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Introduction

The study of human reasoning and the study of human language have been closely connected in European philosophical thought reaching all the way back to Aristotle (384–322 BCE ). Except for the Buddhist thinker Dign ā ga (fi fth century CE ), these two areas of study have not been connected in classical India. However, the connection which Dign ā ga made between inference ( anumā na ) and meaning ( artha ) in his theory of exclusion ( apoha ) is a distinguishing feature of Buddhist philosophical thought in classical India and, for that reason, it is useful to treat the Indian Buddhist views of reasoning and meaning together. Yet, before we turn to Indian Buddhist refl ections on these two topics, let us fi rst bear in mind some very general things about language and reason.

Humans use language. Humans also reason: that is, taking some things to be true, humans conclude that other things are true. Now, the fact that a human uses a lan-guage does not mean that the person using the language can formulate the rules whereby its acceptable expressions are distinguished from its unacceptable ones. Simi-larly, the fact that a human reasons does not mean that the person reasoning can formulate the rules whereby good reasoning is to be distinguished from bad. Clearly, then, just as the fact that humans use language is no guarantee that those who do so refl ect on which expressions are acceptable and which are not, so also the fact that humans reason is no guarantee that those who do so refl ect on which reasoning is good and which is bad. Thus, just as the activity of using a language and the activity of refl ecting on a language are distinct, so the activity of reasoning and the activity of refl ecting on reasoning are distinct. And thus, too, just as the formulation of the grammar of a language results from refl ection on the use of language, so the formula-tion of the rules of reasoning results from refl ection on the use of reason.

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Language and Logic in Indian Buddhist Thought

BRENDAN S. GILLON

C. Language and Logic

A Companion to Buddhist Philosophy, First Edition. Edited by Steven M. Emmanuel.© 2013 John Wiley & Sons, Inc. Published 2013 by John Wiley & Sons, Inc.

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Not every classical civilization tried to formulate rules to identify which expressions are part of the civilization ’ s classical language and which are not. The classical Greek and Indian civilizations did, however. The earliest extant grammar to give the rules of Greek is the Techn ē grammatik ē of Dionysius Thrax (c. 100 BCE ), while the earliest extant grammar to give the rules of Sanskrit is the Aṣṭā dhy ā y ī (“Eight Chapters”) of P āṇ ini, the great Sanskrit grammarian of early classical India (c. sixth–fi fth century BCE ). Nor did every classical civilization try to formulate rules whereby to distinguish good from bad reasoning. But, again, the classical Greek and Indian civilizations did. The earliest known formulation of rules of reasoning in classical Europe is that due to Aristotle; the earliest known formulation of rules of reasoning in classical India is not clear, but works attempting to do so date from at least the beginning of the common era.

Logic, at least as traditionally conceived, seeks to distinguish good reasoning from bad. More particularly, it seeks to identify the general conditions under which what one concludes is true, having taken other things to be true. This raises the questions of what it is which is true and what it is which is false. In contemporary philosophy, truth and falsity are usually taken to apply to linguistic expressions, declarative sentences, for example. But they can also be taken to apply to cognitive entities, such as thoughts or beliefs. Indeed, Aristotle ( De Interpretatione , ch. 1) took truth and falsity to apply prima-rily to thoughts or beliefs and, by extension, to the sentences expressing thoughts or beliefs. After all, one can use a sentence to express a thought. If a thought is true and a sentence accurately expresses it, then the sentence expressing the thought is true.

This, in turn, suggests that reasoning can be seen as a sequence of thoughts, wherein, taking some thoughts to be true, one concludes that some other thought is true. Let us call such sequences of thoughts inferences. At the same time, Aristotle ’ s observation suggests equally that reasoning can be seen as a sequence of sentences, where, taking some sentences to be true, one concludes that some other sentence is true. Let us call such sequences of sentences arguments. In this way, inference and argument are but two sides of the same coin: an argument can be thought, and hence become an inference; an inference can be expressed, and hence become an argument.

