Therefore, because of being originated,

sound is non-eternal.

Here 'sound1, 'originated' and 'noneternal' represent respectively the subject, the probans, and the probandum and are comparable respectively to the minor term, the middle term, and the major term of an Aristotelian syllogism.

We now proceed to analyze

in detail these aphorisms and to study the nature of each of the five steps. 3.

The First Step:

the concepts of Subject

and Probandum. The Thesis, or the first step, has been described by Gotama as the statement of what is to be proved.

'What is to be proved' is ambiguous."'"

One

of its possible meanings is 'the proposition to be proved'.

VatsySyana's comment makes it clear that

it is this sense that is intended here:

"The Thesis

which states what is to be proved is the statement

37

which makes known the characterized (dharmf) as qualified (visista) by the character (dharma) to be proved (to belong to it].

Such as

1

eternal " (comment on 1.1.33).

1

sound is non-

VatsySyana's defi-

nition of Thesis makes it evident that the Thesis comprises the statement of two terms, namely, (1) the characterized (dharmi) and (2) the character (dharma) and that the character must be predicated of the characterized.

The characterized corresponds

to the minor term of the Aristotelian syllogism. refer to it as the 'subject1.

We

The character corre-

sponds to the major term of an Aristotelian syllogism. We refer to it as the 'probandum1.

The conception

of the probandum as the property predicated of the subject and to be proved to belong to it is analogous to Aristotle's conception of the major term as the predicate of the conclusion.

The conception of

the subject as the characterized of which the character to be proved is predicated is analogous to Aristotle's conception of the minor term as the subject of the conclusion. Though VStsySyana's example of the Thesis, namely, 'sound is noneternal,' looks like an indefinite proposition, in actual import it is a universal proposition.

'Sound is noneternal' naturally

means that all sounds are noneternal', and there

38

can be little doubt that this is what is meant.

On

many other occasions VStsySyana has left the quantifier understood, and it has to be gathered from the context what the quantifier is intended to be. This practice of leaving the quantifier understood in this way is, of course, un-Aristotelian.

Aris-

totle's syllogistic examples always contain an explicit quantifier.

It would be a mistake, however,

to think that quantification was not important to VStsySyana and hence that he did not pay much attention to whether the quantifier is explicitly mentioned.

Though the quantifier is understood, it is

undoubtedly there.

Supplying an explicit quantifier

partly depends on the general linguistic habits and peculiarities of a particular language.

In English

a proposition like 'man is mortal' is regarded as a universal proposition.

But cases of universal pro-

position lacking a quantifier are far more common in Sanskrit.

In fact in idiomatically good Sanskrit

a universal proposition like 'all sounds are noneternal' could normally be expected to be expressed as 'sound is noneternal'. Though VStsySyana would sometimes leave the quantifier understood, unlike Aristotle, he wanted to make the order of the subject and the predicate in the Thesis (and consequently, in the Outcome) specific.

Aristotle often used the two forms 'S is

39

P1 and 'P belongs to S1 as interchangeable.

Thus he

did not hesitate to use both the forms 'All S is P1 and 'P belongs to all S1 within the same argument. In the latter case P would still remain the logical predicate, though it is the grammatical subject, and S would remain the logical subject, though it is part of the grammatical predicate. with VStsyayana. He writes: is of two kinds:

Probably not so

What is to be proved

the character belonging to the

characterized, as noneternality belongs to sound; or the characterized (dharmi) qualified by the character (dharma), as sound is noneternal.

Here. . .

the latter is the case" (comment on 1.1.36).

The

point is that a sentence like 'sound noneternal' (with the copula understood in the Sanskrit sentence) may be interpreted in either of two ways.

It may

be taken as 'sound is noneternal' or as 'noneternality belongs to sound'.

VatsySyana is saying

that of these two possibilities, only the former should be regarded as the Thesis to be proved.

More-

over, he is not saying this specially for one particular case.

He is saying in general that the form

of the Thesis is 'the characterized is qualified by (or has) the character' instead of 'the character belongs to the characterized'.

This prevents using

both of these forms interchangeably as Aristotle has

40 done.

In this particular respect VStsyayana is 2

adopting a formalistic

attitude, while Aristotle

is not. 4.

The Second Step

The first variety of Reason: probans:

the concept of

Gotama's definition of the second step is:

The Reason is /that from which we get/ what proves the probandum by virtue of universal concomitance /stated/ in the Exemplification. is the name of the second step.

'Reason' (hetu) It consists in stat-

ing the probans (hetu) by virtue of which the conclusion is to be proved.

Thus Gotama has given the

same name, namely, hetu, to both the probans and second step which supplies it. In connection with defining the second step, Gotama has also clarified part of the concept of a probans.

The probans (comparable to the middle term)

is that which proves the probandum by means of universal concomitance (or universal exclusion) stated in the Exemplification, or the third step.

It is

stated in the latter that the probandum is universally concomitant with the probans.

This means that

the property chosen as the probandum is stated to be present everywhere the property chosen as the probans is present.

The word 'property' (dharma)

here should be taken in a very broad sense.

It does

41 not signify property as an ontological category distinct from substance, relation, and so on.

'Pro-

1

perty or 'character' is used with as much generality as the word 'thing' in English.

The NySya logicians

refer to anything related by any conceivable relation to a thing as a property or character of the latter, and the latter is referred to as the characterized (dharmi).

Taken in this broad sense smoke

and fire may be regarded as characters.

The proposi-

tion 'wherever there is smoke there is fire' expresses the univeral concomitance between smoke and fire.

Similarly, the proposition 'all men are mortal'

expresses the universal concomitance between humanity and morality.

A similar analysis is given for both

of these two cases.

The former case asserts the

universal coexistence of smoke and fire.

The latter

case is also analysed to assert the universal coexistence of humanity and morality.

This intensional

3

analysis is correlated with an extensional analysis. Thus the latter case would be taken to assert that the class of men is included in the class of mortals, or that the extension (desa) of the class of mortals is wider than (or at least as wide as) that of the class of men.

Similarly, the former case would be

taken to assert that the class of smoke possessing things is included in the class of fire possessing

42 things.

The universal concomitance (or its equiva-

lent obtained by contraposition) between the probans and the probandum must be stated in order that the conclusion may be entailed by the premises. VStsySyana comments:

"The Reason is that which

makes known what proves the character to be proved by virtue of the universal (sgmSnya) [as stated in or known through] the exemplification. . . . 'because of being originated'.

Such as

What is originated

is well known to be non-eternal."

The 'universal'

in this passage should refer to the universal concomitance

between the probans and the probandum as

stated in the third step.

VStsyayana has made that

clear by following up the citation of the probans with the universal proposition that what is originated is noneternal.

Being originated is the probans.

Being noneternal is the probandum.

The proposition

states the universal concomitance between these two properties.

This universal proposition is not a part

of the Reason or the second step.

It has been taken

over from the third step to explain the point of mentioning 'being originated' as the probans.

The sec-

ond step consists in citing the property to be used as the probans without relating it to the subject. Thus the second step is not a complete proposition, but merely presents the probans as that through which the existence of the probandum is going to be proved.

43

The word samanya in the previous passage is ambiguous.

Like the word sadharmya, it may literally

mean either a universal characteristic or a similar characteristic (or abstract properties formed out of these, namely, universality and similarity).

A per-

fectly good sense consistent with our view of what VStsySyana has said also can be made by taking the word to mean similarity or a similar characteristic. In this context similarity stands specifically for the similarity between the subject and the positive example, that is,

an instance where the proban-

dum is present along with the probans and is constituted by the fact that the probans belongs both to the subject and that instance.

In the earlier ex-

ample sound is the subject, originatedness is the probans, noneternality is the probandum, and the plate, which is both originated and noneternal, is the positive example, that is, it is an instance where the probandum noneternality is present along with the probans originatedness. also belongs to sound.

Originatedness

Hence sound is similar to

the plate in the respect that both sound and the plate are originated.

The subject is required to be

similar not just to one positive example or some positive examples, but more strictly to be similar only to positive examples or instances where the

44 probandum is present.

By implication the subject

is required not to be similar to instances where the probandum is absent.

It should be remembered that

the similarity between the subject and the positive example is in the respect that the probans belongs both to the subject and the positive example.

Hence

if the probans happens to be present in an instance where the probandum is absent, the subject would turn to be similar to that.

This would violate the

condition that the subject is similar only to positive examples.

The preceding condition can be ful-

filled only if the probans is absent wherever the probandum is absent.

Thus if similarity is construed

in the strict sense, the universal concomitance between the probans and the probandum, the statement of which is required for making the reasoning valid, would be necessarily implied.

As Uddyotakara says:

"By stating similarity with the [positive] example similarity with what is not a [positive] example is ruled out by implication. emphasis (avadhSrana).

Or it is ruled out by

By similarity with [positive]

examples is meant similarity with [positive] examples alone. . ." (NDFC, p. 527).

Vatsyayana himself says:

"In the former kind of example (i.e., a positive example which has to be supplied in the case of a probans having sadharmya) with respect to those two characters which are seen to be related as what

45 proves and what is proved, it is inferred that they are related as what proves and what is proved also with respect to the subject. . . . This is not possible for a pseudo-probans. , ." (comment on 1.1.37). Again he says:

". . . the two characters are known

to be in the same place and related as the probans (=what proves) and the probandum (=what is to be proved) by way of sadharmya 'as a rule' (or without exception:

Vygvasthita)."

Further, "When it is

known through examples that two characters are related as the prover (=that which proves) and the proved 'without exception' (vyavasthita), that character which is the prover is taken as the probans, but not from mere similarity or mere dissimilarity" (comment on 1.1.39).

It is clear from these passages

that in the case of a probans characterized by sadharmya , it becomes known through particular instances: (1) that the probans is related to the probandum by way of the 'prover' and the proved as a rule without exception; (2) that this relationship is not possible for pseudo-probantia; and (3) that this relationship must be distinguished from mere similarity.

Thus a

deviant (vyabhicSri) probans, which is present both where the probandum is present and where the probandum is absent, can possess mere similarity. possess similarity as a rule.

But it cannot

The conception of a

46

rule (vyavastha) takes us beyond particular cases to a universal connection.

Otherwise it cannot be

explained why sadharmya is not possible in the case of a deviant probans.

Since a deviant probans is

present in some instances where the probandum is present, the subject can indeed be said to be similar to those instances.

But what is not realizable in

this case is similarity as a rule or similarity restricted to only positive examples, because the subject will also be similar to instances where the probandum is absent.

The concept of sSdharmya-vyavastha

unmistakably amounts to the concept of a universal connection between the probans and the probandum. vatsyayana has also said:

"The Reason is the

statement of a character as the probans after synthesising the knowledge of its belonging to the subject with its 'synthetic knowledge1

(pratisandhana) in

the Exemplification" (comments on 1.1.34).

Here the

use of the technical concept of pratisandhana is significant.

It refers to the synthesis of several

cognitions and noticing the interconnection.

Such

synthesis is involved in knowing that in some cases the probans is accompanied by the probandum, which may lead to the generalization that the probans is pervaded by the probandum.

Thus the use of the

concept of pratisandhana suggests that a universal premise is involved.

47

Moreover it is significant that in the aphorism 1.1.34, Gotama refers to the probans as the sSdhana of the probandum, that is, as that which proves the probandum.

It will be gathered from the next chap-

ter that according to Gotama, if a probans is not universally concomitant with the probandum but is deviant, it cannot be regarded as a sSdhana.

From

this it becomes clear that universal concomitance and not similarity is the basis of the reasoning. 5.

The second variety of reason:

Further

discussion of the concept of probans. Gotama said in the aphorism 1.1.35: by virtue of [universal] exclusion."

"Likewise

Taken in the

context the aphorism means that "likewise the Reason is that from which we get the probans which proves the probandum by virtue of universal exclusion stated in the Exemplification,"

Universal ex-

clusion means that the probans must be absent wherever the probandum is absent.

The proposition 'all

men are mortal' states the universal concomitance between the properties humanity and morality.

The

universal exclusion between these two properties is stated by the proposition 'all nonmortals are nonmen'. Thus a proposition stating universal exclusion is what can be obtained from a proposition stating universal concomitance by contraposition.

Gotama held that a

probans must be related to the probandum either by

48 way of universal concomitance or by way of universal exclusion.

This strongly suggests that he was aware

of the logical equivalence between the statement of universal concomitance and that of universal exclusion and held that a probans of either type could be used in a pentapod. Since Gotama held that the probans should be related to the probandum either by way of universal concomitance or by way of universal exclusion, he obviously had in mind something like what is expressed by the traditional dictum de omni et nullo: "What can be predicated universally of anything else, whether affirmatively or negatively, can be predicated in the same way of all that is contained under it" (from Aldrich's Logic in Eaton's General Logic, p. 90).

Universally predicating affirmatively corre-

sponds to the statement of universal concomitance between the probans and the probandum.

Universally

predicating negatively corresponds to the statement of universal exclusion between the same.

In the

fourth step of the pentapod, as we will see, the probans is either predicated affirmatively of the subject or the negation of the probans is denied of the subject.

On the strength of that and either

the universal concomitance or universal exclusion stated in the third step, it is concluded that the probandum belongs to the subject.

49 Vatsyayana's comments on the second variety of Reason are as follows:

Is this alone the definition of Reason? No. . . . The Reason is also [that from which we get] what proves the probandum by means of [universal] exclusion [stated] in the Exemplification.

How so?

Sound is

non-eternal because of being originated. What is non-originated is well known to be eternal like the substance soul, etc.

In VStsySyana's example the statement of the probans is followed by a statement of the universal exclusion between the probans and the probandum chosen together with a particular instance.

This

does not really belong to the second step but belongs to the third step.

But as he did in the pre-

vious case, he is explaining the point of choosing 'being originated' as the probans. The most striking thing about VStsyayana's example, however, is that he expresses the universal exclusion incorrectly.

He puts it as "What is non-

originated is well known to be eternal," and so on. This amounts to saying that the probandum is absent wherever the probans is absent or that the absence of the probans is pervaded by the absence of the probandum.

But what is required to be said is that

the probans is absent wherever the probandum is

50 absent or that the absence of the probandum is pervaded by the absence of the probans.

Since 'being

originated' is the probans and 'noneternality' is the probandum, the correct statement of universal exclusion is 'what is eternal (that is, not noneternal) is nonoriginated, etc.' is elementary.

VStsyayana's error

Since the probans is the pervaded

and the probandum is the pervader, the absence of the former follows from the absence of the latter but not vice versa.

The absence of the pervaded

does not imply the absence of the pervader. The relevant text of VStsySyana is as follows: anutpattidharmakam nityam yaths Stmadi dravyam.

