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The Encyclopedia of Indian Philosophies v2.c15.s8: Logical Theory

The Encyclopedia of Indian Philosophies v2.c15.s8

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Contents

Logical Theory

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All systems of Indian philosophy except the Cārvākas accept inference as an instrument of valid knowledge. The science of reasoning (*nyāya*) is alluded to in very early Indian texts, and the name of the Nyāya school indicates that Indian intellectuals looked to this school as the authority in matters of detail connected with logic. Not that Naiyāyikas had a corner on the subject. Most of the other systems proposed theories in the area of logic and reasoning, and some (notably Sāmkhya) may well have antedated the Naiyāyikas on certain important points. In particular the logical theories of Buddhists of Dignāga’s school were viewed by the Naiyāyikas as rivaling their own in subtlety and importance.

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An extended history of Indian logic has yet to be written. Little is known of the beginnings of these reflections. Argument is indulged in in the earliest texts, the Vedas and Upanishads, and there are references in the Upanishads to a science of “dialogue,” though it is unclear what this consisted of. During the Buddha’s and Mahāvīra’s period, argumentation was enriched. The Buddha’s method of answering questions is noteworthy: asked whether a metaphysical proposition was true or not, he sometimes answered by denying that it was true, false, both, or neither; this method became the touchstone of Nāgārjuna’s Mādhyamika system. Mahāvīra developed a “logic of perhaps,” the so-called *syādvāda* or sevenfold predication, which made much of the different points of view from which propositions, might be taken to be true, false or possible. Some of the *suttas* of the Buddhist canon mention *tārkikas* or logicians, and a chapter of the Majjhimanikāya is called *anumānasutta*, the chapter on inference. Manu and the epics refer to logic and logicians, sometimes taking a dim view of their ways and warning the devout against them.

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The specific topic of the proper form of argument (somewhat misleadingly referred to as the theory of the “syllogism” by certain writers)

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can be traced back at least to the Jain writer Bhadrabāhu, who had a 10-membered argument.¹ His 10 members are different from another set which Vātsyāyana addresses himself to later on. By the time of Caraka (ca. A.D. 78), the writer on medicine, we have a 5 membered argument form. Caraka’s time closely approximates Kaṇāda’s and is not far before Gautama. There is also reason to believe that at this same period the Sāṃkhya philosophers knew and used a 5 membered argument form.²

I. The Terminology of Inference

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Before summarizing the logical theories of our writers it will be well to arm ourselves with appropriate terminology for describing those theories.

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As we have seen, *Nyāya* is used to suggest logical theory. A more specific term meaning “inference,” however, is *anumāna*, which is the name for the second of the 2 Vaiśeṣika, and 4 Nyāya, instruments of knowledge. Through inference we are able to gain knowledge about things not available at the moment to perception. For example, we can come to know the cause of an occurrence by inferring on the basis of observed lawful relationships even though we failed to observe the causing event; or we can know that a certain universal qualifies a given particular because it is pervaded by another which is seen to pervade that particular. These are two samples of what comes to be called “inference for oneself” (*svārthānumāna*). A different, but equally important, use of inference is to convince others of the truth of a judgment. This is called “inference for others” (*parārthānumāna*). The adumbration of theories about inference among the Nyāya-Vaiśeṣikas largely concerned this latter role of inference.

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According to our philosophers, all valid inferences-for-others can be analyzed in such a way that they can be perspicuously represented in an argument form which has 5 members and 5 terms. Each of these members has a Sanskrit name, as does each of the terms : I shall propose English equivalents for the names of the members, and abbreviations for the terms. It is easiest to grasp the roles of these members and terms by considering a stock Nyāya argument.

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(1) This mountain is fire-possessing.
(2) Because it is smoke-possessing.
(3) Whatever is smoke-possessing is fire-possessing like kitchen, unlike lake.
(4) This mountain, since it possesses smoke, possesses fire.
(5) This mountain is fire-possessing.

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In the Sanskrit terminology : (1) is called the *pratijñā*; it is what is put forward to be proved, and we may call it the “hypothesis”; (2) is called the *hetu* or “reason”; (3) is the *udāharaṇa* or “example” (actually it states the general principle which underlies thein ference as well as providing evidence in the form of examples which are intended to show not only that there are things which are both smoky and fiery but also that absence of smoke and of fire are concurrent); (4) the *upanaya* or “application,” as its name implies, applies the property whose presence is to be proved to the subject of the inference (this mountain); finally, (5) the *nigamana* or “conclusion” asserts the hypothesis as proved.