In addition to seeing reasoning cognitively and linguistically, one can view it sym-bolically, as contemporary logic does. Contemporary logic formulates rules whereby, when certain strings of symbols in a notation are taken to be true, another string of symbols in that notation is also taken to be true. The inspiration is clearly linguistic, for it seeks to put into a notation what is expressed in language, namely to specify that a sentence is true, if certain other sentences are true.

We see, then, that there are three perspectives on reasoning: the symbolic, the lin-guistic, and the cognitive. These perspectives differ according to what each takes the locus of truth to be: a thought, a sentence, or a string of symbols in a notation. However, they all share the idea of characterizing reasoning as, when some things are true, something else is true.

The linguistic perspective on reasoning suggests still a fourth perspective. A shared language makes it possible for one person to communicate his or her thoughts to anyone else who speaks the same language. More specifi cally, a shared language makes it possible to formulate arguments to communicate inferences. Indeed, humans often do so with the express aim of persuading other humans that something is true. Thus,

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reasoning, insofar as it is formulated as an argument, can also be viewed as a sequence of sentences where, accepting some sentences as true, one should accept another as true. Such is the dialectical perspective on reasoning.

Finally, there is the ontic perspective on reasoning. While, in one sense of the word “express,” sentences may express one ’ s thoughts, in another sense, sentences express the state of affairs which the corresponding thought takes to be its object. Thus, instead of asking, under what circumstances do certain thoughts being true require another thought to be true, one can ask under what circumstances do certain states of affairs, the ones corresponding to the true thoughts, require other states of affairs, the ones corresponding to the other true thought.

While we fi nd in Aristotle all fi ve perspectives, in classical India we fi nd only the ontic, the epistemic, and the dialectic, and neither the linguistic nor the symbolic.

It is perhaps useful to illustrate the distinction between a linguistic approach and an ontic approach to logic with examples of how Aristotle, on the one hand, and various classical Indian thinkers, on the other, formulated the three laws of logic: the law of non-contradiction, the law of excluded middle, and the law of double negation. Let us begin with the law of non-contradiction. Here is an example of Aristotle ’ s ontic formu-lation: “that a thing cannot at the same time be and not be” ( Metaphysics , bk 3, ch. 2, 996b29–30). However, he also provides linguistic formulations, as exemplifi ed by the following: “Contradictory statements are not at the same time true” ( Metaphysics , bk. 4, ch. 6, 1011b13). Classical Indian thinkers, too, formulated the law of non-contra-diction, but its formulation is always ontic. Thus, for example, the Buddhist philosopher Ā ryadeva (third century CE ) asks the rhetorical question: “Moreover, how can one property be existent and also non-existent?” (Tucci 1929 , 51, l. 7).

The law of excluded middle is formulated ontically by the classical Indian philoso-pher and grammarian Bhart ṛ hari (sixth century CE ), who says in his work the Vā kya-padī ya (“On Sentences and Words”) (bk 3, ch. 9, verse 85): “A thing is either existent or non-existent. There is no third.” In contrast, the formulations by Aristotle tend to be linguistic: “One side of the contradiction must be true. Again, if it is necessary with regard to everything either to assert or to deny it, it is impossible that both should be false” ( Metaphysics , bk. 4, ch. 8, 1012b10–12).

And, fi nally, the classical Indian thinkers also formulated the law of double negation ontically. This is how the Buddhist philosopher Dharmak ī rti (seventh century CE ) puts it in his Pram āṇ a-v ā rttika (“Gloss on the Means of Epistemic Cognition”): “What other than affi rmation is the negation of a negation?” (ch. 4, verse 221).

