Definition and Induction: A Historical and Comparative Study 9780824851286

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DEFINITION AND INDUCTION: A HISTORICAL AND COMPARATIVE STUDY

DEFINITION AND INDUCTION A HISTORICAL AND COMPARATIVE STUDY Kisor Kumar Chakrabarti

MONOGRAPH NO. 13 SOCIETY FOR ASIAN AND COMPARATIVE PHILOSOPHY University of Hawai'i Press Honolulu

© 1995 University of Hawai'i Press All rights reserved Printed in the United States of America 00 99 98 97 96 95

5 4 3 2 1

Library of Congress Cataloging-in-Publication Data Chakrabarti, Kisor Kumar. Definition and induction : a historical and comparative study / Kisor Kumar Chakrabarti. p. cm. ~ (Monograph no. 13, Society for Asian and Comparative Philosophy) Includes bibliographical references and index. ISBN 0-8248-1658-7 1. Definition (Logic) 2. Induction (Logic) 3. Philosophy, Comparative. 4. Philosophy, Ancient—Oriental influences. 5. Philosophy, Indie. 6. Nyaya. I. Title. II. Series: Monograph ... of the Society for Asian and Comparative Philosophy : 13. BC199.D4C48 1995 161~dc20 95-7339 CIP University of Hawai'i Press books are printed on acid-free paper and meet the guidelines for permanence and durability of the Council on Library Resources Camera-ready copy prepared by the author

CONTENTS

Acknowledgments

vii

Abbreviations

ix

Introduction

1

PART ONE Chapter One: Aristotle's View of Definition

7

Chapter Two: The Stoic View of Definition

25

Chapter Three: The Epicurean Attack on Definition

33

Chapter Four: The Nyaya View of Definition

39

PART TWO Chapter 5: Aristotle on Induction and Inference from Sign

65

Chapter 6: Epicurus on Methods

83

Chapter 7: Stoic and Later Epicurean Views on Sign

93

Chapter 8: Early Nyaya View of Induction and Inference from Sign

. 103

Chapter 9: Carvaka-Humean Critique of Induction and Some Indian/Western Responses Chapter 10: Induction and Probability

141 165

Chapter 11: Later Nyaya View of Induction and Inference from Sign . 181 Selected Bibliography

215

Index

227 v

ACKNOWLEDGMENTS

We express our deep gratitude to the following institutions for their financial and other kinds of material support: the Fulbright Foundation, the Alpha Fund of the Institute for Advanced Study, Princeton, the Indian Council of Philosophical Research, the University of Calcutta, and the Center for Philosophy of Science, the University of Pittsburgh. We have immensely benefited from the critical comments and suggestions provided by Professors John T. Kearns, James Lennox, Michael Ferejohn, Greg Cooper, Gerald Massey, Nicholas Rescher, Morton White and the anonymous readers of the publisher.

We also

gratefully remember the many years of invaluable philosophical education sitting at the feet of my teachers of Indian philosophy:

(late)

Madhusudan Nyayacharya, (late) Narmada Tarkatirtha, (late) Panchanan Sastri, (late) Gopinath Bhattacharya, Visvabandhu Tarkatirtha, Ashoke Kumar Ganguly and Narayana Chandra Goswami. Last, but not the least, this work would not have been completed without the active help of my wife, Dr. Chandana Chakrabarti.

vii

ABBREVIATIONS

Adv. Math. Sextus Empiricus, Against the Logicians, Library, London, 1929

I and II, Loeb Classical

An. Post.

Aristotle, Posterior

Analytics

ATV

Udayana, Atmatattvaviveka, ed., Dhundiraja Sastri, Kashi Sanskrit Series 84, Chowkhamba, Benares, 1940

BP

Visvanatha, Bhasapariccheda, with six commentaries, ed., C. S. R. Sastry, Sri Balamorama Press, Madras, 1923

BPP

Visvanatha, Bhasapariccheda, with Muktavalisamgraha, Pancanana Sastri, Sanskrit Pustak Bhandar, Calcutta, 1984

Categ.

Aristotle, Categories

De An.

Aristotle, On the Soul

DI

Aristotle, On Interpretation

De Int.

Do

De Part. An.

Aristotle, Parts of Animals

DL

Diogenes Laertius, Lives of Eminent Philosophers, Library, Cambridge and London, 1950

GD

Gadadhara, Gadadhari, I and II, 2nd edn, ed, V. P. Dvivedi, etc., Chowkhamba, Benares, 1970

Hist. An.

Aristotle, History of Animals

IGW

J. W. Sedlar, India and the Greek World, Rowan and Littlefield, Totowa, New Jersey, 1980 ix

ed.

Loeb Classical

x

Abbreviations

JI

R. Swinburne, ed, The Justification of Induction, Oxford University Press, Oxford, 1974

KKK

Sriharsa, Khandanakhandakhadya, Chowkhamba, Benares, 1970

LFP

R. Carnap, Logical Foundations of Probability, Chicago Press, Chicago, 1950, 2nd edn, 1962

LS

A. Long and D. Sedley, eds, Hellenistic Philosophers, Cambridge University Press, Cambridge, 1987

Met.

Aristotle, Metaphysics

Meta.

Do

NBD

Dharmakirti, Nyayabindu, with Tika and Pradipa, ed. D. Malvania, K. P. Jayswal Research Institute, Patna, 1955

ND

Gotama, Nyayasutra, with Bhasya of Vatsyayana, eds., P. Sastri and H. Sukla, Kashi Sanskrit Series 43, Chowkhamba, 1942

NE

Aristotle, Nicomachean

NK

Udayana, Nyayakusumanjali, with Nyayabodhani, Prakasika and Makaranda, Chowkhamba, Benares, 1935

NKS

Bhimacarya Jhalkikar, Nyayakosa, Institute, Poona, 2nd edn, 1978

NKV

Udayana, Nyayakusumanjali, with Vistara, ed. U. Viraraghavacarya, Kendriya Sanskrit Vidyapeetha, Tirupati, 1980

NP

Udayana, Nyayaparisista, with Pancika, ed, S. N. Srirama Desikan, Kendriya Sanskrit Vidyapeetha, Tirupati, 1976

NS

Gotama, Nyayasutra

NSB

Gotama, Nyayasutra, with Bhasya of Vatsyayana, eds, P. Sastri and H. Sukla, Kashi Sanskrit Series 43, Chowkhamba, 1942

NV

Uddyotakara, Nyayavarttika, eds, V. P. Dvivedi and L. S. Dravida, Chowkhamba, Benaras. 1915

Kashi Sanskrit Series,

197,

University of

I and II,

Ethics Prakasa,

Bhandarkar Oriental Research

Abbreviations

xi

OP

Sextus Empiricus, Outline of Pyrrhonism, London

Loeb Classical Library,

PA

Aristotle, Prior Analytics

Ph.

Aristotle, Physics

Phys.

Do

PKM

Prabhacandra, Prameyakamalamartanda, Sagar Press, Bombay, 1941

PO

Aristotle, Posterior

Post. An.

Do

PV

Dharmakirti, Pramanavarttika, with Vrtti, ed, Dvarikadas Sastri, Bauddha Bharati, Benares, 1968

Rhe

Aristotle, Rhetoric

SD

Madhavacarya. Sarvadarsanasamgraha, ed, V. S. Abhyankar, Bhandarkar Oriental Research Institute, Poona, 1978

SL

Gangesa, Siddhantalaksana, with Didhiti, Jagadisi, etc., 2nd edn, ed, G. P. Sastri, V. V. Prakashan, Benares

Strom.

Clement of Alexandria, Stromata, in the Writings of Clement of Alexandria, tran, W. Watson, I and II, Edinbourgh, 1869-71

SVF

von Arnim, Stoicorum Veterum Fragmente, Leipzig, 1923, 1924

TC

Gangesa, Tattvacintamani, with Prakasa and Tarkacudamani, vol. II, part I, ed. N. S. Ramanuja Tatacarya, Kendriya Sanskrit Vidyapeetha, Tirupati, 1982

TCP

Gangesa, Tattvacintamani, with Mathuri, vol. I, ed, K. Tarkavagisa, Motilal Banarasidass, Delhi, 1974

Top.

Aristotle, Topics

TPS

Jayarasi, Tattvopaplavasimha, 1930

ed, M. K. Sastri, Nirayna

Analytics

N.

Gaekward Oriental Series, Baroda,

xii

Abbreviations

TRP

J. M. Keynes, A Treatise on Probability, Macmillan, London, 1948

TS

Annambhatta, Tarkasamgraha, with Dipika, translation and elucidation by Gopinath Bhattacharya, Progressive Publishers, Calcutta, 1976

TSD

Do

TT

Vacaspati Misra, Nyayavarttìkatatparyatika, ed, R. S. Dravida, Kashi Sanskrit Series 24, Chowkhamba, Benares, 1925

INTRODUCTION

Definition is an important scientific and philosophical method. In all kinds of scientific and philosophical inquiries definition is provided to make clear the characteristics of the things under investigation. Definition in this sense, sometimes called real definition, should state the essence of the thing defined, according to Aristotle. In another (currently popular) sense, sometimes called nominal definition, definition explicates the meaning of a term already in use in an ordinary language or the scientific discourse or specifies the meaning of a new term introduced in an ordinary language or the scientific discourse. In yet another sense definition specifies the unique characteristics of what a (simple or complex) term is about. A term may be about a natural object, a theoretical entity, another term or linguistic expression or even a nonentity. [When a term is about a non-entity, the question whether it can by analysis be shown to be about real entities may here be left as open.] Still there may be one or more unique characteristics which determine the ground of the application of a term and what it is about (as also what it is not about). Definition explicitly formulates such unique characteristics and the ground of the employment of a term. Definition in this sense combines the purposes of both real and nominal definition and is promoted by the Nyaya philosophers of India. Another important method of science and philosophy is induction. In a narrow sense induction is a method of generalization to all cases from the observation of particular cases. This narrow sense is found in Aristotle's epagoge and also in Mill's account of induction as "the operation of discovering and proving general propositions." In a broad sense induction is a method for reasoning from some observed fact to a different fact not involved in the former. This sense includes both reasonings to particular facts and universal generalizations. This is found in many contemporary authors on induction and also in the ancient notion of sign (semeion in Greek, linga in Sanskrit). We understand induction in the broad sense though more often we shall actually be concerned with induction in the narrow sense. We shall discuss the modus operandi of induction (while discussing ancient views), but the focus will be on a central epistemological problem of justifying induction. That is, how can

1

2

Introduction

our limited experience of nature provide the rational basis for making knowledge claims about unobserved phenomena, specially generalized knowledge claims? We shall study definition and induction from a historical and comparative point of view—their formulation in the Greek and the Sanskrit traditions. Relying on Aristotle's testimony one can say that Socrates introduced both definition and induction into Greek philosophy. "For two things may be fairly ascribed to Socrates—inductive arguments and universal definition ..." {Met. M 4 27-29) In the Indian tradition both definition and induction play significant roles in Gotama's Nyayasutra, the oldest systematic logical work in Sanskrit. A comparative study of Greek and Indian logical views (though no such book-length study has been made so far) is only natural, for Greece and India are the only two ancient cultures in which well developed and systematic logical traditions are found. [An indigenous and ancient logical tradition also existed in China, but it was superseded after Indian logic was introduced in China early in the Christian era.] There are also remarkable structural affinities between Greek and Indian views, as we shall see. In spite of the similar philosophical views held by the Greeks and the Indians the two traditions may have developed independently and there is no hard evidence to rule this out. The similarity may be explained on the grounds of deep linguistic affinities between Greek and Sanskrit as well as cultural affinities. There are also questions from the considerable physical distance between Greece and India and from difficulties of communication due to language difference. But, at the same time, the possibility of Indo-Greek philosophical contact cannot be discounted. Since there were Greek kingdoms for more than a century in and around the northwest frontiers of India after Alexander's invasion of India in the second half of the fourth century B. C., substantial political contact and contact through trade and commerce during that period is fairly certain. (IGWchapters 8-10) Even before that one may conjecture about some Indo-Greek contact through the Persian court, for the Persians had extended their sovereignty to both parts of Greece and parts of northwest India in the sixth century B. C. (IGW chapter 3) While all these, together with the fact that many Greek and Indian philosophical views are similar, raise the possibility of Indo-Greek philosophical contact, none of these suffice to prove beyond a reasonable doubt that such was probably the case. But there is more. Diogenes Laeritus says in a carefully documented biography that Pyrrho, the founder of Greek skepticism, came to India with the army of Alexander. ("Pyrrho" 9.61-63 in Diogenes, Lives of Eminent Philosophers, II, 475-77, tran, R. D. Hicks,

Introduction

3

Loeb Classical Library, London, 1931) Since there was a powerful skeptical tradition in India from the late Vedic period, the interest of Pyrroh in meeting Indians of similar persuasion is not hard to imagine. The great Neo-Platonist Plotinos is reported to have left for India with the army of the Roman emperor Gordianus III, but is said to have abandoned the mission after Gordianus' death. (Porphyry, "Life of Plotinos" in Plotinos, Complete Works, ed., K. S. Guthrie, London, 1981, P. 8) The very fact that Plotinos wanted to undertake a journey to India proves the seriousness of his interest to meet Indian monists of whom there were plenty. Additional evidence from Megasthenes, Strabo, Plutarch, Clement of Alexandria, Basileides, Bardaisan, Philostratos, Lucian, Eusabios, Porphyry, etc., (/GW part II) is of considerable weight. Finally, although this has escaped the attention of recent scholars, six Greek sources like Diogenes Laertius, Megasthenes, Suidas, etc., report that Democritus, the Greek atomist of the fifth century B. C., visited India. (Diels-Kranz, Fragments, vol. II, section on Democritus) These sources come from a period later than Democritus and their authenticity (the investigation of which is beyond the scope of this study) should be carefully evaluated. However, Democritus travelled widely and authored technical writings on navigation, ocean-study, etc. This puts his trip to India within the realm of believability in spite of his early date. Since an old and well developed tradition of atomistic cosmology is also found in India (although some scholars remain sceptical about asserting or advocating that any well known Greek, apart from Alexander the Great and his generals, ever visited India), the above evidence cannot be summarily dismissed out of court. Needless to say, much of the evidence is presumably lost and the philosophical contact between Greece and India may never be proved as certain. But if the evidence from available ancient sources is put together, the accumulated weight for the hypothesis of Indo-Greek philosophical contact may meet the standards of legal probability. In a court of law decisions are made by considering on which side there is preponderance of evidence. The balance of evidence appears to be tilted on the side of the Indo-Greek philosophical contact. Much serious study is needed before one can determine who influenced whom and how much. But (1) the Sanskrit tradition is older; (2) there is no reference to the Greeks in any Sanskrit philosophical work; (3) there are numerous references to India in Greek authors of distinction and (4) the Hellenistic Greeks look upon India as the land of wisdom and some kind of Utopia. Hence, on the face of it, the chances of Indian philosophers having influenced Greek philosophers, rather than vice versa, are greater. For one obvious question is: if Indian philosophers took any Greek philosophical views seriously, discussed them and were influenced by them, why are not there any references to any Greek thinker in any

4

Introduction

Sanskrit philosophical work? Another obvious question is: if the Indians did not make any contribution to Greek philosophy, why are a number of distinguished Greek authors saying so openly and definitively? Unless compelling evidence is produced to the contrary (no such evidence has been produced so far), one cannot justifiably claim that such specific Greek testimony is deliberately misleading or otherwise mistaken. Further, specific assertions about Democritus or Pyrrho as having visited India cannot be set aside merely by pointing out such general difficulties as the physical distance or the language barrier between the Greeks and the Indians. For, in spite of such difficulties, some Greeks did come to India and Democritus or Pyrrho could be among them. The specific evidence about specific Greeks can be set aside only by specific rebuttal (e.g., a detailed chronology of the events in the life of Democritus showing a trip to India is highly unlikely); but no such specific rebuttal has been forthcoming. In a court of law an unrebutted testimony is considered to be weighty. Hence the testimony of such Greek authors as Megasthenes or Diogenes Laertius should be given the due weight (although the mere fact that such testimony has not been shown to be false does not prove it to be true). Again, even if one finds good evidence for Greek influence on some other aspects of Indian civilization, that by itself would not suffice to prove Greek influence on Indian philosophy (given the lack of any references to the Greeks in any Sanskrit philosophical work). For early Indian philosophical schools were somewhat secretive and moved in relatively small circles. This did not prevent the philosophical views from being widely circulated, for ample references to them are found in the Sanskrit literature. But the chances of any foreigner being admitted to such smaller circles are very small or rather virtually nil. Moreover, the roots of the Indian philosophical schools (including the Nyaya) can be invariably found in the Vedas. The extremely high standards found (by those who have been properly trained by the pundits) in the early Sanskrit philosophical writings also makes any uncorroborated speculation about outside influence unproductive. Under the circumstances, since there is no evidence of any ancient Indian philosopher expressing any interest in Greek philosophy, but there is evidence of Greek philosophers expressing interest in Indian philosophy, the issue of Indian influence on Greek philosophy should be investigated thoroughly and impartially. There are many difficulties in a study of this kind. For one thing, not only an astronomically large body of secondary literature on Greek and Indian philosophies, but also a very sizeable mass of source literature in different ancient languages have to be explored. For another, the interpretation of ancient texts always poses a serious challenge. [This is particularly true of the Sanskrit works, for one would miss much of what

Introduction

5

is going on if one reads them on one's own without being trained by a pundit.] We have tried to be impartial and not to gloss over important differences in the interest of forcing a comparative study. We have carefully noted both major similarities and major differences and tried to preserve the distinctness of each point of view. However, this work moves within certain limited parameters. It is not the aim of this kind of comparative work to provide a comprehensive coverage of Greek or Indian views that one might get from works exclusively devoted to one of them. Moreover, the scope of our study is limited. We have concentrated on Aristotle, the Stoics and the Epicureans on the Greek side and on the Nyaya for the Indian side. Our preparation for the Greek side is also much more limited than that for the Indian side. Still we have not hesitated to use our own translations of Greek texts (although we have often used standard Oxford or Loeb translations). We have not also avoided taking a stand on matters of interpretation for some of the giants of Greek philosophy. Thus we have tried to give an account of essentialistic definition and Aristotle's view of what we have called working or provisional definition which, we believe, holds more philosophical worth than usually acknowledged. We have tried to show that Aristotle's contribution to the study of inductive reasoning, contrary to the opinions of many Aristotelian scholars, is substantial, and some of the mistakes attributed to him are the results of questionable interpretation. We have also offered a tentative interpretation of the Stoic theory of definition according to which nonessential but peculiar properties are allowed in definition. The Epicurean attack on definition as well as the Stoic and the Epicurean views of method and inference from sign have been studied. For the Indian side we have focussed, as said, on the Nyaya views. Other Indian views have either been mentioned briefly or by-passed, because a much larger work would be needed to cover them. For the Nyaya views, too, only some major thinkers have been covered and not at great depth even at that. We have tried to show that the Nyaya view of definition captures what, for many Greek philosophers and contemporary philosophers, definition in an important sense should be, viz., that it should fulfil the conditions of economy, non-circularity and commensurability. References to a few recent views have been included in this connection. On induction and inference from sign we have given an account of these in early Nyaya. We have shown that the Carvaka critique of induction is similar to the Humean critique. We have explained that the later Nyaya justification of induction includes what may be called the subjunctive argument, the argument from belief-behavior contradiction, the argument from causation and the argument from universals. An

6

Introduction

overview of the recent philosophy of induction has been included. We have tried to make the case that the Nyaya view is a viable alternative alongside the contemporary views and has certain advantages over some of them. It would be an understatement to say that the Nyaya has merely anticipated many modern ideas. The clarity, precision and thoroughness with which the Nyaya philosophers have discussed the issues make their views fully relevant to the contemporary debate. Without any doubt the Nyaya justification of induction remains open to criticism from philosophers of various persuasion. However, be that as it may, there is perhaps no other (Indian or Western) attempt at justifying induction which fares any better. Finally, a note about diacritical marks. Although these are needed for accuracy of spelling and pronunciation, we have kept them to the minimum and omitted them from names. Further, the computer on which the manuscript has been typed does not allow the insertion of overdots and underdots. So these have been left out altogether.

PART ONE CHAPTER ONE ARISTOTLE'S VIEW OF DEFINITION

Referring to Aristotle's theory of definition Robinson has said: "It has been more widely adopted, and less often reviled, than any other part of the original theory of logic drawn up by Aristotle." (Nl) Again, according to the author of a currently popular textbook of logic, the Aristotelian type of definition is, "the most important kind of definition," because "it is more generally applicable than any other technique." (N2) These remarks serve to indicate the extent of interest in Aristotle's theory in recent times. There can be little doubt that according to Aristotle, a word has a meaning by itself, in isolation from the context of a proposition. This is borne out by the definition of a sentence as a significant sound, some part of which is significant in separation. (DI 16b26-27) A definition as an expression of meaning must be, Aristotle assumes, a complex expression (logos), i.e. consist of more than one term. (101b38) Although some single-term definitions are found in Top. VI 2 (as examples of faulty definitions which are metaphorical or obscure), Aristotle clearly disallows them: "People whose rendering consists of a term only, try it as they may, clearly do not render the definition . . ., because a definition is always a phrase." (102a2-4) In the discussion that follows (102a4-17) Aristotle says that single-term specifications are 'definitory', but provides no justification for disallowing them as definitions. This assumption that a definition is a longer expression than the term defined is exploited in rejecting those definitions of compound notions which are equimembral. (148b33-149a7) They are faulty for the very reason that they merely exchange the same number of terms: "there are no more terms used now than formerly; whereas in a definition terms ought to be rendered by phrases, if possible, in every case, or if not, in the majority." (149al-3) Aristotle is more cautious here; he implicitly allows that in a minority of cases a definition may possibly be not a phrase but a single term. 7

8

Aristotle's View of Definition

Nevertheless, the requirement that a definition must be a complex expression containing more than one term is frequently endorsed by Aristotle. Another fundamental assumption is that a definition states the essence of the thing to which the term applies. This is closely connected with the idea that a definition expresses the meaning of the term: What the definiens signifies is, presumably, an essence (ti en einai) or nature (phusis). Thus a definition expresses the essence in words and specifies what features are essential to things—as distinguished from other traits which are accidental. In other words, a definition states what the thing defined has to be in order to be a thing of that kind. At any rate, Aristotle connects the notions of definition and essence in numerous places. (N3) The idea that a definition is a mirror in language of what a thing is seems to be a motivating reason behind the considerable space devoted to definition in Aristotle's various writings. The connection between definition and essence is utilized in the following argument designed to show that it is possible to reason to a thing's definition and essence: "If a definition is an account signifying the essence of the thing and . . . genera and differentiae are predicated in what it is, . . . the account containing them will of necessity be a definition; it is impossible that anything else should be a definition, seeing that there is not anything else predicated of the object in what it is." (Top. 153al5-22) (N4) This passage contains another important idea which underlies the discussion of definition in the Topics: the essential predicates of a thing are of two types—genus and differentia. It also implies that a definition indicates the essence in the strict sense so that properties, which are characteristics following from the essence and possessed exclusively by the subject, are excluded. Only if the definition includes the genus and the differentia—and nothing else-can it indicate the essence of the thing. Here are two more passages in which Aristotle indicates his preference for the genus-differentia model of definition: " . . . the framer of a definition should first place the object in its genus, and then append its differences" (139a28-30); ". . . a correct definition must define a thing through its genus and its differentia." (14b26-27) Top. VI 4 contains an argument in favour of the genus-differentia model of definition. The argument may be paraphrased as follows. The purpose of a definition is to make known what the definiendum is. Hence one should employ in a definition, not any random terms, but only those terms which are prior and more intelligible. Unless it is required that the terms are prior and more intelligible, there would be more than one definition of one and the same subject. But that cannot be, for then the different definitions should represent different essences, while the essence of each thing is single. What is prior and more intelligible absolutely,

Aristotle's View of Definition

9

however, should be distinguished from what is prior and more intelligible to particular persons. The latter varies from person to person and even may vary in the same person at different times. Hence the terms in a definition should be prior and more intelligible absolutely; only then can it be that there is only one definition for each subject. Now the genus and the differentia are prior to the species absolutely, for if the genus and the differentia are annulled, the species is annulled too. The genus and the differentia are also more intelligible than the species absolutely, for the knowledge of the species presupposes that of the genus and the differentia, but not vice versa. Since the genus and the differentia are prior to and more intelligible than the species absolutely, it follows that a definition should consist of these. It may be noted that in this argument that a definition expresses the essence has been used as an implicit premise to rule out the possibility that there should be more than one definition of the same thing and to show eventually that the terms in a definition should be prior and more intelligible (gnorimoteron) than the definiendum. This shows that the thesis that a definition expresses the essence is more basic and has a higher priority than the thesis that a definition consists of the genus and the differentia. In fact while Aristotle has found it necessary to argue for the latter thesis, he has at no point felt the need to argue for the former. That a definition expresses the essence is indeed a fundamental assumption of his theory. Another premise in the above argument is that knowledge should proceed from what is prior and more intelligible absolutely to what is posterior and less intelligible absolutely. This is a familiar doctrine and has played a large role in the Posterior Analytics (e.g., I 1-2). Without any doubt, therefore, the above argument is substantial and definitive. The importance in the Topics attached to the thesis that a definition consists of the genus and the differentia should come as no surprise. It is clear that Aristotle is conscious of an ideal of definition; it is only the genus-differentia model which can fulfill that ideal. Moreover, since a definition displays the essence and the essence of each subject is single, there is no room for variation in degrees among definitions; only the ideal definition is the definition. Since the thesis that a definition expresses the essence is more basic than the thesis that it consists of the genus and the differentia, we agree with J. D. G. Evans when he says: "it is less certain that the definition should contain genus and differentia." (N5) Still the favorite view in the Topics is that a defiition in the absolute or ideal sense must contain genus and differentia and nothing else. The genusdifferentia model of definition stating the essence goes well with an important metaphysical doctrine in PO 1.4 that corresponding to every natural kind there is a group of essential characters [that are within "the

10

Aristotle's View of Definition

what-is-it" (to ti esti) of a thing] which something must possess in order to belong to that kind. This provides the basis of the distinction between necessary, per se (Kath auto) predications and contingent, per accidens (kata sumbebekos) truths, only the former being the proper concern of demonstrative science. [One may consult the valuable discussion in chapters 3-6 in Michael Ferejohn, The Origins of Aristotelian Science, Yale University Press, New Haven, 1991.] Definitions stating the essences and conveying "the what-is-it" of things can serve as necessary premises of demonstration. PO 1.4 also endorses the Platonic thesis in the Theaetetus that knowledge is of what "cannot be otherwise" (adunaton allds ekheiri). (73a20, also 88b31) Definitions expressing the essence are necessarily true and live up to such epistemological requirement. Another important (presumably later) development is the thesis of Met. Z 12 that for definitions arising out of divisions the final differentia is the substance of the thing and its definition. Although there can be only one ideal definition of each thing, Aristotle, of course, has no objection to the use of what can be called 'relative' or 'working' definitions which are not in the genus-differentia model. Indeed, he goes on to say that in dealing with persons who cannot recognize things through terms which are prior and better known absolutely, it may perhaps be necessary to frame the definition, not through terms that are prior and better known absolutely, but through terms that are prior and better known to them. (141b 17-22) Since the purpose of a definition is to increase understanding, the state of the person to be instructed will have to be taken into account. This is fully consistent with the methodological recipe that we should start our inquiry from what is more intelligible to us (something accessible to sense experience and so on), but less intelligible absolutely, and proceed to what is more intelligible absolutely, but less intelligible to us (for being removed from sense experience and requiring an exact and exceptional understanding). (De An. B2, 413all; Met. Z3, 1029b3-12) What is absolutely intelligible is not intelligible to all, but only to those who are in a sound state of understanding. (142a9-ll) For a person in sound intellectual condition a definition will consist of genus and differentia. A definition containing genus and differentia is a complex formula; how then can it express a single essence? To put the matter differently: assuming that a man is defined as a two-footed animal, how can 'man', which is clearly one notion, be synonymous with two different notions of 'animal' and 'two-footed'? The answer to these questions takes us to the heart of Aristotle's theory of definition and deep into his metaphysics of the distinction between essential and accidental predicates. The answer seems to be that complex expressions, which are not definitory and which involve accidental predicates, do not designate a single essence or

Aristotle's View of Definition

11

constitute a single notion, irrespective of whether there is a single name for it or not. For example, granting that it is an accidental feature of a man that he happens to be white, the complex notion 'white man' does not stand for a single nature (although it so happens that in some languages there is a single word for 'white man'). On the other hand, in the case of a complex expression which is a definition, only one notion or predicate is involved and one nature or essence designated. Thus, being a two-footed animal is not to have the property of being an animal and the property of being two-footed (Met. Z12 1037bl4), but the property of being an animal of the two-footed kind which is a species of the genus animal. Here it is not the case that two properties are being ascribed to the same thing (as it is in the case of 'white man'); rather 'two-footed animal' functions as a unitary predicate in the way 'man' does. In other words, accidental predicates, even when ascribed to the same thing, do not combine to form a unity (De Int. 11 21 a9- 10); but in the case of essential predicates several predicates unite to form a single predicate (De Int. 11 20b32). Met. Z12 seems to suggest that for definitions reached by divisions only one ( = the last) differentia constitutes the essence of the thing. It is supposed that the genus may not exist absolutely apart from the species, or that if it did, it would exist as matter or something indefinite and that its differentia makes the species, i.e., it is only through the differentia that it can become something definite. (Met. Z12 1038a58)