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The 5 terms are these. First, the subject of the inference, that whose property is proved, in the above argument *this mountain*, is called in Sanskrit the *pakṣa*, which we shall abbreviate as *p*. The property which is proved to qualify *p* is the *sādhya*, or *s*. In the above argument *s* is *fire-possessing*. The argument is that this mountain possesses fire because it is *smoke-possessing*, that is, because it is known to have another property which is related in an appropriate way to the *s*. This property is called *h*, the *hetu*. In the third member of the argument two kinds of examples are offered : one is positive, one negative. The positive example is called *sapakṣa*, *sp*, while the negative one is *vipakṣa*, *vp*. In the argument above, *kitchen* is the *sp* while *lake* is the *vp*.

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Note that though I have called these last 5 things the “terms” of an inference it should not be inferred that *p*, *s*, *h*, *sp* and *vp* are linguistic entities, words or phrases. They are, as the Naiyāyikas see it, things and properties. I have italicized them,r ather than writing them in quotes, in order to suggest this important point. One implication we should note immediately is that an argument is not well-formed unless all 5 terms are present (with certain exceptions mentioned below), and that it is not enough to merely mouth a word or phrase to make them present—they must in fact exist!

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Now a successful inference is one where there is the relation called “pervasion” (*vyāpti*) between *s*-ness and *h*-ness. In the illustration above, the validity of the argument as a whole depends fundamentally on the fact that *fire-possessingness* pervades *smoke-possessingness*. That pervasion is a relation among universals was emphasized quite early in the development of the system, although it is apparent that some of the early writers were unclear on the point.

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The topic of inference received early attention because by proper understanding of the nature of an argument one may hope to identify the conditions under which the truth can be ascertained. Historically, it would appear that the systematic theory of inference owed a great deal to attempts by early practitioners of debate to develop fool-proof methods for winning arguments, as well as providing judges with applicable procedures for telling a winner from a loser. A remarkable feature of the *Nyāyasūtras* is the extended attention that these debating categories receive in the last book of the work.

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In particular, the theory of debate has close connections with a topic at the heart of Nyāya discussions of inference, the topic of fallacies. Even by the close of our period, Naiyāyikas were just beginning to think carefully about positive formulations of the conditions sufficient and necessary to guarantee that pervasion is present, and the problem, which may be insoluble, is fundamental in much Navya-nyāya literature. Without the identification of positive conditions for pervasion, one is forced to rely on negative procedures, that is, one is forced to rely on the identification of fallacies in distinguishing apparent pervasion from the real thing. Thus it is that in the actual assessment of arguments for validity Naiyāyikas proceed by examining the arguments for fallacies, and as a result a clear and sweeping list of types of fallacy is a prime desideratum.

II. Nature and Function of Inference

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Kaṇāda and Gautama viewed inference primarily as a means by which we ascertain causal conditions, or sometimes the effects of known causes. Kaṇāda includes inference from contradictory qualities too. As we have seen, Naiyāyikas view inference as consisting of judgments whose referents are existing things, not, as we in the West are prone to do, as relating to words or concepts. Thus where we conceive of the validity of an inference as compatible with the failure of its members to refer or be true of anything, the Naiyāyika views nonreferential words as ill-formed and excludes them from any inference.

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This fact seems to me to show that Nyāya is not concerned with "formal" logic in the way that Western logicians have characteristically been. However, this does not contradict Bochenski's view that "in India too a formal logic developed. That it really was a formal logic is shown by the fact that the formulae constructed by the Indian thinkers concern the fundamental questions of logic, the question of 'what follows from what.' "3 Of course Indian logicians were interested in what follows from what. But their logic was not "formal" in a different sense : it did not have to do with abstract relations among terms, where the abstraction was from all questions of reference. A

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Western logician views the inference "all animals are pigs; all pigs have wings; therefore all animals have wings" as formally valid, though unsound. The unsoundness does not in his view, detract from the logical interest of the example as instantiating a valid form of inference. The Naiyāyika's view of this example is that it is a *nyāyābhāsa*, something which is only apparently an argument but really is not. It is, in short, ill-formed because its members are known to be false.

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As a result, a great deal of time has been wasted, it seems to me, by writers who attempt to compare the Nyāya 5-membered inference with the Aristotelian syllogism.⁴ A more fruitful comparison can perhaps be found with John Stuart Mill's canons of inductive reasoning.⁵ When the Nyāya method of assessing inferences in practice is carefully studied it becomes quite apparent that the assessment of "validity" is a matter, not of comparing the inference with abstract models to see if it instantiates one of the "valid forms of inference," but rather of trying to detect subtle errors in the adducing of evidence for the constituent judgments.