We

have translated it as 'what is non-originated is eternal such as the soul substance, etc.' This is because in the text 'nonoriginated' occurs first followed by 'eternal'.

This translation gives us

an erroneous statement of the universal exclusion. But there is no fixed word order in Sanskrit, and the writer has the option of putting the subject of the sentence after the predicate.

Hence it is pos-

sible that though 'eternal' comes after 'nonoriginated' , the former is intended to be the subject. that case the translation should be: is nonoriginated, etc.'

In

"what is eternal

This would give us a correct

statement of the universal exclusion.

Since the text

taken by itself may be interpreted either way, there

51 is no conclusive reason, it may be felt, for saying that VStsySyana was mistaken here. But there is further evidence that points to the same mistake. VatsySyana says:

While commenting on 1.1.37 "After realising that in such in-

stances as the soul non-eternality is absent due to the absence of originatedness the reverse is inferred for sound that sound is non-eternal because of being originated."

Here VStsyayana is clearly saying that

the absence of originatedness is the ground for the absence of noneternality.

This gives rise to the

presumption that the intended generalization is that wherever there is the absence of originatedness there is the absence of noneternality, or, in other words, whatever is nonoriginated is eternal.

Moreover,

VStsySyana has put 'nonoriginated' before 'eternal' in all other places where neralization.

he mentions the said ge-

This confirms the suspicion about

his error. The error was duly noted by the Nyaya writers. Vacaspati Misra comments, while referring to the same example:

"Here the author of the Bhasya'

(=V5tsyayana). . . has spoken of the absence of the probandum on the ground of the absence of the probans.

That is incorrect" (NDFC, p. 567).

VStsySyana

was probably misled by the fact that, in the particular example chosen by him, both the probans and

52 the probandum have an equal extension.

In this

particular case it remains true to say that wherever there is the absence of the probans there is the absence of the probandum.

But usually the proban-

dum, which is the pervader, is the wider class.

In

such cases though it is correct to speak of the absence of the probans on the ground of the absence of the probandum, the reverse is not true. The word vaidharmya has been used by Gotama in a technical sense as a correlative of sadharmya to mean universal exclusion.

The word vaidharmya, how-

ever, may mean literally 'dissimilarity1, and many modern writers have taken it in this sense.

The con-

ditions for a valid argument may be obtained even if vaidharmya is taken to mean 'dissimilarity'.

But

then a proviso would be needed, as was needed in the previous case when sadharmya was understood to mean 'similarity'.

As Uddyotakara says:

"Here also dis-

similarity with [negative] examples means dissimilarity with whatever is a [negative] example and not with whatever is not a [negative] example" (NDFC, p. 538).

Examples are of two kinds, namely, posi-

tive examples and negative examples.

A positive

example is where the probandum is present (together with the probans).

A negative example is where the

probandum is absent (and the probans is also absent).

53 In this passage 'example' refers to a negative example.

'Dissimilarity' means the dissimilarity be-

tween the subject and the negative example.

The

subject is dissimilar to the negative example in the respect that the probans is present in the subject but not in the example.

The subject is required to

be dissimilar to whatever is a negative example. That means the probans must not be present in any negative example.

If the probans were present in

a negative example, the subject would become similar to that negative example, because the probans belongs to the subject as well.

The requirement that

the subject is dissimilar to every negative example implies that the probans is absent wherever the probandum is absent.

The latter is nothing other than

the relation of universal exclusion between the probans and the probandum. We translated the aphorism 1.1.35 as 'likewise the Reason is [that from which we get] what proves the probandum by virtue of the universal exclusion [stated] in the Exemplification' na's restoration).

(based on Vatsyaya-

Here we have taken the word

vaidharmya to mean 'universal exclusion' and udsharana to mean 'Exemplification' or the third step.

In the

light of Uddyotakara's analysis we now give an alternative translation of the aphorism.

The word

54 udaharana may also mean an 'example' (in this case, a negative example), and vaidharmya, 'dissimilarity.' The aphorism could then be translated as:

'Likewise

the Reason is [that from which we get] what proves the probandum by virtue of [the subject's] dissimilarity with [whatever is] an example (= a negative example)'.

The point is that the word udaharanavai-

dharmya in the text is a compound.

The compound le-

gitimately may be broken to mean 'dissimilarity' with whatever is an example', if the words udaharana and vaidharmya are taken to mean 'example' and 'dissimilarity' respectively. Similarly, we have translated the aphorism 1.1. 34 as:

'The Reason is [that from which we get] what

proves the probandum by virtue of the universal concomitance [stated] in the Exemplification'.

There

we have taken sadharmya to mean 'universal concomitance' and udaharana to mean 'Exemplification'. sadharmya and udSharana are taken to mean

1

If

similarity'

and 'example' respectively, the aphorism may alternatively be translated as:

'the Reason is [that from

which we get] what proves the probandum by virtue of [the subject's] similarity with [only] examples (= positive examples)'.

Once again udSharana-sSdharmya

in the text is a compound and may legitimately be broken to mean 'similarity only with examples'.

55 As in the case of sSdharmya vaidharmya also

in the case of

VStsySyana has himself stressed

that vaidharmya should not be taken to mean just dissimilarity. lowing passage:

We have already mentioned the fol"When it is known through examples

that two characters are related as the prover and the proved, that character which is the prover is taken as the probans, but not from mere similarity or mere dissimilarity."

Again he has said, as we

have already seen, that vaidharmya is one of the defining characteristics of a probans.

This implies

that vaidharmya could not be a characteristic of a pseudo-probans, because if it were, the definition would have been too wide.

This can be explained

only if vaidharmya is taken to mean universal exclusion.

If it meant dissimilarity, a deviant pro-

bans also could be characterized by it, because it could very well belong to the subject and also be absent in some instances where the probandum is absent, so that the subject would be dissimilar to those instances.

But the subject, in this case,

could not be dissimilar to all negative examples, because the deviant probans would be present in some instances where the probandum is absent.

All this,

together with the fact that VStsyayana has linked the mentioning of a probans with the statement of a universal connection between the probans and the

56 probandum, proves that he took vaidharmya to mean universal exclusion. 7.

The Third Step:

The First Variety of Exem-

plification. Gotama defined the first variety of the third step called the Exemplification (udaharana) as follows:

"The Exemplification is [that from which is

obtained] an instance where that (=the probandum) is present in accordance with the [universal] concomitance [of the probans] with the probandum."

Since

the first step is the statement of what is to be proved and the second step merely cites the probans without relating it to the subject or the probandum, this is the first step of the pentapod which contains a premise in the genuine sense (see also section 9). It states that the probans is universally concomitant with the probandum.

This statement or its lo-

gical equivalent is indispensable for the validity of the argument.

It corresponds to the major premise

of an Aristotelian syllogism.

But it substantially

differs from an Aristotelian major premise, because it contains a supporting instance for the universal concomitance stated as well.

In this case the sup-

porting instance has to be of the positive type, that is, an instance where the probandum is present (together with the probans).

The explicit mentioning

57

of a supporting instance bears testimony to the in4 ductive aspect of the nySya.

While formulating the

principles of nyaya, Gotama was concerned with more than mere formal validity.

The nySya was conceived

to be a source of true knowledge.

Hence it was nec-

essary that the premises used in a nygya were true propositions.

We believe that the supporting in-

stance indicated that the generalization involved in asserting the universal concomitance has been properly done.

VStsyayana said, as already mentioned,

that the corrobarative instance enables us 'to know that two characters are universally concomitant as a rule1.

He also said:

"The udSharana is so called

because it exemplifies the relationship of that which proves and that which is to be proved" (comment on 1.1.36).

According to us, 'the relationship of that

which proves and that which is to be proved' refers to the universal concomitance between the probans and the probandum.

It is clear from VatsySyana's

example that both the universal concomitance and a supporting instance were stated in the third step. His example of the first variety of Exemplification is:

"What is originated is noneternal like a plate,

and so forth."

'Being originated' is the probans,

and 'noneternality' is the probandum, as previously mentioned.

58 That both the universal concomitance and a supporting

instance were stated in the third

step

is also borne out b y the account of PrasastapSda, the Vaisesika

commentator:

The Exemplification kinds:

(nidarsana) is of two

through sSdharmya or universal

concomitance and through vaidharmya or universal exclusion.

There, exemplifica-

tion of sadharmya is the statement of inclusion of the class of the probans in the class of the probandum.

For example,

whatever possesses motion is well known to be a substance like an arrow pp.

[PDS,

598-599).

In Pras'astapada' s example the Thesis to be proven is 'air is a substance 1 is the probans.

and

'possessing motion'

Most significant

in this passage is

the categorical assertion that the exemplification of sSdharmya means the statement of universal concomitance.

Consistently, later NySya

logicians

have interpreted Gotama's aphorism on the Exemplification as requiring the statement of universal concomitance.

Thus Vacaspati Misra said:

After the probans have been mentioned,

it

cannot be established as the probans unless

59

it is pervaded by the probandum.

The state-

ment of pervasion also does not take place without the Exemplification.

That is why he

[Gotama] has defined the Exemplification as being the logically relevant thing after defining the Reason [NDFC, p. 562].

Here VScaspati Misra is explaining why Gotama defined the Exemplification after defining the Reason. He says that Gotama did so because the property mentioned as the probans in the second step cannot do its job as the probans without being pervaded by the probandum, and the statement of pervasion takes place only in the third step.

Thus Vacaspati Misra inter-

preted Gotama's definition of Exemplification as requiring the statement of pervasion, which in the first variety of Exemplification would be the statement of universal concomitance. 8.

The Second Variety of Exemplification.

Gotama1s aphorism 1.1.37 dealing with the second variety of Exemplification merely states: the opposite in the reverse of that." unintelligible as it stands by itself.

"Or

This is quite It can be

made intelligible only if it is understood with reference to the immediately preceding aphorism dealing with the first variety of Exemplification.

That

supplies a positive example where the probandum is

60 present together with the probans in accordance with the statement of universal concomitance between the probans and the probandum.

By contrast, the second

variety of Exemplification supplies the opposite kind of example, namely, a negative example, where the probandum is absent together with the probans being absent, in accordance with the statement of the reverse of universal concomitance, that is, universal exclusion.

Gotama has already said that the

probans should be related to the probandum either through universal concomitance or through universal exclusion.

Since the first variety of Exemplifica-

tion states universal concomitance, the reverse of that, to be stated in the second variety of Exemplification, should be construed naturally as universal exclusion.

Thus VatsySyana's restoration of

1.1.37, carefully imitating the wording in 1.1.36, may be regarded as authentic:

"The Exemplification

is [that from which is obtained] an instance where that (=the probandum) is absent [together with the probans being absent] in accordance with the universal exclusion [of the probans] along with the probandum."

What is stated in the second variety

of Exemplification is the contrapositive of the universal concomitance stated in the first variety of it together with a negative example. previous case here

As in the

also the negative example

61 indicates what kind of inductive evidence is available for the general proposition 9.

stated.

Two Varieties of Application.

Gotama defined the fourth step or Application as: tion

"The Application (upanaya) is the characterisaof the subject as so or not so depending on

[the nature of] the Exemplification."

Since the

Exemplification may be of two different kinds containing either a statement of universal concomitance or universal exclusion, Application, in which the probans is predicated of the subject, has also to be of two different kinds.

As Gotama says, it may be

the statement that the subject is so or the statement that the subject is not so.

Thus the Application

may be either an affirmative statement or a negative statement.

By the statement that the subject is so

is meant the statement that the probans belongs to the subject or that the subject is characterized by the probans.

This form corresponds to the first

variety of Exemplification stating the universal concomitance between the probans and the probandum.

The

statement that the subject is not so is the statement that the probans is not absent in the subject or that the subject is not characterized by the absence of the probans.

This form is matched with the second

variety of Exemplification stating the universal

62 exclusion between the probans and the probandum. Gotama has not said which form of the Application should be matched with which form of Exemplification. But this has been clarified by the comments of VStsy5yana:

In the case of Exemplification containing the universal concomitance with the probandum, such as 'what is originated is well known to be non-eternal like a plate etc. 1 , the characterisation of the subject sound by originatedness is in the form that sound is so originated.

In the case of the Exemplifica-

tion containing the universal exclusion with the probandum, such as 'what is non-originated is well 5 known to be eternal like the soul etc.',

[the Application is of the form that]

sound is not so [i.e., sound is not nonoriginated] .

From the denial of the char-

acterisation of non-originatedness [follows] the characterisation of originatedness.

These

two varieties of characterisation are in accordance with the two varieties of Exemplification [comment on 1.1.38].

Thus the affirmative form of the Application is matched with the statement of universal concomitance and the negative form, with that of universal exclusion.

The passage also contains an application

of the law of double negation.

'Sound is not non-

originated' is said to imply that 'sound is

63 originated'.

It is thereby implied that the affirma-

tive form of Application may also be obtained in other cases where the Application is in the negative form. The difference between the second and the fourth steps of the pentapod is obvious.

The second step

tells us which property is going to be used as the probans.

It is always put in the ablative and, the

ablative serves as a sign to identify the probans. But the probans is not related to the subject in the second step.

It is in the fourth step that the pro-

bans is predicted of the subject, in either of the above two ways.

Vatsyayana says:

Upanaya, the property which is

"without the

the probans would

not be predicated of the subject and would be unable to prove the object" (comment on 1.1.39).

Thus it

is clear that according to VStsySyana the probans is not predicated of the subject in the second step but is so predicated in the fourth step.

Hence the latter

is a complete proposition and becomes a premise in the genuine sense.

It is one of those two steps of

the pentapod (the other one being Exemplification) which suffice to entail the Thesis that the probandum belongs to the subject. 10.

The Outcome (nigamana), or the Fifth Step.

Gotama defined the fifth and final step of the pentapod as:

"The Outcome (nigamana) is the

64 repetition of the Thesis as qualified by the probans." Thus it is obvious that the fifth step is not a mere repetition of the Thesis.

The probans (hetu) stated

in the second step is also contained in it.

This be-

comes abundantly clear when we look at the illustration of VStsySyana.

To quote:

"Therefore, because

of being originated, sound is noneternal" (comment on 1.1.39).

'Being originated' is the probans.

The

Thesis that sound is noneternal is explicitly being stated as qualified by the probans in the fifth step. Under these circumstances it is quite remarkable that many modern writers (see, for example, HIL) have assimilated the fifth step of the pentapod to the conclusion of an Aristotelian syllogism.

To prevent

this confusion we have avoided the usual translation of nigamana as conclusion. an outcome.)