Consistently with the thesis of the unity of definition Aristotle has maintained that the genus and the differentia belong to one and the same category of essence (Top. VII 5 154a27-8) and has even asserted that they are synonymous (Top. 123a29, 127b5-6; Cp. Categ. 5 3al7-20 and 3a33ff.). However, in Top. IV 2 we are told that a thing's differentia never signifies its essence, but rather some quality (Top. 122M6-7; Cp. Top. VI 6 144al8-22). Moreover, in Top. 128a20 that the differentia belongs to the category of essence is mentioned to be the view of only some people. These passages have generated controversy among Aristotelian scholars. (N6) These may be taken to suggest that genus and differentiae belong to different categories; while genus is in the category of substance, differentiae are qualities. Such a view creates some difficulty for the thesis of the unity of definition. In spite of this it should be added that further indirect support for the unity of definition is found in Top. V13 where it is shown that definitions of the forms (1) X is 'A and B' (150al-21), (2) X is 'the product of A and B' (150a22-6) and (3) X is 'A + B' are faulty for various reasons. A definition of the first type (which defines a term as these things) will be wrong if it merely presents the constituent parts into which a whole thing can be analyzed and overlooks the fact that the

12

Aristotle's View of Definition

subject as a whole is more than a mere aggregate of the parts. Definitions of the second type (which define a term as what is made from these things) may be faulty if (a) the parts cannot as a matter of fact form a unity, (b) that in which the subject as a whole inheres is not the same as those in which the parts inhere, (c) there is some discrepancy between the characters of the whole and those of the parts, etc. Definitions of the third type (which define an object as this together with that) may be resolved into definitions of the first or the second type and, therefore, be subject to the same objections. Further, such a definition will be faulty if (a) the two elements which are conjoined in the definition cannot jointly inhere in any subject, (b) cannot exist in the same place or time, etc. Aristotle, however, stops short of asserting that all such definitions are faulty and significantly does not bring into play any argument from the thesis (as he does in Top. Z4) that there can be only one definition for each subject which is fulfilled only in the genus-differentia model. Rather his discussion gives the impression that these types of definitions were in vogue and his concern was not to condemn them outright, but to warn how certain types of blunders could be committed in them. This is confirmed by what Aristotle actually says. While stating the objection to the first type of definition mentioned above, he says: "a man who defines in this way seems (my italics) to assert that the parts are the same as the whole." (150al7) This suggests that if the man who defines in this way does not assert that the parts are the same as the whole, Aristotle may not press the said objection against him. Aristotle also says: "The arguments are particularly appropriate in cases where the process of putting the parts together is obvious," (150al8). This too suggests that the objections might not be considered to be appropriate for all cases. Again, as an example of a definition of the first kind, Aristotle supposes justice to be defined as 'temperance and courage'. Then of two persons each of whom has one of the two only, the definition will be true of both and yet of neither of them; for both together have justice, and yet each singly fails to have it. This objection lacks merit; if neither of two persons has justice, it follows thereby that they together do not have justice either. It is unlikely that Aristotle was not aware of this point. Although he has more to say on this objection, it is possible that the entire objection was advanced as an ad hominem argument against particular persons who harboured the relevant misconception. (N7) This would lend support to the possibility that Aristotle was not concerned, at least in the Topics VI 13, to reject all definitions of these three kinds. The discussion, however, makes one thing clear. The model definition through genus and differentia should not be construed as a definition of any of these three kinds in such a way as to be open to any of the listed objections. If genus

Aristotle's View of Definition

13

and differentia are understood together to form a unitary predicate, the possibility of all such objections is ruled out ab initio. In other places Aristotle has drawn a contrast between two kinds of definition. In the De An. (403a25-403bl9) he distinguishes between a physicist's definition and that of a dialectician. The former defines by assigning the material conditions, the latter by assigning the form. For example, the essence of a house is specified in a dialectician's account as 'a shelter against destruction by wind, rain and heat', but the physicist would describe it as 'stones, bricks and timbers'. It is clear that this distinction is similar to the contrast between the model definition through genus and differentia and a definition of one of the said three kinds. The physicist's account is not condemned as unworthy of being called a definition; rather the discussion suggests that both the physicist's and the dialectician's accounts may be useful from different points of view, and Aristotle takes note of the possibility that the two accounts could be combined. (403b8) [Indeed he seems to suggest in Met. Z17-H2 that this is the best option.] A similar distinction has been drawn with greater force in some aporetic passages in Met. B3 998a20-998bl4. Here Aristotle not only asserts that a definition by genera is different from that which states the constituent parts of a thing, but he also adds that the formula of the substance is one (998bl2)-which reminds one of the argument in Top. VI4. He states unequivocally that it is the genera which are the principles of definition (998b4) and goes on to assert flatly that it is not possible to describe both the constituent elements and the generic universals as the principles. (998bl0) But here, too, Aristotle does not explicitly refuse (nor grant) the title of definition to an account of the constituent elements. It should be clear that side by side with a narrower conception which requires that a definition must express the essence, we find in the Topics and other writings a broader conception which allows an account which does not express the essence at least to be called a definition (though admittedly in a secondary and less satisfactory sense). Aristotle himself has emphasised that 'definition' has several meanings {Met. Z4 1030al8). In Top. VI 139a25-35 Aristotle has listed five conditions for a definition which are as follows: a definition (1) should not be too narrow, (2) should put the object in its appropriate genus, (3) should not be too wide, (4) should express the essence, and (5) should be precise (kalos) in the sense of not containing obscure, metaphorical or ambiguous language and not containing superfluous material. A sixth condition which may be added from the discussion in Top. Z4 is that a definition should be by means of terms that are prior and more intelligible. This may be understood in an absolute or a relative sense, as we have already seen. One important way in which an account could fail to satisfy this

14

Aristotle's View of Definition

condition (to which we have not alluded before) is by way of being circular and using either directly or indirectly the term defined itself. A seventh condition {Top. VI 143bll-144a4) is that a definition should not be in the negative when it can be in positive terms. Finally, an eighth condition (Top. VII 152b4) is that what is signified by the term and the definitional expression should be the same. The conditions are neither mutually exclusive nor collectively exhaustive. Still this list will suffice for the purpose of catching a glimpse of the broader conception of definition. It seems that an account (such as X is 'made from these things') which satisfies the conditions 1, 3, 5, 6 (in the relative sense), and 8 may satisfy the broader conception of definition. But it will fail to conform to the narrower and stricter conception if it does not fulfill the conditions 2, 4, 6 (in the absolute sense) and 7. Without any doubt such a broader conception, or something fairly close to it, was familiar to Aristotle and currently in vogue. Being a promoter of the dialectical method, which acknowledges the importance of beginning by examining common views, he could not possibly ignore it. A definition which satisfies the broader conception, but not the narrower and stricter conception, cannot be a definition in the absolute or ideal sense; but it can at least be accepted as a relative or working definition. This explains why in many places Aristotle's own definitions are not explicitly in the genusdifferentia model. For example, hot is defined as that which associates things of the same kind, while cold is defined as that which associates homogeneous and heterogeneous things alike (329b26-30). Such examples show that a broader and more flexible conception of definition was used by Aristotle in many places. Many such definitions may of course be reformulated, after suitable revision, in the genus-differentia model. Further, since, as already said, there is only one definition for each subject, a relative definition can at best serve a limited purpose and will ultimately have to make way for the definition consisting of genus and differentia. Thus the stringent requirement that a definition should express the essence and consist of genus and differentia which together form a unitary predicate represents Aristotle's fundamental view. But it is likely that in laying down the stringent conditions Aristotle's purpose was to refine and transform a broader and current conception along the line of his basic metaphysical and epistemological views, and not to banish it completely. The following passage (among many others) illustrates how Aristotle criticised a definition which could satisfy the broader conception, but not his stricter conception: " . . . see whether, though the object is in a genus, it has not been placed in a genus . . . e. g., the definition of 'man', supposing any one to give it as 'that which knows how to count': for it is not stated . . . what it is that knows how to count; whereas the

Aristotle's View of Definition

15

genus is meant to indicate just this." (Top. VI 142b23-9) Although the ostensive purpose of this passage is to show why the genus should be included in a definition, it also shows how Aristotle objected to the supposed definition of 'man' as 'that which knows how to count'. The latter may fulfill the conditions of the broader conception. But it is clearly unacceptable, for it fails to state what a man is, which the definition of 'man' must do. Another objection that he would have, which he does not explicitly indicate here, is, of course, that the supposed definition includes a property, instead of the differentia. That Aristotle would not be satisfied with the broader conception, but would require more of definition is not in the least surprising, given his long association with Plato and the Academy. Plato's aim at least in certain of his later dialogues, seems to have been to determine what a thing is by means of the method of division which marks out a given definiendum from other things and shows the forms in which it participates—a method worked out in some detail in the Sophist and the Statesman. Speusippus apparently subscribed to the doctrine that knowledge of each thing requires knowledge of its differentia in respect to everything else, which implies that we cannot specify the differentia of one species without doing it for all. (N8) Aristotle disagreed (An. Post. II, 97a6 ff.) and held that in a division we should specify the differentia in which the definiendum is contained, and that it is not necessary to specify the differentiae which are excluded. He also reformed the academic procedure by requiring that in a division each differentia should be a further specification of its predecessor, so that the last differentia would imply all its predecessors and suffice by itself. This leads to the idea that a proper definition specifies a kind by supplying the proximate genus and the last differentia-which is a corollary of the ontological thesis that a species is the actualization of the genus in the final differentia. Though this particular formulation of the method of division as an instrument for establishing a definition is Aristotle's own, the following passages from the Statesman (285b) clearly shows its kinship with the Platonic recommendation: The right way is, if one has first seen the common nature of many things, to go on and not to turn away until one has found all the differentiae contained in it which form distinct species; nor again should one be able to stop with the various dissimilarities seen in a multitude of things until one has subsumed all of them under a single similarity and embraced them within the being of a single genus. In fact, the kinship is stronger than what is suggested by Cherniss when he says: "As for Plato himself, . . . the method must have been conceived in an essentially different fashion. He does not distinguish

16

Aristotle's View of Definition

genus and species ontologically or give any indication of the priority of the one to the other." (N9) In the above passage, at least, Plato is making use of the three notions of genus, species and differentia. Moreover, the recommendation is not only to search for a definite idea which is the genus, but also to search for the differentiae which constitute distinct species. These recommendations presumably played a vital role in giving shape to Aristotle's view, though Plato himself cannot be said to have explicitly formulated the genus-differentia model of definition. In fact, in the Top. 120b21-35 the Platonic definition of the soul as that which is self-moved has been criticized on the ground that motion does not belong to the soul essentially, so that the definition shows a confusion of genus and accident. The charge of including what cannot be the genus has also been levelled against the definition of Xenocrates that the soul is a selfmoving number. According to the Top. 123al 1-14, since the soul is neither odd nor even (which are the only species of number), it cannot be a number. The Top. 123a23-26 also makes the point that if the soul participates in life, and number does not, number cannot be the genus of the soul. In the Top. 140b2-6, however, Aristotle says first that in the definition of the soul as a 'self-moving number', 'number' is superfluous, for the soul is just 'the self-moving'. But then he goes on to say that perhaps the essence of the soul cannot be expressed if 'number' is eliminated. He finally declares that it is difficult to determine clearly what really is the case. Thus the different ingredients of the genusdifferentia model of definition were provided by the views of the members of the Academy (and also to some extent by Socrates, as Aristotle has acknowledged in Met. M4, 1078bl9). Aristotle put the notions of genus, differentia and species together in a systematic way to arrive at his own theory. He went on further to develop the position that the genus is the matter of which the final differentia is the form and held that this position alone could explain the unity of definition as well as essence. Although Aristotle has attached a lot of importance to the unity of definition, in De Part. An., 13 it is clearly held that the essence of a species is determined by a multiplicity of differentiae. In Hist. An. he has used differentiae such as the following: (1) bodily parts and shapes, (2) bodily activities and functions, (3) psychological dispositions, etc. (N10) According to Leszl, the requirement of more than one differentia is not incompatible with the unity of definition. (N11) But the situation is far from clear. Let us look at the following passage: Now if man was nothing more than a Cleft-footed animal, this single differentia would duly represent his essence. But seeing that this is not the case, more differentiae . . . will necessarily be required to define him; these cannot come under one division; for each branch of a dichotomy ends in

Aristotle's View of Definition

17

a single differentia, and cannot possibly include several differentiae belonging to one and the same animal. (644a711) According to this passage, it is impossible to reach any ultimate animal species by division by single differentiae. The method of dichotomy was revised by Aristotle to account for the unity of essence and definition and he ruled out the introduction of any division which is not a differentia of the essence of the previous differentia. If the essence is specified by many differentiae which cannot be reached by such dichotomy, we are left with no explanation of wherein lies the unity of essence and definition. It is possible that in connection with actually defining animal species Aristotle, in the light of the considerable amount of empirical data available at his command, was constrained to adopt a more flexible stand. Although the Topics contains numerous other issues regarding definition, we now turn to the discussion in the Post. An. In the latter we find a distinction (nowhere mentioned in the former) between an account of what a thing is and an account of what a word or phrase signifies (,sSmainei) (92b6-7, 15-16, 26-28, 93b30-31)-a distinction which is the ancestor of the later distinction between real and nominal definitions. An account of what a name or name-like expression signifies, Aristotle says, is a type of defintion which "signifies, but does not prove (deiknusi)" (93b38). He also says (in a dialectical chapter) that of something nonexistent one may know what the account or the name signifies without possibly knowing what it is; he explains with the famous example of goatstag that one may know what 'goat-stag' signifies, but it is impossible to know that a goat-stag is (96b6-7). [This is crucial to the programme in PO I.] Again he says (in the same dialectical chapter) that if a definition is an account signifying the same as a name without having anything to do with what a thing is, there will be absurd consequences (atopon) such as that there will be definitions of what is not an essence or even nonexistent, that all accounts, including works like the Iliad, would be definitions, for a name can be given for any account, etc. (92b25-34). Elsewhere too he says that 'definition' has several meanings (Met. 24 1030al8), but categorically denies that an account of the meaning of a word is a definition: We have a definition not where we have a word and a formula identical in meaning (for then all formulae would be definitions; for there will be some name for formula whatever, so that even the Iliad would be a definition), but where there is a formula of something primary. (1030a710) It appears from the above that Aristotle's attitude towards an account of the meaning of a word is far from clear. He has said (in

18

Aristotle's View of Definition

different places) both that such an account is a (type of) definition and is not a definition. Since, however, Aristotle has unambiguously asserted in numerous places that a definition is of the essence and since an account of word-meaning is not so, both Greek and Latin commentators have resolved the matter by holding that the latter is not, properly speaking, a definition. Thus, according to Philoponus, such an account is not a genuine definition, but an "accidental definition" (sumbebSkotos estin horismos). (N12) Again, St. Thomas says: "that which explains the signification of a name . . . is different from the definition, because it does not express what a thing is as does a definition." (N13) It is, however, clear that although Aristotle may not have been entirely consistent in his language, he has drawn the distinction between an account of the meaning of a word and an account of a thing's essence and pointed out their crucial difference: the former has no existential import which the latter does. The situation, however, has become complicated because of the way Aristotle has drawn the distinction between a definition and a hypothesis: A posit which assumes either of the part of a contradiction, i.e., that something is or that something is not, I call a hypothesis; one without this, a definition. For a definition is a posit, since the arithmetician posits that a unit is what is quantitatively indivisible, but not a hypothesis, for what a unit is and that a unit exists are not the same. (72al9-24) Thus although both definitions and hypotheses are posits (theseis), the former lacks the feature of an existential assertion which the latter has. The example makes it clear that an account of what a unit is (ti esti) does not imply that a unit exists. This seems to suggest that both an account of what a name signifies and an account of what a thing is lack existential claim. Accordingly, scholars like Heath and Ross have held that definitions, for Aristotle, do not have existential import; in the words of Gomez-Lobo "a definition of "F" has to be understood as stating necessary and sufficient conditions for something to be an F." (N14) But this interpretation is hard to reconcile with Aristotle's view of knowledge of essence. According to Aristotle, we cannot know what it is to be something {to ti en einai) without knowing that it exists, for we cannot know what a thing is (ti esti) if we are ignorant of whether it exists (93al9-20). He also holds that we search for the reason why (to dioti) when we know the fact—sometimes they may come simultaneously, but it is not possible to know the reason why before the fact (93al7-19). It seems, therefore, that a definition, in so far as it is an account of what a thing is, has existential import. This need not obliterate the distinction between a definition and a hypothesis. Although an account of what a thing is includes an existential claim, it does not by itself amount to the

Aristotle's View of Definition

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further claim that a given subject actually fulfills the conditions specified. It is this further claim which is presumably laid down in a hypothesis, so that and such being the case, a conclusion may follow. Such a reading naturally fits 76b35-39 which explains the nature and role of a hypothesis. While an account of a thing's essence has existential import, an account of what a name signifies makes no such claim. We, therefore, find it misleading when Bolton says that nominal definitions, for Aristotle, have existential import. (N15) The exact force of Bolton's claim is not clear, for he says: "Strictly speaking, a nominal definition is as much a definition of a thing ("of what something is" (93b29-30) as a real definition is." (N16) This seems to blur the distinction that Aristotle has made between an account of word meaning and an account of a thing's essence. As already said, an account of what something is makes an existential claim. On the other hand, if words are the subjects of nominal definition, as Bolton is willing to allow, (N17) such a definition, in so far as it is an account signifying the same as a name, lacks existential import. This is clearly implied in Aristotle's assertion, already referred to, that one can know what "goat-stag" signifes although it is impossible to know what a goat-stag is. Here is one more passage which is to the point: "we assume what a unit or what straight and triangular signify, and also that the unit and magnitude are; but we have to prove that the others are." (76a35-36) Further light on an account of what a name signifies is thrown by 93b29-36. With reference to such an account Aristotle says: Having grasped that this is (hoti esti), we inquire why it is (dia ti estin). However, it is difficult thus to grasp that of which we do not know that it is, the reason (aitia) of the difficulty, as stated before, being that we do not know, except accidentally, whether it is or not. This passage is difficult and compressed, and scholars have differed widely in their interpretations. Our reading agrees to a certain extent with that of Bolton, Sorabji and Gomez-Lobo. (N18) The first sentence seems to refer to a case where an account of what a word means includes something of the object named. Such an account would differ from an account of a name-like expression, such as "goat-stag", corresponding to which nothing exists. According to 93a21-22, we may become aware of the existence of something either accidentally or by grasping something of the thing itself (ti autou tou pragmatos). If, however, we have an accidental awareness of the existence of something, we cannot know what it is. (93a24-26) It seems accordingly that in the present type of an account of word-meaning we have a grasp of an element of the nature of

20

Aristotle's View of Definition

the thing named, so that we can proceed further and enquire into its essential nature as well as its explanation. In the above passage, the second sentence which is truly obscure seems to envisage another possibility. The adverb "thus", we suggest, should not be taken as referring to the previous sentence, but, from the context, to the procedure of defining by way of giving the equivalent of a name. What we have then is a case where an account of the meaning of a name does not include an element of the nature of the thing named. We have accordingly an accidental awareness of the existence of the thing and there is difficulty in conducting further scientific inquiry. If all this makes sense, there are three possibilities for what may be called a provisional definition. First, it may be an account of an empty name; no instances will be identified and scientific inquiry will not get off the ground. Secondly, it may be an account inclusive of some accidental feature of the thing named; this may lead to casual identification of instances and further scientific inquiry will be difficult, if not impossible (93a24-26 suggests that it will be impossible). Thirdly, it may be an account comprising something of the nature of the object itself. Such an account may lead to proper identification of instances and there will be less difficulty in the way of scientific pursuit (93a28). So far as an account of the essence of a thing is concerned Aristotle has repeatedly emphasized that one knows what a thing is if and only if one knows why it is, i.e, one knows its cause or explanation. (N19) This is why Aristotle says, while drawing a contrast from an account of what a name signifies, that "another definition is a formula which makes clear why a thing is" (alios de estin horos logos ho dslOn dia ti estin). (93b3839) Such a causal or aetiological definition is a natural corollary of the account of what a thing is which again may be of three different kinds. (N20) First, there is the definition of those which are immediate (ameson) which is an undemonstrable (anapodeiktos) position (thesis) of what a thing is. (94a9-10) Such definitions are principles (arkhai) and are of things whose cause of explanation is not different from themselves. (93b21-22) An example would be an account of what is a unit which is a basic and primitive mathematical term. As pointed out by Barnes, Aristotle is here hinting at the distinction between primitive and derivative terms. (N21) Since what we are concerned with is something primitive, the possibility of demonstration is ruled out. Second, there are definitions which can be made clear through demonstrations, although they are not demonstrated in or by them. These are accounts of items which have a cause or explanation different from themselves. In such a case an account of what something is can be complete and the nature fully revealed if an only if the cause is included. The reference to the cause answers the why question and includes the

Aristotle's View of Definition

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middle term for a parallel demonstration showing why the defined property belongs to the underlying subject. Such a full-fledged causal definition, Aristotle says, is a deduction (sullogismos) of what a thing is "differing from demonstration in arrangment" (ptOsei diapherOn tSs apodeixeOs). (94al 1-12) For example, thunder is the noise of fire being extinguished in the clouds (94a5). Here 'fire being extinguished in the clouds' is the cause or explanation of the noise in the clouds. It is also the middle term in a corresponding demonstration: all quenching of fire in clouds are noises in clouds; all thunders are quenching of fire in clouds; therefore, all thunders are noises in clouds. (N22) Third, there are definitions which are accounts of what a thing is without displaying the specific cause. For example, thunder is the noise in the clouds. In the words of Aristotle, such a definition is "the conclusion of the demonstration of what it is" (touto de esti tes tou ti estin apodeixeds sumperasma). (94a8-9) It is an initial account of what a thing is on the basis of which instances are identified and scientific inquiry proceeds further into the cause of the phenomenon. It is thus a partial definition which should be supplemented by the addition of the cause or the middle term in order to have a complete definition of the second type mentioned above. In spite of the apparent similarity, it cannot be assimilated to the third possible case of an account of what a name signifies, for it, unlike the latter, is an account of the object itself. (N23) Aristotle has not always carefully preserved the distinction between 'what signifies' (ti sSmainei) and 'what is' (ti esti) and has sometimes moved from one to the other. Hence the textual basis for drawing the distinction is less than full proof. Nevertheless, Aristotle has pressed for the distinction in a number of places; without any doubt, the distinction is important and cannot be overlooked in the interest of clarity and the best reading of the text.

NOTES 1. 2. 3.

Robinson, Richard, Definition, Oxford, Clarendon Press, 1954, p. 1. Copi, I. M . , Introduction to Logic, Macmillan, New York, 7th ed., 1987, p. 129. 141b24-5, 143al7-19, 146b32, 153al4-22, 154a32, Post. An. 82b37-9, 92a7-9, 93al9, Meta. VII 4-6, 10-12, 15, 17, Meta. VII 2-3.

22 4.

5. 6.

7.

8. 9. 10.

11. 12.

13. 14.

15.

Aristotle's View of Definition A similar, but not exactly the same, argument has been criticised in Post. An. B6 on the ground of begging the question. Regarding what this implies about the chronology of Aristotle's works see Maier, H., Die Syllogistik des Aristoteles, Tübingen, 1896-1900, vol. II.2, p. 78 n. 3 and Cherniss, H., Aristotle's Criticism of Plato and the Academy, p. 34 n. 28. Aristotle's conception of essence may have undergone important transformation and a developmental approach may be useful for a fuller study. But for our purposes we have adopted a unitarian approach. Evans, J. D. G., Aristotle's Concept of Dialectic, Cambridge University Press, 1977, p. 112. Bonitz, H., Commentarius in Metaphysica Aristotelis, Bonn, 1849, p. 258; Trendelenburg, F. A., Geschichte der Kategorienlehre (in Historische Beiträge zur Philosophie, vol 1), Berlin, 1876, pp. 56ff.; Ackrill, J. L., Categories and De Interpretatione, Oxford, 1963, pp. 85ff. According to John Ferguson, it is an example of Aristotle's sophistry: Ferguson, J., Aristotle, Twayne Publishers, New York, 1972, p. 47. Taran, Leonardo, Speusippus of Athens, E. J. Brill, Leiden, 1981, pp. 64-72. Cherniss, H., op. cit., p. 46. Hist. An. I 1, 487all and De Part. An. I 2-4; also, see Balme, David, "Aristotle's Use of Differentiae in Zoology" in Articles on Aristotle, ed. Barnes, J., Schofield, M., Sorabji, R., London, 1975 and chapters 1 , 4 , 11 and 12 in Philosophical Issues in Aristotle's Biology, ed. A. Gotthelf and J. G. Lennox, Cambridge University Press, Cambridge, 1987. Leszl, Walter, Logic and Metaphysics in Aristotle, Editrice Antenore, Padova, 1970, p. 55. In Aristotelis Analytica Posteriora Commentaria, ed. Wallies, M., (Commentaria in Aristotelem Graeca, vol. 13, pars 3), Berlin, Teimer, 1909, p. 372. Commentary on the Posterior Analytics, translated by Larcher, F. R., Magi Books, Albany, 1970, p. 194. Gomez-Lobo, A., "Definitions in Aristotle's Posterior Analytics", in Studies in Aristotle, ed. O'Meara, D. J., Catholic University of America Press, Washington, D. C. 1981, p. 33; Ross, W. D., Aristotle's Prior and Posterior Analytics, Oxford, Clarendon Press, 1949, p. 55 and 365. Bolton, R., "Essentialism and Semantic Theory," Philosophical Review, 85, October 1976, p. 521.

Aristotle's View of Definition 16. 17. 18.

19. 20.

21. 22.

23.

23

Ibid., p. 515. Ibid. Bolton, R., op. cit., pp. 514-544; Gomez-Lobo, A., op. cit., pp. 25-46; Sorabji, R., "Aristotle and Oxford Philosophy", American Philosophical Quarterly, 6, April 1969, pp. 127-135, and "Definitions: Why Necessary and in What Way," in Aristotle on Science, the "Posterioranalytics", ed. Berti, E., Editrice Antenore, Padova, 1981, pp. 205-244. Post. An. I 2, 71b9-12; II 2; II 8; II 10; II 11, 94a20-l; Meta. I 3, 983a25-6; VIII4, 1044bl3; Phys. 11, 184al2-14; 113, 194bl8-19. According to our interpretation, the threefold classification of definition found in 94al 1-14 and 75b31-32, though not so indicated by Aristotle, should be taken to be a classification of the account of what something is and should not be taken to exclude the recognition of an account of what a word means as another type of definition. Barnes, J., Aristotle's Posterior Analytics, Oxford, Clarendon Press, 1975, p. 212. For a critical study and alternative interpretations of this example see J. L. Ackrill's "Aristotle's Theory of Definition" in Aristotle on Science, the "Posterior Analytics", op. cit., pp. 359-384. In this respect our view differs from that of Ross, op. cit., p. 365.