Logic in Indian Buddhism

Logic, as said above, seeks to distinguish good reasoning from bad. Since reasoning is often communicated and, to that extent, expressed in a language, it is natural to use the forms of language to identify the forms of reasoning. Aristotle, for example, devoted much effort to the analysis of language with a view to identifying forms of argument known as syllogisms and to distinguish among them those whose forms preserve truth and those which do not. Classical Indian thinkers were also sensitive to the fact that some forms of language give expression to good arguments and others to bad, though,

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unlike Aristotle, they never availed themselves of variables to describe the forms of the arguments which were their object of study. Their sensitivity is well illustrated by the arguments recorded in a Buddhist work of the third century BCE , Moggaliputta Tissa ’ s Kath ā -vatthu (“Points of Controversy”). This work contains the refutation by Sthavirav ā dins, one of the Buddhist schools, of some two hundred propositions held by other schools of Buddhism. The refutation of a proposition turns on demonstrating its inconsistency. In the passage below, for example, the Sthavirav ā din questions his opponent, a Pudgalav ā din, about whether or not the soul is known truly and ultimately.

S THAVIRAV Ā DIN : Is the soul known truly and ultimately? P UDGALAV Ā DIN : Yes. S THAVIRAV Ā DIN : Is the soul known truly and ultimately just like any ultimate fact? P UDGALAV Ā DIN : No. S THAVIRAV Ā DIN : Acknowledge your refutation. If the soul is known truly and ultimately, then indeed, good sir, you

should also say that the soul is known truly and ultimately just like any ultimate fact.

What you say here is wrong: namely, that we ought to say (a) that the soul is known truly and ultimately; but we ought not to say (b) that the soul is known truly and ultimately just like any ultimate fact.

If the latter statement (b) cannot be admitted, then indeed the former statement (a) should not be admitted.

It is wrong to affi rm the former statement (a) and to deny the latter (b).

One easily abstracts from this the following form, which is repeatedly instantiated throughout Book 1, Chapter 1:

S THAVIRAV Ā DIN : Is A B? P UDGALAV Ā DIN : Yes. S THAVIRAV Ā DIN : Is C D? P UDGALAV Ā DIN : No. S THAVIRAV Ā DIN : Acknowledge your refutation. If A is B, then C is D. What you say here is wrong: namely, (a) that A is B but that C is not D. If C is not D, then A is not B. It is wrong that A is B and C is not D.

Clearly, the author takes for granted the following: fi rst, that the propositions assented to are inconsistent, satisfying the following inconsistent propositional schemata of α , ¬ β , α → β ; second, that it is wrong to hold inconsistent propositions; and, third, that if α → β , then ¬ β → ¬ α – that is, half of the equivalence of the principle of contraposition.

Over the following 500 years, Buddhist, Jain, and Brahmanical thinkers explicitly addressed the problem of distinguishing good arguments from bad. The earliest exam-

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ples of arguments which are precursors to the canonical classical Indian syllogism are found in a commentary to a Brahmanical treatise on rational inquiry. The treatise, attributed to Gautama, who is also known as Ak ṣ ap ā da (c. second century CE ), is enti-tled the Nyā ya-s ū tra (“Aphorisms on Logic”); the commentary, written by V ā tsy ā yana (fi fth century CE ), also known as Pak ṣ alisv ā min, is entitled the Nyā ya-bh āṣ ya (“Com-mentary on Logic”). Here is one of the arguments found in the commentary:

P ROPOSITION ( pratijñ ā ): sound is non-eternal G ROUND ( hetu ): because of having the property of arising C ORROBORATION ( udā hara ṇ a ): a substance, such as a pot, having the property of

arising, is non-eternal A PPLICATION ( upanaya ): and, likewise, sound has the property of arising C ONCLUSION ( nigamana ): therefore, sound is non-eternal because of having the

property of arising

This argument has the following form:

P ROPOSITION ( pratijñ ā ): p has S G ROUND ( hetu ): p has H C ORROBORATION ( udā hara ṇ a ): d has H and d has S A PPLICATION ( upanaya ): As d has H and has S, so p has H and has S C ONCLUSION ( nigamana ): p has S

Many other examples of arguments with essentially the same form are found in the commentary.