(Nigamana literally means

The middle term is never contained in

the conclusion of an Aristotelian syllogism.

The

mentioning of the middle term in the conclusion would violate the structural requirement of an Aristotelian syllogism that each of the three terms should occur exactly twice in the argument.

Since the probans is

mentioned in the Outcome, it is a compound proposition and not a categorical proposition like the conclusion of an Aristetelian syllogism.

Conceptually

also the outcome is different from a conclusion in the usual sense.

As VStsySyana says:

"The Outcome

65 shows the convergence of all [the five steps] on proving the same thing"(comment on 1.1.39).

Thus

the Outcome demonstrates the interrelatedness of all the five steps and shows that they are all directed toward the same goal of proving the proposition stated as the Thesis.

Hence it is more accurate to

regard the Outcome as the summing up of the entire reasoning, rather than as just the conclusion.

When

it is stated that 'because of being originated, sound is noneternal' , it is indeed summing up the whole reasoning. namely, that

1

It is stating what has been proved,

sound is noneternal1, and also the

basis of the proof, namely, the originatedness of sound.

The Outcome certainly contains a conclusion,

namely, that part of it which repeats the Thesis. The Thesis, or the first step, itself cannot be regarded as the conclusion, because it is what is to be proved as distinguished from the conclusion or what has been proved.

But when it is repeated in

the Outcome, it is a genuine conclusion.

It would

be a mistake to take the entire Outcome as the intended conclusion of the pentapod.

This would vio-

late the clear instruction that it is the proposition stated as the Thesis in the first step that is to be proved.

Since the probans is not included in the

Thesis, the entire Outcome cannot be taken as the

66 intended conclusion.

The conclusion of the pentapod

cannot but be the same proposition stated as the Thesis, which is a subject-predicate proposition saying that the subject is qualified by the predicate to be proved to belong to it.

Hence the con-

clusion of the pentapod is a subject-predicate proposition like its Aristotelian counterpart.

But the

Outcome, though it contains the conclusion as a part, is not itself the conclusion, but is the summary of the whole reasoning. In VatsySyana's illustration, the same proposition is stated as the Outcome for both forms of the pentapod.

Whether 'being originated1

is stated

1

to be related to noneternality' by way of universal concomitance or by way of universal exclusion, implying relevant differences in the Application, the Outcome for both cases is: sound is noneternal'. be so in general:

'because of being originated,

He also says that this should

"Although the probans is of two

different kinds, the Exemplification is of two different kinds and the Application is of two different kinds, [the outcome] is the same" (comment on 1.1.39). This proves that the two forms of the pentapod were regarded as two alternative and equivalent methods of proving the same conclusion.

It implies the

metatheorem that whatever can be proved by the first

67 form of the pentapod can be proved by the second 6 form of it and vice versa. 11.

The Illustration of VgtsySyana.

While commenting on 1.1.39 (which deals with the fifth and final step of the pentapod), VStsySyana has put together all the five steps of his illustration as follows: In the case of the probans stated to be universally concomitant:

the sentence

'sound is non-eternal' is the Thesis. 'Because of being originated' is the Reason. known

'What is originated is well to be non-eternal, such as a plate'

is the Exemplification.

'Sound is so

originated'is the Application.

'Therefore,

because of being originated, sound is noneternal' is the Outcome.

Again in the

case [of the probans] stated to be universally excluded [from where the probandum is absent]:

'Sound is non-eternal,1

'Because of being originated1, 'What is non-originated is well known to be eternal, such as the soul', 'Sound is not so non-originated1 and 'Therefore, because of being originated, sound is non-eternal.

These are the only fully articulated illustrations of the pentapod provided by VStsySyana. It may be noted that in VatsySyana's illustration the Exemplification lacks an explicit universal

68 quantifier.

But there can be no doubt that the

Exemplification is a universal proposition.

It is

not necessary to write down the quantifier explicitly to make the proposition universal.

In general early

Indian logicians do not insist on stating a universal proposition with an explicit quantifier.

Though in

many cases explicit quantifiers like yatra yatra or sarva are supplied, it is not supplied everywhere. If it is clear from the context that a proposition is universal, it is accepted as a universal proposition.

In this particular respect early Indian logi-

cians have placed less emphasis on the linguistic form for specifying the quantity of a proposition than their Western counterpart.

In a valid Aristo-

telian syllogism the major premise (except in the moods Disamis and Dimaris) is not only required to be a universal proposition, its linguistic expression is also required to be in the form of a universal proposition with either of the two quantifiers 'all' or 'no1.

In a valid Indian syllogism

the Exemplification is also required to be a universal proposition, but no rigid requirement about the linguistic form of the expression is imposed. In the illustration of VStsyayana the Thesis lacks an explicit quantifier.

Consequently, in the

fourth and fifth steps also the subject has been stated without any explicit quantification.

But

69 when VStsySyana says that sound is noneternal, what is obviously meant is that all sounds are noneternal. Thus the Thesis is a universal proposition.

There is

the option of treating the Thesis as a singular proposition.

But since 'sound' is a general term and

the reference is to all particular sounds, it is more natural to treat it as a universal proposition.

In

other words we prefer to regard the subject here as a quantified expression with the quantifier understood. But simply because the Thesis in these illustrations is a universal proposition, it does not follow that the Thesis of a pentapod is always a universal proposition.

No such restriction has been

stated or implied in any account of the pentapod given by an Indian logician.

Gotama's account of

the pentapod leaves it quite open for the Thesis to be a particular proposition or a singular proposition as well. We have already remarked that in the Nyaya logic subject-predicate propositions are analyzed to state the concomitance between two properties.

'All men

are mortal', for example, is analyzed to mean 'whatever has humanity has mortality'.

Such analysis is

not restricted to universal propositions but is extended to particular and singular propositions as

70 well. as

1

Thus 'some men are honest' may be analyzed

some having humanity have honesty' and 'space

is endless' as 'that which has space-ness has endlessness . " The Thesis in Vatsyayana's example is subjected to the same analysis.

'Sound is noneternal' is

taken to mean 'what has sound-ness (=the sound universal or the common property of all sounds) has noneternality'.

Similarly, though the Application

is expressed as 'sound is originated', it is taken to mean 'what has sound-ness has originatedness'. This is why VStsyayana has said repeatedly that originatedness and noneternality are the probans and the probandum respectively.

In other words,

though the proposition is expressed in the form 'S is P', it is taken to mean 'what has S-ness has Pness' and to assert the concomitance between two properties.

Hence later logicians describe the

vyapti or pervasion between the probans and the probandum as the universal concomitance between the probans and probandum (sSdharmya, later called anvaya) and conversely the universal concomitance between the absence of the probandum and the absence of the probans (vaidharmya, later called vyatireka). Since every subject-predicate proposition is analyzed to mean the concomitance between two

71 properties, it follows that every subject-predicate proposition is reducible to one basic form, namely, that the subject is characterized by the predicate. Now it is not difficult to understand why VStsyayana held that the Thesis always asserts that the subject of the pentapod is characterized by the probandum. Since the Thesis is a subject-predicate proposition, it is analyzed to mean that the subject of the pentapod is characterized by the predicate chosen as the probandum.

From this point of view both affir-

mative and negative propositions are reducible to the same basic quasi-affirmative form, namely, that the subject is characterized by the predicate.

The

predicate characterizing the subject may be either positive or negative.

A negative proposition is

analyzed to mean that the subject is characterized by a negative predicate.

For example, 'no sound is

eternal' is taken to mean that 'all sounds are noneternal 1 . 12.

The Two Forms of the Pentapod.

In the light of the preceding discussion the two forms of the pentapod may be laid down as follows.

Following Gotama we first express the forms

by using general concepts rather than variables.

A

1.

The subject is characterized by the probandum.

72

2.

Because of the probans

3.

Whatever is characterized by the probans is characterized by the probandum, as in the case of (a positive example)

4.

The subject is characterized by the probans

5.

Therefore, because of being characterized by the probans, the subject is characterized by the probandum.

B

1.

The subject is characterized by the probandum.

2.

Because of the probans

3.

Whatever is characterized by the absence of the probandum is characterized by the absence of the probans, as in the case of (a negative example)

4.

The subject is not characterized by the absence of the probans

5.

Therefore, because of being characterized by the probans, the subject is characterized by the probandum.

The same forms may now be expressed by using the variables S, P, and M, where S stands for the subject, P for the probandum, and M for the probans. For the sake of simplicity we use forms of the verb to be.

A

1.

(all, at least n or this) S is P

2.

Because of M

3.

All M is P, for example, X (= a positive example)

73 4.

(all, at least n or this) S is M

5.

Therefore, because of being M, (all, at least n or this) S is P.

B

1.

(all, at least n or this) S is P

2.

Because of M

3.

All non-P is non-M, for example, Z (= a negative example)

4.

(all, at least n or this) S is non-M

5.

Therefore, because of being M, (all, at least n or this) S is P.

It may be noticed that while stating the forms by using variables, we have indicated explicitly that the Thesis could be a universal, a particular (or numerical) or a singular proposition, requiring the same specification in the fourth and the fifth steps.

It was not necessary to do so when the forms

were stated by using general concepts.

When the

Thesis is described as the statement that the subject is characterized by the probandum, it leaves open the possibilities that it may be a universal, a particular or a singular proposition.

But when

the forms are expressed through variables, it is desirable to indicate all the different possibilities.

We will later analyze some sample arguments

of Gotama

conclusions of which are sometimes uni-

versal, sometimes particular and sometimes singular propositions.

Hence it is necessary to make

74

provision for all the three possibilities within each basic form of the pentapod. We have said that each of Gotama's two basic forms of the pentapod is found to have three distinct forms within it when the quantity of the subject becomes explicitly specified.

This adds up to

six different forms of the pentapod.

There is no

positive proof that each of them was analyzed distinctly by Gotama himself.

But his account of the

pentapod makes provision for all of them.

There is

no reasonable ground for leaving any of them out of his theory of the pentapod.

The distinction

of these forms within each basic variety of the pentapod is possible only if the subject of the pentapod could be a quantified expression.

In the ex-

amples discussed so far no explicit quantifiers are found to be supplied.

Nevertheless we decided to

treat a sentence such as 'sound is noneternal' as a universal proposition and the subject 'sound' as a quantified expression with the quantifier understood. We shall also later come across some examples where the subject is an explicitly quantified expression. Moreover, Uddyotakara (and before him Diiinaga) distinguishes between 'properties that belong to the whole of the subject' (sadhyavySpakadharma), 'properties that belong to a part of the subject'

75

(sâdhyaikadesavrttidharma), and 'properties that do not belong to the subject1

(sadhyavrttidharma). This

shows that quantification of the subject was systematically studied by ancient Indian logicians.

It

is possible at least that they explicitly set forth certain distinctions that are implicit in Gotama's theory and could not possibly be mentioned explicitly within the severe limitation of space in a siltra work. Though we hold that the quantity of the subject could be specified in different ways and accordingly, the Application step and the conclusion could be a universal or a particular or a singular proposition, there is no scope for making such distinctions for the Exemplification step.

What is required to be

stated in the latter is that the probans is pervaded by the probandum.

It can only be a universal propo-

sition if this requirement is fulfilled. Keeping these points in mind and reminding the reader once again that the following distinctions were not explicitly made by Gotama himself, we now proceed to state the different forms.

For our pre-

sent purposes we isolate only the deductive core and omit the first and the second steps as well as the reference to the corroborative examples in the third step.

With this editing the three forms in the first

basic variety of the pentapod are as follows:

76 A

B

C

1. 2.

All M is P All S is M

3.

Therefore, all S is P.

1. 2.

All M is P At least n S is M

3.

Therefore, at least n S is P

1.

All M is P

2.

This S is M

3.

Therefore, this S is P.

A and B correspond to Barbara and Darii of Aristotle's syllogistic.

C does not correspond to anything in

Aristotle's own syllogistic, because Aristotle left singular terras out of it.

But singular terms are

allowed in syllogism by medieval logicians. ingly, C may be called Barbara

Accord-

to indicate that its

minor premise and conclusion are singular propositions . The three forms in the second basic variety of the pentapod (once again supplying only the deductive core) are as below:

D

E

1.

All non-P is non-M

2.

No S is non-M ("All S is not non-M' is misleading.)

3.

Therefore, all S is P.

1.

All non-P is non-M

2.

At least n S is not non-M

3.

Therefore, at least n S is P.

77

G

1.

All non-P is not non-M

2.

This S is not non-M

3.

Therefore, this S is P.

None of these correspond to Aristotelian syllogistic forms, because a term and its negation are counted as two distinct terms in Aristotle's syllogistic. It should be pointed out in this connection that probably in VStsySyana's view Aristotelian forms

like the Celarent where the conclusion is ne-

gative, would not be regarded as distinct forms which could be adopted in a pentapod.

He would rather re-

duce the Celarent to the Barbara form by replacing 'no S is P' by its obverse 'all S is non-P'.

Vats-

yayana has nowhere discussed obversion, and there is no firm evidence to prove that this was his view. But this seems to be implied by his conception of the nature of the Thesis that it is the statement of the subject as characterized by the probandum. It is also clear that Aristotelian forms like the Darapti, where the quantification over the minor term changes from the minor premise to the conclusion, could not be adopted in a pentapod.

This follows from

the fact that there is no provision for changing the subject as stated in the Thesis in any way in the

78 fourth and fifth steps.

Hence there is no possi-

bility that the Application could be a universal proposition while the Thesis and its repetition in the Outcome as the proved conclusion could be a particular proposition. 13.

Gotama's Own Examples.

Gotama did not provide any examples of the pentapod with all the five steps articulatedly stated. There are, however, numerous philosophical arguments spread throughout his work which may be reconstructed to make their form explicit. now.

We study some of them

We avoid restoring them as pentapods.

Rather

we restore them to the forms of their deductive core with three steps as in an Aristotelian syllogism. A.

"Perception is inference, because of being

knowledge of [objects of which only] a part is given" (2.1.30).

There is nothing unusual about the way the

argument has been stated in this aphorism.

This is

the customary way of stating a nyaya in Indian logic, namely, by stating only the three terms with the premises suppressed.

Here 'perception' is the subject,

'being inference1 is the probandum, 'being knowledge of objects of which only a part is given' is the probans .

It may be set out as follows:

All knowledge of objects of which only a part is given is inference. Perception is knowl-

79 edge of objects of which only a part is given. Therefore, perception is inference.

We have treated 'perception' as a singular term. Alternatively, the conclusion could be put as 'all perceptions are inference1, making a similar change 7

in the second step. B.