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It is a consequence of this view of inference as mainly inductive that the instrument of knowledge called "inference for oneself" is said by Gautama to "follow on perception." Inference is a distinct means of knowledge because it gives us knowledge about things we are not immediately acquainted with—but the things in question must be such that we could immediately be acquainted with them if the world, including ourselves, were different from what it is now. In particular, in inference for oneself we must actually perceive *h* and *p*, and we must have a memory of an observed concomitance between *s* and *h*—thus we must either be observing or have observed all 3 terms in the argument. If this condition is not satisfied we have the fallacy called "unproved terms" (*asiddha*). Uddyotakara, presumably following some earlier teacher(s)⁶ introduces the notion of *liṅgaparāmarśa* as a condition which must be satisfied in addition to the ones above: his idea is that the fourth member of the argument, the "application," reports the actual perception of the *s*-pervaded *h* as residing in *p*. Uddyotakara, in opposition to Buddhists, Mīmāṃsakas, Sāṃkhyas, and Vedāntists, argues vigorously that this synthetic condition is the proximate cause of a successful inference for oneself.

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But what of inference for others? Is not this, after all, formal? I use inference to convince you of something you do not know already; if you had perceived it, you would not need an argument. Thus inference for another cannot require that the hearers have perceived the terms and the pervasion and residence relations among them.

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Even here, however, the Naiyāyika characteristically requires perception on the part of the person one is trying to convince, an extraordinary (alaukika) kind of perception, to be sure. The argument's purpose is to get the hearer to see that *p* possesses *s*-pervaded *h*, from which he will be able to conclude the truth of "*p* is *s*."

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To return to the remark with which I began this section: Kaṇāda and Gautama viewed inference as primarily about causal relations. In the *Nyāyasūtras*, as well as in the writings of Hindu logicians of the same period representing other systems such as Sāṃkhya and Mīmāṃsā, one finds reference to a classification of inferences into 3 varieties: *pūrvavat*, *śeṣavat*, and *sāmānyatodṛṣṭa*. It is not clear what Gautama means by these 3 terms, and Vātsyāyana apparently did not understand them very well either, since he offers two distinct explanations of the *sūtras* in question. This has given rise to several historical reconstructions among modern scholars.⁷

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One of Vātsyāyana's interpretations makes Gautama to be distinguishing (a) inference from cause to effect (*pūrvavat*), as when we infer rain from clouds gathering; (b) inference from effect to cause (*śeṣavat*), as when we infer rain upstream from the swollen river downstream; (c) inference from general correlation (*sāmānyatodṛṣṭa*), which would cover correlations not involving the temporality of before and after. Thakur thinks Vātsyāyana's other interpretation indicates his acquaintance with Vaiśeṣika thought, since it runs along lines developed in e.g., Candramati.⁸ Candramati divides inferences into *dṛṣṭa* and *adṛṣṭa*. The former is inference based on perception of a property held in common between two things; the latter is inference based on our failure to perceive the properties of one thing in another. Praśastapāda actually uses the term *sāmānyatodṛṣṭa*, but gives it a complex meaning: it is inference which occurs when two things have different universals but because of general correlation we infer the property of one from the other.

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It is apparent from later writings that no one is very sure what Gautama's *sūtras* meant, and that one interpretation is as good as another, depending on one's theory. Uddyotakara has still another explanation. As he sees it, the threefold distinction being drawn may be construed as that between only-positive, only-negative, and positive-negative inferences. This distinction is an important one in the subsequent literature, as the others mentioned above are not, so let us turn to the last mentioned division and leave historical questions aside.

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The distinction between only-positive, only-negative, and positive-negative inferences is this. In the stock case about smoke and fire on the hill, set out above, it is possible to provide both positive examples (e.g., *kitchen*) and negative ones (e.g., *lake*). But Uddyotakara, criticizing Dignāga, holds that not all inferences are such that both sorts of examples can be given, and this not because of any defect in principle but because of the nature of what is the subject of the inference. Thus in the inference "this pot is nameable, because it is knowable," we cannot give a negative example, not because we are lazy, but because according to Nyāya assumptions everything whatever is both knowable and nameable. That is, knowable and nameable both have as their extension the universal class, if you will, and since a negative example has to be something which lacks both *s* and *h* it is evident that under these circumstances no such example can be provided. In such a case Uddyotakara says we have a case of only-positive (*kevalānvayin*). Likewise, in the inference "Sound is eternal, because it can be perceived by an external sense organ," if one (e.g., a Buddhist) believes that nothing is eternal one cannot in the nature of the case provide a positive example. This is, then, an "only-negative" (*kevalavyatirekin*) inference. The stock example of smoke and fire, where both examples are available, is "positive-negative" (*anvayavyatirekin*).

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Uddyotakara held that all three kinds of inference were such that valid instances of them can be cited, and this view has been characteristic of Naiyāyikas since, although there have been some deviations—e.g., Jayanta seems to have rejected only-positive inferences as not valid, and Udayana appears to have had misgivings about only-negative ones. Most Naiyāyikas in our period, however, allow both as valid in principle. Indeed, the Nyāya rejection of presumption (*arthāpatti*) as an independent instrument depends on their being able to classify presumptive arguments under only-negative type inference.