As noted by Randle ( 1930 , ch. 3, sec. 4), the argument is clearly an argument from analogy. However, there soon emerged an argument of a similar form, which we would classify as a deductively valid argument. The earliest extant works which attempt to specify a related deductively valid argument are those of the Buddhist phi-losopher Vasubandhu (fi fth century CE ). Vasubandhu is thought to have written three works on logic, only two of which have survived and neither of them in their original Sanskrit. One is the Vā da-vidhi (“Rules of Debate”), extant only in Tibetan fragments, which were collected by Frauwallner ( 1957 ) and translated into English by Anacker ( 1984 , ch. 3). Another is extant only in Chinese. This text, whose title in Chinese is Rú shí lùn (“Treatise on Truth”), is best known under the Sanskrit title Tarka- śā stra(“Treatise on Reasoning”) given to it by Tucci ( 1929 ), who translated the Chinese translation back into Sanskrit. The third is the lost text entitled Vā da-vidh ā na (“Pre-cepts of Debate”).

In the Vā da-vidhi , Vasubandu identifi es the various parts of an argument as well as defi nes and illustrates the technical terms he uses. First, he identifi es the argument ’ s thesis ( pratijñ ā ), which comprises a term denoting the argument ’ s subject ( pakṣ a ) and a term denoting the property to be established ( sā dhya ) in the subject. He also identifi es the term for the ground ( hetu ), which, in the argument, is ascribed to its subject. He explains that the ground bears the relation of indispensability ( a-vinā -bh ā va , literally, not being without, or being sine qua non ) with respect to the property to be estab-lished. Finally, he identifi es a term denoting a corroborating instance ( dṛṣṭā nta ) which

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illustrates the indispensability relation borne by the ground to the property to be established.

From the illustrations of the various parts of an argument, one can glean the fol-lowing complete argument:

T HESIS ( pratijñ ā ): sound is non-eternal G ROUND ( hetu ): because of resulting from effort C ORROBORATION ( dṛṣṭā nta ): whatever results from effort is observed to be non-eternal,

like a pot

From this, one easily abstracts the following clearly valid form of argument:

T HESIS ( pratijñ ā ): p has S G ROUND ( hetu ): p has H C ORROBORATION ( dṛṣṭā nta ): whatever has H is observed to have S, like d

(where d is an instance of something recognized to have both H and S). In his Tarka- śā stra (T 1633, 30c, l. 20), Vasubandhu deploys an idea whose precise

origins are presently unknown but which proves to be central to all subsequent treat-ments of the classical Indian syllogism, the so-called tri-rū pa-hetu (three-formed ground) – that is, the three conditions of a ground ( hetu ). The fi rst condition is that the ground (hetu ), or H, should occur in the subject of an argument ( pakṣ a ), or p. The second is that the ground ( hetu ), or H, should occur in things similar to the subject ( pakṣ a ). And the third is that the ground ( hetu ), or H, should not occur in things dissimilar from the subject ( pakṣ a ) (Katsura 1986a , 165).

While these last two conditions are clearly intended to defi ne when the property to be established is indispensable for the ground, they are stated rather imprecisely. First, similarity and dissimilarity are stated with two relata, though these relations are not binary relations but, rather, ternary relations. After all, it is not contradictory for one thing to be both similar and dissimilar to another. Thus, for example, two things are similar insofar as both are leaves, yet they are dissimilar from one another insofar as one is an oak leaf and one is a maple leaf. Nothing in the statement of the three condi-tions specifi es in what respect things are to be similar to the subject of an argument and in what respect they are to be dissimilar. Second, it is made precise neither whether or not the ground occurs in some or all of the things which are similar to the subject of the argument, nor whether or not the ground does not occur in some or all of the things which are dissimilar to the subject of the argument.

Dign ā ga (c. fi fth–sixth century CE ), building on the insights of Vasubandhu, played a decisive role in the development of the canonical classical Indian syllogism (Steinkell-ner 1993 ). His ideas are set out in his three extant works, his magnum opus , the Pram āṇ a-samuccaya (“Compendium on Epistemic Cognition”), Hetu-cakra- ḍ amaru (“The Drum Wheel of Reason”) and Nyā ya-mukha (“Introduction to Logic”). Unfortunately, again, the original Sanskrit texts have been lost, all three texts surviving in Tibetan translation and the last alone surviving also in Chinese translation.