"Perception and so on are nonsources of

knowledge, because of not being related [to the objects of knowledge] in any to the three orders of time [that is, on account of not being able to precede or succeed or be contemporaneous with the objects of knowledge]" (2.1.8).

'Perception and so on'

refer to the four sources of knowledge admitted by Gotama—perception, inference, analogy, and authoritative statements.

It may be noticed that an inflec-

tion meaning 'because of' always helps to identify the probans.

The argument may be reconstructed as

below: Whatever is not related to the objects of knowledge in any of the three orders of time is a non-source of knowledge. Perception, inference, analogy and authoritative statement are not related to the objects of knowledge in any of the three orders of time. Therefore, perception, inference, analogy and authoritative statement are non-sources of knowledge.

80 It may be noticed that the subject in this argument is a compound term formed through conjunction.

It

would sound better in English if we write 'perception and so on are not sources of knowledge', instead of 'perception and so on are nonsources of knowledge'.

But in the aphorism the negation is

attached to the predicate.

In this case also the

conclusion and the minor premise could be restated O

in the form of a universal proposition. C. "[This] is a nonprobans, because of being deviant" (4.1.5).

In this case the subject is under-

stood as is not very unusual in Indian logic.

The

argument is: Whatever is deviant is a nonprobans. This is deviant. Therefore, this is a nonprobans.

D.

"Everything is noneternal, because of having

origin and decay" (4.1.25).

Of several possible

interpretations of this argument we suggest the following :

Whatever has origin and decay is noneternal. All things have origin and decay. Therefore, all things are noneternal.

81

E.

Everything is eternal, because of the eternality

of the five elements."

"No, because of the cause of

origin and decay being known [for some things]" (4.1. 29 and 4.1.30).

These two aphorisms synthesized to-

gether yield the argument that 'not everything is eternal, because the cause of origin and decay is known for some things.' 4.1.30 is:

VatsySyana's comment on

"Since the cause of origin and the cause

of decay is known [for some things], eternality of everything is falsified."

Thus it is abundantly

clear that the word 'no' in 4.1.30 stands for the denial of the proposition stated in 4.1.29, namely, that everything is eternal.

This denial is consis-

tent with Gotama's philosophical position, because in his metaphysics there are such eternal things as the soul, while the composite objects are noneternal. 'Not everything is eternal' is equivalent to 'some things are noneternal'.

The argument may be re-

constructed :

Everything for which the cause of origin and decay is known is noneternal. Some things are things for which the cause of origin and decay is known. Therefore, some things are noneternal.

82

14.

Miscellaneous questions.

One possible criticism of the pentapod is that 9 its first two steps are redundant.

it is true that

the last three steps omitting the corroborative instance in the third step suffice to express a valid deduction. misdirected.

Nevertheless, the criticism is entirely The first two steps could be criticized

as redundant, only if they were regarded as premises, in spite of not being needed as premises.

But it is

obvious that Gotama did not regard the first two steps as premises in the proper sense.

He defined

the first step as the statement of what is to be proved.

It is clear from this definition that he

did not regard the first step as a premise.

On the

other hand it is a healthy practice to write down first what one is going to prove, and there is nothing inelegant or unusual about it.

Similarly, the

second step merely cites the probans.

There is no

reason to think of it as a premise of the deduction. But it is useful to declare what one is going to use as the probans when the Thesis is going to be proved on the basis that the probans belongs to the subject and is pervaded by the probandum. The criticism also overlooks the purpose for which the five steps are recommended.

The pentapod

was conceived as a method of demonstration to others, particularly philosophical opponents.

As a method of

83 demonstration to philosophical opponents all the five steps are necessary to prevent deliberate trickery and deceitful practices.

Gotama, however, realized

that in order to be a successful method of demonstration, the pentapod must contain a valid deductive core.

Hence he required that the two crucial steps

called Exemplification and Application must be .. . 10 supplied. In Aristotle's logic universal propositions have an existential import.

It is necessary to en-

sure the validity of moods like the Darapti.

Modern

logicians, on the other hand, analyze universal propositions without any existential import.

It may be

asked what was the view of Gotama and VStsyayana on this point.

The answer is that their view cannot

definitely be determined either way from the meager information we have.

They have not provided any kind

of analysis of universal propositions that suggests that universal propositions have an existential import or that they do not.

Unlike Aristotle, they

did not admit any valid syllogistic or nonsyllogistic forms which require the existential import of universal propositions for their validity.

Their prac-

tice of supplying a corroborative instance for universal propositions stated in the third step of the pentapod might suggest that universal propositions

84 were understood as having an existential import. But it furnishes no conclusive evidence.

Thus the

view of Gotama and VStsySyana on the question of existential import has to be left open.

85

NOTES 1. The word sadhya (literally, what is to be proved) came to mean, at a later time, only the probandum. The early Indian logicians, however, used this word to mean three different things, namely: (1) the probandum, (2) the proposition to be proved (called the Thesis) containing both the subject and the probandum and, (3) the subject. Since the subject is a part of the conclusion to be proved, it was not unnatural to refer to the subject also as the sadhya. Sometimes the subject was distinguished from the probandum by describing the former as the sadhya-dharmi (dharmi = the characterized) and the latter as the sadhya-dharma (dharma=the character). Quite often one has to decide from the context which of the three different senses of the word 'sadhya' has been used. 2. It is well known that Aristotle's syllogistic is formal, but not formalistic in the sense in which Stoic logic, for example, is formalistic. Perhaps it should be added that in spite of the point noted here, NySya logic as a whole is not formalistic. 3. This analysis, it may be noted, is intensional, because it is in terms of class-properties; and two or more class-properties may correspond to the same class. 4. We have not dwelt upon the inductive aspect of nyaya. For this the reader may consult HIL, pp. 500-503 and BL, pp. 297-300; where comparison between the nySya and Aristotle's syllogism has been made.

86 5.

The correct version of the Exemplification

as noted earlier (p. 50) is:

'what is eternal is

non-originated like the soul and so on. 6.

This metatheorem was later rejected by NySya

logicians like Uddyotakara.

But the issue involved

is too compl icated to he discussed within the scope of this work. 7.

The aphorism 2.1.30 anticipates the position

of many contemporary philosophers that perception of objects involves an inferential element.

It is fol-

lowed by a keen examination of this philosophical doctrine. 8.

The aphorism 2.1.8 introduces a brilliant

examination of philosophical skepticism. 9.

The pentapod was the target of severe cri-

ticism by other schools of Indian philosophy.

The

MimamsS writers held that either the first three or the last three steps suffice for the proof, and the rest are redundant.

The Jains maintained that only

the first two steps are important and the rest redundant.

Some Buddhists argued that only the second

and the third steps are useful and yet some other Buddhists that only the third and the fourth are useful.

It would take a lot more space than we have at

our disposal to discuss the proper basis and motivation for these various criticisms, and the matter has to be dropped without any further discussion.

A

scholarly account (in Bengali) of the controversy is found in ND, vol. 1 (2d ed), pp. 290-295. 10.

The distinction between inference for one-

self and that for others was explicitly drawn by other logicians, see ILES, pp. 160-161 and BL, pp. 276-278.

Also see ILES, pp. 161-162 for an account

of the five extra steps that the pentapod had when it was a ten-step argument.

The extra steps included

psychological factors like desire to know, doubt,

87 and so forth. VatsySyana held that though these enter into a reasoning process, they should be lopped off, because they are not steps in a demonstration to others. This shows that Gotama was concerned to not have redundant steps in the pentapod.

CHAPTER 4 Hetvabhasa or Pseudo-Probaris In previous chapters we have referred to Gotama's distinction between a probans (hetu) and a pseudoprobans (hetvabhasa).

It is now time to explain

this distinction more fully by discussing Gotama's doctrine of pseudo-probans.

Though Gotama as usual

has not supplied any definition of a pseudo-probans, the very name hetvabhasa (= an apparent probans) throws light on its nature. as:

Vatsyayana defines it

"what appears as a probans because of being

similar to a probans, but is not a probans because of not having [all] the defining characteristics of a probans" (comment on 1.2.4).

Thus a pseudo-pro-

bans is similar to a probans because of possessing one or more of the properties of a probans but is still not a probans because of not possessing all the defining properties of a probans.

One might ex-

pect that Vatsyayana would state explicitly what are the defining characteristics of a probans, but he has not done so.

He indeed has said in one place that

the requirement that "the probans is that which proves the probandum by virtue of universal concomitance stated in the Exemplification" does not give the only defining character of a probans.

Another defining

89 character of a probans is that "it proves the probandum alternatively by virtue of the universal exclusion stated in the Exemplification."

But nowhere

has he given a complete list of all the defining characteristics of a probans.

Every pseudo-probans

discussed by us, however, will indirectly throw light on the nature of the probans as well.

Since

a pseudo-probans will lack one or more defining characteristics of a probans, it will become known by implication what the defining characters of a probans are. The first pseudo-probans in Gotama's list is called the deviant (savyabhicara).

Gotama has said

that "the deviant is inconclusive (anaikSntika)" (1.2.5).

By deviation (vyabhicSra) is meant the pre-

sence of the probans in an instance where the probandum is absent.

This furnishes conclusive evidence

that the probans is not related to the probandum, either by way of universal concomitance or by way of universal exclusion.

If the probans is present where

the probandum is absent, it is no longer true to say that the probandum is present wherever the probans is present and that the probans is absent wherever the probandum is absent.

If the probans is not per-

vaded by the probandum, the presence of the probans in the subject would fail to prove the presence of the probandum there.

Since the probans is deviant

90

and is also present where the probandum is absent, there is nothing to rule out the possibility that in the subject also it is present along with the absence of the probandum. Since what is deviant is a pseudo-probans, it follows by implication that a probans is nondeviant, that is, is not present anywhere the probandum is absent.

Thus nondeviation (avyabhicara) is a de-

fining character of the probans.

It is this char-

acter that is missing in a deviant pseudo-probans. At a later time one of the common definitions of pervasion (vyapti) between the probans and the probandum was that it is the relation of nondeviation of the probans from the probandum.

Gotama's

clear and unambiguous assertion that what is deviant is a pseudo-probans is a firm evidence for saying that he recognized that a probans has to be nondeviant from the probandum and, therefore, that he was well aware of the concept of pervasion (though he did not use the word vySpti) . Since Gotama has not given any examples, it is fruitful to turn to the comments of VStsySyana on 1.2.5:

Deviation means not being restricted to one end. . . . For example, 'sound is eternal because of being intangible; a pot is known to be non-eternal and tangible, sound is

91 not so tangible; therefore, because of being intangible, sound is eternal'.

The example

does not show the two characters of tangibility and non-eternality to be related as that which proves and that which is to be proved; an atom is tangible and eternal. If the soul, etc. are [cited as] examples in accordance with the aphorism that probans is

1

the

what proves the probandum

by virtue of the universal concomitance [stated] in the Exemplification',

[it would

be pointed out that] intangibility as a probans deviates from eternality: intangible and non-eternal.

cognition is

Since there

are both kinds of examples, there is deviation; there is no relation between that which proves and that which is to be proved; hence [it] is not a probans for lacking a defining character [of a probans]. nal ity is one end, other.

Eter-

noneternality is the

What remains in one end [only] is

conclusive, the opposite is inconclusive because of spreading to both ends.

In this passage Vatsyáyana first of all points out that a deviant probans is not restricted to only one end, or side, or alternative.

Toward the end

of the passage he mentions eternality and noneternality as the two ends.

Thus the two ends are

the probandum and the negation of the probandum.

A

deviant probans is concomitant with both the probandum and the negation of the probandum.

For example,

intangibility is concomitant with the probandum

92 eternality; there are some intangible things which are eternal like the soul.

It is also concomitant

with the negation of the probandum, namely, noneternal ity; there are some intangible things which are noneternal, like cognition.

VStsySyana has

pointed out that if the probans were restricted to only one of either end, it could be conclusive.

But

when the probans spreads to both ends, it can prove neither, that is, neither that the probandum belongs to the subject, nor that the negation of the probandum belongs to the subject.

All one can assert

truthfully in the Exemplification step in the cited case is that 'some intangible things are eternal' or alternatively, that noneternal'.

1

some intangible things are

The arguments to prove that sound is

eternal or that sound is noneternal respectively will both be invalid (even if the Application step is free from any errors), being vitiated by a fallacy analogous to the undistributed middle in Aristotelian logic. Vatsyayana has quoted the illustration of the fallacy from an unidentified source. tion:

The illustra-

'sound is eternal because of being intangible;

a pot is known to be noneternal and tangible; sound is not so tangible; therefore, because of being intangible, sound is eternal1. His refutation of the fallacious argument is twofold, depending on two different interpretations of the reasoning.

The first

93 refutation is only ad hominem after the argument has been interpreted to be based on mere dissimilarity. A pot is tangible and noneternal.

Sound is dis-

similar to a pot in being intangible; therefore it is eternal.

VStsyayana's ad hominem reply is

that the concomitance of tangibility and noneternality in a pot proves nothing; tangibility is also concomitant with eternality in an atom. Hence that sound is dissimilar to a pot in being intangible while the pot is tangible, fails to prove that sound is eternal.

By the same kind of

logic one could cite an atom as an instance and prove that sound is noneternal. In the other interpretation the argument is not based on mere dissimilarity.

Now the evidence

cited is not a pot but the soul.

The soul is a

proper corroborative instance, because the probandum eternality and the probans intangibility are present in it.

In the absence of a counter example,

this kind of corroborative instance would permit one to generalize that whatever is intangible is eternal and assert the universal concomitance between intangibility and eternality in the Exemplification step.

To criticize this, Vatsy5yana now

produces a genuine counter example, namely, cognition, which is intangible and noneternal.

Hence it

is proved that not everything intangible is eternal.

94

Now it can only be stated in the Exemplification step that some intangible things are eternal, and the argument will be invalid. We have analyzed the last passage from VStsySyana after quoting it practically in full, because two different kinds of wrong interpretations arising from it have been suggested by modern writers. Randle has found in it evidence for saying that VStsySyana had no conception of a genuine counter example to a universal proposition.

He says:

The Western formalist. . . would say that the objection brought against the present argument, on the ground that atoms although eternal are tangible, is altogether out of place: for the fact that some tangible things are eternal is perfectly consistent with the supposed major premise 'All intangible things are eternal', so far as 'formal consistency' is concerned. There is really no point in examining non-M's, cases where the middle is not found. . . . The relevant formal counter instance will be a case of non-P which is M (ILES, n. 1, p. 193).

We do not agree with Randle's criticism of VatsySyana. Contrary to what Randle says VStsyayana has given a relevant, formal counter-instance.