III. The Members of an Argument

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We have seen which the 5 members of a full-scale inference for others are as illustrated in the stock case of the claim that the hill is fiery because it is smoky. But (1) why are these just the members? Could not an argument be successfully couched in less? Or on the other hand, are not there additional members which have been overlooked? (2) What are the peculiar functions of each of the 5 members? And in particular, why do we need 2 members—the hypothesis and the conclusion—which apparently are identical in form and content?

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First, why 5 members and not fewer? In arguments which actually appear in the course of philosophical polemics the characteristic form of an argument is briefer. It tends to be stated something as follows: "that hill has fire, because it has smoke, like a kitchen and unlike lake." This short-form argument sets out all 5 terms in their appropriate places. Why is it not sufficient, and why should we not reject the additional material in the 5 membered Nyāya argument as redundant or dispensable? Mīmāṃsakas, Advaitins, and Buddhists all consider the Nyāya argument unnecessarily prolix.

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Our philosophers labor to make a case for each of the 5 members. For example Vātsyāyana seems to have thought that in a full-scale argument all 4 of the valid instruments of knowledge come into play, and that each of the first 4 members of the argument form represent an instrument, the conclusion stating the judgment as proved by all 4 instruments in tandem. So he identifies the hypothesis as given to us through verbal testimony, the reason as being inference proper (the second of the 4 instruments), the example indicating the perceptual material, and the application representing the use of comparison.⁹ I think it is safe to say that this account is pretty well ignored by later writers.

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What is more plausible is that the difference between the first and last members, and also between the second and fourth members, is the difference between what Ingalls calls "ascripts" and "assertions."¹⁰ The hypothesis ascribes *s* to *p*, whereas the conclusion asserts that *p* has *s*. The reason ascribes *h* to *p*, whereas the application asserts that *p* has *s-pervaded h*. This distinction Ingalls traces back to Vātsyāyana. It appears to be appealed to by Praśastapāda in distinguishing the hypothesis from the conclusion.

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This is not quite the same as saying that the difference between the first two and the last two members is that the former merely mention their terms whereas the latter assert something about them. Śrīdhara seems to have something of this sort in mind when he says that in the reason the *h* is merely mentioned but it is not stated there that it is a property of *p*. Randle takes Śrīdhara to task here; clearly the reason does more than merely mention *h*—"that mountain has fire, because smokepossessing" makes no sense unless it is implicit that it is that mountain which possesses the smoke.¹¹

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A different sort of reason why the hypothesis must be differentiated from the conclusion stems from the fact that among the faults which may vitiate an inference many Naiyāyikas include cases where only *s* and *p* are involved. It is sometimes taken to be a fault in one's argument if the proposition one is trying to prove is contradicted by perception. If one can see all the mountain and can see that there is no fire on it, it is a mistake to argue that it possesses fire. Or again, if one is trying to prove the truth of "my mother is barren" one is wasting one's time; but the reason one is wasting one's time has nothing to do with anything other than the contradiction between being a mother and being barren. Now since these faults cannot be classified as fallacies of the *h*, the *sp* or the *vp*, and since the conclusion asserts a proposition on the basis of its nonfallaciousness, in order to test the argument for these sorts of fallacies we have to formulate the proposition which it is intended to prove for the purposes of testing it for contradictoriness. Such, one might suppose, may have been part of Praśastapāda's rationale in justifying the hypothesis as a separate member. Others, notably Uddyotakara, deny that these are faults, or else classify them under fallacies of the reason or examples. They, therefore, must appeal to different reasons for distinguishing the hypothesis as a member.

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Uddyotakara reminds us that the hypothesis is not, as we Westerners are prone to think, a judgment or statement but rather the complex object *p* accompanied by *s*. What we have been calling fallacies or faults are in fact, literally, in Sanskrit called *ābhāsa*—"appearances (of something as what it is not)." Thus the hypothesis, since it is an object, cannot be fallacious, although one may take something which appears to be an object (but is not) to be one. It follows that a "self-contradictory hypothesis" is a kind of category-mistake; if something is a hypothesis it cannot be self-contradictory (since objects can not be self-contradictory), and if something is self-contradictory it cannot be a hypothesis, not being that kind of thing. We have, then, a fundamental cleavage here between the Vaiśeṣikas Praśastapāda, Vyomaśiva, and Śrīdhara on the one hand, and Naiyāyikas such as Uddyotakara on the other, about the nature and function of the members of an inference. The Vaiśeṣikas take these members to be judgments or propositions, the Naiyāyikas take them to be objects which the corresponding judgments are about.