CHAPTER TWO THE STOIC VIEW OF DEFINITION

Definition continued to be a topic of central interest in Stoic logic and dialectic. Chrysippus is reported to have held the opinion that common nouns have contraries while definitions do not. (Nl) This suggests that in his view a definition (perhaps following the lead of Aristotle) was regarded as a complex expression. However, a definition was required to be brief and to be a means of making one understand what is meant by words. This may be seen from the following passage: Some [i.e., the Stoics] have given these definitions: . . . . 'A definition is that which by a brief reminder brings us to a conception of the things underlying words.' (N2) We now look at some other passages for more light on the Stoic view. Chrysippus says that a definition is a representation of a peculiar characteristic, i.e., that which expounds the peculiar characteristic. Antipater the Stoic says: 'A definition is a statement expressed with necessary force', i.e., with reciprocal force. For the definition is meant to be reciprocal. (N3) A definition is, as Antipater says in On definitions book I, 'a statement of analysis matchingly expressed'. (N4) Three main ideas which emerge from these passages about the Stoic conception of definition are (1) that a definition is the statement of a peculiar characteristic (Idiou apodosis), (2) that it is a statement expressed with necessary (kat anagken) or reciprocal (kat antistrophen) force and (3) that it is a statement of analysis matchingly expressed (logos kat analusin apartizontOs ekpheromenos). These ideas are not at bottom fundamentally different. What is meant by a peculiar characteristic is a characteristic 25

26

The Stoic View of Definition

which is neither too wide nor too narrow. Such a characteristic is convertible and co-extensive with the definiendum. For example, in the definition 'man is a mortal rational animal', both of the following are true: 'if something is a man, that thing is a rational mortal animal'; 'if something is a rational mortal animal, that thing is a man'. This convertibility of the definiendum and the definiens is captured in the idea that a definition is meant to be reciprocal and also in that it is a statement of analysis matchingly expressed. These also suggest that what is signified by the term and the definitional expression should be the same, so that the latter simply gives us the meaning of the former. According to Sextus Empiricus, the Stoics held that a definition has the same meaning as a generalized conditional proposition and differs from it only in syntax. For 'man is a rational mortal animal' means the same as 'if something is a man, that thing is a rational mortal animal'. This is so because both the former and the latter apply to all cases subsumed without exception and are liable to be refuted by a single counter-example. (N5) Since, however, a definition is meant to be reciprocal and to be a matchingly expressed analysis, it should be equivalent to the conjunction of two corresponding conditional propositions (i.e., to a biconditional). Thus a definition of the form 'a is V would be equivalent to the joint assertion of both 'if something is a, that thing is b' and 'if something is b, that thing is a ' . A single counterexample of something which is a and not b would falsify the first of these two conditionals and refute the definition. Similarly, a single counterexample of something which is b but not a would falsify the second conditional and refute the definition. The rephrasing of a definition as a conditional with indefinite terms ranging over individuals has a special Stoic import. Neither Platonic Forms as super-individuals nor Aristotelian universals as primary objects of science have the status of reals (called 'somethings') in the Stoic ontology. Individuals alone are real (are 'something') and universals are mental constructs (phantasmata psukhSs). The rephrasing shows that a definition which appears to be about a universal is at bottom about individuals. This implies a significant departure from the Platonic/ Aristotelian tradition which views a definition as being mainly concerned with relations between universals/Forms. Like Aristotle the Stoics distinguished between a definition and a description (hupographs: literally, an outline) although the exact distinction between these two, as understood by the Stoics, is not clear. Diogenes Laertius reports: "A description is a statement introducing us to things by means of a sketch, or which conveys the force of the definition more simply than a definition does." (N6) But it is not clear

The Stoic View of Definition

27

precisely how a description which is a sketch, would convey the force of a definition more simply than a definition. One thing that could be meant is that while a description gives an account of a thing by stating any peculiar characteristic, a definition does so by stating a character which is not only peculiar but also essential. Indeed, the implication of a description conveying the force of a definition in a more simple way could be that a description too suffices to distinguish the thing from everything else by stating any characteristic which is co-extensive with the definiendum; but a definition does more and states the fundamental nature. Such a reading of the distinction would have to presuppose that a definition, for the Stoics, must state the essence and this is supported by leading scholars. (N7) While such an understanding of the Stoic position is plausible and cannot be ruled out, it should be pointed out that we do not have sufficient evidence to know for sure that a defining character is required by the Stoics to be not only peculiar but also essential. For Aristotle an ideal definition indicates the essence and should be in the genus-differentia model. We do not have conclusive evidence that this is also the Stoic view. First of all, while in some of the available Stoic definitions of a definition a defining characteristic has been clearly said to be a peculiar characteristic, in none of them has a defining property been explicitly required to be also essential. Under the circumstances, such a view should not be attributed to the Stoics without some compelling evidence. Secondly, the issue cannot be settled by an examination of the numerous Stoic definitions of various concepts. In many of them the definition appears to be in the genus-differentia model and could qualify as essential. (The crucial issue, of course, is the differentia, since the genus is not an idion in the requisite sense.) But this does not provide conclusive evidence for from the very nature of the case such characteristics are also peculiar characteristics. Moreover, there are other cases where what looks like a definition is not explicitly in the genusdifferentia model. For example: (1) "A proposition is that which is either true or false ..." (N8) (2) "A predicate is that which is said of something ..." (N9) (3) Rhetoric is "that which concerns the embellishment and order of a set speech." (N10) One could of course say that these are descriptions and fall short of definitions proper. But we have no proof that such was the intention of the Stoics themselves and no evidence to rule out the possibility that these were offered as definitions. Thirdly, Alexander of Aphrodisias has observed: Those [i.e., the Stoics] who say that a definition is a statement of analysis matchingly expressed (meaning by 'analysis' the filling out of the definiendum, and in succinct

28

The Stoic V i e w of Definition

fashion, and by 'matchingly' that it is neither broader nor narrower) would say that the definition is no different from the representation of the peculiar characteristic. ( N 1 1 ) Alexander's point is that a peculiar characteristic may very well turn out to be an inessential characteristic. Although what Alexander says may not necessarily reflect the Stoic view, it would be unwise to assume that he said so solely because he was under Aristotelian influence and either misunderstood the Stoic position or deliberately misrepresented it. It is certainly possible that his understanding of the Stoic position was correct and his observation justified. Fourthly, in some cases more than one definition of the same notion were proposed by the same Stoic thinker. For example, all of the following were coined by Sphaerus (who, according to Cicero, was rated as the best framer of definitions by the Stoics) as the definitions of courage: (1) Courage is a tenor of the soul obedient to the supreme law in matters requiring endurance; (2) courage is the maintenance of stable judgment in undergoing and warding o f f those things which seem fearsome; (3) courage is scientific knowledge of things fearsome, the opposite of fearsome, or to be completely ignored, maintaining stable judgment of those things.(N12) While these definitions of courage are somewhat similar, they are obviously not identical, and there is no indication that Sphaerus himself preferred one of them to the others. N o w the question is: if Sphaerus thought that while defining courage he was spelling out its essence, why should he advance more than one definition? Such was certainly not the practice of those who held that a definition must state the essence; since the essence of each thing is single, there can only be one definition for each subject. On the other hand, if to define means to state the peculiar characteristic, there could be more than one definition of the same thing: the same thing could have more than one peculiar characteristics. Of course, one could maintain that only one of these acconts was meant by Sphaerus to be the definition and the others, to be descirptions. But the point is that w e have no proof that such was actually the case. For all we know, all these accounts might have had been offered as definitions and Sphaerus might have had held that to define was to supply a unique characteristic. Here is another example of different definitions offered for the same notion: A predicate is what is asserted of something, or a state of affairs attachable to one or more subjects, as Apollodorus says, or an incomplete sayable attachable to a nominative case for generating a proposition. ( N 1 3 ) Fifthly, the Stoics unambiguously rejected the doctrines of both the transcendent universal and the immanent universal and, as already said,

The Stoic View of Definition

29

regarded the universals as figments of the human reason. They held that only particulars are real and 'species' in their usage can include even individuals. Thus the ontological motivations of the Stoics are quite different from those of the Platonists. Under the circumstances, when a Stoic thinker would bring, while defining, the subject under the genus, one should not hastily conclude that he meant to specify a part of the metaphysical essence. After all the genus, being a figment of the mind, is in the Stoic terminology 'neither something nor qualified, but a quasisomething and quasi-qualified'. Accordingly, the use of universal concepts by the Stoics may have been for linguistic purposes as it was indeed thought by some ancient authors: "... Forms were introduced ... neither for the usage of linguistic convention, as Chrysippus and Archedumus and the majority of the Stoics later believed ..." (N14) This shows that at least certain versions of definitional essentialism should not be attributed to the Stoics. Thus we should not think that for the Stoics a definition is of a Form or a universal with a primary ontological status of its own. Nor should we think that a Stoic definition is causal, that for the Stoics one knows what a thing is, i.e., its definition, when one knows its cause. If some peculiar, though non-essential, characteristic were acceptable from the Stoic point of view as a defining character, the distinction between a definition and a description might have had been understood as follows. It would still not be easy to find in many cases defining characteristics which are co-extensive with the definiendum, or even when found, such characteristics may not be easily expressible or may not be easily comprehended by particular persons. In such cases it would be useful to have a description as a preliminary account or as an account which seeks to clarify and introduce the subject by using familiar and well known features. Thus a description could serve the purpose of a 'working definition' and make clear what is unfamiliar through what is familiar and as a stepping stone towards a proper definition. In particular, a description could capture what the Stoics called preconception (prolSpsis) understood as the "natural conception of the general characteristics of something" (ennoiaphusikS tön katholou). (N15) In this sense a description would contain a relatively undeveloped conception as distinguished from a well thought out and articulated definition. For example, according to the Stoics, gods are preconceived as immortal, blessed and benevolent. (N16) The definition is a developed version of this: "a living being (zöori), immortal, rational, perfect in happiness (teleion en eudaimonia), unreceptive of any evil, provident over the world and its contents. (N17) Whether a definition was, for the Stoics, required to indicate the essence or not, the practice of careful definition was thought to be a guide

30

The Stoic View of Definition

to truth and a way of escape from error. A large number of definitions of the basic terms in the system, such as fate, providence, the supreme good, virtue, etc., as well as of a wide range of logical, epistemological and linguistic notions were formulated, in particular by the later members of the school. A few of them, are mentioned here as samples. An impression is an affection occurring in the soul, which reveals itself and its cause. Imagination is an empty attraction, and affection in the soul which arises from no impressor. (N18) A cognitive impression is one which arises from what is and is stamped and impressed exactly in accordance with what is and of such a kind as could not arise from what is not. (N19) An argument is a complex of premises and a conclusion. What they call its premises are the propositions adopted by agreement for the establishing of a conclusion. A conclusion is the proposition established from the premises. (N20) Of arguments, some are invalid, others valid. Invalid are those the contradictory of whose conclusion does not conflict with the conjunction of the premises. (N21) It appears thus that the role of definition as an integral part of philosophizing was fully utilized and recognized by the Stoics.

NOTES

1. 2. 3. 4. 5. 6. 7.

SVF, 2.174. Galen, Medical definitions 19.348,17-349,4; LS I p. 191, LS II p. 194. Scholia on Dionysius Thrax, 107, 5-7; SVF, 2.226; LS I p. 190, LS II p. 192. D L 7.60; LS I p. 190, LS II p. 193. Sextus Empiricus. Against the professors II.8-9; SVF, 2.224; LS I p. 180-1, LS li p. 184-5. D L 7.60-1; LS I p. 191, LS II p. 193-4. "But there seems no d o u b t . . . that 'peculiar characteristic' (idion) is an expression intended by the Stoics to apply only to features which are not just unique but also essential." LS I p. 194.

The Stoic View of Definition 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

31

DL 7.65. DL 7.64. SVF 2.297. Alexander, On Aristotle's Topics 42, 27-43,2; SVF 2.228; L S I p. 191, LS H p . 194. Cicero, Tusculan disputations 4.53; LS I P. 191-2; LS II p. 195. DL 7.64; SVF 2.183; LS I p. 197, LS II p. 199. Syrianus, On Aristotle's Metaphysics 105, 21-4; SVF 2.364; LS I p. 180, LS II p. 184. DL 7.54; SVF 2.105; LS I p. 242, LS II p. 243. Plutarch, De communibus notitiis 1075E DL 7.147; SVF 2.1021; LS I p. 323, LS II p. 321. Aetius 4.12.1-4; SVF 2.54; LS I p. 237, LS II p. 239. Sextus Empiricus, Against the professors 7.248; SVF 2.65; LS I p. 243, LS II p. 245. Sextus Empiricus, OP 2.135-6; LS I p. 213, LS II p. 214. DL 7.77; LS I p. 212, LS II p. 213.

CHAPTER THREE THE EPICUREAN ATTACK ON DEFINITION

According to the Platonic tradition, a philosopher should pursue a dialectical process leading up to definition. One of the significant movements that enriched the Greek tradition was the development of a diametrically opposite standpoint by Epicurus and his followers. Reason rather than sense experience inevitably plays the primary role in Platonic definition. The Epicureans were committed to the priority of sensation and, not surprisingly, opposed the view that definition should play a central role. The Epicureans were concerned that definitional exercise could boil down to being exclusively linguistic, divorced from the real objects, the definition's referents. Evidence of such concern is found in the following passages. They reject dialectic as redundant and hold that it suffices for natural philosophers to proceed in accordance with the words belonging to things. (DL 10.31, Usener 257) Of enquiries, some are about things and others about mere utterance. (DL 10.34, Usener 265) Epicurus held that the first concepts of enquiry should not be required to be demonstrated because that opens the door for an infinite regress. (Letter to Herodotus 37, similar to Aristotle's view regarding first principles in PO I 1-2.) He might have also held that the basic concepts should not be required to be defined for the definiens should be prior to the definiendum (as Aristotle held) and nothing is prior to the basic concepts. At any rate, if every concept must be defined in a noncircular way, there will be the threat of infinite regress of definitions. Since it is impossible to define every term and since some terms must remain undefined, definition must in the ultimate analysis be held to be superfluous. The following well known passage states the dilemma of definition.

33

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The Epicurean Attack on Definition

If we are to explain the words familiar to everyone, we should explain either all or some. But to explain each is impossible while to explain some is pointless. For we shall expound them either through familiar or through unfamiliar expressions. But unfamiliar words appear to be unfit for the task, for the recognized rule is to explain what is less known by what is better known. On the other hand, familiar words, by being on the same footing with them, will be uninformative for throwing light on language, as said by Epicurus. The informativeness of language is typically ruined when it is bewitched by an account, as if by a homeopathic drug. (Erotianus 34, 10-20, Usener 258) Erotianus does not explain why using familiar words in a definition would make it uninformative and why such words must be on a par with the subject to be defined and could not be better known. But it is this relative uninformativeness of the definitions which made them unattractive to the Epicureans. The Platonists claimed that definitions would supply the most valuable information about things by indicating their essences; but to the Epicureans the so-called search for essences amounted to turning away from the actual observation of things and indulging in speculation based on a priori assumptions. As Epicurus put it: "one must conduct an inquiry about nature not in accordance with empty axioms and stipulations (kata axidmata kena kai nomothesias) but as the phenomena dictate (ekkaleitai)." (Letter to Pythocles 86) This sentiment also underlies the following view attributed to Epicurus: "Epicurus says that names are clearer than definitions." (ta onomataphesin saphestera einai ton hordn: Anonymous commentary on the Theatetus, 22.39-42) The superfluity of definitions is also broadly hinted in the following words attributed to the Epicurean spokesman Torquatus: "Who is there who does not know what pleasure is or who wants a definition to understand it better?" (Cicero, On Ends, 2.6) Although the Epicureans were opposed to definitions, they were not opposed to providing descriptions so that an investigation could proceed methodically and everyone participating in it could agree on the subject matter. Indeed, descriptions which do not toe the line of Platonic definitions are found in the writings of both Epicurus and his followers. The Epicureans agreed with the Platonists on the point that the subject of an inquiry should be clear from the beginning. (Nl) This is fully consistent with the first rule of inquiry as formulated in the Letter to Herodotus where Epicurus requires that an inquirer should have clear notions corresponding to the words used. (N2) Descriptions or outline accounts (hupographS) thus had to be supplied to ensure that the

The Epicurean Attack on Definition

35

investigators participating in a discussion had a clear understanding of the relevant concepts. As an example one may refer to Epicurus' famous description of god (in the Letter to Menoeceus 123) as "an indestructible and blessed creature" and his comment that such is the common idea of god in outline (he koine tou theou noesis hupegraphe). Epicurus goes on to say that one should not attach to god anything which does not agree with indestructibility or blessedness and should add everything that preserves the combination of indestructibility and blessedness. This serves to show how Epicurus distanced himself from Platonic definitions and used descriptions or outlines to clear up possible ambiguities. Such descriptions were not meant to indicate the essence, but to lead one to the concepts underlying words by stating some experientially important features that are generally well known. The aim is not to fix some ideal meaning, but to lay bare in outline what is empirically learnt and commonly understood. It may be useful at this point to look at some more specimens of descriptions provided by the Epicureans. Thus a world is said to be a certain envelopment of a heaven. It is cut off from the infinite, and ends in a terminus which is rare or dense, on the destruction of which everything contained in a world will collapse. (Epicurus, Letter to Pythocles 88) Again, an opinion is a movement inside us of mind atoms. (DL 10.51) A preconception (prolSpseis) is a sort of recognitive perception (katalSpsis) or correct opinion or conception or universal notion stored in the mind, that is, a memory of that which has often become evident from outside. (DL 10.33) In the version of Clement of Alexandria a preconception is a contact with some self-evident thing and with the self-evident conception (epinoia) of the object. (Strom. 2.4, Usener 255) Justice is a mutually beneficial pledge among men on the basis of which they agree not to harm one another in order that they may not be harmed themselves. (BD 31, 32, 36) A perusal of these outlines or descriptions shows that Epicurus' rejection of definition is not a rejection of the demand for clarity and does not reflect a lack of concern for the problem of ambiguity. His objection was to definitions as a priori explanations of the meanings of terms which would replace ordinary concepts as the norms of inquiry. Nevertheless, clarity had to be restored and ambiguities removed, and this task could be achieved through outlines or descriptions. In fact, Epicurus authored a book called Peri Amphibolias, which is lost. (N3) It seems then that Epicurus opposed definitions but endorsed descriptions. This was consistent with his overall opposition to a priorism and his advocacy of empiricism. It is to be noted, however, that in none of the extant writings of Epicurus or his followers do we find any detailed account of

36

The Epicurean Attack on Definition

descriptions nor is there any clear evidence that a full fledged theory of descriptions was developed systematically. The distinction between definitions (horoi) and descriptions or sketches (hupographai, hupotuposeis) was, however, well known. Cicero has made it clear in the exchange with Torquatos that while a definition discloses and makes evident what is implicitly contained in the ordinary notion of a thing, a description serves as a reminder of the ordinary notion itself. (On Ends 2.5) Galen has said that descriptions are definitions of our concepts that do not go beyond what all men know, but are not accepted as definitions in the strict sense. (SVF 2.229) Galen has also said that in distinction from a definition proper a description is made out of manifest characters (ek tdn enargos huparkhontdn) and of manifest phenomena (ek ton enargos phainomenon). (Subfiguratio Empirica 7 p. 63.4-10 D) Ammonius has indicated that a definition consists of essential attributes (ek ton kata ousian huparkhontdn), but a description, of accidental characters (ek ton sumbebS kotori). (In Porphyrii Isagogen: 2.15: Commentaria in Aristotelem Graeca, vol. 4 pt. 3, ed. A. Busse, Berlin, G. Reimer, 1891, pp. 54-55) (N4) The three main features of a description that emerge from these accounts are that a description should consist of characters which are (1) part of the commonly understood concept of a thing, (2) are empirically evident and (3) are accidental or non-essential characters. Of these the second feature, viz., that of being manifest or evident in sensing, would seem to be the most important from the Epicurean point of view. The other two features are clearly connected with this feature. An empirically given character was not acceptable from the Platonic stand-point as an essential character. The Epicureans tacitly agreed with that, although with the added proviso that the talk about an ideal essence was superfluous as well as conjectural. Further an empirically acquired characteristic could be expected to be part of the ordinary notion of the things, for common opinion is based on sensing. However, the essentialists held that an ordinary empirical feature was merely a concomitant accidental feature and would have to be superseded. For an accident is a feature which a particular may or may not have while being the same (kind of) thing. For example, our skin-color is incidental to our being human. If one includes such accidents among marks of being human, things people agree are human would be excluded. But, for the Epicureans, the Platonic distinction between the essential and the accidental is based on a priori speculation and, therefore, unacceptable. The Epicureans implicitly seem to agree that a description should not be too wide or too narrow. This is probably why a description is required to include characters which are part of the commonly shared concept of a thing. For one point of a character being part of the common concept

The Epicurean Attack on Definition

37

presumably is that the character is not too narrow (nor too wide). But, more importantly, for the Epicureans, our ordinary experience and understanding provides an ultimate criterion. A description making use of empirical features and serving as a brief reminder of the ordinary conception was thus designed to play a crucially important role. Further light on the Epicurean view is thrown by considering the fact that Epicurus proposed the following ostensive description of man: "this kind of ensouled structure" {to toioutoi morphOma meta empsukhias: Sextus Empiricus OP 2.25 and Adv. Math. 7.267; Usener 310). (N5) Thus the empirically given form of man and the empirically ascertained feature of having soul in it (i.e., being alive) are taken to provide the account of man. The ostensive description may have been provided to avoid an infinite regress of descriptions. But it also underscores the importance of the empirical features for giving an account of man. It is only some directly observed characteristic, such as having a certain shape, which can be sought to be communicated through ostentation. The reference to the soul, it may be noted, does not introduce something unobserved or non-empirical. Epicurus' concept of soul is a far cry from, for example, that of Plato who regarded the soul as a spiritual substance which pre-exists before birth and survives the death of the body. For Epicurus the soul is a kind of physical substance: "The soul is a body with fine parts permeating the whole aggregate. It most closely resembles breath mixed with heat." (Letter to Herodotus 63) Thus the reference to the soul draws attention to another empirical feature, viz., that of being animated. The emphasis on the ordinary conception and the observed features gives a special flavor to the Epicurean account of concepts. But notably, according to Philodemus, the first century B. C. Epicurean, the preconception of man is "rational living being" (z is non-a." Since such a general premise is required to be reliable, the Nyaya philosophers became interested in the methods of generalization and related issues of induction from the very beginning. In fact, the said general premise (usually) includes the citation of a particular specimen. This is thought to indicate that there is adequate inductive evidence in support of the genenral premise. Such a general premise, as already said, states that the probans is pervaded by the probandum. Accordingly, two of the conditions required to be fulfilled by a probans are as follows: (1) The probans ( = the pervaded) should be present in some particular cases where the probandum ( = the pervader) is known to be present. These may be called positive instances (called variously in Sanskrit sapaksa, sadharmya-drstanta, anvayi-drstanta and tajj&tiya). For example, for the general statement 'whatever is smoky is fiery', a kitchen (where fire is known to be present and also smoke) is a positive instance. (2) The probans should be absent from some particular cases where the probandum is known to be absent. [For formal validity the probans is required to be absent from wherever the probandum is absent.] These may be called negative instances (called variously in Sanskrit vipaksa, vaidharmya-drstanta, vyatiraki-drstanta and tajjatiyaanya). For example, for the above general statement a lake (where fire is known to be absent and also smoke) is a negative instance. [For a fuller exposition see TSD, the chapter on inference (anumana)]. It should be clear that a nyOya as an argument is partly inductive and partly deductive. When, in the inference of fire from smoke, it is asserted that 'whatever is smoky is fiery, such as a kitchen, etc., and a lake, etc.', an induction is involved. The induction is from sentences describing particular instances (e.g., the kitchen has smoke and fire; the lake has neither fire nor smoke) to a general proposition that whatever is smoky is fiery. This is followed usually by an observation report, such as that 'the hill has smoke.' Then the conclusion that 'the hill has fire' is deduced from the above two steps. In other words, in a nydya we first

Early Nyaya View of Induction and Inference From Sign

105

reach a general proposition from sentences describing particular cases. Then the general proposition is used, together with another premise (which is often, but not always, an observation report), as a premise to derive a conclusion (which may be a universal, a particular or a singular proposition). The above account of nyOya is commonplace in later Nyaya. We begin our more detailed study of the Nyaya view by tracing how some of these ideas begin to surface in early Nyaya with the focus, of course, on induction and inference from sign. It may be noted that the notion of linga (a name for the probans) is close to the Greek notion of semeion (sign). Linga literally means "what makes known something hidden" (iTnam gamayati). In a typical, paradigmatic case the linga is evident or perceived (pratyaksa) and serves as the means or ground (sGdhana, hetu) for inferring something non-evident or unperceived (paroksa), e.g., unperceived fire is inferred from perceived smoke. We first look at the account of the 'exemplification' (ud&harana) step of the pentapod argument (panc&vayavany&ya) (N2) provided in Gotama's Nyayasutra 3.1.36: "Exemplification is [that from which is obtained: yatah] the example possessing those characters in accordance with the universal concomitance (sOdharmya) [of the probans] with the probandum." (N3) The words 'those characters' here stand for the probans and the prbandum. Thus, in spite of the admitted brevity and ambiguity, the prescription laid down in this aphorism may be interpreted (generations of Nyaya philosophers have interpreted it so) as to supply a statement of universal concomitance between the probans and the probandum together with a supportive particular specimen. The role played by the particular specimen is of crucial importance for our present purposes. What Gotama is prescribing is that a particular specimen should be supplied which will possess both the properties named by the probans and probandum. This will lend support to the claim made in the premise that the probans is universally concomitant with the probandum. In other words, in order to vindicate the reliability of the premise that the probans is universally concomitent with the probandum, one should cite particular objects possessing the properties named by the probans and the probandum. Gotama's account is cryptic, but the substance of the matter is neither unclear nor confused. It is the thesis that a generalization is supported by positive instances (sOdharmya/anvayi-drst&nta). (N4) Gotama described the structure of a nydya very briefly without providing any actual, fully articulated specimens. In a specimen of a nyaya supplied by Vatsyayana, the earliest commentator, the relevant exemplification step is as follows: "What is originated is non-eternal, such as a plate, etc." (A© p. 32) (N5) It is clear that in Vatsyayana's example the exemplification step consists of a universal proposition

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together with a positive instance. The fact that a plate, etc., are both originated and non-eternal supports the reliability of the general premise that all originated things are non-eternal. It is significant that Vatsyayana has added the word "etc." after citing a plate as a particular specimen. This obviously indicates that other observed particulars which are both originated and non-eternal also lend support to the said generalization. In other words, what Vatsyayana has in mind (when he speaks of "a plate, etc.") is the class of all known particular things which are both originated and non-eternal. The method prescribed is precisely that in order to generalize that all a is b, one should observe particular things which are both a and b. In other words, by borrowing later Nyaya terminology, the observation of the co-presence (anvaya) of two properties in some particular cases supports the generalization that the two properties are copresent in all cases. This may be called the method of co-presence (anvaya). In Nyaya terminology anvaya (which means co-presence) is also the name of this method of co-presence. For a second method of generalization we now look at NS 1.1.37: "Or the opposite in accordance with the negation of those." Since this aphorism is too brief to make any sense standing alone, we must look at two earlier aphorisms for a better understanding of the context: "The reason (hetu) is [that from which is obtained: yatah] that which proves the probandum on the basis of the universal concomitance (sadharmya) stated in the exemplification." (NS 1.1.34) "Likewise on the basis of universal non-concomitance (vaidharmya)." (NS 1.1.35) The last aphorism, when read in conjunction with the previous aphorism, is taken to be an abbreviated version of the following aphorism: "Likewise the reason is [that from which is obtained] that which proves the probandum on the basis of the universal non-concomitance stated in the exemplification." At least this is how Vatsyayana has restored it. (ND p. 30) Similarly, when read with NS 1.1.36, quoted earlier, NS 1.1.37 should be taken to be an abbreviation (as suggested again by Vatsyayana: ND p. 31) of the following aphorism: "Or exemplification is [that from which is obtained] the example lacking those characters in accordance with the universal non-concomitance [of the probans] with the probandum." The restored version of NS 1.1.37 contains the following prescription: alternatively, the exemplification step should state the universal non-concomitance between the probans and the probandum together with a supportive particular specimen. What is meant by the universal non-concomitance between the probans and the probandum is that the probans is excluded from everything from which the probandum is excluded, i.e., that whatever lacks (the property named by) the probandum also lacks (the property named by) the probans. Once again,

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the role played by the particular specimen is of crucial importance for our present purposes. The prescription is that a particular specimen should be supplied which lacks both the properties named by the probandum and the probans. This will lend support to the claim made in the general premise that everything lacking the probandum also lacks the probans. In other words, in order to vindicate the reliability of the premise that the probans is universally excluded from where the probandum is excluded, one should cite particular objects lacking the properties named by the probans and the probandum. Once again, in spite of the crypticness, the substantial thesis is clear, viz., that a generalization is confirmed by negative instances (vaidharmya/vyatireki-drst&nta, N6). In Vatsyayana's specimen the said step is as follows: "What is eternal is non-originated, such as the soul, etc." (ND p. 30) (N7) Once again, it is clear that in Vatsyayana's example the exemplification step consists of a universal proposition together with a supportive instance. The fact that the soul, etc., are both eternal and non-originated confirms the general premise that all eternal things are non-originated. It is noticeable that Vatsyayana has added the word "etc." after citing the soul as a particular sample. This indicates that other known particulars which are both eternal and non-originated also lend support to the said generalization. In other words, when Vatsyayana speaks of the soul, etc., what he has in mind is the class of all known particular things which are both eternal and non-originated. The method prescribed is that in order to generalize that all non-fe is non-a, one should observe particular things which are neither b nor a. In other words, (by borrowing later Nyaya terminology) the observation of the co-absence (vyatireka) of two properties in some particular cases supports the generalization that the two properties are co-absent in all cases. This may be called the method of co-absence (vyatireka) In Nyaya terminology vyatireka (which means coabsence) is also the name of this method. Gotama and Vatsyayana are well aware of the fact that a generalization is falsified by counter-examples. This may be gathered from NS 1.2.5: "The deviant is inconclusive." This implies that only the non-deviant sign can be conclusive. Commenting on this Vatsyayana says: Deviation is lack of being restricted to one side. . . . For example: suppose one argues that sound is eternal because of lacking touch. The soul, etc., may be cited as examples in pursuance of the [aphorism] that the reason is [that from which is obtained] what proves the probandum on the basis of the universal concomitance stated in the exemplification. But the sign 'non-possession of touch' deviates from eternality: cognition does not possess touch and is non-

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eternal. (ND pp.40-41) The point for our present purposes is the following. The soul, etc., may be cited as examples in support of the generalization that all things which lack touch are eternal. But the generalization is false, for cognition lacks touch, but is non-eternal. The same moves are found in NS 2.2.22 and 2.2.23 (which belong to a section devoted to refuting that sound is eternal: "[Sound is eternal] because of lacking touch." (2.2.22) "No, for motion is non-eternal [and lacks touch]." (2.2.23) Gotama's point is that one may argue that sound is eternal because of lacking touch; but the argument is faulty, for it is based on the false generalization that all things lacking touch are eternal. That the generalization is false is shown by the counter-example of motion which lacks touch but is non-eternal. The role of the counter-example is also highlighted in NS 2.2.13-2.2.15: "[Sound is non-eternal] because of having an origin. . . . " (2.2.13); "No, for absence of a [destroyed] pot [has an origin] but is eternal. ..." (2.2.14); "There is non-deviation, for the principal sense [of eternality] should be distinguished from the secondary sense." (2.2.15) To explain: One may object to the argument that sound is non-eternal because of having an origin, by pointing to the counter-example of absence of a destroyed pot. Since the self-same pot, once destroyed, cannot be brought back into existence, its absence, consequent upon its destruction, has a beginning but no end; such an absence accordingly may be described as eternal. This allegedly refutes the generalization relied on in the said argument, viz., that all things having an origin are non-eternal, for the absence of a destroyed pot has an origin but appears to be eternal. This seems to prove that the sign, viz., having an origin, deviates from the probandum, viz., non-eternality, and is faulty. In reply Gotama points out that we should distinguish between the principal and the secondary senses of being eternal. In the principal sense eternality means having neither an origin nor an end and this is the sense intended in the present context. Since absence of the destroyed pot is not eternal in the principal sense, it is not a genuine counter-example to the said generalization; it fails to show that the sign has deviated from the probandum, i.e., that the sign belongs to something lacking the probandum. Gotama's use of the word non-deviation (avyabhicara) is significant. Non-deviation is another name of what was later called pervasion (vyapti): it is the requirement that the probans should not belong to anything which lacks the probandum. The requirement of nondeviation together with the recognition of the role played by a counterexample in refuting a general proposition provides further evidence that Gotama's nyaya is not merely analogical argument from a particular premise to a particular conclusion. It shows that in Gotama's view too,