Dign ā ga ’ s fi rst contribution is to make explicit the intimate connection between inference and argument, calling the former inference for oneself ( sva-artha-anum ā na )

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and the latter inference for another ( para-artha-anum ā na ). Second, Dign ā ga addressed the shortcomings of the three conditions of a ground mentioned above. He made clear that things are similar or dissimilar to the subject of an argument with respect to the property to be established. In addition, he reformulated in a more rigorous way the three conditions of a ground ( tri-rū pa-hetu ), pressing into service the Sanskrit par-ticle eva (only) (Katsura 1986a , 163; 1986b , 6–10; see also Randle 1930 , 180–9) to ensure that it characterized more accurately the form of the syllogism.

Lastly, and most strikingly, Dign ā ga gave an alternative and an essentially equivalent characterization of the truth conditions of his syllogism, which he called the wheel of grounds ( hetu-cakra ). The so-called wheel of grounds is a three by three matrix, which distinguishes a proper from an improper ground, and is equivalent to the last two forms of the three conditions of a ground ( tri-rū pa-hetu ). It comprises, on the one hand, the three cases of the ground (H) occurring in some, none, or all of the property-possessors where the property to be established (S) occurs, and, on the other, three cases of the ground (H) occurring in some, none, or all of the property-possessors where the prop-erty to be established (S) does not occur. Letting S be the property-possessors in which S occurs and S ′ be the property-possessors in which S does not occur, one arrives at what is set out in table 19.1 .

Dign ā ga identifi ed the arguments corresponding to the top and bottom cases of the middle column as good arguments and those corresponding to the other cases as bad.

The view of Dign ā ga ’ s work as an attempt to identify a formally valid syllogism raises two questions. First, why did Dign ā ga hold that the major premise, or statement of corroboration ( dṛṣṭā nta ), must have associated with it an example, even though exam-ples are irrelevant to the validity of an argument? Second, why did Dign ā ga regard as a bad argument any argument corresponding to one whose major premise, or state-ment of corroboration ( dṛṣṭā nta ), corresponds to the middle case of the middle column, which is, in fact, a valid argument?

Some scholars think that these questions arise from a misunderstanding of what Dignā ga was striving to do. According to some, such as Oetke ( 1994, 1996 ), Dign ā ga and some of his predecessors and contemporaries were striving to spell out a defeasible form of argument (see Taber 2004 for a critical assessment of Oetke ’ s view). According to others, such as Hayes ( 1980; 1988 ch. 4.2), Dign ā ga was striving to work out not a deductively valid form of argument, but rather a good inductivist form of argument. A third view – my own – is that Dign ā ga was indeed trying to pin down what we today would call a deductively valid argument, but that he had not managed to disentangle fully the purely logical features of an argument from its dialectical features.

Table 19.1 Wheel of grounds

H occurs in: all S all S all Sall S ′ no S ′ some S ′

H occurs in: no S no S no Sall S ′ no S ′ some S ′

H occurs in: some S some S some Sall S ′ no S ′ some S ′

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However much scholars may disagree about Dign ā ga ’ s aim in the formulation of the syllogism, all agree that his works set the framework within which subsequent Bud-dhist thinkers addressed philosophical issues pertaining to inference and debate. Thus, Ś ankarasv ā min (c. sixth century CE ) wrote a brief manual on inference and argument for Buddhists called the Nyā ya-prave ś a (“Beginning Logic”), based directly on Dign ā ga ’ s work. Not long thereafter, Dharmak ī rti (c. seventh century CE ), the great Buddhist metaphysician, also elaborated his views on inference and debate within the framework found in Dign ā ga. At the same time, these same ideas came to be adopted by Jain and Brahmanical thinkers. Whether or not the ideas were arrived at independently or were borrowed from the Buddhists is not clear.