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Very well, then, we need at least 5 members, say the Naiyāyikas and Vaiśeṣikas. But why, let us ask next, only 5? Vātsyāyana mentions 5 additional members that some older philosophers had included—the desire to know, doubt about the truth of the hypothesis, the possibility of getting a solution to the question, the purpose of the inquiry, and the resolution of the doubt. Recent scholarship suggests that a 10 membered argument form was espoused by Sāmkhya; just these 10, in fact, are apparently found in the *Yuktidīpikā*.¹² Vātsyāyana's attitude toward these added entries is that they are properly cited as psychological conditions and/or stages in inference for oneself but that they are out of place in a list of the steps required for inference for others. Udayana expatiates: the reason why the additional 5 members are out of place is that although their presence assists inference to take place they do not need to be known and understood by the person to whom the argument is addressed, while the approved 5 members must be appreciated in order that the argument succeed.

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A good deal of discussion is occasioned over the function of the fourth member, the application. A question which troubled many of our philosophers was this: since everything has a cause, and since an inference issues (when successful) in the establishment of a conclusion, a key to understanding inference is to know, not merely what the steps are but what is the essential cause of the successful demonstration. What, then, asked our philosophers, is the essential cause of a successful demonstration?

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Now, the conclusion of our stock inference is "this mountain possesses fire." The Buddhists thought that the essential cause for the knowledge of this fact on the part of the person to whom the demonstration is addressed is just the realization that this mountain has smoke, the information set forth in the second step. (Of course in Buddhism's view there are no more steps!) Most Naiyāyikas would agree that the second member sets forth this fact (technically referred to as pakṣadharmatā), but many would not agree that the knowledge of this fact on the part of the person being convinced is the essential, or at least the last crucial, step in the process. Uddyotakara in particular champions the fourth step as that which sets forth a relationship which is the most essential and proximate cause of success, a relationship which he calls liṅgaparāmarśa. This relationship is that which holds between p and s-pervaded h, a relationship of qualification. As emphasized before, Uddyotakara is careful to insist that the relationship itself is not judgmental; it is a fact of nature, and it is this fact which is the cause of the addressee's correct judgment that p has s.

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Śrīdhara, on the other hand, says that the Vaiśeṣika view is different from Uddyotakara's, that the fourth member has the function of conveying the pakṣadharmatā. He can say this because, we will recall, he holds the second member merely to mention the h, not to ascribe it to p. Randle argues that in fact Śrīdhara identifies pakṣadharmatā with liṅgaparāmarśa, as they are both now associated with the fourth member.13

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These subtleties go beyond what is said by the authors of the sūtras and their initial commentators (Vātsyāyana and Praśastapāda).

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These oldest writers apparently thought of the fourth member as merely arguing by analogy from the fact that in a kitchen one finds both *s* and *h* to the fact that on this mountain one finds both *s* and *h*, coupled with the fact, established in the third member, that this mountain is an instance of a general concomitance between *h* and *s* as instanced by the negative example, lake. In other words, the oldest writers treated the fourth member merely as the particular instantiation of the general relation; they do not raise the question as to which member states the most essential or proximate cause of successful inference. It is probable that they did not distinguish clearly the notion of a member as a linguistic or epistemic item—a judgment or statement—from that of a member as a complex fact about which we form judgments or make statements.

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It is Uddyotakara’s care in distinguishing these that leads him to emphasize the role of *liṅgaparāmarśa*. As he sees it, it is not our judgments which make inferences successful but the facts themselves; thus in particular it is not the judgments that *h* resides in *p* and that *s* pervades *h* that cause a successful inference, but only the complex fact of *p*’s possessing *s*-pervaded *h* which causes it. It is particularly the Buddhists that Uddyotakara opposes. Buddhist logicians such as Dignāga, since they do not admit objects independent of knowledge, must perforce view inferences as constituted of judgments, and more particularly they must trace the causes of success in inference not to facts but to judgments. Uddyotakara is cleverly forcing the Buddhists to see what he believes to be the shortcomings of an idealist theory of knowledge and inference.

IV. Pakṣa and Sādhya

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In the case of the terms, there is no real disagreement among the schools about their number, but there is some discussion over just what exactly the terms are, i.e., what constitutes a *p*, an *h*, or an *s*, or one of the examples.