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as in the view of later Nyaya logicians, the probans is required to be stated as being related to the probandum by way of universal inclusion and/or universal exclusion. Quite interesting is also the way in which Gotama diffuses the counter-example to save his premise. The theory he wants to defend is that sound is non-eternal. In defense of the theory he brings in the general law-like statement that all originated things are non-eternal (and points out that sound is originated). The counter-example he cites is by no means trivial. For posterior absence of a thing has an origin (when that thing is destroyed) but is endless, has the semblance of eternality and seems to refute the law-like statement. In response Gotama clarifies the distinction between the primary and the secondary senses of the theoretical term 'eternal' (as a scientist might when facing a counter-example to a favored law), shows that the counter-example does not apply to the primary sense and saves the law. Thus in spite of the crypticness the high level of sophistication can be unravelled if one probes patiently. We have so far analyzed some cryptic statements of Gotama and Vatsyayana's comments thereon to show that they anticipated two basic inductive methods, viz., the method of agreement in presence and the method of agreement in absence. We have also seen that they adequately recognized the role played by a counter-example in refuting a generalization. We now move on to consider some other contributions made by them in the study of inference from sign. NS 1.1.5 contains a threefold classification of inference: "Next, inference which is based on those, is of three kinds, viz., purvavat, sesavat and samanyatodrsta." Gotama has not explained what he means by "those", nor what he means by purvavat, etc. Such excessive crypticness may be disconcerting; but it should be kept in mind that these aphorisms are meant to be nothing more that mnemonic aids in an instructional process—mnemonic aids waiting to be filled in by the instructor who knows what these mean for the benefit of the students. At any rate, under the circumstances it is useful to turn to the gloss of Vatsyayana: By "based on those" reference is made to cognition of the relationship between the sign and the signified. By cognition of the sign and the signified as related reference is made to the remembrance of the sign [i.e., to the remembrance of the sign as pervaded (vydpya) by the signified]. On the basis of the remembrance and cognition of the sign something unperceived (or not given: apratyaksa) may be inferred. (ND p. 14) When Vatsyayana speaks of the relationship between the sign and the signified, he has in mind the requirement that the sign should be pervaded

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by the signified. What is meant by the relationship of pervasion, as already said, is that the sign (the probans) is related to the signified (the probandum) by way of universal inclusion and/or universal exclusion, i.e., that the signified (the probandum) belongs to everything to which the sign (the probans) belongs and/or the sign (the probans) is excluded from everything from which the signified (the probandum) is excluded. Vatsyayana has laid down the two basic conditions of the inference of something unperceived (or not given). These are (1) cognition of the sign (the probans) and (2) cognition of the relationship (of pervasion) between the sign and the signified. The mere knowledge of the sign is not an adequate basis of the inference; it must also be known that the sign is pervaded by the signified. Vatsyayana has described the cognition of pervasion as a remembrance. What he means is that in order to legitimately infer the signified from the knowledge of the sign it must already be known that the sign is pervaded by the signified. The force of the word "remem-brance" is to point to the epistemic priority of such knowledge for the process of inference. Unless the sign is already known on the basis of previous experience to be pervaded by the signified, the inference (anumdna) of the signified from the sign cannot be reliable (pramdna). Vatsyayana has explained the threefold classification of inference as follows: Purvavat: where the effect is inferred from the cause (k&rana), e.g., that there will be rain from the massiveness of clouds. Sesavat is that where the cause is inferred from the effect (karya), e.g., that it has rained from the fullness of the river and the swiftness of the current and the difference of the river's water from its previous condition. Samdnyato Drsta: the observation of something at a place different from its previous location presupposes that the thing has moved; this is so with the sun; therefore, there is the sun's motion although unperceived. It appears from this passage that Vatsyayana has interpreted "purva" as cause and "sesa" as effect. Since purva and sesa signify respectively the predecessor and the successor and since the cause precedes the effect, such an interpretation makes sense. Purvavat means "that which contains the predecessor"; accordingly purvavat stands for an inference containing a cause as the sign. Such inferences should not be thought to be merely casual surmises. Nyaya philosophers steadfastly held on to the position that such inferences are reliable and the causal link is invoked to show that they are reliable. Inferences of future and past rain in Vatsyayana's examples may appear to be notoriously unreliable. But Vatsyayana has mentioned

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specific factors like massiveness of clouds, fullness of the river, swiftness of the current, etc., to give substance to such inferences. Other Nyaya philosophers too have attempted to salvage the element of reliability in such cases. This may be gathered from the following observations of Uddyotakara: Who says that the existence of the effect may be known from the cognition of the cause? Who, too, says that where there is the cause, there is the effect? What the aphorism [really] means is that the effect should be inferred from an appropriate qualification of the cause as its subordinate (guna). . . . This applies also to Sesavat, etc. Here, too, the cause should be inferred as the effect's subordinate (anga) That there will be rain from the amassing of clouds is an example of the inference of an effect from the cause. How should this be construed? These clouds are rainmakers, because while they are massive, there are roaring thunders, numerous swans and flashing lightnings, like a rainmaking cloud. It is clear that Uddyotakkara has tried to minimize the risk of error in predicting a future rain by adding carefully those factors which make a rain virtually an imminent certainty. He has offered similar comments on the inference of the past rain. His position is that while ordinary causal inferences couched in careless, general terms are not reliable, inferences of specific causes from specific effects as well as inferences of specific effects from specific causes are reliable in case appropriate qualifications and specifications are taken into account. The cause may be inferred from the effect and the effect may be inferred from the cause only as the subordinate (guna, anga) of the other. This means that such inferences are permissible only when the cause or the effect may be ascertertained to be pervaded (vyapta) by the other. In other words, such inferences are allowed only if it is known that a specific effect always follows a specific cause or that a specific cause always precedes a specific effect. Uddyotakara is well aware that observations may be misleading and has specially warned that hasty generalizations must be avoided. But he is confident that careful observation may lead to causal generalizations which are reliable. The same point has been made by Vacaspati Misra: "Although the bare cause [i.e., the cause without appropriate specifications] deviates from the origin of the effect, the researcher should specify it carefully, so that there is no deviation." (7Tp. 174) He has mentioned the inference of the origin of a piece of cloth from the last conjunction of the threads as an example of an inference of an effect from a cause. (77* p. 175) In the Nyaya view a piece of cloth as a substantial whole (avayavin) comes

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into being immediately after all the threads used in it are weaved together and conjoined. Each of the numerous threads are conjoined in succession and the piece of cloth as the final product (antya-avayavin) is not produced until the time of the final conjunction between the last remaining thread and the rest. The origin of the piece of cloth, however, is considered to be an event distinct from the final conjunction of threads and is said to take place one moment after that conjunction. Since the piece of cloth as the final product is still non-existent at the moment the final conjunction occurs, it cannot be perceived at that very moment. But its origin may be inferred with confidence at that time. This example shows where the Nyaya quest of reliability within the world of observation could lead. We have seen how Uddyotakara added several empirical factors seeking to reduce the risk of error in the inference of rain. But Vacaspati Misra has opted for a different strategy to forestall sceptical objections to the claim of reliability made for causal inferences. He might have thought that the addition of various empirical factors, however carefully done, may not by itself suffice to answer sceptical doubts. So he has taken up an ordinary causal inference and shown how it can be said to have reliability by suitable philosophical analysis. He is well aware that the inference that there will be a finished piece of cloth when the threads are being woven together is problematic. So he points to the only stage in the causal process when such an inference may legitimately be said to be reliable, viz., the stage of the final conjunction of threads. He does not say so explicitly, but he implies that the sum total of causal conditions (which includes the absence of obstructions) needed for the production of the cloth is available at that stage; under these circumstances, the origin of the cloth is a certainty. The cloth could of course be destroyed soon afterwards. But the (usual) Nyaya view, backed by various metaphysical arguments, is that the cloth would have to exist at least for two moments before it could be destroyed. Hence the inference that there will be a piece of cloth is reliable under the said conditions. Because of their interest in inferences based on causation the Nyaya philosophers have carefully analyzed the notion of a causal condition (kdrana). Briefly stated, a causal condition (as defined by later Nyaya philosophers) is that which is indispensably relevant (ananyathasiddha) and is invariably present in the effect's location at the moment immediately preceding the effect's origin. (BP p. 102) For example, the potter, the wheel, the rod, water, clay, etc., are all causal conditions of a clay pot. An effect cannot be produced unless the totality of causal conditions (with the absence of obstructions being usually thrown in as a causal condition) is available at the moment immediately before the effect's origin. Hence the very fact that an effect has come into being is

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a reliable sign that all the causal conditions were available at the moment before the effect's production. Thus the inference from an effect to a cause may legitimately be said to be reliable when the nature of the inference is clarified by precise analysis. The quest for reliability in causal inferences, so pronounced in Uddyotakara and Vacaspati Mistra, is consistent with the views of Gotama and Vatsyayana. They too clearly held that the sign should be related to the signified by way of non-deviation—a relation which provides the basis for stability. The subsequent Nyaya philosophers had to wrestle with a persistent current of sceptical thought within the Indian tradition. They sought to meet the sceptic on the familiar grounds of common sense metaphysics and epistemology. They held on to the belief that the sceptical challenge, although formidable, is not insurmountable and can be adequately met by working out their metaphysics and episistemology in sufficient detail and precision. We now turn to the third kind of inference called samányato drsta. In Vatsyayana's example what is inferred is something imperceptible, viz., the sun's movement. The strategy seems to be that facts about celestial phenomena, which are unobservable, may be inferred on the basis of generalizations true of observable earthly phenomena. In Vatsyayana's examples of the other two kinds of inference what is inferred is in each case something perceptible. But this by itself does not prove that the first two kinds of inference are restricted to things which are perceptible. In fact, an inference to something imperceptible based on a cause or an effect serving as a sign may be classified under one or the other of the first two kinds of inference. Similarly, the fact that in Vatsyayana's example of the third kind of inference what is inferred is something imperceptible does not by itself prove that the third kind is restricted to inferences of things which are imperceptible. Since Vatsyayana has not said in so many words what specifically the sámányato drsta kind stands for, its precise distinction from the other two kinds is not clear. One plausible clue, however, is that the first two kinds have been described as inferences from a cause or an effect. This might be taken as an indication that the third kind includes inferences where the sign is not related to the signified as a cause or an effect. This is how Uddyotakara has interpreted this kind: "Samanyatodrsta is that in which a subject as characterized is inferred through a character which is invariably concomitant without being related as a cause or an effect." {NV p. 47) Uddyotakara has offered the inference of water from the presence of swans as an example. The inference is as follows: a certain place having trees, etc., also has water because swans reside there and because there is water wherever swans reside, like places X, Y, etc. having water and constantly frequented by swans. The point is that in this

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inference the sign, viz., being a place where swans reside, cannot be strictly said to be the cause or the effect of the signified, viz., the presence of water. With regard to Vatsyayana's example of the inference of the sun's movement Uddyotakara has observed that what should first be inferred is the sun's presence at a place different from the previous location; from that the sun's motion may be inferred in the next step. Thus 'presence at different locations' and 'motion' turn out respectively to be the sign and the signified of the latter inference. Since, however, motion and presence in different locations are related as cause and effect, the inference should be included, Uddyotakara observes, under the second kind. This confirms our earlier remark that the inference of something imperceptible may also be included under the first two kinds. Vatsyayana has offered a second explanation of Gotama's threefold classification of inference: Alternatively, pürvavat: where of two things perceived as before, one which is unperceived is inferred from the perception of the other, e.g., fire from smoke. Sesavat is the same as parisesa. And that is concluding with propriety to what remains after the negation of the relevant alternatives when no other alternative remains. For example: it may be shown, without excluding substance, quale or motion, that sound is not a universal, nor an ultimate individuator, nor again inherence on such grounds as that sound possesses [the universal] being, is non-eternal, etc. This leads to the question whether sound is a substance, or a quale or a motion; but not a substance, for a single substance is its inherent cause; nor a motion, for it becomes the cause of other sounds; thus it becomes known that it is that which remains, i.e, that sound is a quale. Sámünyato drsta: where the relationship between the sign and the signified being unobservable, the signified, which is imperceptible, is inferred from the sign's generic [or universal] connection with something else, e.g., the soul from desire, etc.; desire, etc., are qualia; qualia are supported by substances; that which is their support is the soul. (ND pp. 14-15) According to this explanation, pürvavat is the inference of something unperceived for the time being from the perception of its (invariably concomitant) sign. "Pürvavat" may literally be taken to mean "as before"; and this is how Vatsyayana has construed it here. When he speaks of "two things perceived as before", he implies two things which,

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on the basis of previous experience, are already known to be invariably concomitant. When he speaks of "one which is unperceived", he means the pervader (vydpaka) which is temporarily unperceived. The inference of fire from smoke is a stock example in the Nyaya tradition. Vatsyayana has mentioned the same example elsewhere: "for example, the knowledge of unperceived fire from perceived smoke is inference." (ND p. 75) The implication is the following. It is already known from the previous perception of co-presence of smoke and fire in the kitchen, etc., that wherever there is smoke there is fire. Then, if smoke is perceived in some place, such as a hill, but fire is not perceived, the latter may be inferred to be there, for it is known that smoke is invariably concomitant with fire. In this way, when something is known to be invariably concomitant with something else, the latter, though unperceived, may be inferred from the perception of the former. It should be clear that both the inference of an effect from a cause and the inference of a cause from an effect, which are called purvavat and sesavat respectively under the first explanation, may be described as purvavat under the second explanation. It may also be noted that although Vatsyayana has here spoken of only signs which are perceived, Nyaya philosophers like Vacaspati Misra have suggested that in this context "perception" should be broadly construed as knowledge in general: "In two things perceived" there is indirect reference to all sources of knowledge. Thus from the knowledge of the presence in the subject of one character, i.e., of the character which is the probans, the other, i.e., the character which is the probandum, is inferred." (77"p. 179) In other words, if something is invariably concomitant with something else, then, if the former is perceived or otherwise known to belong to some subject, the latter may be inferred to belong to the same subject. It is this sense which is widely prevalent in the Nyaya tradition. Vatsyayana may have spoken of the perceived sign to single out the most typical case of purvavat, clearly the most common case is where something unperceived is inferred from the perception of its invariably concomitant sign. He might have done so also to highlight the foundational role of perception in acquiring the premises of the inference. According to the second explanation, sesavat is an inference in the form of a disjunctive syllogism. Vatsyayana has laid down the requisite conditions for the formal validity as well as the soundness of such an inference. He has indicated the correct form by saying that all but one of the alternatives must be eliminated and that the remainder should be deduced as the conclusion. In order to preserve soundness he requires that the alternatives should be mutually exclusive and collectively exhaustive. (N8) His example is a well known metaphysical argument to prove that

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sound is a quale. The six recognized kinds of positive reals are: substance, quale, motion, universal, ultimate individuator and inherence. By mentioning them Vatsyayana has considered all relevant alternatives, i.e., all alternatives which are mutually exclusive and collectively exhaustive. He has given reasons, each true from the stand-point of Nyaya ontology, for eliminating five of these six alternatives and derived the only remaining alternative. Sámányato drsta, under the second explanation, is unambiguously described as the inference of something imperceptible. Since the signified is imperceptible, its relationship of pervasion with the sign, too, cannot be known through perception. This is why this kind differs frompürvavat (under the second explanation) where the signified is not necessarily imperceptible and where, consequently, perception may normally be expected to play the foundational role in knowing the relationship of pervasion between the sign and the signified. Vatsyayana's example is the inference of the soul. Although the sign, viz., desire, etc., is introspectible and, therefore, perceptible, its relation of pervasion with the signified, viz., belonging to the soul, cannot be known by perception, for the soul, according to Vatsyayana, is imperceptible. The same will be true of any other sign that may be chosen for the purpose. The way out sought by Vatsyayana in this situation is to bring into play the genus of the sign and point out something true of the genus. (Sámányato drsta could be taken literally to mean "known through the genus.") He points out that since desire, etc., are qualia and qualia belong to substances, it follows that desire, etc., too, belong to a substance. He concludes in the next step, without further elaboration, that the substance to which desire, etc., belongs is the soul. This is in keeping with Gotama's own view: the aphorism 1.1.10 declares desire, etc., to be the signs of the soul. Gotama has not explained specifically in what way desire, etc., serve as the signs of the soul. There is obviously a difficulty here; since the soul is imperceptible, the connection between the signified and whatever is chosen as the sign cannot be known through perception. Vatsyayana has shown the way out of the difficulty by utilizing, as already noted, the genus of desire, etc., and relying on two related generalizations which can be supported by positive instances. The first, as noted above, is that desire, etc., are qualia; the truth of this can be certified by introspection. The second is that all qualia belong to substances; the truth of this can be supported by such positive examples as color, etc., which are qualia and belong to substances. The methodological point suggested by Vatsyayana is the following. If no positive or negative examples can possibly be found to support the generalization stating that the chosen sign is pervaded by the signified, one should explore whether relevant generalizations involving the genus of the sign can be supported by positive or negative

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examples, so that those generalizations may be used as premises to get the desired conclusion. In this connection Uddyotakara has observed as follows: It is known that desire, etc., are qualia. Through that character desire, etc., are inferred to be qualia of the soul. Desire, etc., are dependent on something other than themselves, because they are qualia like color. This inference proves dependence on something else; how can dependence on the soul be proven? Dependence on the soul [is proven] through eliminative reasoning (parisesa) on the grounds of being introspectible by the self and being imperceptible by the external sense organs. [Desire, etc.,] are not qualia of [material substances like] earth, etc., for the latter's qualia are observable both by oneself and by others and are also perceptible by external sense organs. Desire, etc., are perceptible by oneself, but are not perceptible by external sense organs. . . . No other substance remains. The soul [alone] remains. Therefore, [desire, etc.] are dependent on the soul. (NV p. 52) Thus, according to Uddyotakara, a supplementary eliminative reasoning is needed to show that desire, etc., could not belong to any other kind of substance. The argument as a whole has two stages. The first stage proves that desire, etc., are dependent on something other than themselves. This is in the form of a categorical syllogism: Desire, etc., are qualia; all qualia are dependent on substances; therefore, desire, etc., are dependent on substance. The second stage proves that desire, etc., are dependent on the soul by eliminating other available substances. This is in the form of a disjunctive syllogism: Either desire, etc., are dependent on the soul or desire, etc., are dependent on some other substances like earth, etc.; it is not the case that desire, etc., are dependent on some other substances like earth, etc.; therefore, desire, etc., are dependent on the soul. (N9) Accordingly, the inference of the soul turns out to be a two-stage argument the first of which is in the form of a categorical syllogism and the second of which is in the form of a disjunctive syllogism. This is significant and shows that in the Indian tradition arguments in the categorical syllogistic form have been combined together with arguments in the disjunctive syllogistic form in order to yield the desired conclusion. It may here be pointed out by way of comparison that there are plenty of arguments in the form of a categorical syllogism in the Aristotelian tradition. There are also plenty of arguments in the form of a disjunctive syllogism in the Stoic tradition. But there is no case in the Greek tradition where an Aristotelian or a Stoic logician has deliberately combined arguments in the categorical and disjunctive

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forms to get to the final conclusion. The fact of the matter is that Aristotelian and Stoic logicians shared an attitude of hostility towards each other; perhaps they never realized that the Aristotelian syllogistic logic and the Stoic logic of truth-functional connectives were complementary to each other and that there was no real opposition between the two. This is probably why no Aristotelian or Stoic logician ever tried to combine the fruits of the work of each other to further the study of logic. The fact that early Nyaya logicians were able to combine the fruits of syllogistic logic and truth-functional logic is an indication of the high level of understanding achieved by them. We now look at the section on the critical examination of inference where Gotama considers and answers objections to the status of inference as a source of knowledge. The aphorism 2. 1. 37 says "Inference is not a source of knowledge because of deviation due to obstruction, destruction and similarity." Vatsyayana comments: "Not being a source of knowledge" means not leading to reliable knowledge of things even once. A river is found to be full also due to obstruction; then the inference of rain in the upper region is false. Ants' eggs are dispersed also due to the destruction of the nest; then the inference that it will rain is false. A person too can imitate the cry of a peacock; then inference from the similarity of the sound is false. (A© 71) It is clear that Vatsyayana has linked the aphorism 2.1.37 with the inferences cited by him under his first explanation of Gotama's threefold classification of inference. He has taken "obstruction" to suggest an objection to the inference of past rain in the upper regions of a river from the observation of the fullness of the river. He points out that such fullness could be also due to some obstruction, such as a dam, whence the inference could be false. Then he has taken "destruction" to suggest an objection to the inference of future rain from the ants' running away with their eggs. He notes that ants could run away with their eggs also if their nest were destroyed, so that the inference could be false. Finally, he has taken "similarity" to suggest an objection to an inference from what appears to be the cry of a peacock. It is not clear what exactly is to be inferred here. Perhaps what is to be inferred is the presence of a peacock from hearing what seems to be the cry of a peacock. He observes that since even a human being could imitate the cry of a peacock, such an inference, too, could be false. Thus it is clear that even well known cases of inference could go astray. The crucial word in Gotama's said aphorism is "deviation". That inference is not a source of knowledge is said to be due to deviation. What he obviously means is that inference cannot be a source of knowledge if the sign deviates from the signified,

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i.e., if the sign is not invariably concomitant with or pervaded by the signified. Vatsyayana explains through various examples how this can happen in different cases. The general point made in the objection described by Gotama is the following. Since the sign is known to deviate from the signified in some cases of inference, the doubt (samsaya) that it may do so also in other cases cannot be ruled out. As long as the doubt about the possibility of deviation is not ruled out (and the objection implies that such doubt cannot be ruled out), inference cannot be accepted as a source of knowledge even in a single case. Gotama's reply is: "No [i.e., it is not true that inference is not a source of knowledge]; for there is difference from a portion, fear and similarity [i.e., the signs actually used in the relevant inferences are different from those supposed to be so by the objector]. (2.1.38) Vatsyayana explains: This is not deviation in an inference, but [the objector is] mistaking what is not an inference for an inference. How so? That which lacks specification does not qualify as a sign. By seeing the rain water to be different from the water before and the swiftness of the current and the drifting of numerous fruits, leaves, woods, suds, etc., it is inferred that it has rained . . . in the upper region of the river, not from the rise in water alone. From the carrying of eggs by a large number of ants in rows it is inferred that it will rain, not from a few. This is not the cry of a peacock, but only a sound similar to it—the false inference results from not realizing the difference. For one who grasps the distinctive cry of a peacock and distinguishes it from similar sounds it serves as a sign in so far as he grasps it with specification, as do snakes, etc. Thus it is the fault of the person inferring and not of inference, i.e., of the person who seeks to infer through the awareness of the thing without specification something which can be inferred only through the thing with specification. (ND p. 72) Thus it appears that Vatsyayana has taken "portion" to suggest fullness of a river resulting from the blockage of a portion of the river, "fear" to suggest the carrying of eggs by ants out of fear after their nest has been destroyed and "similarity" to suggest similarity with the cry of a peacock. He has shown that in each case what the objector thought to be the sign is not the actually intended sign and that when the latter is spelt out with the specifications, it becomes non-deviant from the signified. He has taken the battle right into the camp of the objector by claiming that the latter has not considered cases of inference at all, but only cases of pseudo-inferences. As contented by Gotama and Vatsyayana, the sign is

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non-deviant in every case of inference and the fact that it is not so in some pseudo-inferences cannot impugn the status of inference. Thus the objector's claim that inference is not a source of knowledge because of deviation can itself be shown to be a pseudo-inference. In other words, it is a pseudo-inference with 'inference' as the subject (paksa), 'not being a source of knowledge' as the signified and 'having deviant signs' as the sign. Since the characteristic of having deviant signs does not belong to any inference, there occurs the fault called svarUpdsiddhi. (N10) In this connection Uddyotakara has observed: When it is said that inference is not a source of knowledge, is 'not being a source of knowledge' predicated of all inferences or of a particular inference? What is the point of this? Let it be supposed that no inference is a source of knowledge. But then the sign could not belong to the subject as a whole and could belong to only a part. Although all inferences have been subsumed under the subject, there could not be deviation in each inference. There can be no deviation in the respect of deviation proving the lack of the property of being a source of knowledge. . . . thus it fails to belong to the subject as a whole and must be a pseudo-probans. On the other hand, it may be said that only those in which there is deviation are not sources of knowledge. . . . this would amount to proving what is already accepted: what is deviant cannot be a source of knowledge. (NV pp. 251-52) Uddyotakara is arguing to the effect that the objection that inference is not a source of knowledge is either trivial or self-refuting. If the objector is simply saying that those inferences which contain deviant signs are not sources of knowledge, he is making a point which is already accepted by the Nyaya. (Seeking to prove a point which is already accepted is considered to be a ground of defeat in the Nyaya tradition.) Hence to join issue with the Nyaya the objector must claim that no inference is a source of knowledge. But then, in order to prove his point, the objector must make use of an inference containing 'possession of deviant signs' as the sign. (In other words, the objector must claim that since all inferences have deviant signs, none is a source of knowledge.) Now the question is: is this sign in this particular inference (seeking to prove that no inference is a source of knowledge) itself deviant or not? The objector cannot afford to say that this sign is deviant, for then inference could be a source of knowledge in spite of containing deviant signs. But if the said sign is non-deviant and if the said inference seeking to prove that no inference is a source of knowledge is itself sound, it refutes itself (and the sign cannot belong to the subject [ = inference] as a whole). Thus there is

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'inconsistency between the thesis and the reason' (pratijM-hetvosca virodhah). It appears from the above that the Nyaya logicians have adopted a twofold strategy to meet the objection that inference is not a source of knowledge. They have shown in the first place that the socalled inferences in which the signs are found to be deviant are only pseudo-inferences and that in each case the inference may be carefully reformulated with sufficient specifications to rule out the charge of deviation. In the second place, they have resorted to a dialectical argument to the effect that the claim that no inference is a source of knowledge because of having deviant signs is itself an inference which, if sound, is self-refuting. We now move on to consider some pseudo-rejoinders (jati). Gotama has mentioned 24 of these, but we consider only a few of these which are important for the study of induction and inference from sign. Gotama's aphorism 5.1.2. says: "In the event of concluding on the basis of similarity (sQdharmya) and dissimilarity (vaidharmya) counterreasonings (upapatti) through that character and its absence are respectively parity per similarity (sSdharmya-sama) and parity per dissimilarity (vaidharmya-sama)." What Gotama is saying is that one may argue analogically by pointing out the similarity of the subject with something else X having the desired character or by pointing out the dissimilarity of the subject with something else Y lacking the desired character. In such a case one may counter-argue by pointing out the similarity of the subject with something else W lacking the desired character or by pointing out the dissimilarity of the subject with something else Z having the desired character. This is consistent with the definition of a pseudo-rejoinder given earlier: "A pseudo-rejoinder is a counterargument ipratyavasthanam) on the basis of similarity or dissimilarity." (1.2.18) Vatsyayana's comments on 5.1.2. are: When it is concluded on the basis of similarity, counterarguing and rejoining on the basis of similarity itself by utilizing the absence or presence of the character which is the probandum, so that there is no difference [in the epistemic status] from the supportive reason, is the rejoinder called parity per similarity. Illustration: the soul has motion because of having a quale which is the cause of motion of substances. A stone is a substance which possesses a quale which is the cause of motion and also has motion. The soul is so. Therefore, [the soul] has motion. When it is concluded thus, it may be counter-argued on the basis of similarity itself. The soul is motionless, for a ubiquitous substance is motionless; the dk&sa (the substratum of sound) is ubiquitous and motionless; and the

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soul is so [i.e., ubiquitous]. Therefore, [the soul] is motionless. There is no reason to make a difference [to the epistemic status of the two arguments], [The soul] should have motion because of similarity with what has motion; but no; [the soul] should be motionless because of similarity with what is motionless. Since there is no reason to make a difference, the rejoinder is of the nature of parity per similarity. Parity per dissimilarity is next. A stone is known to have a quale which is the cause of motion and also to be of a limited magnitude; the soul is not so. Therefore, [the soul] does not have motion, as does a stone. There is no reason to make a difference. [The soul] should have motion because of similarity with what has motion; but no; [the soul] should be motionless because of dissimilarity with what has motion. Since there is no reason to make a difference, there is parity per dissimilarity. (ND p. 232) Thus the conclusion that the soul has motion is drawn on the basis of its similarity with a stone (which has motion) in the respect that both possess a quale which is the cause of motion in substances. The conclusion is drawn on the basis of this similarity without using any such universal premise as that whatever has the quale which is the cause of motion, has motion. The counter-argument to this consists in showing that the soul is motionless because it is similar to dk&sa (which is motionless) in the respect that both are ubiquitous. The counter-argument, too, is drawn on the basis of this similarity without using any such universal premise as that whatever is ubiquitous is motionless. This is an example of 'parity per similarity', for, as Vatsyayana points out, the counter-argument is equally matched with the original argument in its probative value and provides no ground for preferring the former to the latter. This is also (partly) why it is a pseudo-rejoinder, for it is understood that an effective rejoinder should provide a decisive ground for preferring it to the original argument. (The full explanation of why this is called a pseudo-rejoinder will be provided later.) Both the argument and the counter-argument seize on particular things which possess or lack the character to be inferred. The original argument uses the example of a stone as something which has the probandum, viz., the soul, on the ground of the latter's similarity to a stone in a specific respect. The counter-argument uses the example of dk&sa as something which lacks the probandum and argues to the absence of the probandum in the subject on the ground of the latter's similarity to ak&sa in a specific respect. The same kind of logical moves are found in 'parity per dissimilarity' except for that here the counter-argument is drawn from

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dissimilarity rather than similarity. In Vatsyayana's example the conclusion that the soul has motion is drawn on the basis of the soul's similarity with a stone in the respect that both possess a quale which is the cause of motion. In the counter-argument the conclusion that the soul does not have motion is drawn on the basis of the soul's dissimilarity with a stone in the respect that while the stone has a limited magnitude, the soul is ubiquitous. Once again, both the argument and the counterargument seize on particular examples and do not make use of any universal premises like 'what possesses a quale which is the cause of motion, has motion' or 'what is ubiquitous is motionless'. The point of the original argument is that since the soul and the stone are known to be similar in a given respect, they should also be similar in the respect under contention. The point of the counter-argument is that since the soul and the stone are known to be dissimilar in a certain respect, they should also be dissimilar in the respect under contention. Thus both the original argument and the counter-argument are equally matched in their logical worth and the latter provides no ground for preferring it to the former. Hence, as pointed out by Vatsyayana, this is a specimen of 'parity per dissimilarity'. One noticeable feature of Vatsyayana's example is that the same particular example, viz., the stone, has been used both to support and to oppose the same conclusion, viz., that the soul has motion. Since the supportive argument is based on similarity and the rejoinder is based on dissimilarity, it has been possible to use the same example for both. After explaining how such pseudo-rejoinders arise when the proponent's argument is based on similarity, Vatsyayana has explained how these arise when the proponent's argument is based on dissimilarity: And when the conclusion is based on dissimilarity: The soul is motionless because of being ubiquitous; substances possessing motion are known to be non-ubiquitous, such as the stone; the soul is not so; therefore, [the soul] is motionless. The rejoinder on the basis of dissimilarity: ak&sa which is a motionless substance, is known to be devoid of any quale which is the cause of motion; the soul is not so; therefore, [the soul] is not motionless. And there is no reason to make a difference. [The soul] should be motionless because of its dissimilarity with what possesses motion; but no, [the soul] should possess motion because of its dissimilarity with what lacks motion. Since there is no reason to make a difference, there is 'parity per dissimilarity'. Next comes 'parity per similarity'. The stone which possesses motion, is known to possess a quale which is the cause of motion; the soul is so; therefore, [the soul]