He has mentioned

cognition which is intangible and noneternal.

This

is a genuine counter-example to the supposed major

95

premise or Exemplification that things are eternal'.

1

all intangible

Randle is mistaken to think

that an atom, which is tangible and eternal, has been cited as a counter example to 'all intangible things are eternal1,

As already explained, the ci-

tation of an atom is connected with a different interpretation of the fallacious argument quoted by VStsySyana.

In that interpretation sound is sought

to be proved to be eternal because of being intangible and dissimilar to a pot which is tangible and 2

noneternal.

It is a sufficient refutation of this

kind of argument based on mere dissimilarity to a particular instance to point out that an atom is tangible and eternal.

VStsyayana, however, is well

aware that the citation of an atom would not be a counter example, if the conclusion sought is to be based on the universal premise that things are eternal1.

1

all intangible

Hence he cites cognition, which

is a genuine counter-example, to show that the required universal premise could not be used in a nySya.

(Since the nyaya is conceived as a source of

objective truth, it is rightly required that its premise must be true.) A different interpretation of savyabhicSra or the deviant pseudo-probans has been given by Vidyabhusana.

He holds:

"The erratic [our deviant] is the

reason which leads to more conclusions than one"

96 (HIL, p. 63).

He has interpreted the example of

Vatsyayana as yielding two different pentapods, each containing a valid syllogism, but the conclusions of which are mutually contrary.

The essential steps of

the two pentapods reconstructed by him are as follows :

(a) Whatever is intangible is eternal, as atoms, so is sound

intangible.

Therefore sound is eternal.

(b) Whatever is intangible is noneternal, as cognition. So is sound intangible. Therefore sound is noneternal.

Chatterjee is subscribing to a similar view when he says:

"...

from such a middle term we can infer

both the existence and the non-existence of the major term" (NTK, p. 284). The position of Gotama and VStsyayana, however, is that since a deviant probans is concomitant with both the probandum and its negation, it is inconclusive and can prove neither that the probandum belongs to the subject nor that the negation of the probandum belongs to the subject.

Since intangibility is per-

vaded neither by eternality nor by noneternality, it is not possible to use truthfully, as premises, the universal propositions 'whatever is intangible is

97

eternal' and 'whatever is intangible is noneternal', as Vidyabhusana does in his reconstruction of the argument.

What would have to be used as premises are

the particular propositions 'some intangible things are eternal' and eternal'. case.

1

some intangible things are non-

The argument would be invalid in either

Hence a deviant probans is not one that proves

both of two contrary conclusions (in which case it would have led to an antinomy), rather it is inconclusive and proves neither. The second pseudo-probans mentioned by Gotama is called the opposed (viruddha).

He defines it as

"The Opposed is what is opposed to the proposed conclusion" (1.2.6).

This is the pseudo-probans which

is pervaded by the negation of the probandum instead of being pervaded by the probandum, as required.

For

example, 'sound is eternal because of being originated'.

The probans 'being originated1 is pervaded

by noneternality instead of eternality, which is the probandum.

Hence in the place of proving that sound

is eternal, it goes to prove the opposite, namely, that sound is noneternal.

While the deviant probans

merely fails to prove the desired conclusion, the opposed probans goes one step farther and proves the falsity of the desired conclusion.

Hence it is pro-

perly labeled as 'opposed to the conclusion proposed' . 3

98 We next mention the pseudo-probans called sadhyasama

(literally, comparable to the probandum).

Gotama defines it as:

"Sadhyasama is that which is

like [or indistinguishable from] the probandum in the respect that it would have to be proved long to the subject]"

(1.2.8).

[to be-

The previous two

pseudo-probantia are related to the Exemplification step.

The present one relates to the Application

step of the pentapod.

To prove that the probandum

belongs to the subject it is necessary that the probans belongs to the subject.

If the probans does

not belong to the subject or even if it is doubtful whether the probans belongs to the subject, the proof cannot be accomplished.

This fallacy refers to such

a situation where the property chosen as the probans either does not belong to the subject or is not certainly known to belong to it.

Since that the proban-

dum belongs to the subject presupposes that the probans belongs to the subject, the proof remains inconclusive until the probans is proved to belong to the subject.

Hence Gotama describes this pseudo-pro-

bans as being like or indistinguishable from the probandum

in the respect that it also would have to be

proved to belong to the subject.

The expression

'would have to be proved' has the negative force of suggesting that the putative probans may not be proved to belong to the subject.

VStsyayana's ex-

99 ample is as follows:

"'Shadow is a substance' is

what is to be proved; 'because of having movement' is the probans . . . .

Since this is also unproved,

it would have to be proved like the probandum" ment on 1.2.8).

(Com-

VStsyayana goes on to say that what

has to be ascertained is whether shadow moves or whether what seems to be the movement of the shadow is really the movement of substance obstructing light.

Until it is proved that movement actually

belongs to the shadow, having movement cannot justifiably be used as a probans to prove that some other characteristic, namely, that of being a substance, belongs to the shadow.

The point is that (a part of)

the basis of inferring that the probandum belongs to the subject is that the probans belongs to the subject.

If the basis of inference is questionable the

product of inference becomes questionable as well. Like other kinds of pseudo-probans this variety also lacks a defining character of a probans.

That

defining character has not been explicitly stated by Vatsyayana. But it is clear by implication what it is, namely, that the probans 'has to belong to the subject'

(paksasattff) .

It was ascertained earlier

that a probans must be nondeviant or be absent from wherever the probandum is absent.

Now we gather that

belonging to the subject is another essential characteristic of a probans.

100 It is abundantly clear that the fallacies just discussed are all material fallacies.

'Thus the

point of interest in the case of the deviant probans is whether it is present in an instance where the probandum is absent and in the case of sSdhyasama, whether the probans actually belongs to the subject. This is rightly so because the nyaya is conceived to be a source of objective truth.

Hence care is

taken to see that no false premises are introduced in the course of the reasoning.

Nevertheless, the

discussion has an indirect bearing on the validity of the deductive core of the pentapod.

Two char-

acters of the probans that are gathered from this discussion are nondeviation and belonging to the subject.

If these two conditions are fulfilled, it

can be truthfully stated in the Exemplification step that the probans is pervaded by the probandum and in the Application step that it belongs to the subject.

From these two statements the conclusion that

the probandum belongs to the subject follows •i 4 necessarily.

101

NOTES 1. Avyabhicara, or nondeviation, must have been an earlier na,tie for vyapti. The concept of avyabhicara occurs explicitly in Gotama's aphorism 2.2.15. It is interesting that VStsySyana illustration there is a universal proposition with an explicit quantifier. "None of the effects of the kind to which sound belongs is eternal. Such is nondeviation." It may also be added that another synonym for vyapti, namely, niyama or necessary connection, occurs in Gotama's aphorisms 3.2.11, 3.2.65, and so on. Vatsyayana's comments on 3.2.11 contains, as an illustration of niyama, a universal proposition with the quantifier yatra yatra tatra tatra or 1

wherever-there'. 2. There was a pre-Gotama stage of Indian logic when the conclusion that the probandum belongs to the subject was sought to be proved on the basis of the mere similarity or mere dissimilarity of the subject to a particular instance cited. The passage from VStsyayana shows that he is rejecting this kind of reasoning as having very little probative value. Modern writers have interpreted the pentapod of Gotama and Vatsyayana to be basically the same kind of reasoning that Vatsyayana is clearly rejecting in the passage. Contrary to the interpretation of modern writers, Gotama and VStsyayana required that the citation of a particular instance has to be linked with a universal connection between the probans and the probandum. VStsyayana has said that the deviant probans lacks the 'relation of that which proves and that which is to be proved' (sSdhya-

102 sSdhanabhSva).

This relation has been

interpreted

b y N y S y a logicians to b e the relation of pervasion. 3.

O u r a c c o u n t of t h e o p p o s e d

pseudo-probans

is b a s e d o n h o w G o t a m a ' s v i e w h a s b e e n interpreted.

traditionally

T h i s i n t e r p r e t a t i o n is c o n s i s t e n t w i t h

Gotama's definition of the opposed.

But

VStsySyana's

e x a m p l e of t h e o p p o s e d is t h a t of i n c o n s i s t e n c y b e tween two philosophical taneously.

statements accepted

T h e e x a m p l e is:

terally, modification)

" . . .

simul-

the effect

(li-

ceases to b e manifested b e -

c a u s e o f t h e n e g a t i o n of e t e r n a l i t y .

. . .

In s p i t e

of t h e c e s s a t i o n t h e e f f e c t e x i s t s b e c a u s e o f t h e negation of destruction"

(comment o n 1 . 2 . 6 ) .

The

p o i n t is t h a t t h e n e g a t i o n of e t e r n a l i t y a n d t h e g a t i o n o f d e s t r u c t i o n w i t h r e g a r d t o t h e same are mutually incompatible.

Jayanta Bhatta

(NM, vol.

2, p. 158) p o i n t s o u t t h a t t h i s t y p e o f d e f e c t included under

account

is u n s a t i s f a c t o r y , b e c a u s e it m a k e s v i r u d d h a 4.

is

'the g r o u n d o f defeat' ( n i g r a h a s t h a n a )

c a l l e d pratijTiSvirodha. H e n c e V S t s y S y a n a ' s distinguishable

ne-

thing

from

in-

pratijftgvirodha.

Gotama has mentioned two varieties

pseudo-probans which we have not discussed. b o t h are important, we have avoided their

of Though

discussion

because they have no b e a r i n g on the validity of the deductive core of the

pentapod.

CHAPTER 5 Disjunctive Syllogism From the point of view of the historical development of Indian logic the pentapod reasoning was certainly the single most important logical contribution of Gotama.

It was, however, by no means

his only important contribution to logic.

It also

goes to his credit that he discovered the disjunctive syllogism as a distinct kind of reasoning where the validity or invalidity depends on the propositional or term connectives used.

Gotama's own name

for it is sesavat anumSna (literally, inference in which there is the residue). 'proof by elimination1.

Keith has called it

Randle has called it 'eli-

minative inference1, adding that it was an innovation on the part of Gotama that he recognized it to be a separate kind of inference embodying a principle distinct from that of the pentapod argument.

Bar-

lingay has referred to it by its Sanskrit name. Faddegon has observed that sesavat anumSna is identical with what is known as disjunctive inference in Western log ic (VS, p. 313).

We will call it dis-

junctive syllogism, because that is a common name traditionally assigned to this kind of inference in Western logic.

104 We already know that sesavat anumSna has been mentioned by Gotama in the aphorism 1.1.5 as a distinct kind of inference without any explanation of what is meant by it.

However, he has provided us

with a reasoning in the form of the disjunctive syllogism in the second section of the third chapter where he is arguing at length to prove that it is the soul which is the substratum of knowledge and other internal states.

We quote a few aphorisms that

will enable us to see the form of reasoning: "[Knowledge]

belongs neither to the [external] sense organs

nor to the objects because knowledge may persist even after their destruction" (3.2.18).

"[Knowl-

edge] does not belong to the internal sense organ because of the nonsimultaneity of cognitions of knowables" (3.2.19).

"Through eliminative reasoning

(parisesad) and because of reasons already mentioned [it follows that the soul is the substratum of knowledge] " (3 . 2 . 39) .

The eliminative reasoning referred

to in the last aphorism may be reconstructed as follows:

The objects or the external sense organs or

the internal sense organ or the soul is the substratum of knowledge;

(for specified reasons) the ob-

jects, the external sense organs and the internal sense organ are not the substratum of knowledge; therefore, the soul is the substratum of knowledge. The argument is clearly in the form of a disjunctive

105 syllogism, and the word parisesad, meaning "through eliminative reasoning," helps us to see how the argument moves.

But this falls short of an explicit

statement of the principle of disjunctive syllogism. For such an explicit statement we have to look at VStsySyana's comments, on the aphorism 1.1.5 supplying the second explanation of sesavat anumSna : "Sesavat is "reasoning through elimination' (parisesa), and that is the ascertainment of what remains after the cancellation of certain alternatives, when there is no other alternative." Vatsyayana's example is:

As for example, by characterizing sound as existent (sat) and non-eternal, which properties are common to substance, quale and motion, it is differentiated from universal, ultimate individuator and inherence; then facing the doubt whether it is substance, quale or motion, [elimination is made as follows]:

it is not substance, because it

inheres in a single substance; it is not motion, because it produces another sound; then it is what remains, and thus it is proved that sound is a quale.

The first premise left implicit in this reasoning is that sound is substance or quale, or motion, or universal, or ultimate individuator, or inherence. Vatsyayana cancels three of the six alternatives in

106 one stroke by saying that sound is existent and noneternal.

This step is really the outcome of a penta-

pod argument (compressed by Vatsyayana in the customary manner), the three essential steps of which are as follows:

Everything that is existent and noneternal is different from universal, ultimate individuator and inherence (example).

(All) sound is

existent and noneternal. Therefore, (all) sound is different from universal, ultimate individuator and inherence.

What is noticeable about this argument is that both its middle term and its major term are compound terms made out of simple terms by using connectives like conjunction, disjunction, and negation.

The

use of compound terms containing such connectives is a distinctive feature of NySya logic.

It shows

that these ancient logicians had a thorough understanding of the principle on which the validity of the argument depends and realized that these principles do not change in any significant manner if compound terms, instead of simple terms, are used. Returning to Vatsyayana's example we find that after the elimination of three alternatives, there are three more remaining.

Of these the alternative

that sound is a substance is eliminated on the ground that sound inheres in a single substance.

Another

107 alternative, that sound is motion, is rejected because it produces another sound

(that is, another

object of its own kind, while motion never does that).

It should be pointed out that these two steps

also are the results of pentapod argument, the essential steps of which are as follows:

(a) Everything that inheres in a single substance is different from substance, (example). (All) sound inheres in a single substance. Therefore,

(all) sound is different from

substance. (b) Everything that produces another thing of

its own kind is different from motion,

(example). (All) sound produces another thing of its own kind. Therefore,

(all) sound is different from

motion.

With the rejection of last two alternatives five of six alternatives have been eliminated.

The only

alternative remaining is that sound is a quale.

And

that is the conclusion reached by VStsySyana as the result of reasoning. Now that we have briefly explained the example of VStsySyana, we may start analyzing the logical structure of disjunctive syllogism in early NySya logic.

It is obvious in the first place that no

108 restriction was put on the number of alternatives in such a reasoning.

In the preceding example there

are six alternatives, in Gotama's example mentioned earlier in this chapter the alternatives are four. Vatsyayana has correctly laid down what is necessary to make the reasoning valid, namely, that all but one of the (finite number of) alternatives must be eliminated and the remaining alternative deduced as proved. All this is clear enough.