Of course, Buddhist, Jain, and Brahmanical thinkers had different views, both epis-temological and ontological, yet they all came to adopt the classical Indian syllogism and the specifi cation of its validity in terms of the three conditions of a ground. Part of the attraction is that the underlying concepts are easily construed in terms of com-mon-sense realism. Let us see how this is so.

The three terms used to specify the three parts of the three conditions on a ground – namely, “subject of an argument” (“ pakṣ a ”), “ground” (“ hetu ”), and “property to be established” (“ sā dhya ”) – draw on three basic kinds of entities: the relation of possession and its two relata of property ( dharma ) and property-possessor ( dharmin ). An argu-ment ’ s subject is a property-possessor, while the ground and what is to be established are properties. A converse equivalent of the possession relation is the relation of occur-rence: a property-possessor possesses a property just in case the property occurs in the property-possessor.

These entities are easily construed in terms of the common-sense ontology of Indian realists such as the Naiy ā yikas. According to their view, the world consists of individual substances, or things ( dravya ), universals ( sā m ā nya ), and relations between them. They thought that the relation of occurrence ( vṛ tti ) is of two kinds: contact (saṃ yoga ) and inherence ( samav ā ya ). So, for example, one individual substance, a pot, may occur on another, say the ground, by the relation of contact. In this case, the pot is the property and the ground is the property-possessor. Or, a universal, say treeness, may occur in an individual substance, say an individual tree, by the rela-tion of inherence. Here, treeness, the property, inheres in the individual tree, the property-possessor.

As we saw above, essential to the formulation of the three conditions of a ground are the relations of similarity and dissimilarity. Realists, such as the Naiy ā yikas, have a ready explanation of what these relations consist in. What accounts for two things being similar to each other in some respect is that they share an entity known as a universal ( sā m ā nya ). Thus, for example, two things which are both leaves share the universal of being a leaf and they thereby are similar to each other in that respect. If one is a maple leaf and the other an oak leaf, then they are also dissimilar to each other insofar as one has the universal of being a maple leaf and the other does not, while the other has the universal of being an oak leaf and the one does not.

However, Buddhists cannot appeal to universals as part of an account of similarity and dissimilarity, since universals are eternal and the Buddha taught that everything is impermanent. However, the Buddhists did not content themselves just with relying

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on scripture. Starting with the Abhidharmika thinkers, they formulated arguments to support this teaching of the Buddha. One argument has been succinctly stated by Mark Siderits as follows.

1 Only what is causally effi cacious is real. 2 To be causally effi cacious is to produce an effect at a particular time. 3 Something eternal would be unchanging. 4 There would be no reason for an unchanging thing to produce an effect at any one

time and not another. 5 Hence nothing eternal could be causally effi cacious. Therefore no existing things

are eternal. (Siderits 2007 , 214)

In addition, Dign ā ga himself formulated an argument to show that universals do not exist (see Hayes 1988 , ch. 5.2.3.). The argument is based on two principles: fi rst, that nothing can wholly exist in two places at once; and, second, that all entities are partless. Since all entities are partless, universals are partless. Since no entity can exist wholly in two places at once, no universal can. Yet, universals are entities which exist wholly in more than one location at a time. Furthermore, Dign ā ga argued that, even if universals exist, they are unknowable. To know a universal one must know all the things in which the universal has inhered. But there are many things outside of the ken of any person in which universals inhere. Therefore, any person of limited knowl-edge cannot know a universal.

So, if Dign ā ga could not draw upon universals to account for similarity and dissimi-larity, crucial to the formulation of the three conditions of a ground, how could he make sense of the second and third conditions of a ground ( hetu )? The answer is that Dignā ga drew upon the notion of exclusion ( apoha ). Unlike realists, such as the Naiyā yikas, who take the fundamental relation to be explained to be that of similarity and who then explain similarity as two things sharing a universal, Dign ā ga takes simi-larity and dissimilarity to be by-products of our use of words, and he seeks to explain how humans come to use words correctly through exclusion ( apoha ).