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possesses motion. And there is no reason to make a difference: should be motionless because of dissimilarity with what possesses motion; but no, should possess motion because of similarity with what has motion. Since there is no reason to make a difference, there is 'parity per similarity'. (ND pp. 232-233) The logical moves here are exactly of the same kind as those above. No universal premises are involved and the reasonings are from particulars to particulars. Vatsyayana again makes it clear that we have 'parity per similarity' or 'parity per dissimilarity' when both the proponent's argument and the opponent's rejoinder are based on considerations of similarity/dissimilarity and there is no logical ground for preference of the latter over the former. The discussion shows that 'parity per similarity' could arise in two ways: (1) when an argument based on similarity is countered by a rejoinder based on similarity or (2) when an argument based on dissimilarity is countered by a rejoinder based on similarity. In the same way there is 'parity per dissimilarity' either when (1) an argument based on dissimilarity is countered by a rejoinder based on dissimilarity or (2) when an argument based on similarity is countered by a rejoinder based on dissimilarity. In the Nyaya view the soul is ubiquitous and is, therefore, motionless. In other words, the following is a sound argument: 'Whatever is ubiquitous is motionless, e.g., X; the soul is ubiquitous; therefore, the soul is motionless. Nevertheless, Vatsyayana has no hesitation in allowing an argument to prove that the soul is motionless to be equally matched by an argument to prove that the soul possesses motion. He allows this even though the former argument makes use of the fact that the soul is ubiquitous and of that the substances possessing motion are non-ubiquitous. The reason for this is that although the argument is making use of the right facts (from the Nyaya point of view), it is not using them in the right way. The argument does say in so many words that the soul is motionless because of being ubiquitous. Still the intention is not to prove that the soul is motionless by using the universal premise that whatever is ubiquitous is motionless. Rather, as made clear by Vatsyayana, the intention is to prove that the soul is motionless on the ground of its dissimilarity to the stone in the respect that the soul is ubiquitous while the stone is not. Thus the soul's ubiquitousness enters into the argument to prove the soul's motionlessness not as a part of a universal premise, but as the ground of the soul's dissimilarity with the stone. There is no verbal difference between the usual abbreviated version of a nyaya and that of the analogical argument discussed here. A nydya involving the same terms, too, could be abbreviatedly stated as 'the soul is motionless because of being ubiquitous like the tikdsa'. But the

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logical structure of a nydya is substantially different from that of the said analogical argument: while a nydya must include a universal premise stating the pervasion (vydpti, avyabhicdra) between the probans and the probandum, no such universal premise is included in the analogical argument. The latter is by no means a trivial argument. On the contrary, Vatsyayana has shown how one can construct substantial analogical arguments with true premises. Still the logical status of such arguments is inferior, from the Nyaya point of view, to that of a nydya. And one of the grounds of the inferiority is precisely that while a nydya is based on a universal connection between the probans and the probandum, the analogical argument is not. This is also why an equally matched counterargument with true premises leading to a logical stalement can be more easily found for analogical arguments than for a nydya. One may speculate that such analogical arguments were probably the precursors of nydya and dominated the Indian logical scene before Gotama's time. Gotma might have invented nydya while searching for a surer footing for logic; accordingly, he and Vatsyayana devoted considerable space under the discussion of jdti to distinguish such analogical arguments from a nydya. The discussion also shows the high level of sophistication reached by early Nyaya logicians. Since Vatsyayana allows the use of true premises in pseudo-rejoinders, he clearly separated questions of logic from questions of truth or falsity. The avowed purpose is to show that in spite of the use of true premises, such analogical arguments do not measure up to the logical rigour of a nyaya. One of the advantages of a nydya, as perceived by Gotama and Vatsyayana, is that it can help to resolve the kind of logical stalemate resulting from analogical arguments indicated above. This point is made by the aphorism 5.1.3.: "The proof of that has the characteristic of proving that something is a cow on the basis of cowness." What Gotama means by "the proof of that" is a proof through the modalities of a nydya of some such proposition as that the soul is motionless. The point of "proving that something is a cow on the basis of cowness" is to drive home the point that the proof is based on a universal and invariable connection between the probans and the probandum. In proving that something is a cow on the basis of cowness 'being a cow' is the probandum and 'cowness' is the probans. It is known that cowness is pervaded by being a cow: whatever has cowness is a cow and whatever is not a cow does not have cowness. In the view of Gotama cowness, humanity, etc., are real universals. These are objective, mindindependent entities which are eternal and inherent in many particulars. ( N i l ) The relationship of inherence (samavdya) between cowness and a cow does not admit of any exceptions; thus cowness can serve as a sure sign of something being a cow. The lesson of all this is that if the proof

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is based on a universal connection (vyápti), a rejoinder based on the similarity or the dissimilarity of the subject with something in some respect lacks merit. This is a basic reason why these are called pseudorejoinders. Such a rejoinder could be said to be equally matched with the original argument if the latter, too, were based on similarity or dissimilarity, but not if the latter is based on a universal connection. Clearly a rejoinder based on similarity/dissimilarity is not falling back on a universal connection and hence cannot be an equal match of the original argument. For example, if one proves that the soul is motionless on the ground that the soul is ubiquitous and that being ubiquitous is pervaded by being motionless, the proof cannot be effectively countered merely by pointing out that the soul is similar to some mobile substance like a stone in some respect or is dissimilar to some motionless substance like the akasa in some respect. In spite of such similarity or dissimilarity the premises could still be true. To effectively counter the proof the objector should question and attack the premises on which the proof is actually based, viz., that the soul is ubiquitous and that whatever is ubiquitous is motionless. Of these two premises the truth of the latter can hardly be questioned; if something is ubiquitous, it cannot move. But the objector could question the truth of the other premise and try to show that the soul is not ubiquitous. He could also attack the arguments advanced by the Nyaya philosophers to prove that the soul is ubiquitous. In stead of any of this the objector has resorted to 'parity per similarity' or 'parity per dissimilarity' on the wrong assumption that the proof is based on the soul's similarity with something motionless in some respect or the soul's dissimilarity with something moving in some respect. Since the objector has misunderstood the nature of the premises actually used and since the original conclusion does follow soundly from the original premises, Gotama labels such an objection as a pseudo-rejoinder (jati). The same point may be made by looking at another favorite example of inference, viz., that sound is non-eternal because of being originated and that whatever is originated is non-eternal, like a plate, etc. This argument is usually stated in the abbreviated form as: sound is noneternal, because of being originated, like a plate, etc. An objector may be misled by this and take it to be an argument based on sound's similarity with a plate, etc. He may take it as: since sound is similar to a plate, etc., in the respect of being originated, it should also be similar to them in the respect of being non-eternal. Accordingly, he may reply by way of 'parity per similarity' or 'parity per dissimilarity': sound is eternal, because of being touchless (asparsatvat) like the aküsa (which is eternal), or because of being shapeless unlike a pot (which is non-eternal). As already said, philosophical debate was probably conducted through this kind of analogical argument and counter-argument before Gotama.

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Gotama introduced an important change here. He pointed out that the above argument should be understood, not as an argument from sound's similarity with a plate, etc., in the respect of being originated, but basically as an argument from the relationship of non-deviation (avyabhic&ra) between being originated and being non-eternal. According to this understanding, since sound is originated, it cannot but be noneternal, for whatever is originated is non-eternal, like a plate, etc. With this new understanding the above counter-arguments turn out to be inadequate and are labelled as pseudo-rejoinders. It appears that the discussion of pseudo-rejoinders provides a clue to the pre-Gotama stage of Indian logic. It also provides further evidence for one of Gotama's most important contributions, viz., the requirement that in a nydya the probans should be related to the probandum by way of non-deviation, i.e., that there should be no case where the probans exists without the probandum. It is this relationship of non-deviation which is emphasized by proving that something is a cow on the basis of cowness. As already noted, from the point of view of Nyaya ontology cowness is related to being a cow by way of non-deviation. The same relation of non-deviation holds in other examples of inference. Thus being originated is related to being non-eternal by way of non-deviation, and so is being ubiquitous to being motionless. Vatsyayana's comments on 5.1.3. are: If the probandum is proposed to be proven on the basis of mere similarity and mere dissimilarity, there should be 'lack of decisiveness' (avyavastha). But this is not rationally justifiable if there is a character [i.e., a sign, a probans] which can make a difference. On the basis of the common character of cows, i.e., on the basis of the particular universal called cowness, it is proven that something is a cow, and not on the basis of having a dewlap, etc. Again, it is through cowness serving as the ground for excluding horses, etc., that it is proven that something is a cow, not on the basis of difference in qualia, etc. (ND p. 233) Vatsyayana makes it clear that an analogical argument on the basis of similarity or dissimilarity alone cannot be decisive, for it can be equally matched by a counter analogical argument as he has already explained. But lack of decisiveness is avoided if there is a character which can make a difference, i.e., if there is a probans which can settle the issue by proving that the probandum belongs to the subject and can exclude the counter-thesis that the probandum does not belong to the subject. This happens when the probans belongs to the subject and is non-deviant from the probandum. Vatsyayana explains why Gotama has chosen cowness as the probans for proving that something is a cow. He implies that if

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something were proven to be a cow on the basis of some other character found in cows, such as having a dewlap, having horns, etc., there could be doubt about whether such a character is non-deviant. But, given the stand-point of Nyaya ontology, when cowness is chosen as the probans, the possibility of non-deviation is excluded. Proving that something is a cow implies that it is not some other kind of animal, such as a horse. Once again, it is cowness and not some other character found in cows which serves as the ground of exclusion and, therefore, the possibility of deviation is ruled out. Clearly, an inference like 'this is a cow, because it has cowness', is not the kind of inference which one commonly comes across in everyday life. Gotama might have deliberately chosen this example to forestall sceptical objections about the possibility of the probans deviating from the probandum. Modern scholars like Keith, Stcherbatsky, Randall, Potter, etc., have held that in Gotama's original formulation and in Vatsyayana's exposition the ny&ya was an analogical argument without involving the notion of non-deviation. (N12) This interpretation is largely based on the fact that Gotama has used the words sadharmya and vaidharmya (which could literally mean similarity and dissimilarity respectively) in the account of ny&ya and has also retained particular examples within the body of a nydya. But neither of these provide the needed basis for such an interpretation. The words sadharmya and vaidharmya are compounds and, as pointed out, could also literally mean universal inclusion and universal exclusion respectively, depending on the way the compounds are construed in accordance with the rules of Sanskrit grammar. Where is the evidence to show that sddharmya and vaidharmya should not be construed in this latter way, particularly when generations of Nyaya philosophers as well as philosophers belonging to other Indian schools have done so? The retention of particular examples in a nyaya does not provide the requisite evidence, for the role of the example is to indicate that there is supportive evidence for the general premise stating the relation of non-deviation between the probans and the probandum. The following remark of Vatsyayana is to the point: "Thus in the one thing [i.e., in the example (drstdnta)] the probans-probandum relation of the two characters is apprehended as decisive (vyavasthita) through sddharmya. After realizing this in the example . . . " (ND p. 31) If sddharmya means similarity, how can it be decisive, i.e., prove that the probandum belongs to the subject and rule out that the probandum does not belong to the subject? As Gotama and Vatsyayana have shown in the discussion of pseudorejoinders, analogical arguments based on similarity/dissimilarity alone cannot be decisive, for they can be equally matched by counter arguments based on analogy. However, if sddharmya means universal inclusion, it could be decisive and the probans-probandum relation signify the relation

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of non-deviation. As Vatsyayana says, it is the probans-probandum relation which is made evident by the example. Thus the function of the example is to show that the probans is related to the probandum by way of non-deviation. Again, if sodharmya and vaidharmya mean nothing more than similarity and dissimilarity, why should Gotama and Vatsyayana take such pains in the discussion of pseudo-rejoinders to show that a ny&ya is not based on similarity or dissimilarity alone? Why should also a universal proposition be included in the exemplification step when a ny&ya is stated in full? Surely the universal proposition is redundant for demonstrating similarity which could be sufficiently brought out merely by citing the example. But if sQdharmya and vaidharmya mean universal inclusion and universal exclusion respectively as they could literally mean, the inclusion of the universal proposition becomes necessary. Again, as already discussed, Gotama and Vatsyayana have mentioned the relation of non-deviation between the probans and the probandum while defending their claim of inference being a source of knowledge against sceptical objections. Finally, they have also insisted that a deviant (savyabhic&ra) sign is inconclusive (anaikantika: N5 1.2.5). This clearly implies that in order to be conclusive (aikdntika) a sign must be non-deviant (avybhic&riri). That is, a sign must be related to the probandum by way of universal inclusion or universal exclusion and not merely by way of particular inclusion and particular exclusion. (N13) None of these make sense if the nyaya is reduced to an argument based on analogy alone. It thus appears that the opinion of some modern scholars that the ny&ya in the early stages of the development of the Nyaya school is nothing more than an analogical argument lacks merit. It would have helped if Gotama had used less ambiguous expressions like anvaya and vyatireka to mean universal inclusion and universal exclusion respectively as the later Nyaya logicians did and a modern reader may find the use of highly ambiguous expressions to convey crucial notions objectionable. But a modern reader is used to reading a written work without the help of others and expects the author to communicate in such a way that the ideas can be adequately grasped without the assistance of any one else. There is no evidence to show that Gotama wanted to live up to any such expectations. He belonged to the sutra age when in all probability whole works were memorized without being written down and handed down orally by the teacher to the student. In fact Gotama did everything possible to economize his expressions and cut down the size of his work, presumably to facilitate memorizing and oral instruction. He might have also opted for familiar, though ambiguous, expressions to help memorizing and, thereby, the survival of his work. It is reasonable to assume that Gotama expected a qualified teacher of his work to explain the ambiguities and fill up the necessary

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gaps for the benefit of a qualified student. This is precisely what a pundit does even today. The important thing is that the Nyaya tradition is alive and a modern reader who is trained by a pundit should have no real difficulty in deciphering the ambiguities and getting the sense. It should also be kept in mind that a sQtra is expected to be multi-directional (visvatomukha). It is not only expected to convey a lot of ideas in the briefest possible space, but also to convey them in such a way that they may be developed in more than one directions, depending partly on the level of interest and competence of different learners. From this point of view the use of ambiguous expressions like sQdharmya is not necessarily a disadvantage. One obvious gain of Gotama's doing so is that it enabled him to lay down through the same expressions the basic structure of ny&ya including the notion of non-deviation and at the same time indicate the strength and weakness of reasoning by analogy. We now return to the discussion of pseudo-rejoinders. Two other pseudo-rejoinders are 'parity per addition' (utkarsa-sama) and 'parity per deletion' (apakarsa-sama). (NS 5.1.4.) The former is the addition of some non-existent and unacceptable feature and the latter is the deletion of some existent and accepted feature. (NV p. 532) For example, one may argue that sound is non-eternal, because it is a product like a pot. The opponent may counter-argue that since a pot has color, sound also should be admitted to have color. This illustrates parity per addition (color being a non-existent and unacceptable feature of sound). Alternatively, the opponent may counter-argue that since a pot is not audible, sound also should be admitted not to be audible. This illustrates parity per deletion (audibility being an existent and accepted feature of sound). (NP p. 15) A variant of these two pseudo-rejoinders is called 'parity per diversity' {vikalpa-sama). (NS 5.1.4) Here some (seemingly) significant difference between the confirming instance and the subject (paksa) is made the basis of the rejoinder that the latter should lack the probandum rather than have it. (N14) Thus with reference to the above argument to prove that sound is non-eternal it may be pointed out that the confirming instance, viz., a pot, differs from the subject, viz., sound, in the respect that while a pot can never result from the disjunction (vibhaga) of parts, sound does result from disjunction, or again, that while a pot has color, sound does not. (NV p. 533) Such diversity (vikalpa) shows, it may be claimed, that while the probandum belongs to the confirming instance, it may very well not belong to the subject. The opponent is demanding, as Vatsyayana observes, that differentiating grounds should be provided if the alternative that the subject lacks the probandum is to be rejected (viparyaye v& viseso vaktavyah: NB p. 234). Another interesting specimen of parity per addition (the specimen may, with suitable changes be alternatively viewed as parity per deletion)

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is the following (TTpp. 599-600, NP p. 16): a theist may argue that the first effect is caused by a conscious agent because it is an effect like a pot. The theist may argue further that his implicit general premise, viz., whatever is an effect is caused by a conscious agent, is confirmed by both positive instances (like a pot or any artifact) and negative instances (like atoms or anything eternal which are neither caused by any conscious agent nor effects) and that there are no undisputed counter-examples (for things like rivers and mountains do have, according to the theist, a conscious agent, viz., God, as a causal condition. The atheist may, then, counterargue that since all known conscious agents have bodies, the conscious agent of the first effect should also have a body. By adding this requirement of a body the atheist virtually comes out a winner, because an embodied God is totally unacceptable to the theist. This is, however, a difficult case and a proper discussion would require a lot of space. Gotama points out that such rejoinders are ineffective, because analogies are offered only in certain respects (kiftcit-s&dharmyat) which is compatible with disanalogy in certain other respects. (NS 5.1.5) Uddyotakara adds that if each and every feature of the subject and the confirming instance were to be the same, it would be a case of identity rather than similarity. (NVp. 533) Further, if the proponent is arguing merely on the basis of the analogy between sound and a pot in respect of a shared feature, viz., being a product, the rejoinders may have a point. [There is room for such misunderstanding if one considers only the usual abbreviated version of the argument: sound is non-eternal because of being a product like a pot.] But that is far from the case. The proponent is relying on the implied general law that whatever is a product is noneternal (and is offering a pot as a confirming instance for the law). But the opponent cannot fall back on any such general laws as that whatever is a product has color or that whatever is a product is inaudible or that whatever lacks color is eternal (such general claims being easily falsifiable.) (NP pp. 15-16) Once the full implications of the argument are brought out, the inadequacy of the rejoinders becomes patent. The moral to be derived is that a philosopher or a scientist should take guard against his theory or explanation being frustrated by unwanted additions or unwanted deletions or superficial disparities. He may do this by showing that his theory or explanation derives support from some accepted general law while the attempted addition or deletion or disparity does not. We now consider the pseudo-rejoinder called 'parity per counterexample' (pratidrst&nta-sama). (NS 5.1.9) A legitimate use of a counterexample is not a pseudo-rejoinder, but a genuine rejoinder. (TT p. 678) It proves that the mark is deviant (savyabhic&ra) and such a mark is recognized as a variety of pseudo-probans (hetvtibhasa: N15). It shows

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that the proponent's argument is not sound, because the implied general premise is false. But at the same time Gotama warns against a possible misuse of the counter-example. This happens if (in stead of merely claiming to have shown that the proponent's general premise is false) the opponent claims to have proven the counter-thesis with the help of the counter-example. (NV pp. 536-7) For example, one may argue that the self has motion, because it possesses a motion-causing characteristic like a missile. The opponent may then cite ubiquitous space (N16) as the counter-example and try to prove that the self is motionless on the very same ground, viz., that it has a motion-causing characteristic. (NB p. 236) All that the opponent is saying here is true from the point of view of Nyaya ontology. According to the Nyaya, the self does possess a motion-causing characteristic, but is till motionless. [Space too is motionless in spite of possessing a motion-causing characteristic.] So the proponent's argument is faulty with a false general premise, viz., whatever has a motion-causing characteristic has motion, and a false conclusion, viz., the self has motion. The falsity of the general premise is conclusively shown by the counter-example of space which has a motion-causing characteristic but is motionless. Still the opponent's misuse of the counter-example reduces his argument into a pseudorejoinder. By citing the counter-example the opponent does not succeed in proving the counter-thesis. It still remains true that some things having a motion-causing characteristic do move, as the proponent's example of the missile shows. So the implicit general premise in the opponent's argument, viz., whatever has a motion-causing characteristic is motionless, also would turn out to be false. The discussion of this pseudo-rejoinder is particularly interesting and shows a high level of sophistication in correctly distinguishing between the proper and improper use of a counter-example. It illustrates how a counter-argument should be limited to only what is logically warranted. It also shows that early Nyaya logicians were aware that an argument may be faulty in spite of consisting of true premises and a true conclusion. Another pseudo-rejoinder is 'parity per questionability' (sOdhyasama). {NS 5.1.4) This happens if the confirming instance is dismissed as questionable. Thus in the above example the proponent cites a pot as something known to be non-eternal. The opponent may disagree and claim that to be as questionable as the thesis to be proved, viz., that sound is non-eternal. Two related pseudo-rejoinders are called 'parity per need of evidence' (varnya-sama) and 'parity per lack of need of evidence' (iavarnya-sama). (NS 5.1.4) These crop up from the attempt to swap between the outstanding feature of the confirming instance, viz., that it is not in need of evidence, and the outstanding feature of the subject (paksa), viz., that it is in need of evidence. Vatsyayana resolves the

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matter by pointing out that a confirming instance is neither in need of evidence nor questionable, because it is invariably something on which both commoners and experts agree. (NB p. 235) The point is further clarified in the discussion of another related pseudo-rejoinder called 'parity per regress' (prasanga-sama). (NS 5.1.9) This arises if the opponent asks for evidence to prove that the confirming instance has the probandum and thereby seeks to open the door of a pseudo infinite regress. (NPp. 29) Such demand for evidence, as Udayana observes, has a point only if something uncertain is offered as certain. (aniscitasya nisc&yakatvOdhy&ropah: NP p. 30) [The various sceptical issues raised here, though formulated in terms of the subject and the confirming instance, apply to the relation between evidence and conclusion in general.] Gotama answers as follows; "That [the sceptical regress] is uncalled for just as the regress from procuring a lamp is uncalled for." (NS 5.1.10) Vatsyayana elaborates: When such is asked, this should be noted. Who get a lamp? And for what purpose? Those who want to see, for seeing what can be seen. Now, why do not those who want to see the lamp get another lamp? Since the lamp is seen without another lamp, it is fruitless to get another lamp to see it. Now, for what purpose is the confirming instance cited? For the purpose of making known something not known. Now why is evidence demanded for the confirming instance? If for making known, the confirming instance is [already] known. Indeed: "That with regard to which object there is agreement of opinion among commoners and experts is a confirming instance." (NS 1.1.25) Thus it is fruitless to adduce evidence to make that known. Such is the resolution of parity per regress. (NB p. 236) As Nyaya logicians are never tired of saying: no enquiry is conducted in an absolute vacuum, but only within the framework of various things which are known or accepted and various other things which are disputed. Even about disputed things something must be known, for otherwise no meaningful inquiry about them could be initiated at all. Indeed, things under inquiry and questioning are such that they are known in general terms (samanyatah jMtah) but not in specific terms (visesatah ajMtah). Accordingly, evidence is required neither for what is completely known (nirntta) nor for what is completely unknown (animtta). (NB p. 4, pp. 58-9) Thus it is the presupposition of any rational inquiry that there exists broad consensus over certain matters. The confirming instances are chosen from within the area of such broad consensus. This is highlighted by requiring that they are such that both

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commoners and experts agree on them. Hence the only legitimate rebuttal of what is produced as a confirming instance is to show that the item is not agreed upon by both commoners and experts or that there is no broad consensus over it or that it goes against something known or accepted. In other words, any such rebuttal must presuppose various things which are known-things about which no doubt or denial is permissible. Thus while it is proper to try to show that what is put forth as a confirming instance is not such, what is not proper is to accept something as a confirming instance and still demand evidence for it. Absolute scepticism (atyanta-samsaya) is doomed on either count. Either the sceptic accepts the confirming instance as such and cannot question it any further and, therefore, renounces absolute scepticism. Or he tries to dislodge it by showing that it conflicts with something else known—which also amounts to renouncing absolute scepticism. A related pseudo-rejoinder is 'parity per doubt' (samsaya-sama). (NS 5.1.14) There is occasion for this if the opponent counter-argues merely on the ground that the subject (paksa) shares common features (sam&na-dharma) both with things having the inferred character and with things lacking it. Take, for example, the argument that sound is noneternal because it shares, with non-eternal things like pots, the character of being caused by volition. The opponent may counter-argue that sound is eternal because it shares, with eternal entities like universals, the character of being perceptible. (NB pp. 237-38) Gotama observes: "Although there can be doubt from common features (sadharmya), there can be no doubt if there are [also] discriminating features (vaidharmya); if there is doubt in spite of both [common and discriminating features being available], the consequence will be absolute scepticism {atyanta-samsaya)." (NS 5.1.15) Vatsyayana explains that one may, for example, be in doubt about the thing in front being a stump or a man if (the light is insufficient or for some other reason) one sees only features common to both a stump and a man, such as similar height. But the doubt is gone if one notices some discriminating feature (visesa), i.e., a feature which is compatible with only one of the choices. In the above example the fact that the subject shares features with both things having the inferred property and things lacking it may cause doubt if that is all that is known about it. But that is not the case. The property of being caused by volition is also a discriminating feature because it is incompatible with being eternal. Hence the rejoinder fails. If the doubt is not resolved in the face of discriminating features, the consequence will be, Gotama adds, absolute scepticism (for there always remains the possibility of finding some 'common features'). But absolute scepticism is untenable. [The thorough examination of absolute scepticism by Gotama, Vatsyayana, etc., cannot

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be taken up for discussion here for lack of space.] Another closely related pseudo-rejoinder is 'parity per counterbalancing' (prakarana-sama). (NS 5.1.16) In this case also the opponent tries to neutralize the proponent's argument through some 'common features' (with Vatsyayana adding that this can be also extended to uncommon features: NB p. 239). But the opponent goes a step further and actually tries to prove the counter-thesis with the help of a counter (pseudo) nyOya. For example, it may be argued that sound is non-eternal because of being caused by volition like a pot and because whatever is caused by volition is non-eternal. The opponent may seek to counterbalance it by arguing [the Mimamsa philosophers actually hold that (preexistent) sound is only manifested and not created] that sound is eternal because of being audible like sound-ness (the eternal common character of all particular non-eternal sounds) and because whatever is audible is eternal. ( 7 T p . 681) The opponent's general premise, viz., whatever is audible is eternal, has some plausibility. The proponent too accepts that sound-ness is audible and eternal. So the opponent can show that the general premise is confirmed by a mutually accepted positive instance. There are also no undisputed counter-examples, particular sounds being the bone of contention and the only other audible entities. Still this is nothing more than a pseudo-rejoinder, for the two arguments are not equally matched (tulya-bala: TT p. 683). The proponent is in a position to bring supplemental arguments in favor of his general premise. He can, for example, argue that if something were eternal and already existent, no effort would have been needed to produce it. The opponent is unable to do any such thing if his general premise is challenged. In other words, the two rival arguments may appear to be equally matched when they are taken in isolation and set against each other. But the picture changes when they are considered in the larger framework of supplementary arguments and connected theories. Once the proponent succeeds in showing that this thesis goes well with other accepted views and the opponent fails to do so to an equal extent, the balance is tilted in favor of the former. If, however, the opponent does succeed in continuing to counter-argue with equally cogent supplementary arguments and theories, we shall have, not a pseudo-rejoinder classified under j&ti, but a genuine rejoinder classified with the same name (a later name being satpratipaksa) under pseudo-probans (hetvabhasa: N17). Then the opponent succeeds in showing that the proponent's so called ny&ya is a pseudo-wytfya (ny&y&bhasa) and, as long as both sides remain equally matched, neither proves his case. Things do not have contrary or contradictory features; so either the thesis or the counter-thesis should prevail in the long run. But until that happens, withholding the assent is the only rational choice.

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We now come to an end of the discussion of early Nyaya views of induction and inference from sign. We have shown that, contrary to the opinion of scholars like Keith and Randall, early Nyaya logicians from Gotama onwards had a good grasp of a process by which one moves to a general proposition from the observation and description of particular cases. We have alluded to this process as induction. Two methods that were identified as part of this process are the method of co-presence and the method of co-absence. Gotama and others also had a clear understanding that a general proposition confirmed by positive and negative instances may be falsified by a single counter-example. In these respects the early Nyaya conception of induction is similar to that of Aristotle. Aristotle looked upon induction as the source of the premises of deduction. There can be little doubt that early Nyaya logicians shared that point of view. They realized that a general proposition is indispensably required as a premise in a ny&ya to get to the last step or the conclusion called an 'outcome' (nigamana). (NS 1.1.39) Hence they became interested in understanding and describing the process by which one may arrive at a general proposition. There are also broad similarities in the early Nyaya notion of sign (linga) and the Greek notion of sign (semeion). Both share the general idea that something perceived or evident must serve as the witness of something unperceived or nonevident. However, early Nyaya does not look upon induction as leading up to first principles which are the most knowable or intelligible in principle, as Aristotle does. In the Nyaya epistemology as a whole there is a pervasive commitment to fallibilism which would conflict with such a point of view. Early Nyaya also shows a deep concern for certain sceptical issues over induction and sign-inferences. To meet the sceptical challenge Vacaspati Misra provided a fine-tuned analysis of causal inferences focussing on the stages of the causal process where the claim of reliability can be legitimized. The two kinds of causal inferences identified as reliable are the following: (1) inference of the cause from the effect, for the latter does not come into being without the former and the plurality of causes is to be discounted. (2) The inference of the imminent origin of the effect when the sum-total of causal conditions (including the absence of obstruction) is available. The evidentiary value of examples (drst&nta) was also defended with substantial arguments. The study of such sceptical issues did not gain prominence in the Greek tradition.

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NOTES

1. 2. 3.

4.