What is not clear

is whether the alternatives to be used in such reasonings are alternative predicates (or subjects) or alternative propositions.

Vatsyayana's definition

does not help us much because it is not specific enough to decide either way.

Hence all we can do is

study the examples provided.

Unfortunately, the ex-

tremely cryptic style of writing prevents us from reaching a clear decision even in that way.

As we

have already noticed, the first step stating the alternatives has been left implicit in VatsySyana's example analyzed by us (and similarly in Gotama's example).

If the first step were explicitly written

down, we could immediately decide whether the alternatives were written down as alternative terms or as alternative propositions.

But all we have been ex-

plicitly provided with are the eliminative steps and the conclusion.

Regarding the eliminative steps,

however, we could try to find out whether these are

109 complete propositions.

If these are propositions,

this would indicate that the alternatives are also alternative propositions.

On this point again we

find that in the example analyzed, though the subject (sound) has been explicitly mentioned in the first eliminative step, it has been left unstated in the other two.

Hence the question is whether the

subject is understood in the other two alternatives, in which case they would still be complete propositions; or it is not there at all, in which case the alternatives were presumably alternative terms. Since we can not settle the question from the statements of Gotama and VStsySyana, let us look at one more inference in the form of the disjunctive syllogism taken from Uddyotakara, the commentator on Vâtsyâyana: "Because the negation of one of two implies the acceptance of the second. . . for example, from the statement 'Does not eat during the day' it follows that "Eats at night'" (NDBVTV, p. 576). This specimen shows that the habit of writing down reasonings in a cryptic manner continued down the line of commentators.

When Uddyotakara says that

the negation of one of the two implies the acceptance of the second, it is impossible to decide from this statement alone whether he is speaking about two alternative terms or two alternative propositions. He has also spoken of two things (vastu) where 'thing' has been used in a very general sense that is

110 applicable both to terms and propositions. his example help us any further.

Nor does

It may be formu-

lated in either of the two following ways, and there is not much ground to choose between them:

A

Either X eats during the day or X eats at night. X does not eat during the day. Therefore, X eats at night.

B

X either eats during the day or eats at night X does not eat during the day. Therefore, X eats at night.

Here the formulation A would give us two alternative propositions while B gives two alternative predicates. In the absence of any decisive evidence there is room for conjecture.

One fact relevant for our

purpose is that, in the examples of Gotama and VâtsySyana (though not in the example of Uddyotakara), the eliminative steps are the results of covert pentapod arguments.

The probandum and the probans of

these arguments have been explicitly supplied, and the subject has sometimes been left understood— as is not unusual in Indian logic.

But whether the

subjects are supplied or understood, they are undeniably there, because without them the arguments cannot be carried out.

Hence in the examples of

Ill Gotama and VStsySyana the subject in each eliminative step not explicitly supplied has to be regarded as understood.

This lends support to the possibi-

lity that each eliminative step in a disjunctive syllogism is a complete proposition and not merely a term.

This indicates that the alternatives in the

example of Gotama and VStsySyana are alternative propositions and not alternative terms.

In that

case the form of the disjunctive syllogism in early NySya logic would be as follows:

1.

S is P. or S is P_ or . . . or S is P 1 2 n.

2.

S i s not P. and . . . and S is not P , 1 n-1.

3.

Therefore, S is P

n.

where S, P , . . . P are terms and n is any finite 1 n number greater than or equal to 2.

However, a num-

ber of alternative subjects could also be attached to a common predicate as is presumably the case in Gotama's example, in which case the form is as follows: 1. 2. 3.

S., is P or S is P or . . . S is P. 1 2 n It is false that S^ is P and . . . and it is false that Sn-1 , is P. Therefore, S is P. ' n

112 Construed as either A or B, the disjunctive syllogism would belong to the logic of propositions However, we have carefully shown that the alternatives were attached to either a common subject or a common predicate.

Such is the case in all three

examples that we have considered.

There is no case

to our knowledge where both different subjects and different predicates have been used in different alternatives.

This fact would lend support to the

possibility that the alternatives could be alternative terms.

In that case the forms of the disjunc-

tive syllogism would be as follows:

C

1.

S is P, or P 1 2

or , , . or P n.

2.

S i s not Pn1 and . . . and not P_n-1. n

3.

Therefore, S is P

1. 2.

s. or s„ or . . . or s is p. 1 2 n It is false that sn or . . . or s .. 1 n-1

3.

Therefore, sn is p.

and

are p.

On this construction the disjunctive syllogism belongs to the logic of terms.

113

Though it is difficult to decide whether the alternatives used in a disjunctive syllogism were alternative terms or alternative propositions (or both?), what is most important is that the disjunctive syllogism was recognized by Gotama and VStsyayana to be a distinct kind of valid reasoning.

Even

if it belonged to the logic of terms, its addition would yield a significantly richer logic of terms than that comprising only syllogistic reasoning. Another distinction that needs to be made is that between modal and truth-functional connectives. We may ask whether the disjunction used in early Nyaya logic was modal or truth-functional in nature. As in other ancient systems of logic the alternatives used by these logicians were always relevant to each other.

There was also an attempt to make the

alternatives mutually exclusive and collectively exhaustive.

But none of this is inconsistent with

the extensional point of view, and there is nothing in the meaning of the connectives themselves that makes them modal in nature.

We do not have ex-

pressions like 'this is necessarily a man or a post', and such necessity also is not implied by the connectives used.

Hence though the meager information

we have does not warrant a decisive answer, the disjunction was in all probability a truth-functional disjunction.

114 With regard to the meaning of the connectives, there are again three possibilities for a truthfunctional disjunction:

(a) the connective may

unambiguously indicate the inclusive or, such as the wedge, 'V', in modern symbolic logic and vel in Latin; (b) the connective may be unambiguously an exclusive or, such as aut in Latin; and (c) the connective may be ambiguous, sometimes used in an inclusive sense and sometimes in an exclusive sense. Such is the case with the English or_. We may ask how far these distinctions can be made with regard to the disjunction in early Nyaya logic. In answer we may point out that there is first the connective va, which is exclusive in nature. No formal definition of vS has been supplied; but it is clear from the usage that it is so.

In other

words whenever two or more alternatives are connected by vS, we can tell from the very meaning of va that the alternatives are intended to be mutually exclusive. Second, there is the expression anyatara, which is also frequently used by VatsySyana. It means 'either of two alternatives' without firmly implying that only one of the alternatives is true.

Thus

anyatara may be interpreted to signify inclusive disjunction, though no" formal definition of it has been supplied by early NySya logicians, and hence

115

there is doubt regarding its precise meaning.

At

a much later time it was defined to stand for inclusive disjunction by Navya-NySya logicians (Ingalls, Materials, pp. 63-64). Third, there is the expression anyatama, which means 'one of many (two or more) alternatives'. Though no formal definition of it has been provided, it is used in an exclusive sense to signify that only one of the many alternatives is true.

In this

respect anyatama has the same semantic function as that of vs.

Grammatically, however, va, is a con-

junction, while anyatara and anyatama are used as nouns or adjectives, though they often play the role of a conjunction.

Also when the alternatives

are connected by anyatara or anyatama, these words are written at the end of the expression, while va may be written either in the middle or at the end of the expression.

There are, finally, the expres-

sions ekatara and ekatama, both of which have an exclusive meaning.

Ekatara means 'one of two alterna-

tives', and ekatama, 'one of many alternatives'. These two are also used as nouns or adjectives. In the disjunctive syllogism described so far, one of the alternatives is affirmed by way of a denial of the rest, this kind is traditionally known in Western logic as modus tollendo ponens.

In this

kind the validity of reasoning is not affected by

116

whether the connective used is exclusive or inclusive in meaning.

In the other kind of disjunctive syl2

logism, known as modus ponendo tollens,

one of the

alternatives is affirmed and the rest are denied. In this kind, the reasoning is valid only if the connective is exclusive in meaning.

We now consider

some evidence that shows that this second kind of disjunctive syllogism was used in early NySya logic. This evidence is found in the discussion of doubt (sartisaya).

Gotama says:

Doubt is 'knowledge of incompatible characters with regard to the same object1 (vimarsa) where there is need for [knowledge of] 'differentiating factors' (visesa) . . . [1.1.23].

Gotama's point is that doubt arises when we are faced with two or more incompatible alternatives with regard to the same object and that the doubt may be removed if we find any distinguishing factor that makes only one of the alternatives applicable to the object, to the exclusion of the others.

Thus we may

be in doubt about whether sound is substance, or quale, or motion, until we find something about sound that makes only one of the alternatives applicable to it, to the exclusion of others.

As Vatsyayana says:

"Doubt is whether it (sound) is substance or quale or motion. . . . I do not apprehend a property that

117 1

makes

[only] one of the alternatives'

applicable" (comment on 1.1.23).

(anyatama)

Though this be-

longs to the discussion of doubt, it is not difficult to discern the form of reasoning that is implicit.

(For the sake of simplicity we will confine

ourselves to two alternatives only, though there could be more.)

We start with two alternatives

joined by exclusive disjunction, namely, 'A is B or* C

or 'A or B is C'.

We assert (upon some

ground) one of the alternatives and exclude the other.

The form of the reasoning may be set out as

follows :

A

1.

A is B or C.

2. 3.

A is B Therefore, A is not C.

1.

A or B is C

2. 3.

A is C Therefore, B is not C.

and

B

Two more forms could be distinguished by setting out the alternatives as propositions.

The discussion

of doubt definitely suggests that the modus ponendo tollens kind of disjunctive syllogism was known to Gotama.

118 Within the Western logical tradition both varieties of disjunctive syllogism were discovered by Stoic logicians.

Our first kind corresponds to

the fifth 'indemonstrable' and the second to the fourth 'indemonstrable' of Stoic argument forms, (Mates, Stoic Logic, pp. 72-73), in both cases the nature of disjunction being exclusive.

One dif-

ference between early NySya logic and Stoic logic on this point is that, in the latter, the alternatives are definitely known to be propositions, while it is difficult to decide—as we have seen—whether in the former the alternatives were terms or propositions, or both. Before ending this chapter we would like to remark on a question of historical detail. has said:

Randle

"For all practical purposes the sesavat

form is disregarded by the Naiygyika himself" (ILES, p. 153).

Barlingay has also remarked that "In later

logic this [=disjunctive syllogism] was identified as saitisaya and was not regarded as anumSna, as it does not require vyâpti" (MIIL, p. 157).

Unfortunately,

neither writer has supplied any evidence to support his statements.

So far as our information is con-

cerned these statements seem to be plainly wrong. It cannot be true that the sesavat form or the disjunctive syllogism has been disregarded by NaiySyikas or NySya logicians, when we find that not only

119 VStsyayana, b u t also subsequently commentators as U d d y o t a k a r a

(NDFC, p. 2 9 8 ) , V a c a s p a t i

Misra

(NDFC, p. 321) a n d so o n h a v e c o m m e n t e d u p o n

it.

W i t h regard to the first part of Barlingay's ment,

such

it h a s to b e s a i d t h a t e x c e p t t h r o u g h

stateconfu-

s i o n n o one c o u l d i d e n t i f y a f o r m o f r e a s o n i n g w i t h sartisaya or d o u b t .

W i t h r e g a r d t o t h e s e c o n d p a r t of

h i s s t a t e m e n t , c o n t r a r y t o w h a t is s t a t e d , l o g i c i a n s d i d t r y t o s u p p l y a v y S p t i for syllogism

disjunctive

(a m o v e o p p o s e d b y m a n y o t h e r s ) .

is a s s e r t e d b y V a c a s p a t i M i s r a : reasoning

many

(parisesa)

(NDFC, p. 322).

"the

Thus

it

eliminative

is a n o t h e r n a m e for

vyatireki"

T h e s a m e a s s e r t i o n is f o u n d in h i s

Sartikhyatattvakaumudi:

" T h e r e s e s a v a t is a v i t a . "

" A v i t a is.

. . that w h i c h proceeds b y w a y of

vyatireka"

(pp. 141, 1 4 0 ) .

vacaspati Misra's

a m p l e o f s e s a v a t is the f o l l o w i n g :

ex-

"Along w i t h

n e g a t i o n of d e s i r e a n d so o n b e l o n g i n g to e i g h t s t a n c e s for p r e v e n t i v e r e a s o n s , t h e i r b e i n g

the sub-

qualia

is the v y a t i r e k i p r o b a n s for p r o v i n g t h a t t h e y b e l o n g t o t h e soul"

(NDFC, p. 323).

Thus

Vacaspati

M i s r a b a s i c a l l y h a s g i v e n as t h e e x a m p l e of the same inference w h i c h has been given b y

sesavat VStsyayana

as a n e x a m p l e , as w e h a v e in the s e c o n d c h a p t e r ,

of

samanyatodrsta inference. W e have already shown by a n a l y s i s t h a t t h i s r e a s o n i n g is t h e j o i n t p r o d u c t of a c a t e g o r i c a l s y l l o g i s m a n d a d i s j u n c t i v e

120 syllogism.

The novelty in the statement of Vacaspati

Misra is that this inference is reformulated as a vyatireki argument.

In a vyatireki argument what

has to be used as a premise is the universal concomitance between the negation of the probandum and the negation of the probans.

The probandum here is

'belonging to the soul'; the probans is 'being quale and not belonging to either earth or water or fire or air or akSsa or space or time or manas' (that is, not belonging to eight of nine possible substances, the only remaining alternative being the soul).

The

reasoning may be set out in the vyatireki form as the following:

1.

Whatever does not belong to the soul is not both a quale and something that does not belong to either earth, or water, or fire, or air, or 5kSsa, or space, or time, or manas.

2.

Desire and so on are qualia and do not belong to earth, or water, or fire, or air, or SkSsa, or space, or time, or manas.

3.

Therefore, desire and so on belong to the soul.

This reformulation is done to justify the view to which VScaspati Misra subscribes, that all valid inferences are based on vyapti or pervasion between

121

two (or more) properties.

This movement of thought

has a superficial similarity to the attempt of Aristotelians to reduce all valid inference to categorical syllogisms.

Apart from that we will

refrain from making any other comments about this movement, because our presentation of VScaspati Misra's case is very inadequate and a fuller presentation is impossible within our present framework. Our point is that the reformulation of the disjunctive syllogism as a vyatirekil argument, in order to defend the thesis that all valid inferences are based on vyapti, does not amount to disregarding it nor to refusing to regard it as inference.

122

NOTES 1.

Robinson's Principles of Reasoning, p. 69

2.