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One problem about reading the earlier writings in the school on these topics is that the terms *pakṣa* and *sādhya* were used interchangeably. The reason for this, apparently, is that the term *pakṣa* is found frequently as an alternative way of designating the first member or hypothesis, and apparently the term *sādhya* was used indiscriminately, sometimes to mean the subject of the hypothesis, sometimes to mean its predicate. Tucci¹⁴ points to a passage in the Buddhist work *Nyāyapraveśa* in which the author explains that according to the older masters of logic the argument form has two sections: (1) the *sādhya*, including both its *dharmin* (a thing which has a property) and its *dharma* (the property the thing has); (2) the *sādhana*, which comprised the first 3 members of the argument form discussed above. The idea apparently was that the first section gives us what is to be proved, and the second produces the proof. According to Tucci this tradition is followed by Asaṅga and Vasubandhu, but was rejected by Dignāga and Dharmakīrti in favor of a distinction between the hypothesis, called by them the *pakṣa* or *sādhya*, and the reason plus the examples, called the *sādhana* or proof. It took a bit of doing for the Naiyāyikas to evolve a consistent terminology, since they were addressing themselves to Buddhists whose terminology was not at all clear and who tended to analyze the first member differently than the Naiyāyikas did.

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Just what is it that one is attempting to prove in the stock argument? When one says "this mountain has fire" how should we analyze what this statement is about? This question created controversy between Nyāya and Buddhism, and for that matter among Naiyāyikas themselves.15 Vātsyāyana starts us off: he says that what is being inferred is fire. But both Dignāga and Uddyotakara point out that one does not infer fire from smoke, or even fieriness from smokiness, but rather one infers from the fact that a place has smoke that it has fire. It is the relation between smoke and fire that makes the inference possible, but the inference is to a particular possessing a property, not merely to the property alone.

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But the Buddhists are not very happy with the notion that in "this mountain has fire" we are referring to a universal in a particular. Dignāga therefore espouses the view that what is being proved in the inference is that the place from which the smoke is issuing is a fire-possessing place; the subject of the argument is a particular place on the mountain, and the property of fire-possession is being attributed to that place. Uddyotakara controverts this, it is clear; just what his argument is is not so clear. Vācaspati Miśra appears to think that Uddyotakara's point is that the inference cannot be about that place, since we do not see that place, it being hidden behind the hill. After all, if we could see the place we could see the fire and would not need inference. Randle discusses the passage at length and concludes that Vācaspati's understanding is probably mistaken, and that what Uddyotakara is complaining about is that Dignāga wants to infer from the general presence of smoke to the occurrence of fire at some specific spot, which he could only do if he adduced as his reason that the smoke qualified that particular spot — and that is not the evidence that is given!

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Udyotakara’s own analysis of the hypothesis is that we are inferring, about this particular smoke that we see over the hill, that it is fiery, i.e., that it is accompanied by fire somewhere nearby on the hill. On his view, then, the *p* is this smoke and the *s* is *fire-possessing*; the mountain disappears as a term in the argument because, as Randle puts it, it is an “accidental *dharmin*.” As we shall see, this analysis leads Uddyotakara to have grave suspicions about the crucial relation of pervasion, which will be discussed shortly.

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Generally, the *p* is identified, e.g., by Vātsyāyana, as the thing about which we are doubtful as to whether it does or does not possess the *s*. For one thing, it must not be an empty class. Udayana explicitly points this out, and it is generally assumed. Jayanta adds that it must not overlap the *sp*, and that it must not be identical with the *s*. In general, we may say at this point, all the terms of a well-formed argument must be different. Śrīdhara adds still another requirement: the *p* must not be such that it can have mutually contradictory properties—of the two entities *s* and absence of *s* one or the other but not both must be attributable to *p*. Mīmāṃsakas and others suggest a further requirement intended to rule out “straw man” arguments: *s* must be hitherto unproved to reside in *p*. But Uddyotakara rejects this as too stringent; all that is needed to make an inference have point is that someone claims that *s* resides in *p*.

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V. *The Hetu Term : Its Nature and Requirements*

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In many ways the heart of early discussions of successful inference lies in their treatment of the *h* and when one has a “real” *h* as opposed to only an apparent one. There is more than one way of approaching the requirements for a successful *h*. On the one hand one may attempt to provide conditions necessary and sufficient for a putative *h*’s being a real one. On the other one may set out to specify (exhaustively if he thinks himself able) the kinds of faults discovery of which convicts a putative *h* of being only an apparent one—a *hetvābhāsa*. We shall deal with each of these approaches in turn.

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A. *Necessary and Sufficient Conditions for h*: One of the most famous theories in Indian philosophy, and probably the best known to historians of Indian logic, is that of the “three fold mark” (*trairūpya*) of the *hetu*. The theory is especially associated with the name of Dignāga, but in some form it antedates him considerably. The reason for the association with Dignāga is that he seems to have radically reinterpreted the formula which constitutes the “threefold mark.” This formula runs as follows :

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(1) the *p* must fall completely within the *h*;
(2) the *sp* must occur partially or completely within the *h*;
(3) the *vp* must occur outside of the *h*.

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Unfortunately, this formula as given is ambiguous, and the history of the development of the theory of pervasion is a history of the successive reconstruing of the second and third requirements in the formula.