5.

6.

7.

See my Logic ofGotama Honolulu, Hawaii University Press, 1978, Chapter 3 for detail. See Ibid., Chapter 3 for an account of the pentapod argument. We have translated the word udüharana as 'exemplification' rather than as 'example,' because (1) in the given context it is the name of a sentence which is a step of the pentapod argument and (2) there is another word, viz., drstánta, in the same passage signifying an example. Further we have translated the word südharmya as 'universal concomitance' rather than as 'similarity'. The word südharmya could literally be construed to mean either, but clearly the former meaning is intended in the given context. It may here be noted that we apply the word 'probans' only to those signs which meet the Nyaya requirements of being reliable, so that 'sign', in our discussion of Nyaya, is applicable to both a probans and a pseudo-probans (hetvübhása). While the compound südharmya-drstanta is used in early Nyaya, the compound anvayi-drstünta is more popular in later Nyaya. However, the compound sádharmya-drstánta is not used by either Gotama or Vatsyayana although they both use separately südharmya and drstánta. The word drstünta by itself signifies a positive instance or a negative instance and it may be gathered from the context which one is meant. In another place on p. 30 the word drsta is added to the same specimen. Drsta literally means 'known/seen/found'. It may then be translated as: 'what is originated is known to be non-eternal, such as a plate, etc.' 'Known' is the most appropriate sense of drsta in the present context, for (1) a positive instance or a negative instance may sometimes be imperceptible and (2) such a belief is taken to be reliable and justified. While the compound vaidharmya-drstanta is used in early Nyaya, the compound vyatireki-drstünta is more popular in later Nyaya. However, the compound vaidharmya-drstánta is not used by either Gotama or Vatsyayana although they both use separately vaidharmya and drstánta. In Vatsyayana's text "non-originated' precedes "eternal." The text could also be translated as: "What is non-originated is eternal, such as the soul, etc." Then the argument would turn out to be formally invalid. It is possible that Vatsyayana made the mistake, and if so, this would be the only singular case where a formally

138

Early Nyaya View of Induction and Inference From Sign invalid argument has been accepted as a nyaya in the Nyaya tradition. But it is not certain that Vatsyayana made this mistake. It has to be remembered that only reliable premises are allowed in a nydya. While "what is eternal is non-originated" is true from the point of view of Nyaya ontology, "what is non-originated is eternal" is false. Under the circumstances, since there is no fixed word-order in Sanskrit, Vatsyayana may very well have intended to say that "what is eternal is non-originated", and this is how the text should be translated by invoking the principle of charity. Translating the text thus involves neither any special pleading nor any extra-ordinary attempt to exonerate Vatsyayana of having used a formally invalid argument. Since the existing word order would yield a false premise and Vatsyayana has nowhere else used a false premise in a nyaya, Nyaya philosophers like Vacaspati Misra have opted to reverse the order and read the text in the way we have done. (NDFC p. 546) It should be noted that the oral tradition is of great importance for Sanskrit philosophical schools. Since Sanskrit grammar permits words in a sentence to be moved around to make better sense, Vatsyayana could legitimately count on the instructor to clear up some ambiguities to the student. Not surprisingly, traditional pundits discourage a beginner from reading Nyaya texts on his own and recommend that a beginner seek an instructor and learn from his mouth (gurumukhi vidya).

8. 9.

10. 11. 12.

13.

In another place on p. 32 the word drsta is added to the same specimen. It may then be translated as: "what is eternal is known to be non-originated, such as the soul, etc." See my Logic of Gotama, op cit., chapter 5 for detail. For further detail see "Towards Dualism: The Nyaya-Vaisesika Way", Kisor K. Chakrabarti and Chandana Chakrabarti, Philosophy East and West, vol. 41, 1991, pp. 470-91. See TSD pp. 254-6 for an explanation of svarupasiddhi. See my "The Nyaya-Vaisesika Theory of Universals," Journal of Indian Philosophy, vol. 3., 1975, pp. 363-82. A. B. Keith, Indian Logic and Atomism, Munshiram Manoharlal, New Delhi, 1977, pp. 85-88; H. N. Randle, Indian Logic in the Early Schools, Munshiram Manoharlal, New Delhi, 1976, p. 148; K. H. Potter, "Dignaga and the Development of Indian Logic," in R. S. Y. Chi, Buddhist Formal Logic, Royal Asiatic Society, London, 1969, pp. xciii-xcviii. See my Logic of Gotama, op cit., chapters 3, 4, and the appendix for more detail. Also see S. R. Saha, Perspectives on Nyaya Logic and Epistemology, K. P. Bagchi, Calcutta, 1987, pp. 285-90).

Early Nyaya View of Induction and Inference From Sign 14. 15. 16. 17.

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Vatsyayana's account of this pseudo-rejoinder is different. See NB p. 234. See my Logic of Gotama, op cit., chapter 4. We have made a minor change in Vatsyayana's example by replacing akdsa with space (dik). See my Logic of Gotama, op cit., chapter 4.

CHAPTER NINE CARVAKA-HUMEAN CRITIQUE OF INDUCTION AND SOME INDIAN/WESTERN RESPONSES

It has been shown how Gotama, Vatsyayana, etc., had to defend the status of inference as a source of knowledge. The view that inference is not a source of knowledge was forcefully presented by philosophers of the Carvaka school many of whom held that perception is the only source of knowledge. Unfortunately, however, the writings of Carvaka (6th century B.C.?) and his principal followers are lost (except for Jayarasi to whom we shall turn later). But, fortunately, the Carvaka viewpoint has been preserved in the writings of their philosophical opponents, including the Nyaya philosophers. [In fact, it is customary within the Sanskrit philosophical tradition to state rival views with clarity and precision. The statement of the rival view is called 'the predecessor's view/the preceding view' (purva-paksa) and sometimes even contains improvements on the original. The statement of the favored view is called 'the successor's view/the succeeding view/the later view/the answering view/the accepted view' (uttara-paksa/siddhanta-paksa).] We first look at the great Nyaya philosopher Udayana for an account of the Carvaka position. Like other Sanskrit philosophers Udayana (11th century) writes in a compact style; hence some explaining has become necessary. Carvaka says: That which cannot be perceived does not exist. The opposite exists. God, etc., are not so; therefore, it should better be held that these do not exist. It may be objected that inference, etc., will then be eliminated. But this is not unwelcome. Objection: But then common activities would be impossible. Reply: No. That can be carried out on the basis of expectation (sambhavana) alone. Coherence is

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mistakenly thought to justify the claim of knowledge. (NK p. 334) The Carvaka view as explained here is that if something cannot be perceived by anyone at any time whatsoever, then, since perception is the only source of knowledge, it cannot be admitted to exist. Since God, etc., are imperceptible, it is better not to admit that they exist. Only what is perceived exists (not that all that is perceived exists). Since it is unnecessary to admit the existence of anything imperceptible, it is also unnecessary to accept inference (or any other means admitted to account for the knowledge of imperceptibles) as a source of knowledge. Is not inference indispensable even for common activities, such as going for fire after seeing smoke? The reply is: no. It is indeed necessary to go beyond what is perceived at a given time and form opinions about the past as well as expectations about the future. All such activities can be fully explained in terms of such expectations. For example, one goes for unperceived fire after seeing smoke on the basis of the expectation that there is fire. It is both unnecessary and unjustified to claim that there is inferred knowledge of fire in such cases. When fire is actually found, does not that justify, because of the coherence (samvada) between what was previously expected and what is now perceived, that there is knowledge of fire, so that the acceptance of inference as a source of knowledge becomes necessary? The reply is: no. Success of the action prompted by the expectation does not turn the expectation into knowledge. But such success and coherence suffices to generate confidence in the expectations and make them appear as knowledge. 'Appearing as knowledge' (prümányabhimána) is all that is needed to account for such activities. Rucidatta, the author of the Prakasa commentary on the NK, has described the expectation as a doubt (samsaya) one side (koti) of which is stronger (utkata) than others. (NKp. 334) If each side of the expectation were equally matched, the expectation would not have led to any action. But if one side is stronger than the others, an expectation may lead to action. For example, when one sees smoke, one does not have any rational grounds for being sure that there is fire, but may nevertheless have a strong expectation that there is fire. This is a doubt with two sides, viz., that (1) there is fire and that (2) fire is not there. But the two sides are not equally matched; the first is stronger than the second, for fire has been observed together with smoke on many occasions. Hence it may very well lead to the action of procuring fire. The Carvaka philosopher argues further: Since there is no discriminating factor, how can it be known that although there is deviation in a certain case, there is no deviation in some other case? Thus, since there

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is no reason which can settle the matter one way or the other, the observation of togetherness itself is the ground of the apprehension (samka) of deviation (vyabhicara). How then can it be groundless? It may be said that that there is deviation in some cases and not in some other cases is due to the nature of things and that it is the nature of things which provides the discriminating factor. But by what signs can the nature of things be determined with certainty? This question should be considered carefully. For what is confirmed in hundreds of cases is also found to be refuted. It may be said that where no counter-example is known [and the two have been observed together], there that is so [i.e., one has a valid reason for generalizing]. But from the fact that no counter-example has been found so far, who can legislate that none will be found anywhere at any time? (NK p. 339) Several arguments are compressed in this passage. The Nyaya philosophers have accepted the observation of co-presence (sahacaradarsana) as a method of generalization. It is pointed out first that the method cannot give any valid reason for making such a claim. Even when two things have been observed together in some cases, the one which is supposed to be pervaded is sometimes found to exist without the other (the so called pervader). This establishes the fact of deviation and falsifies the general claim. Hence one cannot have any reason that this is not so in other cases when two things are observed together, for there is no objective ground for discriminating between the two situations, viz., (1) two things are together sometimes and separated sometimes (2) two things are together always. Accordingly, no generalization based on the observation of co-presence can be justified. But then since there is no ground for generalizing, no inferences of the type under consideration can be a source of knowledge, for they all require at least one general premise to the effect that the probans is pervaded by the probandum. Since the premise is baseless, the result of the inference is baseless too. One may criticize the Carvaka position by saying that if inference is not accepted as a source of knowledge and if perception is the only source, the very apprehension of deviation will be groundless. The observed cases cannot provide the ground, for it is already known that the two things are together in each of these cases. In fact, if the so called pervaded were found to be present without the so called pervader in any of the known cases, the generalization would have been refuted and the apprehension replaced by the certainty that the generalization is false. Thus, the ground for the apprehension can come only with reference to the unobserved cases. But the unobserved cases are, ex hypothesi, beyond

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perception as well as knowledge. How could these then be the basis for such apprehension? In reply, the Carvaka says that it is the observation of togetherness itself which provides the ground of the apprehension. No inferential knowledge of the unobserved cases is required for such apprehension of deviation. All that is required is the expectation that there are unobserved cases and that the two things may not be together in some unobserved case. The observation of togetherness can provide the ground for such expectation, for there are previous occasions when one of two things has been observed without the other after both have been observed together in some cases. The Carvaka dismisses the suggestion that the ground of difference between the cases of deviation and those of non-deviation may be found by an appeal to the nature of things. He argues that there are no signs with the help of which the nature of things could be determined with certainty. The Carvaka also dismisses the suggestion that lack of the knowledge of deviation could be the ground for the knowledge of nondeviation. As the Prakasa puts it: "If non-deviation could be ascertained from lack of knowledge of deviation, deviation should be ascertainable from lack of knowledge of non-deviation." ( A ^ p . 340) Further, "If lack of knowledge of deviation were the ground for the knowledge of pervasion, there would not be any doubt regarding pervasion when it is so [i.e., when there is lack of knowledge of deviation]" (NK p. 340) In other words, knowledge of pervasion is opposed to the doubt regarding pervasion. If lack of knowledge of deviation could be the basis for knowledge of pervasion, there would not be any doubt regarding pervasion when there is lack of knowledge of deviation. Finally, the mere fact that no deviation has been noticed in the observed cases could give no reason that no deviation will be found at some other place in some other time, for even what is confirmed in hundreds of cases is found to be refuted by a single counter-example. The Carvaka goes on to say: "Deviation and non-deviation follows respectively from the presence and absence of adjuncts (upadhi)\ but the determination of that [i.e., determination of the absence of adjuncts] is impossible." (NKp. 339) To explain: The co-presence of two things or characteristics may depend on the availability of adjuncts or additional third factors; if so, at least one of those two things/characteristics will be found without the other when the third factors are missing. For example, if one has observed every earthen vessel to be brittle and generalizes thereby that all earthen vessels are brittle, one overlooks that brittleness is not due to being earthen or being a vessel but due to other factors, such as being built or baked in certain ways. In the absence of those other

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factors being an earthen vessel will deviate from brittleness, i.e., an earthen vessel will not be brittle, and the generalization will be falsified. On the other hand, if the co-presence of two things or characteristics is not dependent on any third factor, according to the Nyaya, they are nondeviant and the generalization to the effect that at least one of them is pervaded by the other is true. The Nyaya logicians have held that one must carefully observe if any third factors are involved and that 'the elimination of adjuncts' (upadhi-nirasa) is a requisite step for generalizing. The Carvaka contends that while some third factors may be detected and eliminated, one can never be sure that all third factors have been eliminated. Therefore, no empirical generalization can be justified. It may be pointed out that while an adjunct is anything which leads to the deviation of the mark from the probandum, in the narrower, technical sense, it is defined as "that which pervades the probandum but does not pervade the mark." (NK p. 352) This definition may be explained with the help of the following stock example. While it is true that wherever there is smoke there is fire, it is not true that wherever there is fire there is smoke. This is because fire emits smoke only if the fuel is wet. Thus wet fuel (ardrendhana) is the third factor on which depends the co-presence of fire with smoke. The detection of the adjunct vitiates the generalization and also the inference of smoke from fire. In this inference smoke is the probandum and fire, the mark. It may be noticed that the adjunct pervades the probandum: wherever there is smoke there is wet fuel; but the adjunct does not pervade the mark: fire may be found without wet fuel, as in a red hot iron ball or in an electric heater. When the adjunct is defined in this way, its presence proves beyond all doubt that the mark deviates from the probandum. This may be explained as follows. Let a, b, and c stand respectively for the adjunct, the probandum and the mark. It is given that a pervades b. It follows that the extension of a is equal to or greater than that of b and, therefore, that the extension of b is equal to or less than that of a. It is given further that a does not pervade c. It follows that the extension of a is neither equal to nor greater than that of c. It thus follows that the extension of b is neither equal to nor greater than that of c. In other words, since the intersection of b and the complement of a is empty and the intersection of c and the complement of a is non-empty, it follows that the intersection of c and the complement of b is non-empty. In the language of Nyaya: since the adjunct pervades the probandum and does not pervade the mark, it follows that the latter deviates from the probandum, for what deviates from the pervader of something also deviates from that thing (vy&paka-vyabhicarinah vy&pya-vyabhic&raniyamdt). The formulation of such a law is a pointer incidentally to the

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high level achieved by the Nyaya logicians in formal logic. Now an adjunct may be certain (niscita) or suspected (samdigdha, samkita: NK p. 351). It is certain when it is known that the adjunct pervades the probandum and does not pervade the mark. Such an adjunct proves beyond any doubt, as we have seen, that the mark is deviant and hence it is so called. Wet fuel in the above example is an adjunct of this kind. On the other hand, if either the fact that the adjunct pervades the probandum or the fact that the adjunct does not pervade the mark or both are uncertain, the adjunct is subject to suspicion. A stock example of this kind of adjunct is the following. (TC p. 319-20) One may infer after seeing that all the children born of a woman are of dark complexion that the future child of the then pregnant women will also be of dark complexion. The inference involves the implicit general premise that all children of the woman are of dark complextion. But the general premise and the inference may be falsified; for the fact that all the children born of the woman so far are of dark complexion may be due to some additional third factor, such as the dietary habit (or the complexion of her male partner.) If so and if the woman had changed her dietary habit (or changed her male consort), the future child could very well be of fair complexion. Here the dietary habit is a suspected adjunct, for it is uncertain whether the dietary habit is the actual cause of the dark complexion of those children. Nevertheless, the possibility that such an adjunct is involved renders the general premise and the inference suspect. The Carvaka contends that the elimination of all suspected adjuncts is impossible and that this alone suffices to make any empirical generalization baseless. This is particularly so when it is taken into account that the Nyaya logicians admit the existence of unobservable entities. What could be the ground for knowing that no unobservable adjunct is involved? (NK p. 348; also SD pp. 10-11) Further, pervasion has been defined as a relation (between the probans and the probandum) which is not dependent on any adjuncts (anaupadhika). At the same time an adjunct has been defined as that which pervades the probandum and does not pervade the mark. This shows that while "adjunct" appears in the definition of pervasion, "pervasion" appears in the definition of an adjunct—which is circular. (SD p. 12) In the Tattvacintamani of Gangesa (13th century) the Carvaka position has been succintly stated as follows making points similar to those of Udayana noted above: Inference is not a source of knowledge. Although perceptible adjuncts could be eliminated by means of verified non-apprehension, there will remain the apprehension of deviation stemming from imperceptible

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adjuncts. After all, two things which are together in hundreds of cases are found to be deviant. Common activities towards fire, etc., after seeing smoke, etc., are based on expectation, for coherence gives the appearance of knowledge. (TC pp. 38-9) Some other points are raised in the Tattvacintamani in the chapter entitled "The Method of Generalization" (Vyaptigrahopayaprakaranam: pp. 170-87). It is argued that multiple observations (bhuyodarsana) cannot be the method of generalization. Since each observation cannot singly provide the ground, their collection cannot provide the ground either. It could be said that the impressions produced by the multiple observations provide the ground. But this is of no avail. The impressions could at best provide the ground for only what is contained in them. Since pervasion is not the content of any of them, they could not be the ground. (This is reminiscent of Hume's famous argument against causal power to the effect that causal power is not the content of either impressions or ideas.) Further, multiple observations are not indispensable for generalization. In some cases a legitimate generalization could be made from a single observation. For example, let it be supposed that the particular color and the particular taste of a particular mango is not duplicated anywhere. Then, since there can be no counter-example under such circumstances, the generalization that whatever has that particular color has that particular taste is true although based on a single observation. At the same time, a generalization supported by multiple observations could be false. For example, it is observed in hundreds of cases that something made of earth can be pierced by iron. Still the general statement that whatever is earthen is piercable by iron is false: the diamond is an earthen substance, but it cannot be pierced by iron. Thus not only can sound generalizations be made without multiple observations, but also generalizations based on multiple observations could be false. This shows that multiple observations cannot be the proper ground for generalization. It could be said that repeated observations are needed to dispel the apprehension (samka) that the co-presence of two things in a single case is accidental (kakataliya). But this is not acceptable in the long run; for the same apprehension could remain even after repeated observations. It could again be said that the elimination of adjuncts should precede the generalization and that multiple observations are needed for that (since one has to find out if something does pervade the probandum and does not pervade the mark). Similar considerations could be offered for the elimination of any other third factors which do not qualify as adjuncts in the narrower sense, but which may be found to accompany the so called

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pervader and the pervaded. But even if this were granted, imperceptible adjuncts and other imperceptible third factors could not still be eliminated in this way; therefore, the apprehension of deviation arising from the possibility of imperceptible adjuncts or other third factors would still remain. One could fall back on inference to eliminate imperceptible adjuncts or other third factors. But the inference would itself have to make use of a generalization. Since further justification would be needed for that and since the same issue would arise in each successive step, the process would surely lead to a vicious infinite regress. We finally look at Jayarasi, the author of the Tatttvopaplavasimha and the 8th century Carvaka sceptic, who rejects all sources of knowledge, including perception. While dismissing inference as a source of knowledge, he raises the usual Carvaka objection that knowledge of pervasion (avinübhüva-sambandha) cannot be accounted for. He asks: is pervasion a relation between universals, or between universals and particulars, or between particulars? (TPS p. 65) The first and the second positions are with reference to the Nyaya claim that universals are eternal entities inherent in many particulars in spite of being different from and independent of them. (N 1) This view has some similarity with the view of Aristotle who utilized universals to give foundation to our general knowledge claims about natural phenomena. So far as Jayarasi is concerned, he summarily rejects both the first and the second positions by saying that he has shown elsewhere that universals cannot be admitted to exist. If the third position is advocated, since there is an infinity of particulars, pervasion as a relation among them, he says, could never be known. At any rate, sense experience cannot be the source of such knowledge so far as particulars belonging to distant time/space are concerned. (If sense-experience fails, so too will the other sources of knowledge; for they are ultimately grounded on sense-experience and cannot extend our knowledge to what cannot be known through senseexperience.) One could of course enumerate the cases actually observed and establish the relation of pervasion among them. But this cannot justify the 'inductive leap' to all cases comprising the unobserved cases, past, present and future. (TPS p. 65) Regarding the Nyaya claim that pervasion could be justified as being based on causation, he asks: is a cloth determined to be the effect of the threads on the basis of its coming into being in succession or on the basis of its being cognized in succession? (TPS p. 70) The first view is not acceptable; for then other things coming into being simultaneously with the cloth would also be turned into effects. It could be replied that other things could be eliminated, because they are not related with the threads by way of agreement in presence (anvaya) and agreement in absence (vyatireka). But that cannot give the guarantee for causal

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connection, for things found to be co-present and co-absent may still not be causally connected. In fact, all that can be determined is whether two things have come into being at the same time or in succession. This falls short of proving causal connection. (A similar point is made by Hume also in his critique of causation.) The second view, too, is not acceptable. Even two things which have come into being at the same time and are not related to each other as cause and effect may be cognized in succession, such as the two horns of a cow. Further, two non-entities, such as cowness and horseness, which are not causally related, could also be cognized in succession. Thus being cognized in succession fails to justify a causal connection. (TPS p. 71) We now move on first to consider briefly some Indian responses to the problem of induction. We have looked at arguments intended to show that multiple observations cannot provide the adequate logical basis for generalization. If so, can that basis come from a single observation (sakrd-darsana)! The method of single observation has indeed been favored by Prabhakara, the great Mimamsa philosopher. (TC p. 177) Prabhakara points out that something could pervade something if and only if their co-presence is not dependent on any adjuncts. Thus pervasion is extensionally the same as the absence of adjuncts. The absence of adjuncts is a qualifier (visesana) of co-presence which is the substratum (adhikarana) of the absence. Now, according to Prabhakara, an absence is ontologically reducible to its substratum; hence absence of adjuncts is reducible to nothing other than co-presence. Since co-presence can be known by a single observation, pervasion too can be known by a single observation. (TC p. 178) Although pervasion can be grasped by a single observation, repeated observations are not wasteful. They confirm the generalization by eliminating the apprehension that additional third factors may be involved. (TC p. 180) But the method of single observation could fare no better, for the objections brought against multiple observations apply against single observation as well. In addition, if pervasion could be known by a single observation of co-presence, how could there be any apprehension of deviation? (TC p. 179) Since pervasion is already known once the pervader is observed together with the pervaded, and since such knowledge would remove the apprehension of deviation, the apprehension of deviation should disappear as soon as the co-presence is observed. Finally, even if it were granted that absence of adjuncts were ontologically the same as co-presence, it does not follow that knowledge of co-presence would necessarily include knowledge of absence of adjuncts. For example, Devadatta may be the son of Yajnadatta, but one who sees Devadatta does not thereby automatically know that he is the son of Yajnadatta. Hence although mere co-presence can be known through

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a single observation, it does not follow that absence of adjuncts too can be known through a single observation. (TC p. 183) Indeed, the latter knowledge involves that there are no third factors which pervade the probandum but does not pervade the mark. This goes far beyond the knowledge of co-presence alone. If neither multiple observations nor a single observation suffices for the purpose, can pervasion be justified with the help of a kind of hypothetical reasoning called uha or tarka! This view has been promoted by the Jain logicians. They agree with the Carvakas that perception cannot be the means for knowing pervasion, for " . . . only what is in contact (sannihita) with the sense organs can be known by it ( = perception), and hence it is incapable of grasping pervasion which covers all cases [including past and future cases where there can be no senseobject contact]." (PKM p. 177) Pervasion cannot also be known through inference, for inference "is preceded by knowledge of pervasion; if knowledge of pervasion were based on inference, there would be infinite regress or circularity." (PKM p. 178) In other words, if pervasion is known by inference, since that inference itself would be based on some premise involving some pervasion, the latter too would have to be grasped by another inference and so on to infinity. On the other hand, if pervasion is based on inference and inference, in its turn, is based on pervasion, there would be mutual dependence (anyonyasraya), which is a kind of circularity. The Jains argue further that various other knowledge-sources, such as authority (sabda), etc., which could be offered as the means of knowing pervasion, also turn out to be unsuitable. (PKM pp. 349-53) The Jains, however, accept inference as a source of knowledge and also that inference cannot be without general premises. Accordingly, they offer a certain kind of hypothetical reasoning as the only acceptable means of knowing pervasion. The reasoning is based on perception and nonperception, or more generally, on awareness (upalambha) and nonawareness (anupalambha) to cover pervasion involving unobservables. (PKM p. 348) It is set out as a reasoning 'being explicable thus' (tathopapatti) and 'not being explicable otherwise' (anyathanupapatti). (PKM p. 348) It consists in showing that 'what is intended as the probans' (sadhanatvena abhipretam vastu) exists or is possible only if 'what is intended as the probandum' (sadhyatvena abhipretam vastu) exists or is possible and does not exist or is not possible otherwise. (PKM p. 349) In other words, something can be known to be pervaded by something if and only if it is known that the former exists (or is possible) only if the latter exists (or is possible) and that if the latter does not exist (or is not possible), the former does not exist (or is not possible) either. The crucial difference between the methods of multiple observation and

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single observation on the one hand and the Jaina method on the other is that the latter requires, and the former does not, the demonstration that the pervaded indispensably depends on the pervader. But, to the Carvaka, the method of hypothetical reasoning fails to counter the sceptical challenge. The demonstration of indispensable dependence must presuppose an invariant and universal connection, i.e., pervasion in some form. If the said method is the only means, the pervasion presupposed in the hypothetical reasoning brought in support of pervasion would itself have to be supported by another hypothetical reasoning, and so on ad infinitum. The Jain logicians have themselves rejected the method of justifying pervasion through a typical inference (anumdna) because of the charge of infinite regress or circularity. The important difference between that typical inference and the hypothetical reasoning recommended by the Jains is the following. In the typical inference the general premise incorporating the pervasion between the pervaded and the pervader is stated in the form of a universal categorical proposition. In the hypothetical reasoning the general and indispensable dependence of the pervaded on the pervader is stated in the form of a conditional proposition. How can this mere change in the form of the statement, the Carvaka would say, remove the old and familiar charge? In the process of justifying pervasion the Jain logicians felt the need of going beyond empirical observation and of resorting to the demonstration of the dependence of the pervaded on the pervader. A somewhat similar view has been developed in a different vein by some Buddhist logicians like Dharmakirti (7th century). (N 2) Dharmakirti asserts, agreeing with the Carvaka and the Jains, that pervasion cannot be founded on the observation of co-presence (darsana) or the observation of co-absence (adarsana). (PV verse 31, p. 269) He makes it clear that even if the so called pervaded is observed to be absent from the places where the so called pervader is observed to be absent, it does not follow that the former is non-deviant from the latter and that the possibility of deviation still remains. (PVverse 13, p. 263) He holds that there can be pervasion only if there is a natural connection (svabhava-pratibandha) between two things. (NBD p. 112) He holds further that the only bases of natural connection are identity (tddatmya) and causation (tadutpatti). Accordingly, identity and causation are the only acceptable grounds of pervasion; unless two things are related in one of these ways, there can be no necessity (avasyambhdva-niyama) and no pervasion. (PVverses 312, p. 269) Identity is exemplified in such generalizations as 'all mangoes are fruits' and 'all originated things are non-eternal'. In all such cases there is non-difference (abheda) between the pervaded and the pervader. (NBD p. 113) Non-difference implies essential identity (vastutah

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toddtmyam) in spite of the difference in the cognitive contents {pratyayabheda-bheditvam) of the two expressions. (NBD pp. 159, 162) As the examples show, the relation of identity could hold between classes which are co-extensive (as in the case of originated things and non-eternal things) as well as between those which are not co-extensive (as in the case of mangoes and fruits where the latter is the wider class representing the genus). But in both cases the pervaded suffices by itself alone (bh&va-m&tra-anurodhiri) to provide the connection with the pervader. (PV verse 2, p. 259) For example, being a mango by itself and without reference to any other factor implies being a fruit, just as being originated by itself and without reference to anything else implies being non-eternal. It appears that in cases of identity or non-difference the connection between the pervaded and the pervader is not synthetic (by borrowing modern terminology). [Thus if something is known to be a mango, without any further consideration it can also be known to be a fruit; if something is known to be originated, without regard to any other factor it can also be known to be non-eternal.] At the same time, the connection cannot be described as analytic if analyticity is understood in a linguistic sense: these truths are non-empty and are about the nature of things. Thus the relation of identity, as understood by Dharmakirti, provides general truths which are non-empty although necessary, but neither synthetic nor analytic. (N 3) On the other hand, causation provides general truths which are nonempty, physically necessary and sythetic. In all such cases there is difference (bheda) between the pervaded and the pervader and the former cannot by itself alone provide the connection with the latter. Dharmakirti argues that unless two different things are causally related, their connection cannot be necessary. (PV verse 33, p. 270) He goes on to cite the example of a dress and its color. The color comes into being after the dress. The color is not a cause of the dress and further the inference from the dress to the color would not be based on a necessary connection. The dress could be regarded as an auxiliary cause (sahakarikarana) of the color; still the inference from the dress to the color would not be necessary, for the inference from the cause to the effect is not necessary (ekanta). (PV verse 33, p. 270) It follows that only the cause can be inferred with necessity from the effect and only the effect can be pervaded by the cause and necessarily connected with it, but not vice versa. This is because the effect cannot come into being without the cause; hence the existence of the effect gives a guarantee for the inference of the cause: the effect thus is necessarily pervaded by the cause. But the effect may not come into being in spite of the presence of the cause if some auxiliary cause is missing. Hence the existence of the cause does not provide a guarantee for the inference of the effect: the cause thus is