Robinson's Principles of Reasoning, p. 69.

CHAPTER 6 Arthapatti In this chapter we will explore further contributions of Gotama and VStsyayana to the study of reasonings involving truth-functional connectives, namely, those found in their discussion of arthapatti as a source of knowledge.

Arthapatti is a compound

made out of the two terms 'artha' and 'apatti'.

Both

of these terms have several meanings and the resultant compound, arthapatti, may be broken up in more than one way.

Hence the literal meaning of artha-

patti is, at the least, problematic.

Fortunately,

however, Vâtsyayana himself has broken the compound for us and indicated the precise literal meaning (out of several possibilities) intended in this context.

He says that arthapatti means arthad apatti,

that is, apatti from artha, where artha is meaning (proposition).

He says moreover that apatti means

praptih prasangah, that is, getting or obtaining as a necessary consequence. of arthapatti is:

Thus the literal meaning

'deducing from a proposition what

is implied' or 'deducing from a proposition what is a necessary consequence'.

The term arthapatti has

been translated in several different ways. (p. 196) and Vidyabhusana (HIL, p. 96) have

Jha

124 translated it as 'presumption1, NP as 'postulation1 (vol. 2, p. 105), and Randle as 'implication' (ILES, p. 320).

Though 'presumption' and 'postulation' may

be correct translations of some of the literal meanings of arthSpatti, they obviously are not suitable as a translation of the precise literal meaning spelled out by VStsyayana.

'Implication' is also

not a good translation, because arthSpatti signifies the deduction based upon implication and not implication itself.

In fact the one English word that

comes close to the meaning specified by VStsySyana is 'deduction'.

However, since 'deduction' also

will prove to be too general in the present context, we will retain the Sanskrit term itself. The topic of arthSpatti is introduced by Gotama in the aphorism 2.2.1 by way of an objection that his classification of sources of knowledge is inadequate, because he has left out arthSpatti (and three other sources of knowledge).

Gotama defends

his classification in the following aphorism by saying (among other things) that arthSpatti is included in inference (anumSna). objection is:

His own statement of the

"[The sources of knowledge] are not

four, because aitihya. arthapatti, sambhava, and abhSva are [additional] sources of knowledge." reply:

The

"Since aitihya (tradition) is not different

from sabda (authoritative statement) and since

125

arthapatti, sambhava, and abhava are not different from anumana (inference), there is no refutation [of the view that the sources of knowledge are four, namely, perception, inference, analogy, and authoritative statement]."

From this objection and reply

we know that already before the time of Gotama there were philosophers who subscribed to a narrow view of inference and excluded arthapatti and so on from it as distinct sources of knowledge, as against that Gotama is subscribing to a broad conception of inference that would be inclusive of arthapatti and so on.

We have already referred to this broad concep-

tion of inference in the first chapter. In the aphorisms following those mentioned earlier, Gotama has discussed the question of the validity or invalidity of arthapatti, a question to which we will return later.

But he has not explained

what is meant by arthgpatti. For such an explanation we have to look at VStsyayana, whose definition of arthapatti is as follows:

"Where from a proposition

stated another proposition follows as a necessary consequence, that is arthapatti." This definition of arthapatti makes it applicable to any valid deductive reasoning with a single premise and a single conclusion.

vatsySyana has not emphasized that there

should be a single premise and a single conclusion. He has merely put artha in the singular number.

126

Hence one cannot rule out the possibility that there could be more than one premise.

However, in both of

the examples available from VStsySyana, there is only one premise.

Thus it is probable that what is

meant by arthgpatti is a deductive reasoning with a single premise. VStsySyana's definition of arthapatti does not make it clear on what the implication, between the premise and the conclusion, is based.

His other

remarks and examples, however, help us to see what the basis is.

We will first look at his example.

"For example, if there are no clouds, there is no rain.

What follows from this as a necessary con-

sequence?

That if there are clouds, there is rain"

(commentary on 2.2.1).

It may be noticed that the

premise and the conclusion in this argument are conditional statements.

In the previous chapter on

the disjunctive syllogism, we have seen that Gotama and VStsySyana were concerned with reasonings involving the two connectives of negation and disjunction.

The present specimen shows that reasonings

involving yet another connective, namely, the conditional, occupied their attention.

Moreover, in

this case both the premise and the conclusion are unmistakably propositions, and hence the reasoning belongs, without doubt, to the logic or propositions.

127 Gotama has declared that reasonings of this kind are to be included in inference.

Regarding

that, VatsySyana's comments are as follows:

"In-

ference is knowledge through the given of what is not given, but related [to the given] . . . .

Since

arthgpatti is knowledge of a proposition which is not stated obtained from the precise understanding of the meaning of a sentence by means of the relation of opposition, it is definitely inference" (comments on 2.2.2).

According to this quotation, arthgpatti

is knowledge from the understanding of the meaning of a sentence.

In modern terminology this amounts

to saying that arthSpatti is analytic knowledge and not knowledge obtained by any empirical means. Moreover, the proposition deduced is said to be related by way of 'opposition' to the premise. VatsySyana has clarified what is meant by 'opposition' (pratyanîkabhSva) as follows:

"If there is

no cause, there is no effect1 from the meaning of this sentence is obtained the proposition related by way of opposition that 'if there is cause, there is effect'.

The positive is the opposite (pratyanîka)

of the negative" (comments on 2.2.4).

What is meant

is that 'there is no cause' is related by way of opposition to 'there is cause', and similarly 'there is no effect', to 'there is effect'.

In the propo-

sition 'there is no cause' the Sanskrit sentence

128

shows that what is negated is the proposition 'there is cause' and similarly in the case of 'there is no effect'.

Thus we know from this example that a

proposition and its negation are related by way of opposition. It is now clear that the implication on which the deduction of 'if there are clouds, there is rain1 from 'if there are no clouds, there is no rain' is based on the relation of opposition.

What is re-

quired is that the conclusion should contain negation of the constituent simple propositions in the premise. We have another specimen of arthSpatti in VStsyayana's comments on the aphorism 5.2.16:

"after

1

stating noneternal because of being originated' it is obtained from the meaning that . . . what is eternal is nonoriginated. . . . this is . . . by arthSpatti."

Here 'noneternal because of being

originated' is certainly not intended to be the premise as it stands.

This is rather a synoptic way of

stating a pentapod argument which, as we know from the context, runs as follows:

'sound is noneternal,

because of being originated; what is originated is noneternal" and so on.

The intended premise of

arthSpatti is 'what is originated is noneternal'. This example, however, creates some complications for the correct interpretation of arthSpatti.

In

129

the previous example both the premise and the conclusion are compound propositions.

But in this case

they are categorical propositions.

In fact this

case belongs to the variety of immediate inference known as contraposition in Western logic.

Thus it

is obvious that the premise of an arthSpatti is not necessarily a compound proposition.

It may also be

a categorical proposition, presumably as long as there is only one premise. The next question is whether, in this second case, the conclusion is related by way of 'opposition' to the premise.

There is no question of there

being any opposition between the constituent propositions, as there was in the previous case.

There

is, however, a kind of 'opposition' between the constituent terms in this case.

'Originated' may

be said to be 'opposed' to 'nonoriginated' and 'eternal', to 'noneternal'.

vatsyayana has said

that 'the positive is the opposite of the negative'. He has not specified that 'opposition' may take place only between propositions.

Thus it seems that 'oppo-

sition' is the relation between not only a proposition and its negation but also between a term and its negation. Hence it may be said that there is a relation of 'opposition' between the premise and the conclusion in both of the available specimens of arthSpatti.

130 There is no other specimen available.

It is possible,

therefore, though not so stated in the definition of arthapatti, that the premise and the conclusion are to be related by way of 'opposition'.

This

would certainly amount to an important modification in the concept of arthapatti, and we do not know whether such modification would be proper.

It is

possible that VStsyayana left us with a more general definition of arthapatti, because he wanted to accommodate other cases of inference from a single premise to a single conclusion where the premise and the conclusion are not 'opposed'. Randle has said : "It will be clear that vatsyayana means little more by arthapatti than what Western formalists call the opposition of propositions and immediate inference.

But vatsya-

yana has no doctrine of 'logical opposition' as that embodied in our 'Square of Opposition' (ILES, p. 322).

Now we have seen that there is one example

of arthapatti which belongs to contraposition as a variety of immediate inference (though Randle has not referred to this example at all).

But there

is another example (the only one mentioned by Randle), where both the premise and the conclusion are conditional propositions.

Reasoning of this type is

not traditionally considered under immediate inference.

The only sense in which both the examples

131 o f a r t h S p a t t i m a y b e c h a r a c t e r i z e d as

immediate

i n f e r e n c e is t h a t in b o t h t h e r e is e x a c t l y o n e premise and one conclusion.

S t i l l the

important

d i f f e r e n c e b e t w e e n t h e c a s e of a r t h S p a t t i

dealing

w i t h c o n d i t i o n a l p r o p o s i t i o n s a n d w h a t are

tradi-

t i o n a l l y k n o w n as i m m e d i a t e i n f e r e n c e s h o u l d n o t b e overlooked. S e c o n d , it is t r u e t h a t V S t s y S y a n a h a s s u p p l i e d us w i t h a 'square of o p p o s i t i o n ' .

not But

it

is n o t c l e a r t h a t h e s h o u l d b e e x p e c t e d to d o so. Some of the implications w i t h i n the square of opp o s i t i o n h o l d o n l y b e c a u s e of c o n s t r u i n g t h a t u n i versal propositions have an existential do not know whether VStsySyana construed p r o p o s i t i o n s as h a v i n g a n e x i s t e n t i a l c h a p t e r 3 for f u r t h e r d i s c u s s i o n ) .

import.

We

universal

import

(see

If h e d i d not,

s o m e p o r t i o n s of t h e s q u a r e of o p p o s i t i o n w o u l d b e invalid to him.

T h e r e is r e a s o n t o b e l i e v e ,

how-

e v e r , t h a t s o m e o f the i m p l i c a t i o n s t h a t h o l d through

' o p p o s i t i o n of p r o p o s i t i o n s ' w e r e k n o w n t o

Gotama and VStsySyana.

They undoubtedly knew

that

a universal proposition could be falsified b y prod u c i n g o n e c o u n t e r e x a m p l e w h i c h e n t i t l e s us t o assert the truth of the corresponding

particular

proposition. The first example of arthSpatti was is n o c l o u d , t h e r e is n o r a i n , so

: 'if t h e r e

'if t h e r e is c l o u d ,

132 there is rain'.

This argument is invalid.

VatsyS-

yana notes its invalidity while commenting on aphorism 2.2.3, which says:

"arthapatti is invalid

because of being inconclusive." ments are: rain':

vatsyayana's com-

"'if there are no clouds, there is no

from the meaning of this it is obtained

that 'if there are clouds, there is rain 1 .

But even

if there are clouds, there is sometimes no rain, so that this arthSpatti is invalid." This passage shows that Vatsyayana knew that an argument is invalid if its premise or premises are true and the conclusion is false.

That is why he

is pointing out that the preceding argument is invalid because the premise, namely, 'if there are no clouds, there is no rain' is true, but the conclusion, namely, 'if there are clouds, there is rain' is false. Another important thing in this passage is what it reveals about the nature of conditional propositions.

VStsySyana has referred to the point

of time when there are clouds but there is no rain. This interpretation falsifies the proposition that 'if there are clouds, there is rain'.

The only

condition in which a material conditional is false is when the antecedent is true and the consequent is false.

Vatsyayana correctly identified that con-

dition, though he has not spelled it out in actual

133 words.

Moreover, this interpretation makes the

premise 'if there are no clouds, there is no rain' true.

This shows that VStsyayana correctly realized

that a conditional proposition remains true if the antecedent is false and the consequent true. VStsyayana, however, has not explicitly supplied us with the truth-table of the material conditional as was done by Megarian-Stoic logicians. After pointing out that the argument is invalid, Vatsyayana has gone further to indicate what would be a valid argument in the given circumstances. This is found in his comments on aphorism 2.2.4 that "farthapatti was thought to be invalid] because of considering as arthapatti what is not arthSpatti [proper]".

VatsySyana writes:

That even if there is the cause, there is not effect due to obstructing factors is a causal phenomenon and this is not what is known with certainty by arthapatti.

What

then is known with certainty by it?

'If

there is the cause, there is the effect' [should be changed to] "it is not that there is the effect without there being the cause 1 , this is what is known with certainty by it.

134

It should be remembered that these comments are about the invalid argument VStsySyana is discussing. VatsySyana is telling us in a more general way that what should be deduced from 'if there are no clouds, there is no rain' is not is rain', but

1

1

if there are clouds, there

it is not both that there is rain

without there being clouds'.

This is a valid argu-

ment in the form that 'if not A, not B; therefore, not both B and not A'.

Randle has stated the valid

form specified by VStsySyana as : ergo if B, A'.

1

if not A, not B;

This is not strictly accurate.

1

If

B, A' is logically equivalent to 'not both B and not A', but still a different proposition. One interesting question to ask is why VStsyayana switched from the proposition 'if there are no clouds, there is no rain1 to the more general proposition 'if there is no cause, there is no effect', making similar appropriate changes with respect to the other propositions involved?

There

is more than one answer possible, but the answer that first comes to our mind is that VStsyayana was not concerned with the particular words 'cloud' and 'rain'.

He not only wanted to show that the parti-

cular argument 'if there are no clouds, there is no rain; therefore, if there are clouds, there is rain' is fallacious, but also that the very form of the argument is invalid, so that any other argument put

135

into the same form would turn out to be invalid. Hence VatsySyana used general concepts.

The word

karana, in the present context, may be interpreted as the ground or the antecedent and karya, as the consequent.

Thus vatsyayana's statements amount to

saying that the following form of argument is invalid, namely,

1

if there is negation of the ground

there is negation of the consequent; therefore, if there is the ground, there is the consequent1.

When

he showed that the argument 'if there are no clouds, there is no rain? therefore, if there are clouds, there is rain' is invalid, he may have produced it as a counter example to the invalid argument form. One important ingredient of a logical theory is the method of proving the invalidity of argument forms by producing a counter example, that is, producing an argument in the same form, the premise(s) of which is true and the conclusion false.

It is likely

that Vatsyayana was aware of this method and applied it to the present case.

CHAPTER 7 Conclusion In this monograph we have been able to ascertain a number of significant facts about Gotama's logic. In the first chapter we discussed Gotama's view of the nature of inference.

In the light of the com-

ments of Vatsyayana we found that inference was conceived to be knowledge of what is indicated (lingi) from the knowledge of what indicates (liftgi) on the basis of a necessary connection between what indicates and what is indicated. The second chapter was devoted to Gotama's threefold classification of inference into pürvavat, sesavat, and samSnyatodrsta.