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Stage One: As Vidyābhūṣaṇa asserts, “an example before the time of Dignāga served as a mere familiar case which was cited to help the understanding of the listener.”¹⁶ In the first stage of development requirement (2) of the threefold mark was taken to mean that the *sp* constituted some class or other whose members all share the property of possessing fire, and that at least one of those members also has the property of possessing smoke. To use a Boolean procedure for symbolizing this, (2) required that *ash* ≠ 0 (where *a* = *sp*). Requirement (3), likewise, was construed to mean that the *vp* consists of some class or other whose members all share the property of not possessing fire, and that none of those members have the property of possessing smoke. Thus (3) may be formulated for this stage as *vsh* = 0 (where *v* = *vp*). Requirement (1) is relatively unambiguous; it states that *ph* = 0.

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It is important to note carefully the definition of *sp* and *vp* set forth in this stage, as well as two features of an inference as conceived here. The first feature is this : that satisfaction of the three requirements conjointly does not suffice to entail the conclusion. The situation here is rather that one giving an argument is citing examples to suggest the plausibility of his hypothesis to a listener; we are considering a moment in discussion where one side claims something to be the case and in order to illustrate what he means, as well as to show that his claim is not altogether unreasonable, he provides examples. The second feature to note is this : requirements (2) and (3) are independent of each other. It is possible to satisfy one without satisfying the other.

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Stage Two : In this stage the understanding of requirement (3) undergoes a distinct change, while the other two requirements are interpreted as before. In Stage One the *vp* was taken to be some particular class (e.g., the class of lakes). On the understanding of the second stage the *vp* is to be construed as the class of all fireless things. Requirement (3) now is taken to state that *hs* = 0, that is, that the *h* is completely within the *s*.

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This is a radical change, for it is now the case, where it was not before, that if all three requirements are satisfied the conclusion is entailed, and we have in (1)—(3) the necessary and sufficient conditions for a successful inference. To see this we may construct a diagram.

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TO PROVE: ps = 0 ASSUME: p ≠ 0 s ≠ 0 h ≠ 0 pa = 0 as = 0

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REQUIREMENTS: (1) ph = 0
(2) as ≠ 0
(3) hs = 0

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It will be seen from the diagram that the p falls completely within s, which is the conclusion to be proved. However, the stock example of lake as vp will no longer do. For lakes is not the class of everything which lacks the s-property fieriness. In Stage Two, then, interest has swung from the giving of evidence suggestive of lawfulness to the actual assertion of lawful connection between smokiness and fieriness, a connection which comes to be known as "pervasion." In Stage Two, while sp still serves as positive evidence of concomitance between h and s, vp is no longer viewed as an example but rather as the complement of s. Requirements (2) and (3) on this reading have completely different roles: whereas requirement (2) involves giving evidence for concomitance by citing a particular case instantiating both h and s, requirement (3) asks us to assent to a universal proposition, "all h things are s things" ("all smoky things are fiery things") but does not involve the production of specific evidence.

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Nevertheless the 2 requirements are still independent. One can find an instance satisfying requirement (2) without feeling able to assert pervasion of h by s, and likewise one might feel inclined to assert pervasion without being able to come up with an actual instance of a thing which shares the two properties. It is evident, though, that Stage Two is a halfway house, since if one sincerely believes that requirement (3) is satisfied, that pervasion does indeed hold, then he will have no doubt that an instance of concomitance can be found, even though he might not be imaginative enough to come up with one immediately upon request. So we are led to a third stage.

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Stage Three : Here requirements (1) and (3) are understood as in Stage Two : the change is in requirement (2). In fact, in this Stage requirements (2) and (3) come to the same thing; for the sp is now construed as consisting of the class of all things which have the s-property except the p itself. Requirement (2) now says that the members of h, smoky things, must only occur in the sp, which means now the class of fiery things. Thus requirement (2) must be stated thus : hs= 0, which was precisely the way we found requirement (3) to read as well in Stage Two.

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In this Stage not only are requirements (2) and (3) equivalent, but it follows that one of them is unnecessary. Requirement (1) together with either one or the other of the other two is sufficient to entail the conclusion.