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not pervaded by the effect. Dharmakirti cites smoke as an example of an effect which is necessarily pervaded by fire as the cause and says that there is universal agreement in presence (anuvrtti) between smoke and fire, i.e., every case of smoke is also a case of fire. He points out that if something could come into being without something, the former could not be the effect of the latter. (PV verse 34, p. 270) Where there is both agreement in presence (anvaya) and agreement in absence (vyatireka), something is established as the natural (svabh&va) cause of something else; in such a case the latter could not come into being from anything else. (PV verse 38, p. 271) Without any hesitation he rejects the plurality of causes: he claims that if smoke is produced somewhere, fire must be there too, for if nothing of the nature of fire is there, how could smoke come into being? (PV verse 36, pp. 270-1) Again, "fire is the natural cause of smoke" (dhuma-hetu-svabh&vo hi vahnih) and "has the specific power to produce it (tacchakti-bhedav&n); if smoke were to come into being without its cause, it would have to be uncaused." (PV verse 37, p. 271) Dharmakirti rejects the suggestion that effects are uncaused, for then it cannot be explained why they come into being at specific times and not at other times (k&dacitka). Only what is eternal or unreal is uncaused; the very fact that something comes into being at a certain time and not at any other time proves its dependence on something else which is the cause. (PV verse 35, p. 270) (N 4) Could there be pervasion between two things even if they are related neither by way of identity nor by way of causation? Durveka Misra (the author of the Pradipa sub-commentary on the NyayabinduTika) has considered a number of possible exceptions, such as light and shade, the upward and downward movements of a scale, color and taste (of a fruit), hands and feet, the rise of the moon on the one hand and the rise of the sea or the blooming of night flowers on the other, the rise of a certain star and the rise of another star, etc. (N 5) He points out that although in these cases neither is directly the cause or the effect of the other, both are nevertheless co-effects of the same cause (ekas&magridhlna). He also considers certain other possible exceptions, such as mendicants and their sticks, disturbed mongooses and snakes, etc. He agrees that these are not related by way of either identity or causality, but he rejects these as cases of pervasion. Thus the view that there is pervasion if and only if things are related by way of identity or causation is secured. Dharmakirti's views are highly influential and have been widely discussed. One well known problem is: how can it be known that two different things are causally related? As Prabhacandra argues (PKM pp. 511-3), when fire is claimed to be the cause of smoke, is this relation known from the perception of fire, or from the perception of smoke, or

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from the perception of both? It cannot be from the perception of fire alone; for that tells us only about fire and not about smoke, and without the knowledge of both there can be no knowledge of the relation between the two. For the same reason it cannot also be from the perception of smoke alone. Thus the only remaining alternative is that the causal relation is known from the perception of both. But this too is not acceptable, as Prabhacandra continues to argue in a vein similar to that of Jayarasi mentioned above. The perception of both smoke and fire tells us only about smoke and fire and does not tell us that fire is the cause and smoke is the effect. If the mere perception of smoke and fire suffices for the knowledge that fire is the cause of smoke, from the perception of any two things which are not, admittedly, causally related, such as a pot and a cloth, it should become known that they are so related. It may be said that causation is known, not from the mere perception of two things, but from the perception of succession of one by the other. But this is of no avail, for there could be perception of succession between a pot and a cloth too. It could be said that from the knowledge that smoke exists only where fire exists and does not exist where fire exists not, it is known that fire is the cause of smoke. But then it can justifiably be asserted that all speakers are possessed of attachment. (PKM p. 512) To explain: since average speakers like ourselves are possessed of attachments towards various things and since stones, etc., are neither speakers nor possessed of attachments, it should follow with equal cogency that all speakers have attachment. But this would contradict the Buddhist view, fully supported by Dharmakirti, that although Buddha spoke about the truth, he possessed no attachment. The point is that agreement in presence and agreement in absence cannot provide the guarantee that fire is the cause of smoke any more than it can provide the guarantee that all speakers are possessed of attachment. Finally, the claim that fire is the cause of smoke comprises all fires and all smokes located anywhere and anytime. It is beyond the means of perception to deliver any such knowledge. It may here be pointed out that Dharmakirti himself declared that pervasion could not be known from perception of co-presence and perception of co-absence. He also held that when there is knowledge of agreement in presence and agreement in absence between two things, one of them is known to be the cause of the other. But knowing one thing to be the cause of the other implies that one is pervaded by the other. If pervasion cannot be known from perception of co-presence and co-absence, how can causation, which implies pervasion, be known from that very source? Accordingly, the sceptics of the Carvaka school claim that the problem of induction is insoluble and, therefore, that inferences based on inductive premises are not acceptable as sources of knowledge (pramana). The Carvaka critique of induction and inferences employing inductive

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premises, as already pointed out, is substantially similar to Hume's sceptical attack on induction and inferences regarding matters of fact. Hume says: [Experience] shows us a number of uniform effects, resulting from certain objects, and teaches us that those particular objects, at that particular time, were endowed with such powers and forces. When a new object endowed with similar sensible qualities, is produced, we expect similar powers and forces, and look for a like effect. . . . But this surely is a step or progress of the mind which wants to be explained. . . . For all inferences from experience suppose, as their foundation, that the future will resemble the past, and that similar powers will be conjoined with similar sensible qualities. . . . It is impossible, therefore, any arguments from experience can prove this resemblance of the past to the future; since all these arguments are founded on the supposition of that resemblance. (N 6) Hume's argument shows not merely that induction is fallible or that inductions with true premises cannot always have true conclusions. Rather, it shows much more radically, that the claim that any induction is true is not justified. There are (not surprisingly) substantial differences between Carvaka and Hume. The former does not accept memory as knowledge, the latter does. Some followers of the former refuse the status of knowledge to even perception, the latter does not. The Carvaka thoroughly investigates the nature of adjuncts (upadhi) to show that induction has no rational foundation; Hume does not. The Humean distinction between relations of ideas and matters of fact (the forerunner of the analytic-synthetic distinction) is also far less visible in the Indian tradition. [However, the Indians do separate what is derived from the meaning (arth&ksipta) from what is not and what is discernible as true by the mind alone (manasaiva gamyate) from what is not: for example, that a thousand includes a hundred is derived from the meaning of the symbols involved. Again, that the probandum belongs to the subject is discernible as true by the mind alone if it is given that the probans belongs to the subject and that the probans is pervaded by the probandum. Similarly, that there are no sons of barren women can be discerned by the mind alone while that there are no rabbit's horns cannot.] Still, for Hume, the inductive passage from observed cases to all cases cannot be justified except on the assumption that the nature is uniform and that the future will resemble the past~an assumption which amounts to begging the question. This is similar to the Carvaka argument

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that if the claim of pervasion is justified through inference, one would have to use pervasion itself inviting either vicious regress or circularity. Both refute causality so that the inductive base cannot be provided by the law of causation. Both maintain that practical activities are carried on, not on the basis of knowledge, but on the basis of custom/habit (for Hume) or expectation (for Carvaka), i.e., opinion. Both insist that no grounds can be provided for the inductive leap and conclude that induction is unjustified. Again, the Carvaka (and other Indian) philosophers find the argument from infinite regress and the argument from error to be of great interest in the controversy over the justification of knowledge-claim. This indicates their understanding of internalist concerns in the internalistexternalist debate over the analysis of knowledge [without implying that they were (or were not) internalists] and establishes affinity with the Humean view [without, again, implying that Hume was (or was not) an internalist, given that there are many different interpretations of Hume], Further, the typical paradigm of inference attacked by the Carvaka has three steps: (1) the probans is pervaded by the probandum (hetuh sadhya-vyaptah); (2) the probans belongs to the subject (hetuh paksavrttih) and (3) therefore, the probandum belongs to the subject (tasmat sQdhyah paksavrttih). The Carvaka, throughout its long history, has consistently attacked the first step (which incorporates the generalization) and argued that since the generalization is baseless, so is the conclusion; however, that the conclusion follows from the other steps is not questioned, but, instead, explicitly acknowledged. This is similar to the Humean approach which rejects the rationality of induction, but not of deduction. In this respect the Carvaka-Humean critique differs from that of Sextus Empiricus, the Pyrrhonic sceptic, who attacked syllogism and rejected both deduction and induction. Sextus does not argue that there is no reason for induction or that inductive reasons are not reasons, as the Carvaka-Humean critic does. Again, Sextus distinguishes between indicative signs and associative signs, rejects the former by which we infer something imperceptible from something perceived and appears to lend support to the latter by which we infer from what has been observed something unobserved at present but observable in principle. This differs from Carvaka and Hume neither of whom advocates such a division of signs. Hume's critique of induction led to a vigorous study of induction in recent philosophy. Bertrand Russell, a leading philosopher of this century, holds that all empirically based opinions about the future are based on the inductive principle which experience can neither confirm nor confute. "We must either accept the inductive principle on the ground of its intrinsic evidence or forgo all justification of our expectations about the future." (N 7) If this dichotomy proposed by Russell is sound, both the

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Humean and the Carvaka sceptics would have a cause to celebrate, for it is unlikely that either would be persuaded by an appeal to accept the inductive principle on the ground of its intrinsic evidence. In another work (N 8) Russell has listed five "postulates of scientific inference" as being basic to all non-demonstrative reasoning. The first postulate of quasi-permanence is the following: "Given any event A, it happens very frequently that, at a neighboring time, there is at some neighboring place an event very similar to A." The other postulates are that the world contains separable causal lines, that there is spatio-temporal continuity of causal lines, that structurally similar events ranged about a center usually have a common causal origin, and that analogies are usually reliable. But, in the above enumeration, the vague words 'frequently', 'usually' and 'similar' should be rendered more precise (by specifying how much similar, etc.). However, if they are rendered more precise, different sets of presuppositions would result which would inevitably lead to some varying estimates of probabilities. Hence choosing from among different possible sets of postulates is required, but we do not seem to have any grounds for making the choice. Again, these postulates are factual statements about the world. There appears to be no good reason why the sceptic must accept them as true. Thus it does not seem likely that a resolution of the sceptical challenge to scientific knowledge should rest upon such a basis. (N 9) T o meet the sceptical challenge other philosophers like Strawson have argued that the Humean attack on induction is based on the assumption that only those arguments which are deductive and in which, if valid, the conclusion follows necessarily from the premises are rational. This assumption, Strawson claims, is wrong and overlooks the fundamental difference between deduction and induction as well as the fact that the norm of rationality for induction is different from that of deduction. Since the aim of induction is to produce factual knowledge which is not contained in the premises, the conclusion of an induction cannot necessarily follow from the premises. Rather an induction is rationally justified when it is reasonable and proportionate to the multiplicity and variety of empirical data. Hence if there is a large number of corroborative instances which are appropriately sampled, the induction is rational and justified. To ask if such a method is rational is like asking whether the law is legal. (N 10) But this amounts to claiming that what we mean by induction being rational and justified is that the inductive conclusion is reached by the recommended method. This claim is hard to reconcile with the fact that the method is subject to evaluation, criticism and further revision. Such evaluation and revision presupposes that it makes sense to ask the question whether the currently accepted inductive methods are rational and

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justified. Being rational and justified, therefore, cannot be synonymous with being by passed by the current procedure. It may very well be that the criterion of rationality for induction is different from that of deduction. But even if this were true, it does not follow that fulfilling the accepted inductive requirements automatically amounts to satisfying the said criterion. Further, if the norm of rationality for induction is different from that of deduction, as Strawson grants, how can we know that the same evaluative notion, viz., rationality, is applicable to both? After all, in deduction the conclusion follows necessarily from the premises but in induction, does not. In induction one goes from cases observed to cases unobserved but in deduction, does not. How then can we be sure, without any further ado, that both, in spite of being so importantly different, are rationally justified? Could it not be that since induction is so dissimilar to deduction, it is appropriate to restrict the concept of rationality to the latter and not extend to the former? Still others have claimed that since inductions using accepted procedures have been true or largely true, it follows that induction is justified. (N 11) But such an inductive justification of induction is circular, for the very question raised by Carvaka and Hume is whether regularity in the past can be the proper reason for regularity in the future. R. B. Braithwaite has tried to avoid the charge of circularity as follows. According to him, if a person B believes (1) that the policy of induction is effective and also believes (2) that the inductive principle which supports this conclusion, is effective, B may infer that the inductive policy is effective. This inference is "subjectively valid" and, Braithwaite points out, not circular, because it is not required that B's belief in the conclusion, viz., that the inductive policy is effective, should be a reasonable one. (N 12) This may be so; but the criterion of "subjective validity" is too weak, as the following example shows. Let B believe that all inferential policies are effective and also believe in the principle of inference that any passage from any premise to any conclusion is sound. Then B may infer that all inferential policies are effective. This inference will be subjectively valid and non-circular in Braithwaite's sense. But such a demonstration of the effectiveness of all inferential policies is futile as is the said demonstration of the effectiveness of induction. Braithwaite has proposed to offer a stronger criterion of validity by adding a third condition that the principle of inference in accordance with which the conclusion is reached, should be effective. If this third condition is fulfilled along with the two previous ones, the inference is "both subjectively and objectively valid." (N 13) But then, as he himself concedes, the reasoning will be implicitly circular; for to have a reasonable belief in the effectiveness of the inductive principle an

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inference of exactly the same sort would be required to establish it. Braithwaite holds, in the vein similar to that of Alice Ambrose, that the rule or policy of induction is not a premise of inductive reasonings, but a principle of inference following which inductive reasonings are carried out. (N 14) The charge of circularity, however, as Nicolas Rescher points out, does not disappear. (N 15) For the contention is still that we can show that the inductive rule is justified and validate the belief that this rule is reliable by this rule itself. This argument can be successful only if we already have an independent and adequate justification of the inductive rule, i.e., only if the argument is pointless and dispensable. Thus the inductive justification of induction fails to overcome the Carvaka-Humean objection that one cannot validate the general policy of appealing to experience by an appeal to experience itself. The rule of induction permits us to go from observed cases to unobserved cases and from smaller percentages to larger percentages (including 100%) of the whole class. In a special form this has been interpreted by Reichenbach, Salmon, etc., to prescribe that the probability value is equal to the observed frequency, i.e., that P(A/B) = m/n, where n is the number of observed events B and m is the number of those observed B which have the property A. Reichenbach (who calls the inductive rule the 'straight rule') and Salmon (who calls the inductive rule also the 'rule of induction by enumeration') have argued that if there are any laws of nature to be found, persistence with the inductive rule would lead to their discovery, but there is no certainty that the laws of nature will be found if the rule is disowned. (N 16) In particular, if there is no limit of the relative frequency of the events A in the set of events B, it cannot be specifically determined by any rule; but if there is a limit, it may be possible to discover it and specify its value. Thus the above rule, it is claimed, will work if any will. When it is backed by a sufficiently large number of careful observations and experiments, the law of large numbers would ensure that the probability value is close to the observed frequency. This, then, pragmatists like Reichenbach and Salmon claim, provides a vindication of induction although Reichenbach himself was quick to concede that we are not able to prove that the success of induction is necessary, or even probable. (N 17) Many difficulties in this viewpoint have been pointed out. Thus even if any laws of nature are found by the use of the inductive rule, (since we do not know how many observations will be needed) it would not be possible for anyone to know when they have been found. (N 18) Further, scientists try to predict short-run relative frequencies, but the straight rule does not ensure that such predictions are correct. (N 19) Moreover, Reichenbach himself noticed that the argument for the straight rule recommends equally an infinity of inductive rules, the asymptotic

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rules, which prescribe estimating P(A/B) = m/n + f(n), where f(n) is a function of the number of observations n which decreases to zero with the increase of n. Since there is no objective ground for choosing among these rules, there will also be no objective ground for choosing among our predictions which will vary enormously depending upon which rule is used. (N 20) Again, Carnap has argued that the straight rule would lead to hasty generalizations. (N 21) Finally, even if it were true that the continued use of the straight rule would lead to the discovery of scientific laws, it cannot be claimed, without assuming that the future will resemble the past, that this trend will be maintained. Hence the pragmatist justification, too, if the claim of proving the rationality of induction is included, will be open to the charge of circularity. Another well known recent view is that of anti-inductivism mooted by Karl Popper. (N 22) Popper agreed with Hume that ampliative induction has no rational validity. Accordingly, he sought to substitute the inductive model of empirical sciences by the so-called hypotheticodeductive model and held that valid science is invariably deductive and never inductive. (N 23) While, according to the inductionists, the aim of science is the verification of hypotheses, according to Popper, the proper aim is their falsification. The latter is done by the logical procedure of modus tollendo tollens: if a prediction deduced from a hypothesis turns out to be false, the hypothesis is falsified. For example, the hypothesis that all A is B warrants the prediction that the next A one is about to observe is B and is falsified when that A is actually found not to be B. Popper was well aware that falsification cannot be the whole story, for at a given time more than one hypotheses could pass the most rigorous In such a situation, the choice among competing tests available. hypotheses would depend on which hypothesis has the richer information content, is formulated in a more precise way and provides the explanation of a larger number of facts. (N 24) Popper maintained that all these qualities of a hypothesis or theory normally go hand in hand with a higher degree of falsifiability; for the more general, the more precise and the more comprehensive is a hypothesis, the larger is the set of its potential falsifiers. There is no doubt that the hypothetico-deductive method and falsifiability have their roles to play in science. But these do not necessarily exclude induction and inductionists need not deny the importance of either. But, on the other hand, for the acceptance of a hypothesis or a theory what is more important is not that it is not falsified, but that it has survived rigorous tests that could have refuted it. The more rigorous and the more potentially falsifying are the tests to which the hypothesis is put, the better confirmed and the more acceptable

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is the hypothesis. Thus the measure of severity of the tests is the measure of the degree of confirmation of a hypothesis. The hypothesis does not logically follow from the test although the latter does confirm the former. This shows that induction remains an indispensable part of the scientific method, for the confirmation of hypotheses by tests utilizes it. In fact, a distinction should be drawn between the confrontation of the results of observation with the hypothesis and its acceptance or rejection. The former involves the examination of logical relations between the statement of the hypothesis and the statement of the test result. But the latter is pragmatic in character and involves considering such issues as simplicity, explanatory value, etc., and goes beyond observation and deduction. Popper of course denied that the notion of testing of a hypothesis by observation involves induction. He substituted the notion of confirmation by that of corroboration and held that a hypothesis is corroborated by observation reports only if the latter is an account of the results of genuine attempts to falsify the hypothesis and not attempts to verify it. (N 25) He added that the notion of genuineness cannot be formalized. But, clearly, genuineness cannot be explained in terms of the psychological attitude of the observer, for that would conflict with Popper's sworn aim of ridding scientific methodology of all elements of psychologism and subjectivism. Rather it could be interpreted, consistently with what is said above, as a postulate that if there are experiments which have a high chance of falsifying the hypothesis, the latter should be subjected to them (in preference to other experiments which have a low chance of falsifying it). But, when interpreted in this way, the postulate of genuineness is well known to inductionists and fully consistent with their common understanding of confirmation. Again, the big problem for the notion of corroboration is that Popper gives us no reason to think that highly corroborated theories are more likely to be true. (Thus, why should we care about corroboration?) Further, a major flaw of mere falsificationism, as Nicholas Rescher has remarked, is that falsifying a hypothesis is no more than eliminating one possibility. (N 26) The elimination can be a sure method of drawing near to acceptance only if it is already known that only a finite number of possibilities exists or perhaps it is granted that the human mind has a natural inclination to move towards something better. Short of the justification of such large metaphysical claims, induction remains an indispensable element in the process of confirmation. On the other hand, the contrast between verification/confirmation and falsification is not as pronounced as Popper supposed it to be. For an inductionist, so thought Popper, truth is the only aim of science. But it need not be so and, for inductionists, acceptance by way of induction need be neither infallible nor permanent. An inductionist acknowledges the value of falsification within his method

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and Popper's crusade against induction appears to be misguided. Thus the methodology of science-despite the effort of Popper-can neither banish induction nor ignore the problem of induction. Thus the various Indian and Western theories fail to provide a solution to the problem of induction. However, there is optimism in some quarters that a solution may be found from the study of probability to which we turn next.

NOTES

1. 2.

3. 4.

5. 6. 7. 8. 9.

See my "The Nyaya-Vaisesika Theory of Universals", Journal of Indian Philosophy, 3, 1975, pp. 363-82. Dharmakirti, a great Buddhist philosopher, is the author of such famous works as the Pramanavarttika, the Vadanyaya, etc. His Nyayabindu together with the commentary by Dharmottara has been translated into English with an elaborate exposition by T. Stcherbatsky, Buddhist Logic, vols. 1 & 2, Dover, New York, 1962. For further discussion see my "Svabhavahetu in Dharmakirti's Logic", Philosophy East and West, 37, 1987, pp. 392-401. Dharmakirti may be the first to use this argument explicitly to defend causality. A sharper and more elaborate version of the same argument is found in Udayana and his commentators: NKV, p. 9. Dharmottarapradipa of DurvekaMisra, ed. Dalsukhbhai Malvania, K. P. Jayswal Research Institute, Patna, 1955, p. 115. David Hume, An Enquiry Concerning Human Understanding, ed. L. A. Selby-Bigge, Clarendon Press, Oxford, 1902, pp. 36-7. Bertrand Russell, Problems of Philosophy, Oxford University Press, Oxford, 1959, p. 68. Bertrand Russell, Human Knowledge: Its Scope and Limits, Simon and Schuster, New York, 1948, part 6. R. M. Sainsbury, "On Induction and Russell's Postulates", Minnesota Studies in the Philosophy of Science, vol. 12, Rereading Russell, University of Minnesota Press, Minneapolis, 1989, pp. 200-219.

Carvaka-Humean Critique of Induction 10.

11.

12. 13. 14. 15. 16.

17. 18. 19. 20. 21. 22.

23. 24. 25. 26.

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P. F. Strawson, Introduction to Logical Theory, Methuen, London, 1952, pp. 248-50. See also A. J. Ayer, The Problems of Knowledge, Penguin Books, Harmondsworth, 1956, pp. 74-5. See R. B. Braithwaite, Scientific Explanation. Cambridge, 1953, pp. 255-92. Reprinted in part as R. B. Braithwaite, "The Predictionist Justification of Induction" in the Justification of Induction, ed. R. Swinburne, Oxford University Press, Oxford, 1974, (abbreviated as Jl) pp. 102-26. See also Max Black, "SelfSupporting Inductive Arguments" and the exchange between Peter Achinstein and Max Black in this same book. See further Abner Shimony, "Braithwaite on Scientific Method", Review of Metaphysics, 1 1953-54, pp. 644-60 and H. E. Kyburg, "R. B. Braithwaite on Probability and Induction", British Journal for the Philosophy of Science, 9, 1958-59, pp. 203-20. Jl, pp. 123-4. Jl, pp. 124-5. Alice Ambrose, "The Problem of Justifying Inductive Inference", The Journal of Philosophy, 44, 1947, pp. 260ff. Nicholas Rescher, Induction, University of Pittsburgh Press, Pittsburgh, 1980, pp. 117-9. Hans Reichenbach, Experience and Prediction, Chicago, 1938. Wesley C. Salmon, "The Pragmatic Justification of Induction", Jl, pp. 84-97. Hans Reichenbach, The Theory of Probability, University of California Press, Berkeley, 1949, p. 479. John W. Lenz, "Problems for the Practicalists's Justification of Induction," Jl, p. 99. Ibid., p. 101. Ibid., pp. 98-99. Rudolf Carnap, Logical Foundations of Probability, Chicago University Press, Chicago, 1950, 2nd edn., Chicago, 1962. Karl R. Popper, The Logic of Scientific Discovery, Hutchinson, London, 1959; main text originally published in German as Logik der Forschung, Julius Springer, Vienna, 1934. Ibid., pp. 29-30. Ibid., pp. 113-9. Ibid., pp. 344, 337. N. Rescher, Induction, op cit., pp. 217-8.

CHAPTER TEN INDUCTION AND PROBABILITY In recent studies of induction induction and probability have become closely linked. This may be due to the common conviction that although empirical generalizations and theories cannot be rendered certain on the basis of observation, they can be rendered more or less probable. Accordingly, the justification of induction has been sought to be founded on probabilistic criteria. There are, however, serious differences of views regarding what is this inductive probability on which inductive logic should be based. We now briefly discuss some of the important accounts of probability in modern philosophy. First, we look at the logical interpretation of probability. Although there is no universally agreed meaning of this notion, it draws its inspiration from the idea that probability depends on (some) relationships between sentences. Such relations hold between sentences by virtue of their logical structure which is determined by the connectives, the quantifiers, etc., regardless of the sense of the non-logical contents. J. M . Keynes who first developed a detailed theory of logical probability, thought that the latter is not definable. ( T R P p. 8) For the source of numerical values for the probability calculus he relied on the classical principle of indifference. The latter assigns equal probabilities to those events whose chances of occurrence are not expected to be different. ( T R P p. 65) But he recognized that the principle is not universally applicable, took this to entail that not all probabilities are numerically measurable and held further that some probabilities are not comparable with one another. It was Rudolf Carnap who showed in works dating from 1950s ( N 1) that it is possible to develop a method which gives effective estimates of logical probabilities (called by Carnap 'probability,') for all sentences in a given formal language. [Carnap also recognized what he called 'probability2' the value of which is established empirically and accepted its identification with the relative frequency in certain cases: LFP p. xiv, p. 294] The latter was a standard type of logical language with a finite number of monadic, first-order predicates, F, G, H, . . . (like 'is blue', 'is human', etc., naming properties) and a finite number of individual

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constants a, b, c, . . . (naming individuals). An atomic sentence is an assignment of an individual constant to a predicate, e.g., Fa (like 'John is human'). A state description is a conjunction of sentences containing every atomic sentence or its negation but not both. (LFP p. 71) Thus a state description completely describes the universe in the given language by affirming or denying each property of each individual. The logical range of a sentence may then be defined as the class of state descriptions in which, for each state description, the sentence is true if individuals have exactly those properties assigned to them by the state description. It may be seen that if a sentence p follows logically from a sentence q, the logical range of q is included in the range of p. But if p and q are logically inconsistent, the ranges o f p and q are disjoint. On the other hand, if p and q are logically consistent, but neither follows from the other, their logical ranges would overlap to a greater or smaller extent. Accordingly, in Carnap's view, logical probability is the measure of the degree of overlapping of the logical ranges of sentences. This is called the probability confirmation function and symbolized as 'c'. The value of c(p/q) corresponds to the confirmation of sentence p by sentence q on the basis of the logical relation between p and q. One important kind of confirmation function is the one called 'symmetrical'. In a symmetrical confirmation function all individuals are treated alike; hence one individual constant within the function's scope may be uniformly replaced by another so long as this does not change the given identity between occurrences of those constants. Under these circumstances, it is possible to give the same real number to each state description of any kind. The symmetrical confirmation function which is evaluated thus in any language is called ' c + ' . But it is also possible to suppose on the other hand that patterns of state descriptions, rather than individual state descriptions, should be put on a level with one another. Such a pattern is called a structure description and defined as disjunction of isomorphic state descriptions. (LFP p. 116) Every structure description is a complete description of the world although, as distinguished from a state description, it is a statistical description. The same real number may, under these circumstances, be given to every structure description and a measure be fixed for each of the n disjointed state descriptions within a particular structure description by dividing the number of that structure description by n. A confirmation function which is evaluated thus is called 'c*'. Carnap showed that c + and c* have important differences and approved the latter as appropriate for inductive logic. It was also made clear that any number of other symmetrical cfunctions could be formulated leading to other bases for the a priori measurement of probability understood as a logical relation.