We discussed both of

the alternative explanations of the classification provided by Vatsyayana.

In the first version pür-

vavat and sesavat signify respectively the inference of the effect from the cause and the inference of the cause from the effect.

Sgmanyatodrsta stands

for the inference of something imperceptible on the basis of a general connection established by experience. In the second version, pürvavat was interpreted by us to be an inference which gives the deductive

137 core of the pentapod reasoning.

Now sesavat,

discussed separately in chapter 5, is represented as the disjunctive syllogism of the modus tollendo ponens type.

It was noted that the alternatives

were attached to either a common subject or a common predicate.

We could not reach a definitive judgment

whether the alternatives were alternative terms, or alternative propositions, or could be both.

Ac-

cordingly, four different valid forms of the disjunctive syllogism were distinguished to account for all the possibilities (pp.111-12).

We also presented

evidence that suggests that the modus ponendo tollens variety of the disjunctive syllogism was known to Gotama and Vatsyayana, though its principle was not formulated by them.

The possible forms of the dis-

junctive syllogism of this second type are distinguished on page 117, chapter 5. In the second version also, samSnyatodrsta stands for a method of inferring something imperceptible.

The example of VStsySyana is interesting

because of its being a joint product of a categorical syllogism and a disjunctive syllogism. In the third chapter we discussed the nature of pentapod reasoning.

Though the pentapod has both

deductive and nondeductive aspects, we concentrated on the deductive aspect of it containing a valid argument.

Gotama had explicitly distinguished

138

between two basic varieties of it.

But in doing

so he also made room for three distinct forms within each basic variety.

Of these six valid forms

there are Aristotelian (p. 76 ) and three non-Aristotelian (p. 77).

We discussed why the criticism

that Gotama's pentapod has two extra steps arises from a misconception of the nature of the case.

In

the fourth chapter we gave an account of three fallacies arising from violating the conditions of validity of the deductive core of the pentapod. In chapter 6 we studied the nature of arthgpatti—a reasoning from a single premise which could be either categorical or compound.

One specimen of

it was found to be a case of contraposition.

It was

gathered from VStsySyana's comments on another specimen

that he discerned that the form 'if not-A,

not-B; therefore if A, B' is invalid, while the form 'if not-A, not-B; therefore not B and not-A' is valid. Gotama's contributions to logic are substantial and very impressive considering the fact that he is one of the first systematic logicians of the world. Aristotle's name as a logician naturally comes into mind in this connection.

Both Aristotle and Gotama

formulated certain fundamental principles of reasoning for the first time in their respective logical traditions.

The deductive core of Gotama's pentapod

139

has substantial affinity with Aristotle's syllogism. Aristotle developed one kind of syllogistic theory in great detail and perfection.

By contrast the

severe constraints of the aphoristic style of writing compelled Gotama to express his thoughts through briefest possible hints, without elaborating on what is implied.

(Gotama expressed not only his logic

but his entire philosophy, in less than two thousand words.)

Under these circumstances Gotama's theory

lacks much of the detailed development that is found in Aristotle's theory. There are some obvious differences, however, between the two doctrines.

First, Aristotle's

syllogism is eliminative; it eliminates the middle term from the conclusion.

But Gotama's pentapod is

summative—it retains the probans in the final step, so that the final step gives a summary of the whole reasoning.

It not only gives the conclusion in the

usual sense as stated in the Thesis, or the first step, but also indicates the logical basis of the conclus ion.

The retention of the probans in the

final step may have a deeper philosophical significance.

It may indicate that the connection between

the subject and the probandum cannot be isolated from the connection between the subject and the probans . Hence the proper Outcome of the reasoning is not simply that the subject is qualified by the

140 probandum, but that the subject, because of being qualified by the probans, is qualified by the probandum. Second, according to VStsySyana, the Thesis of the pentapod is always in the quasi-affirmative form that 'the subject is qualified by the probandum' .

Even if the Thesis is a negative proposition,

it is expressed in the quasi-affirmative form with the negation attached to the predicate.

It follows

thereby that Aristotelian forms like the Celarent, Ferio, and so forth could not be directly adopted in Gotama's pentapod.

Before their negative con-

clusion could be written down as the Thesis, they will have to be replaced by the obverse of each, with the negation attached to the predicate. Third, the nature of the subject, as stated in the Thesis, cannot undergo any change in any later step of the pentapod.

Thus if the subject happens

to be universally quantified, the quantifier cannot be changed to a particular quantifier in the Outcome containing the conclusion.

This implies that Aris-

totelian forms like Darapti, Bramantip and so on, where the quantification over the minor term changes from the premise to the conclusion, could not be adopted in Gotama's theory of the pentapod. Fourth, in Aristotle's syllogism a term and its negation count as two distinct terms but not so in

141 Gotama's pentapod.

Gotama allows the use of both

the probans and its negation (and implicitly the use of both the probandum and its negation) within the same pentapod. Fifth, in one respect the early Indian logicians have attached less importance to the form of the linguistic expression of a proposition than Aristotle, namely, with respect to explicitly supplying the quantifier.

Aristotle not only requires that the

quantifier of a categorical proposition has to be explicitly supplied but also that the quantifier has to be specifically one of the three quantifiers 'all', 'no', or 'some1.

But it is clear from the usage of

Gotama and Vatsyayana (and other early Indian logicians) that any ordinary quantifier, such as sarva (everything), yat (whatever), na sarva (not everything) , were acceptable to them.

They also allowed

the quantifier to be often dropped where the Sanskrit usage permits the quantifier to be left implicit. But in another respect Vatsyayana has attached more importance to the linguistic form of the expression of a proposition than has Aristotle.

Aristotle

allows the use of the forms 's is p' or

1

p belongs

to s' interchangeably within the same syllogism. VStsyayana has ruled out the interchangeable use of these forms.

142

Sixth, in Aristotle's theory universal propositions are interpreted as having an existential import.

Modern logicians have departed from

Aristotle's view and interpreted universal propositions to have only a hypothetical import.

With

regard to Gotama's theory there is no conclusive evidence that universal propositions were interpreted to have an existential import.

His theory can be

consistently interpreted from the hypothetical point of view as well. As long as we are making the comparisons between Gotama and Aristotle, it may be pointed out that in one respect the scope of Gotama's logic is wider than that of Aristotle.

Aristotle did not

make any significant contribution to the study of arguments, the validity or invalidity of which depends on the term or propositional connectives involved.

Gotama's logic includes the disjunctive

syllogism.

Moreover, VStsySyana's comments on

arthapatti show that valid and invalid arguments involving the use of conditionals were distinguished. Gotama's influence on Indian logic can hardly be exaggerated.

Throughout the ages commentaries

(and commentaries on commentaries) on his work were written by logicians belonging to the NySya school. His doctrine of the pentapod remained a topic of pivotal interest in the logical works of other schools

143

of Indian philosophy.

His doctrine was severely

criticized, in particular, by Buddhist logicians. It was also attacked by logicians belonging to the schools of Jaina, Mfmamsa, and so on.

These cri-

ticisms prompted a vigorous defense from NySya logicians throughout the generations.

After the

rise of Navya-NySya the focus of the attention of NySya logicians was shifted from Gotama to Gaiigesa, whose TattvacintSmani is generally acclaimed as the pioneer work on Navya-NySya.

But Gotama1s in-

fluence persisted because the TattvacintSmani itself is a work of criticism of some selected aphorisms of Gotama on logical and epistemological topics. Moreover, though the focus of attention shifted from Gotama to Gaiigesa,

the NySya logicians never

lost their interest in Gotama's work.

New Sanskrit

commentaries have been written on his work and the work of VStsyayana even in this century.

The great

importance of Gotama lies in the fact that he is the founder of the NySya school.

The school, which still

has many active adherents, has existed without any real discontinuity from pre-Christian times.

It is

this fact alone that makes it absolutely imperative to the historians of logic to pay proper attention to the logic of Gotama.

Bibliography NySyadarsana (also called NyayasQtra) of Gotama with the BhSsya of VStsySyana. Edited by PadmaprasSda ¿astri and HarirSma ¿ukla. Kashi Sanskrit Series, 1942. . Bengali translation along with a Bengali commentary by PhanibhGsana Tarkavagisa. 5 volumes. Calcutta: Bangiya Sahitya Parisat, 1932-1935. . English translation called Nyaya Philosophy along with a translation of portions of the Bengali commentary of Phanibhusana Tarkavagisa. Edited by D. P. Chattopodhyaya and M. K. Gangopadhyaya. Calcutta: Indian Studies, 1967. . English translation with notes by S. C. VidySbhtlsana. Allahabad: 1931. . English translation with translation of portions of the Vrtti of Visvanatha. Edited by J. R. Ballantyne. Allahabad: 1850-1854. , with the BhSsya of VStsySyana and the commentaries BhSsyachandra, Khadyota and Tippani. Edited by GangSnStha Jh5 and Dhundiraja SSstri. Chowkhamba Sanskrit Series, 1924. , with the commentaries of BhSsya, VSrttika, and TStparyatikS and Vrtti. Volume 1. Edited by Amarendra Tarkatirtha and TSrSnStha Tarkatirtha. Calcutta: Sanskrit Series 18, 1936. ,

with the four commentaries of Bhasya,

Varttika, TStparyatika and Parisuddhi. Volume 1. Edited by Anantalal Thakur. Darbhanga: Mithila Institute, 1967.

145 N y ä y a - S ü t r a s of G o t a m a a n d V ä t s y ä y a n a ' s

Bhäsya.

E n g l i s h t r a n s l a t i o n b y M. G. JhS. Central Book Agency,

1939.

N y ä y a v ä r t t i k a of U d d y o t a k a r a . and Laksana äastri.

Baroda:

E d i t e d b y V.

Dvivedin

Chowkhamba Sanskrit

Series,

1915. N y g y a v a r t t ik a t a t p a r y y a t t k a of V S c a s p a t i Edited by RSjesvara äästri. Series,

Misra.

Kashi

Sanskrit

1924.

T a t t v a c i n t ä m a n i o f Gattgesa w i t h t h e c o m m e n t a r y Mathuränätha.

Edited by Kämäkhyänätha

gxsa. 4 volumes. Society, Delhi:

1884-1901.

one.

1974.

A M o d e r n I n t r o d u c t i o n to

Delhi:

Tarkavä-

Calcutta Asiatic

Reprint, volume

Motilal Barnasidass,

B a r l i n g a y , S. S. Logic.

Calcutta:

of

National Publishing

Indian

House,

1965. B h a t t a c h a r y a , D. C. H i s t o r y of N a v y a - N y ä y a Mithila.

Darbhanga:

Bocheriski, L M.

Mithila Institute,

A H i s t o r y of F o r m a l L o g i c .

t r a n s l a t i o n b y Ivo T h o m a s . Illinois: Calcutta:

T h e N y ä y a T h e o r y of

U n i v e r s i t y of C a l c u t t a ,

C h i , R. S. Y.

Dame,

1950.

F a d d e g o n , B.

New York:

Charles

1931.

The Vaisesika System.

Johannes Muller,

Amsterdam:

1918.

T h e L o g i c of I n v a r i a b l e

in the T a t t v a c i n t ä m a n i . D. R e i d e l ,

Concomitance

Dordrecht,

Holland:

1967.

The Navya-NySya System of Logic.

Varanasi:

Royal

1969.

E a t o n , R. M. G e n e r a l L o g i c . Scribners,

1961.

Knowledge.

Buddhist Formal Logic. London:

Asiatic Society,

G u h a , D. C.

Notre

1958. English

University of Notre Dame Press,

C h a t t e r j e e , S. C.

G o e k o o p , C.

in

B. V. P r a k a s h a n ,

1968.

146 I n g a l l s , D. H. J.

M a t e r i a l s for t h e S t u d y of N a v y a

N y S y a Logic. Press,

Cambridge:

K e i t h , A . B.

University

Indian Logic and Atomism.

The Clarendon Press, Mates, Benson. Angeles:

Oxford:

1921.

Stoic Logic.

Berkeley and Los

U n i v e r s i t y of C a l i f o r n i a P r e s s ,

M a t i l a l , B. K.

T h e N a v y a - N y a y a D o c t r i n e of

Cambridge: .

Harvard

1951.

Harvard University Press,

1968.

E p i s t e m o l o g y , L o g i c a n d G r a m m a r in

Philosophical Analysis.

The Hague:

1961.

Negation. Indian

Mouton,

1971. M c D e r m o t t , A. C. S e n a p e . Logic and Reidel,

Buddhist

Dordrecht, Holland:

D.

1969.

M i l l e r , J. W .

T h e S t r u c t u r e of A r i s t o t e l i a n

London:

K e g a n Paul, Trench, Trubner,

Misra, Umesa. bad:

An Eleventh Century

'Exists'.

Logic. 1938.

H i s t o r y of I n d i a n P h i l o s o p h y .

Tirabhukti Publications,

a n d v o l u m e 2, M o h a n t y , J. N.

1957

1966.

GaTfrgesa's T h e o r y o f T r u t h .

niketan:

Allaha-

v o l u m e 1,

Visvabharati,

Santi-

1966.

PadSrthadharmasaitigraha of P r a s a s t a p S d a w i t h

the

Nygyakandali of ^ridhara. Edited w i t h a H i n d i t r a n s l a t i o n b y D u r g S d h a r a Jha. Benares Sanskrit University, R a n d l e , H. N. Oxford,

I n d i a n L o g i c in E a r l y

Schools.

1930.

Sartikhyatattvakaumudi of V S c a s p a t i M i s r a . t r a n s l a t i o n b y G a n g S n S t h a JhS. Oriental Book Agency, S a n g h v i , S.

Benares:

1963.

1965.

Advanced Studies

Metaphysics. S t c h e r b a t s k y , T. Leningrad:

Calcutta:

in I n d i a n L o g i c 1961.

Buddhist Logic. 1932.

English

Poona:

Volume

1.

and

147 Sugiura, S.

Hindu Logic as Preserved in China and

Japan. Tucci, G.

Philadelphia, Pa., 1900.

Pre-Dinnaga Buddhist Texts on Logic

from Chinese Sources.

Baroda:

Gaekwad

Oriental Series, 1929. Vidyäbhüsana, S. C. Calcutta: . 1921.

Indian Logic

(Mediaeval School).

1909.

A History of Indian Logic.(Calcutta,

AUTHOR: Kisor Kumar Chakrabarti, Ph.D. is a lecturer in the Department of Philosophy, University.

Calcutta