To appreciate better Dign ā ga ’ s appeal to exclusion in connection with the application of words to things, let us consider briefl y the background to the fundamen-tal linguistic issue, which has its origin, if not in grammatical thought preceding Pāṇ ini, then in his Aṣṭā dhy ā y ī . The basic idea underlying P āṇ ini ’ s grammar is this: each Sanskrit sentence can be analyzed into minimal constituents, and the sense of each minimal constituent contributes to the sense of the entire sentence. Thus, a grammar of a natural language should not only generate all and only its acceptable constituents, it should also make clear how the meanings of the constituents compris-ing a more complex constituent determine its meaning. In his Aṣṭā dhy ā y ī , the meanings associated with minimal constituents comprise, among other things, the constituents of situations, namely, actions ( kriyā ) and their participants ( kā raka ) (for details, see Gillon 2007 ).

Consider the sentence “Devadatta is milking a cow.” The activity is milking. This activity has two participants ( kā raka ): Devadatta and a cow. The question arises: how

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do the words get correlated with the individual Devadatta, the activity of milking, and the individual cow? In the case of proper nouns such as “Devadatta,” nothing much needs to be said: one simply has to associate, for each proper noun, the single thing to which it applies. However, in the case of a common noun, there is, in general, no single thing to which it applies, and hence there is, in general, no single thing with which to associate a common noun.

Let us consider an example of the contrast between proper nouns and common nouns. If one person points out Devadatta to a second and tells the second person that Devadatta ’ s name is “Devadatta,” the second person knows all he or she needs to know to apply Devadatta ’ s name correctly to him. No one who, having had Devadatta cor-rectly identifi ed and having been told that the name of that person is “Devadatta,” would apply that name to any stranger which he or she could clearly distinguish from Devadatta, nor would that same person withhold the application of the name “Devadatta” when presented with Devadatta and fully recognizing him as Devadatta. But this is not surprising; after all, what else does one need to know to apply the name correctly, once one knows to whom the name applies? In contrast, suppose that one person points out an animal to a second and says correctly to the second person that the animal pointed out is called a “gayal.” If all that the second person knows is that “gayal” applies to the object pointed out, he or she does not know enough to apply it correctly to other animals. After all, what prevents the second person from applying it incorrectly to a horse and what guarantees that the second person will not, incor-rectly, withhold applying it to a domesticated ox, indigenous to India. Clearly, unlike in the case of a proper noun, just knowing a single thing to which the common noun applies does not provide an adequate basis for its application ( prav ṛ tti-nimitta ) to things he or she may not have previously encountered.

The question arises: is there perhaps some other entity, different from things to which a common noun applies, which could provide a basis whereby one would be in a position to apply it to things other than the ones which have been identifi ed as those to which the common noun applies? For realists, universals provide a basis for the application of a common noun. Once one associates the single entity, a universal, with a common noun, then one has a basis for the application of the common noun: it applies to all and only those things which have the associated universal. But, as we saw, Dign ā ga rejected the existence of universals, and so he could not appeal to them to explain how one knows to apply a word to the things to which it applies. Instead, Dignā ga turned to exclusion ( apoha ). What one learns, according to Dign ā ga, is what a word does not apply to, and, through exclusion, one comes to use the word correctly.

It is easy to see that exclusion does not seem to bring us any closer to a satisfactory account of how one learns to apply a word to things. Just as we saw above, being told that a word applies to a thing provides no basis for its correct subsequent application, so too being told that a word does not apply to a thing provides no basis for what else not to apply it to subsequently. Thus, for example, just as when one person points out some animal to another person and tells the second person that the animal pointed out is called a “gayal,” the second person will have no idea of how to apply the word subsequently, so too should the fi rst person, in pointing out the animal to the second person, tell the second person that it is not called a “gayal,” the second person will have

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no idea of what else it might not apply to subsequently. Rather, just as one must associ-ate with the word “gayal” some characteristic whose possession is both a necessary and a suffi cient condition for the word ’ s application, so one must associate with the word “gayal” some characteristic whose failure to be possessed is both a necessary and a suffi cient condition for the word not to apply. But what characteristic is there which all things not called “gayal” fail to have in common? For the realist, all things which are not called “gayal” fail to have the universal of being a gayal in common. This answer, of course, is not available to Dign ā ga (for discussion, see Hayes 1988 , ch. 5; and Pind 2011 ).