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Carnap's system, however, produces unwelcome results for situations which are regarded typical for induction, his favorite confirmation function c* being no exception. In fact c*(p/q) = 0 where q is an observation report and p is a non-tautological generalization in a universe with an infinite number of individuals. This is unsatisfactory and implies that any generalization over an infinite domain is as worthless as any other. Further, even when the number of individuals in the domain is not infinite, but very large, the values of c* will be very small and tend to zero. This is because a generalization is logically equivalent to a conjunction of singular statements saying of each individual in the domain that it has the given property; hence the larger the number of conjuncts, the fewer are the possible worlds in which the conjunction is true and the lower is the confirmation value. It follows thereby that the degree of reliability of such a generalization would not increase with the increase in the number of confirming observations (even when there are no counterexamples). It is clear that the only cases where the confirmation values of empirical generalizations will not tend to zero are those in which the number of observed objects is close to the total number of objects in the domain (i.e., when 'enumerative induction' comes close to 'summative induction'). Carnap himself was not worried over these difficulties, for he held that scientific activity should be construed exclusively in terms of that which directly serves practical activity and that what is needed is the degree of confirmation of individual hypotheses and not that of universal hypotheses. But such a narrow-minded view of science is clearly unacceptable, for even rational decisions to act in particular situations may sometimes require seeing individual phenomena or particular uniformities in the light of much wider universal laws. Further, while practical technologists like engineers, navigators, etc., may choose to overlook general laws (such as Newton's laws of motion), this cannot be done by theoretical scientists, such as astro-physicists. (N 2) At any rate, whatever may be the merit of Carnap's view of science, his theory does not solve our main problem which is that of justifying inductive generalizations over domains in which the number of individuals is often very large/unknown. (N 3) Another currently discussed interpretation is the subjective or the personalist view of probability. This was mooted by F. P. Ramsey and then developed further by B. de Finetti, L. Savage and R. Jeffrey. (N 4) The fundamental thesis here is that objective probabilities are an illusion or a superstition, and that probabilities depend essentially on someone's beliefs. Thus in Ramsey's view the probability of a statement measures the degree of rational belief of the person making the statement. Beliefs

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or convictions are not understood in terms of introspected feelings; rather they are taken in a behavioristic way as definite actions which should result from beliefs in situations of making a decision. Thus in the situations of making bets on an uncertain event the lowest odds accepted by a person will decide about the belief of that person. For example, if Smith bets at 4 to 1 that the government will fall, but not at anything lower than 4 to 1, he has a 1/5 degree of conviction that the government will fall. Subjective probability is understood as the function of beliefs which are 'coherent' and are not such as to ensure a loss to the bettor no matter what happens. For example, if a person bets 3 to 2 that the government will fall and also bets 4 to 1 that the government will not fall, he will lose no matter what. Such a belief is 'incoherent' and left out of purview. Ramsey and de Finetti proved that a set of degrees of belief that are 'coherent' satisfies the axioms of probability calculus. Subjectivistic theories have allowed extensive use of Bayes's Theorem which puts P(A/B) as being equal to P(B/A~) x P(A1 P(B) where P(B) > 0. Some non-subjectivists prefer a very limited use of the theorem because the initial probabilities in the formula are often unknown. But since there are no objective probabilities from the subjectivistic point of view, there are also no unknown objective probabilities. Hence the investor may begin by assigning a chosen value to the initial probabilities (i.e., by deciding his lowest acceptable betting-odds), before considering the evidence. Once the values are established in this way, the desired probability may be computed with the help of the formula. In actual cases a good deal of empirical data are often accumulated, so that the initial chosen values eventually get rapidly diminishing roles in yielding the answer. Hence, from the subjective Bayesian point of view, differences in prior probabilities are not very material: as more and more evidence is gathered, these differences wash out, the posterior probabilities merge and lead on to the same final degrees of belief. Thus: " . . . the particular form of the prior distribution expressing beliefs held before the experiment is conducted is not a crucial matter. . . . The well-designed experiment is one that will swamp divergent prior distributions with the clarity and sharpness of its results, and thereby render insignificant the diversity of prior opinion." (N 5) Numerous logicians, however, have objected to the idea that probabilities should be identified with belief functions. Thus I. Levi has argued that subjective probabilities lead to counter-intuitive results. For example, if somebody has no reason to believe that some event A will take place rather than not, the correct measure of the degree of belief that

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A will happen as well as that A will not happen would be zero. (N 6) Again, according to Levi, if the degree of belief about hypothesis A is less than equal to the degree of belief about another hypothesis B, the degree of belief about the conjunction of A and B would be equal to the degree of belief about the former. But the probability of a conjunction is usually less than that of each conjunct. This tends to show that beliefs are not probabilities. (N 7) Further, H. Kyberg has shown that the identification of probabilities with the behavior of betting fails in numerous cases. For example, a bet about the truth of a universal statement is meaningless, for it cannot be decided. (N 8) Moreover, the behavior of betting appears to depend on a number of factors, e.g., a person's financial condition, the influence of other bettors, and not merely on the beliefs that some events will or will not take place. This raises questions about the behavioristic interpretation of beliefs. Moreover, it is difficult to accept that there are no objective probabilities whatsoever. It is true that much of statistics is justified and accepted because it works and that the selection procedure is often based on our beliefs and desires. But this does not detract from the common conviction that some things are more/less probable than others. For example, that a fair coin will land heads more than 20% of the times is more probable than that it will land heads less than 5% of the times. The professional gambler, again, is favored to beat the novice, because the former plays the percentages—and the percentages are real. The greater probability of these is not dependent on beliefs or opinions, but, the critic would insist, on objective facts. (N 9) Finally, for the convergence to certainty and merger of opinions results one supposes that all of the Bayesian agents accept the trials to be independently and identically distributed. But such conditions, as Mary Hesse points out, do not hold for scientific inferences in general, particularly when non-statistical hypotheses are involved. (N 10) Different Bayesian agents may also give, as John Earman observes, different estimates of rates of convergence. One may try to estimate the rate of convergence by getting an average of the rates for different evidence sequences which would require assigning weights to the sequences. But it is not clear that all Bayesian agents will agree to the same function for assigning weights. (N 11) Further, as Earman argues, the thesis of convergence to certainty implies that the Bayesian is probabilistically certain from the beginning that the actual world lies in a narrow enough range of possibilities, so that the truth or falsity of any empirical hypothesis can be reliably determined. But this amounts to a claim of dogmatic and substantive a priori knowledge. An astro-physicist, for example, may possess enough information ab initio to guarantee that the truth-value of that most stars have planets and most planets have at

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least one moon is decidable. But it appears to be wrong to require that the astro-physicist begin the inquiry with such a priori knowledge about the nature of the world. (N 12) We now move on to consider the viewpoint that probability is objective. Thus, according to Karl Popper, probability is best understood as a propensity or a disposition of objects towards specific types of characteristics with determinate frequencies. (N 13) This propensity analysis should be distinguished from the frequency analysis favored by von Mises, Reichenbach, etc., according to which probabilities are not related distributively to each member of the reference class, but should be identified with some collective property of the reference class. (N 14) So, for Popper, the 1/2 probability that an unbiased coin will fall tails is a propensity pertaining to each coin-toss and not a relative frequency characterizing the set (sequence) of coin-tosses, as it is for von Mises, etc. Relative frequencies observed in appropriate samples are, for Popper, the external, observable manifestations of the propensity or the hidden dispositional property, but should not be identified with it. The propensity analysis does not have some of the problems of the frequency analysis. From the latter point of view it is difficult to give an account of the probabilities of individual events, for it is features that have relative frequencies. (Indeed, some frequency theorists like von Mises have denied that there is any such thing as the probability of a single event: PST p. 15.) But the former allows assigning probabilities to individual events, for propensities may be regarded as properties of some kind of individual arrangements. Further, the propensity account works for both finite and infinite classes while the frequency account faces difficulties when the reference-classes are infinite. For while each member of an infinite collection cannot be individually examined, the relative frequency value of any finite sub-sequence is agreeable with any value of the limit of relative frequency in the infinite sequence. Still the propensity theory does not have a large following (although the following has grown recently). While the frequency theory states an estimable ratio for actual evaluation of probabilities, the propensity theory does not, for dispositions do not have specific numerical implications. However, for both these theories a probability value is a measure of an empirical, physical fact about the external world. Hence they are opposed to the logical interpretation which holds that probability depends on logical relations between sentences and also to the subjectivistic thesis that probability is an index of rational beliefs or attitudes. Thus Popper thought of propensities as "a new physical hypothesis . . ., analogous to the hypothesis of Newtonian forces." (N 15) Similarly, von Mises said about probability in dice games: "The probability of a 6 is a physical property of a given die . . . analogous to its mass, . . . or electrical

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resistance." (N 16) In this respect, from the point of view of the justification of induction the difference between the two theories is not very great. Since the propensity probabilities are estimated on the basis of observed relative frequencies, an empirical method is adopted by both for estimating probability values. Accordingly, if the probability values are estimated by using primarily inductive methods, the attempt to justify induction with reference to such inductively ascertained probabilities would be open to familiar charges of circularity. The classical and the most discussed theory of probability of course centers around the principle of indifference. According to this principle, if we can discern no reasons for discriminating between alternatives, we should assign equal probabilities to them. Thus, from the point of view of an indifference theory, probability may be defined as the ratio of the favorable cases to the total of equally probable cases. In the words of Laplace: "The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is sought. The ratio of this number to that of all the cases possible is the measure of this probability, which is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible." (N 17) Laplace has avoided any patent circularity, for the word 'probability' does not reappear in his definition. He seems to have given 'equally probable' a sense independently of probability by requiring that (a) they must be "equally possible" and (b) "such as we may be equally undecided about in regard to their existence." But the indifference theory is open to many objections. The theory speaks of 'equipossible' cases which must be such as to which we have no grounds to prefer one to the other. Hence the theory faces difficulty when there is evidence to show that the different outcomes are not equally probable. For instance, it may be known during a long run of trials that one side of a die turns up much more often than any other, but it may not be known which way the die is biased. Under these circumstances, the indifference theorist would still say that the probability of any one side coming up is the same as that of any other which, as remarked by Henry Kyburg, is "strange enough." (N 18) Again, this theory lands in difficulty where the evidence for different outcomes is not symmetrical. For instance, a coin may be found after a long run of throws to land heads twice as often as tails. Here the probability of landing heads may be said to be 2/3 and that of landing tails, 1/3. But this does not make good sense from the point of view of equipossible outcomes. The coin, although loaded, still has only two

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sides of which only one shows the head. How can then it be that the ratio of favorable alternatives to the total of equipossible outcomes is 2/3? Hence, as Kyburg observed, philosophers had no choice but to regard the indifference theory as seriously flawed: " . . . in many cases . . . the only way of arriving at probabilities was not to compute numbers of equally likely alternatives, . . . ." (N 19) Where would, if one is willing to speculate, the Nyaya philosophers stand in the modern controversy over probability? So far as the principle of indifference is concerned, it is accepted as a methodological postulate in the dictum called 'lack of discriminating reason' (vinigamana-viraha: KKK pp. 524-31). It implies that if no discriminating reasons can be found for favoring one out of two or more alternatives, each must be regarded as equally probable. This precludes accepting one and rejecting others until a discriminating reason, i.e., a reason for favoring one alternative (ekatara-paksa-p&tinl yukti) can be found. The principle of indifference also underlies what is called 'counter-balancing' (sat-pratipaksatva: BPP p. 405). According to it, if the opponent produces equally good reasons for the counterthesis, the proponent's case is frustrated; that is to say, when there are equally good reasons for both the thesis and the counter-thesis, both must be regarded as equally probable and the proponent of the thesis cannot be said to have made his case. For an understanding of the Nyaya viewpoint on probability, however, one should look at the analysis of doubt (samsaya, samka). The doubt of deviation (vyabhicOra-samsaya or vyabhic&ra-samka) which underlies the problem of induction, is after all a kind of doubt. Now doubt is an indecisive awareness (anavadharana-jnana), a state of mental undulation (dolayamdnd pratttih). (N 20) When one side becomes dominant or appears to be more likely (utkata-eka-kotika), the doubt is labelled as an 'expectation' or 'probable opinion' (sambhavana ) in the narrower sense. (NKS p. 923) For example, 'there is an 80% chance that it will rain tomorrow' is a 'probable opinion' in this narrower sense. This narrower sense is also found in the closely related word sambhava. (NKS p. 923) Annam Bhatta has pointed out that in a doubt opposed characters become the qualifiers with reference to one and same qualificand. (TS p. 347) For example, 'is sound eternal or non-eternal?' is a doubt: being eternal and being non-eternal are contradictory and they are qualifiers of the same qualificand, viz., sound. Similarly, 'is this a man or a statue?' is a doubt: being a man and being a statue are contrary characters and qualifiers of the same subject, viz., this. However, 'is the soul eternal but cognition non-eternal?' is not a doubt; although two contradictory characters are the qualifiers, they are not qualifiers of the same

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qualificand, but of two different qualificands, viz., the soul and cognition. Similarly, 'is the soul eternal or ubiquitous?' is not a doubt; although two different characters are the qualifiers of the same qualificand, the characters are not opposed. Again 'is there contact with a monkey and absence of contact with a monkey in this tree?' is not a doubt. Contact (samyoga) is not a pervasive relation; hence there may be both contact with a monkey and absence of contact with a monkey in the different parts of the same tree at the same time. According to Gotama, doubt is indecision (vimarsa) waiting for (apeksa) a discriminating factor (visesa) [i.e., a factor which would favor one alternative and exclude others] and is due to the cognition of various common (samana) features, or opposed (viruddha) features, or due to the lack of uniformity (avyavastha) of apprehension (upalabdhi)/nonapprehension (anupalabdhi). (NS 1.1.23) This gives the essential information about doubt in a nut shell. Doubt involves a state of indecision between two or more alternatives and one would be motivated to find something which is compatible with only one alternative and incompatible with the rest, so that the doubt may be resolved. For example, the doubt as to whether the thing in front is a man or a statue is resolved if the thing is noticed to move. Here the movement is a discriminating factor (visesa), for it is compatible with only one alternative and incompatible with the other. Why are we in doubt? One reason is that only common features may be noticed. For example, one may notice only those features which are common to both a man and a statue in the thing in front, such as similar height and width. (NSB p. 25) Another reason is that one may be confronted by conflicting opinions, such as that the soul is eternal and that the soul is non-eternal. By conflict (vyaghata) is meant, as Vatsyayana explains, opposition (virodha) which, in its turn, means lack of belonging together (asahabh&va). (NSB p. 26) When opposed characters are ascribed to the same thing and no ground for settling one to the exclusion of the other is known (na ca anyatarasadhako hetuh upalabhate), there is indecision about what is the case and doubt (tatra tattva-anavadh&ranam samsaya iti). (NSB 26) Later Nyaya philosophers have added that there may be doubt when only what is unique (asSdh&rana) to the subject is known. For example, let it be supposed that all individual sounds and nothing else share a common universal property called sound-ness. Let it be supposed further that there are conflicting claims (1) that sound is eternal and (2) that sound is non-eternal, and nothing is known about sound which proves either to the exclusion of the other. In this situation, although sound may not be known to possess any features which are common (sQdh&rana) to eternal and non-eternal things, there may still be the doubt about whether

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sound is eternal or not, when it is merely known that sound possesses sound-ness (which is unique to sound and, therefore, missing from other things, eternal or non-eternal.) (BPP p. 524) Going back to Gotama, doubt also arises due to the lack of uniformity of apprehension or non-apprehension. What is meant, as Vatsyayana explains with examples, is that we apprehend both the existence of something somewhere (such as that there is water in a tank) and the non-existence of something somewhere (such as that there is no water in a lightning). Similarly, there is non-apprehension of both what is existent and what is non-existent. Hence there may be doubt as to whether what is apprehended is the existence of something or the nonexistence of something, also doubt as to whether what is not apprehended is existent or non-existent. Vatsyayana observes that of these factors involved in the analysis of doubt apprehension and non-apprehension belong to the knower (jndtrstha) and the common features, to the object known {jneyastha). (NSB p. 27) It appears from this brief and rather bald survey of the Nyaya account of doubt that these philosophers have focussed on three different kinds of factors. There are (1) logical factors highlighted by the relationship of opposition; (2) objective factors represented by the common and unique features and (3) subjective factors represented by the lack of uniformity of apprehension or non-apprehension. This throws light on probability for doubt and probability are invariably connected. When, for example, there is doubt whether the thing in front is a statue, it is neither certain that the thing is a statue nor certain that it is not a statue. In fact, if it were certain either that it is a statue or that it is not a statue, the doubt would not have been there. But as long as the doubt persists, there also remains the probability that the thing is a statue as also that it is not a statue. Although sambhdvand/sambhava/sambhdvyatd are the Sanskrit terms for probability, one must look at the analysis of the content-ness (visayata) of doubt for an understanding of the Nyaya view of probability. Now content-ness is a self-relation (svarupa-sambandha). The latter signifies a relation which is not ontologically distinct from the relata, but is reducible to them. (BPP p. 71) So probability may be viewed as a self-relation dependent on and reducible to all the three kinds of factors mentioned above, the logical, the objective and the subjective. (N 21) This in itself does not amount to endorsing the logical or objective or subjective theories of probability. The fuller implication will be explained below. But it may be noted here that the doctrine of selfrelation utilized to explicate probability is a useful methodological tool. This device has been used by Nyaya philosophers (from Udayana onwards) to build epistemic and semantic structures without adding to the ontological burden. It implies that some notions are better explained as

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the nesting or networking of certain entities without assigning a separate ontological slot to the nesting or the relationship itself and without precluding that some of these other entities could themselves turn out to be self-relations (and be subject to further reduction). Thus the main point of introducing the doctrine of self-relation in this context is to avoid reifying our talk about epistemic or semantic notions and promoting the possibility of reductive analysis. What the theory of probability has to gain from this will become clearer as we proceed. We should add that there is no text explicitly saying that probability is a self-relation (what we explicitly have is that the content-ness of doubt is a self-relation); but this is what one Nyaya position undoubtedly amounts to. What follows is somewhat speculative and reflects our perception of the relevance of the above thesis to the modern debate. The Nyaya would seem to both agree and disagree with de Finetti's slogan: probability does not exist. (N 22) What is implied by regarding probability as a self-relation is that it does not exist as an additional, separate entity over and above the others already recognized. But it does exist as a self-relation among certain logical, objective and subjective factors each of which may (or may not) have its distinctive place in the ontological scheme. It would seem that from the Nyaya point of view the modern debate over the logical, the objective and the subjective interpretations of probability is one-sided. Each side would seem to have seized upon one side of the issue and overemphasized it. A more balanced approach would seem to require paying attention to all the three sides and neglecting none. Thus the probability of rain tomorrow would depend on some objective factors, such as wind velocity and direction, cloud density and moisture, etc. It would also depend on some "logical" factors; for example, wind blowing from some direction may (or may not) be "opposed" to raining. [Modern taste would prefer exhibiting the logical relationship among sentences/statements/propositions. Nyaya logicians like to show logical relations not only among sentences, but also at the level of cognitive content-ness (visayatd) as well as at the objective level and have produced a highly sophisticated logical theory.] Further, the probability would depend on some subjective factors comprising our information or lack of information about the relevant variables and be relative to the given evidence. This precludes interpreting probability in exclusively logical, exclusively objective or exclusively subjective terms. One advantage of this more catholic approach to probability is that it avoids some of the seeming pitfalls of the more exclusive approaches. One criticism of the logical interpretation of probability (abbreviated as LIP) is that no merely logical division can determine the probability of one of the logically possible outcomes in the actual world—a point

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emphasized by the supporters of the objective interpretation of probability (abbreviated as OIP). But when probability is viewed as a self-relation (abbreviated as SRP), such a criticism does not arise; for probability is expressly made to depend on conditions in the real world. For the same reason SRP avoids a common objection to the subjective interpretation of probability (abbreviated as SIP) that probabilities do not depend merely on degrees of belief and that certain odds are real and hold no matter what someone believes. In other words, since SRP does take the objective features into account, probability can no longer be labelled as 'subjective' in a pejorative sense. One can still say that there are certain facts of the matter that scientific opinions seek to approximate. At the same time SRP is not open to some of the objections facing OIP. Thus one criticism of the frequency theory is that frequency probabilities cannot be known. The point of the objection is easily seen in the following scenario. Let us suppose that 10,000 cows have been examined of which 1,000 have been found to be black. Then the probability that a cow will be black may be determined as .10. But now suppose that later on we observe some new cows in previously unknown places where the relative frequency of black cows is .20. If this trend persists and we complete 10,000 more observations of such new cases, we would have to say that the relative frequency of black cows in the entire observation is .15. It can be seen that under these circumstances the relative frequency cannot be determined in purely objective terms as long as the possibility of future observations and unexpected variations remains open ended. But this difficulty does not plague SRP, for the latter does take subjective factors into account and allow probability to be relative to given evidence. The recognition of subjective factors in this way, however, does not reduce SRP to a merely subjective interpretation. The objective properties of individuals and of collections of individuals, too, are given due recognition and probability made to depend on them. It seems then that SRP avoids some of the weak points of LIP, OIP and SIP. SRP, however, retains some of the strong points of each of these theories. Thus one virtue of LIP is that it seems to cover every kind of probability and explain the full range of its meaning. This is true of SRP as well. The latter recognizes that probability depends on a wide spectrum of factors: this broad-based approach would allow SRP to address various kinds of probability. Again, OIP is attractive to some empiricists, for it locates probabilities in the objects themselves. This applies to SRP also. The latter, too, makes probability (partially) depend on objective features and recognizes the value of observation in discovering probability. Finally, one good point of SIP is that it permits us to speak of the probability of unique/individual events with greater ease than does, say, the frequency theory. So far as SRP is concerned, it too

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takes subjective factors into account and can begin assigning probability to an event if someone has an opinion on the matter. Needless to say, SRP does not make probability appear to be as objective as 01P does or as subjective as SIP does (and does not render probability a priori as LIP does). But if it did so, it would have been open to the very objections facing each of them respectively. It may be added as a historical comment that in Europe the science of probability did not emerge until the late seventeenth century. The neglect of probability may be due to the pervasive domination of the high road of rationalism prescribing a necessitarian view of nature and the sharp contrast between knowledge and opinion on the one hand and cause and sign on the other. But the rise of modern science finally showed that the so called necessary causes were nowhere to be found in nature. This together with the rise of statistics, the availability of vast quantities of statistical data and philosophical criticism such as that of Hume made the need for the systematic study of probability apparent. (N 23) In India where cultural forces were not the same, the story may be somewhat different. Since gambling was a popular kingly sport and sometimes played a role in deciding royal fortunes, the need for learning to play the percentage was felt early. In the great epic Mahabharata we find Yudhisthira who had a passion for but little understanding of gambling, losing disastrously to Sakuni, the skillful master. In the same epic, in the well known Nala story, we find Rtuparna claiming to be able to estimate the number of leaves and fruits from survey sampling. (N 24) A specimen of what is called a 'Dutch book' is found in the work of the late ninth century mathematician Mahaviracarya. (N 25) All this points to a greater awareness of the need and use of investigation of probability from ancient times.

NOTES

1. 2. 3.

R. Carnap, LFP; R. Carnap, The Continuum of Inductive Methods, University of Chicago Press, Chicago, 1952. L. J. Cohen, An Introduction to the Philosophy of Induction and Probability, Clarendon Press, Oxford, 1989, pp. 121-3. Jaakko Hintikka, inspired by Carnap's ideas, formulated a method for calculating the measures of the range of a universal proposition

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Induction and Probability without making it dependent on the number of individuals in the domain. This avoided the assignment of zero confirmation values to universal statements. (J. Hintikka, "A Two-Dimensional Continuum of Inductive Methods", in Aspects of Inductive Logic, Hintikka, Suppes (eds), Amsterdam, 1966; J. Hintikka, "Towards a Theory of Inductive Generalization", in Logic, Methodology and Philosophy of Science, II, J. Bar-Hillel (ed), Amsterdam, 1964) But many difficulties of the Hintikka-type modification of Carnap's system have been pointed out. See Halina Mortimer, The Logic of Induction, Ellis Horwood, Chichester, England, 1988, pp. 61-71.

4.

5.

6. 7. 8. 9.

10.

11. 12. 13. 14.

F. P. Ramsey, The Foundations of Mathematics, Routledge and Kegan Paul, 1931, pp. 156-98; B. de Finetti, "Foresight: Its Logical Laws, Its Subjective Sources", (1937) in H. E. Kyburg and H. E. Smokier (eds), Studies in Subjective Probability, John Wiley and Sons, New York, 1964, pp. 99-158; L. J. Savage, The Foundations of Statistics, Dover, New York, 1972; R. C. Jeffrey, The Logic of Decision, McGraw-Hill, New York, 1965. P. Suppes, "A Bayesian Approach to the Paradox of the Ravens" in J. Hintikka and P. Suppes, eds., Aspects of Inductive Logic, North-Holland, Amsterdam, 1966, p. 204; quoted in John Earman, Bayes or Bust?, MIT Press, Cambridge, Mass, 1991, p. 142. I. Levi, Gambling with Truth, Knopf, New York, 1967, p. 123. I. Levi, Ibid., p. 124. H. E. Kyburg, Jr., Probability and the Logic of Rational Belief, Wesleyan University Press, Middletown, Conn, 1961. Various revisions and improvements of the subjective viewpoint have been suggested by L. Savage and R. Jeffrey. These modified versions, too, have been shown to open to many difficulties. See H. Mortimer, The Logic of Induction, op. cit., pp. 83-9. M. Hesse, "Bayesian Methods and the Initial Probability of Theories" in G. Maxwell and R. M. Anderson, eds., Induction, Probability, and Confirmation, Minnesota Studies in the Philosophy of Science, vol. 6, University of Minnesota Press, Minneapolis, 1975, p. 78. John Earman, Bayes or Bust?, op. cit., p. 149. Ibid., pp. 215-18. K. R. Popper, "The Propensity Interpretation of Probability", British Journal of the Philosophy of Science, 10, 1959-60. R. von Mises, Probability, Statistics and Truth, 2nd edn., Dover, New York, 1957; H. Reichenbach, The Theory of Probability, Berkeley and Los Angeles, 1949.

Induction and Probability 15.

16.

17.

18. 19. 20. 21. 22.

23. 24.

25.

179

K. R. Popper, Realism and the Aim of Science, Hutchinson, London, 1983, p. 360; quoted in L. J. Cohen, An Introduction to the Philosophy of Induction and Probability, op. cit., p. 54. R. von Mises, Probability, Statistics and Truth, op. cit., p. 14; quoted in R. Weatherford, Philosophical Foundations of Probability Theory, Routledge and Kegan Paul, London, 1982, p. 183. P. S. de Laplace, A Philosophical Essay on Probability, Dover, New York, 1951, pp. 6-7; quoted in R. Weatherford, op. cit., p. 26. Henry Kyburg, Jr., Probability and Inductive Reasoning, London, 1970, p. 33. Ibid., p. 40. Saddarsanasamuccayatika of Gunaratna, Asiatic Society, Calcutta, p. 55. In some cases the Nyaya philosophers favor reducing a self-relation to one of the relata. B. de Fi netti, Theory of Probability: A Critical Introductory Treatment, vol. 1, trans. Antonio Machi and Adrian Smith, John Wiley, New York, 1974, p. x; emphasis in the original. Ian Hacking, The Taming of Chance, Cambridge University Press, Cambridge, 1990. Mahabharata, ed. S. Majumdar, Dev Sahitya Kutir, Calcutta, 1985, p. 325, 346, 427; cited in Ian Hacking, The Emergence of Probability, Cambridge University Press, Cambridge, 1975, pp. 78. The Ganita-sara-samgraha of Mahaviracarya, with English translation and notes by M. Rangacarya, Madras, 1912, p. x; cited in Ian Hacking, Ibid., p. 8.

CHAPTER ELEVEN LATER NYAYA VIEW OF INDUCTION AND INFERENCE FROM SIGN

Induction raises some of the most difficult and most debated problems of contemporary philosophy. The Carvaka-Humean problem of induction is not satisfactorily resolved in the light of the different Indian and Western views discussed earlier, as we have seen. We have also seen in an earlier chapter how some early Nyaya philosophers wrestled with the sceptical attack on induction and inference from sign. The controversy over this age old epistemological problem continued unabated and subsequent Nyaya philosophers addressed the issue with fresh innovativeness, subtlity and depth. We shall not try to summarize all or even most of the diverse viewpoints utilizing highly sophisticated and hairsplitting distinctions that emerged in this process. Rather we shall briefly explain some main arguments developed by the later Nyaya philosophers. We first quote a passage from the Tattvacintamani (abbreviated as TQ of Gangesa. [Gangesa (13th century) is eulogized by modern scholars as the founder of Navya Nyaya or New Nyaya. The commentarial and super-commentarial literature on TC includes a number of outstanding works, such as Raghunatha's Didhiti (15th century) and runs into thousands of pages.] The removal of that [the apprehension of deviation] is sometimes through the subjunctive reasoning (tarka) countering the opposite thesis and sometimes comes of itself (svatah siddhah). Should there be an infinite regress because the subjunctive reasoning is based on pervasion? No. The subjunctive reasoning is resorted to upto the point there is apprehension [of deviation]. Where the apprehension does not arise at all because of conflict, there pervasion is known without the subjunctive reasoning. Thus: if smoke were produced neither by the aggregate excluding fire nor by the aggregate including fire, it would not have come into being. Here there may be deliberation

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as to: Could it be that smoke always comes into being without fire or sometimes comes into being without fire as well or comes into being without a cause? If one is apprehensive that the effect could come into being without the cause with which there is known agreement in presence and absence, why should that very person regularly procure fire for smoke, food for nourishment or words for communication with others? For, after all, that [the effect] could come into being without that. Therefore, the procurement of those itself is the obstruction to that kind of apprehension. (TC pp. 187-94) There are three main points in this passage. (1) The sceptical doubt about induction may be countered by a subjunctive reasoning: a sample is included. (2) The subjunctive reasoning leads onto a follow up argument from belief-behavior conflict. (3) Since the conflict obstructs the sceptical doubt, no additional reasoning is called for when the doubt is removed and there is no infinite regress. We first take up (what for the lack of anything better we have translated as subjunctive reasoning) tarka or uha. The same names, it may be remembered, are given by the Jaina philosophers to a kind of hypothetical reasoning. In the Jaina version the reasoning uses hypothetical propositions with a true antecedent and a true consequent. The hypothetical forms are 'if this, then that' and 'if not that, then not this', where 'this' signifies the pervaded or the probans (vypdta: hetu) and 'that', the pervader or the probandum (vyapaka: sOdhya)\ 'this' and 'that' are replaceable by truth-preserving non-empty names like 'smoke' and 'fire' to generate true conditionals. But in the Nyaya version tarka or Qha stands for a reasoning with a counter-factual hypothetical proposition which is known to have a false (ayathartha) antecedent and a false consequent. The Nyaya philosophers operate with an internal realistic, utility-linked version of correspondence to give an account of truth (ydthdrthya). (N 1) However, they explicitly label the counterfactual proposition as false while granting that it is subservient or conducive (sahOyaka, anugr&haka, upayogin, prayojaka) to truth. (N 2) In the TS tarka is explained as "the factitous supposition (aropa) of the pervader due to the factitious supposition of the pervaded." (p. 351) Thus in a subjunctive reasoning both the antecedent and the consequent of the conditional premise are willfully made false assumptions. Further the assumptions must have an important relationship. The antecedent must be the assumption of the pervaded and the consequent, that of the prevader, so that one can make the counter-factual claim that if the antecedent were true, so would be the consequent. In other words, the conditional premise is such that it can reasonably be ruled out from what

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we know that the antecedent is true, but the consequent, false. [The explicit labelling of this conditional premise as false shows that the Nyaya logicians are not using material implication. If this were a material implication, the conditional would have been true.] As an example, the TS cites the proposition 'if there were no fire, there would be no smoke.' (p. 351) This may refer to the particular inferential situation where it is known that smoke and (therefore) fire are present. Then it would amount to saying that if there were no fire in a given location, there would be no smoke in that location. Alternatively, the conditional may refer to the imagined absence of all fires and all smokes in the universe. On either construal both the antecedent and the consequent are taken to be false. The antecedent contains the absence of fire which is the pervaded and the consequent, the absence of smoke which is the pervader; that is, it is known in each observed case that where there is absence of fire, there is absence of smoke. Since the premise is about the presence of the pervader on the condition of the presence of the pervaded, that the antecedent is true and the consequent is false is ruled out. This is important. Although the conditional is labelled as false, it is still subservient or conducive to truth. If it were a conditional with a true antecedent and a false consequent, its status would have been different. Since, however, both the antecedent and the consequent are taken to be false, each is described as a factitious supposition (