Dign ā ga ’ s theory of exclusion was widely criticized. Non-Buddhist thinkers, most prominent among them the Naiy ā yika Uddyotakara (c. late sixth century CE ) and the Mī m āṃ s ā ka Kum ā rila Bha ṭṭ a (c. early seventh century CE ), and even some Buddhist thinkers, for example, Bh ā vaviveka (c. early sixth century CE ), raised many objections to the theory of exclusion, including ones similar to the one raised above. Uddyotakara and Kum ā rila Bha ṭṭ a, for example, both argued that the theory of exclusion is circular (for discussion, see Hugon 2011 ).

Dharmak ī rti, in his Pram āṇ a-v ā rttika ’ s fi rst chapter, Svā rtha-anum ā na (“Inference for Oneself ”), emended Dign ā ga ’ s exclusion theory to circumvent the criticisms it had encountered (for details, see Dunne 2011 ; Hugon 2011 ; and Tillemans 2011 ). The essence of his proposal is to shift question of the similarity of things to the similarity of the images to which they give rise (see Dunne 2011 ). But this merely shifts the problem of explaining similarity among things to explaining similarity among mental images.

The theory of exclusion ( apoha ) was a peculiarly Buddhist theory, and it remained central to Buddhist thought in India, so long as Buddhist thought survived on the subcontinent. Important contributors to the theory were Ś antarak ṣ ita (c. late eighth century CE ), Kamala śī la (c. late eighth century CE ), Kar ṇ akagomin (c. late tenth century CE ), Jñ ā na ś r ī mitra (c. eleventh century CE ), Ratnak ī rti (c. late eleventh century CE ), and Mokṣā karagupta (c. twelfth century CE ) (see Siderits 2007 , 35–7, for discussion of the views of Ś antarak ṣ ita and of Kamala śī la; see Patil 2011 for discussion of those of Jñā na ś r ī mitra and of Ratnak ī rti).

One other aspect of the relation of words to the things to which they apply should be mentioned. Buddhists maintain that there are only two means by which to learn about things in the world: perception ( pratyak ṣ a ) and inference ( anumā na ). Yet, Bud-dhists also recognize that one learns about the world from what one is told by others. It seems to have been Dign ā ga who fi rst suggested that what one learns about the world from others can be reduced to a form of inference. As part of this reduction, Dign ā ga maintained that words bear an inferential relationship to the things to which they apply. He seems to have been encouraged in this view by the following parallel. First, just as the ground should occur in the subject of an argument, so a word used in a discourse should apply to the subject of the discourse. Second, just as the ground should occur in things similar to the subject insofar as they have the property to be established, so the word must be applicable to objects similar to the subject of discourse. Third, just as the ground should not occur in things dissimilar from the subject, so the word must be restricted in application to that which is to be learned through it (for further details, see Hayes 1988 , ch. 5.2.5; and Pind 2011 ).

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Conclusion

We have seen that Buddhist thinkers played a central role in the development of logic in early classical India. In their earliest texts, there are copious examples of canonical forms of reasoning. Later, Buddhist thinkers helped to transform a canonical form of analogical reasoning into a form of deductive reasoning, not only settling the form of what became the canonical classical Indian syllogism but also setting out its truth conditions. In addition, driven by ontological concerns, Buddhist thinkers tried to develop a theory of meaning for words which eschewed universals by appealing to exclusion. Finally, eager to maintain that there are only two sources of knowledge, inference ( anumā na ) and perception ( pratyak ṣ a ), they sought to use the notion of exclu-sion to include knowledge of the meaning of words in inference.

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