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The three Stages I have just identified can be associated with Buddhist logicians. Stage One presumably antedates Dignāga. Just who was responsible for Stage Two is not entirely clear. Vidyābhūṣaṇa¹⁷ seems to have thought it came in with Asaṅga, but Tucci¹⁸ finds no trace of the trairūpya in Asaṅga. In any case it is likely that it was Dignāga’s position, although this is extremely hard to ascertain, mainly because of the difficulty of maintaining the position of Stage Two without perforce being led on to Stage Three. Stage Three is explicitly and unmistakably formulated by Dharmakīrti in the Nyāyabindu.¹⁹ Stcherbatsky’s²⁰ puzzlement over the trairūpya stemmed from his difficulty in explaining adequately why Dharmakīrti should promulgate as a threefold mark a formula in which one of the requirements is redundant and unnecessary. He was not the firstt to have this difficulty; Dharmakīrti’s commentators, such as Dharmottara, shared it.²¹

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It is especially instructive to note how in the transition from Stage One to Stage Two attention shifts from what is the case to what is asserted. I remarked earlier that Uddyotakara, especially, is sensitive to Buddhism’s tendency to confuse things with judgments about them. In turning the pattern of inference into a formal relation among judgments, the Buddhists discovered something approximating the kind of thing which Western logicians have studied for centuries. It was their idealist proclivities which enabled them to interpret the argument pattern thus without shuddering. Naiyāyikas resisted the transition from Stage One to Stage Two. They continued to interpret the *sp* as a class whose members share the *s*-property and some of whose members (though not necessarily all) have the *h*-property, and they refused to take the *vp* as the complement of *s*. As empiricists and realists they viewed the examples as providing evidence for pervasion, but they generally admit that the statement of pervasion is always fallible—that subsequent examination may show that what seemed to be concomitance between *h* and *s* is not really such. Their attention remained directed toward the evidence, where the Buddhists tended to be drawn off to study formal relationships among judgments abstracted from their relationship with the facts. At least I think it fair to say a Naiyāyika would claim this to be so.

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We find the threefold mark cited by most of our authors as necessary conditions for a valid *h*. Jayanta adds 2 more requirements to the 3 of Stage One above. They are (4) that *h*’s residence in *p* not be refutable by one of the valid instruments, and (5) that *h* not be such that though it satisfies requirements (2) and (3) with respect to *s* it also satisfies them with respect to *s*’s complement. According to Matilal²² the Vaiśeṣika authors count (4) as a requirement on *p* rather than on *h*, although Vyomaśiva at any rate reports with approval the fivefold mark of “Nyāya theorists.”

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B. Fallacies of the Hetu : If one despairs of finding any set of conditions on the *h* necessary and sufficient to insure validity of the inference in question, the alternative is to list and classify as many as one can of apparent *hetus* which are not real *hetus*, i.e., which do not produce a valid inference.

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It is not hard to show why despair may be an appropriate attitude to adopt toward the prospect of finding positive conditions for validity. There are indefinite ways in which an inference which has the look of validity about it fails, and only a small number of these ways constitute violations of the 5 conditions Jayanta accepts. For one thing, participants in an argument are extremely likely to disagree on matters which are presupposed in the very formulation of the hypothesis, or reason, or examples. In such cases the argument may pass all 5 conditions from one party’s point of view but not from the others, so that although it convinces the speaker it fails to convince the hearer. Worse yet, one or both parties may be confused or uncertain about key aspects of the terms, in which case although conviction may be produced the argument is invalid (though possibly temporarily successful!). Then there is the matter of being well-formed semantically and pragmatically (supposing for the moment that it passes muster syntactically). I.e., if one or more of the terms fails to denote anything whatsoever, or if there is a category-mistake involved in relating one thing to another, the argument is not well-formed semantically; and if the terms are equivocal in context, or if the members are asserted at widely separate times, the argument is not well-formed pragmatically or contextually. In Western logic textbooks one sometimes finds discussions of "informal fallacies," arguments which appear formally satisfactory but which misuse the language in some fashion or other. It would be a very unsophisticated logician who thought he could give an exhaustive classification of all the possible faults of this sort that can infect an argument.

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When one turns to consider what Indian logicians have to say about fallacies of the *hetu*, one is struck by the lack of agreement on such topics not only between philosophers of different schools but also between Naiyāyikas themselves. In part this reflects the difficulty felt by everyone about getting any rigorous classification of fallacies, but it is even more apparent that our philosophers were victimized by a horrible confusion over terminology. In what follows I shall try to give hints about this sort of difficulty, although to track down the uses of different terms synonymously and of the same terms in different senses would require that I presuppose more understanding of Sanskrit than I am in fact presuming on the part of my reader.

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Let us start with Kaṇāda. He finds that there are 3 kinds of fallacies which pertain to the *hetu* term. (1) It may be contradictory (*viruddha*). (2) It may be unproved (*asiddha*). Or (3) it may be doubtful (*samdigdha*). It is left to his commentators to explain just what kinds of mistake Kaṇāda had in mind.

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Meanwhile, however, along comes Gautama. He finds 5 varieties, only one of which verbally matches with Kaṇāda’s list. The one that matches is (1) contradictory. His other 4 are (4) an *h* which is indecisive (*savyabhicāra* or *anaikāntika*); (5) where the *h*, though it is intended to establish something, merely produces doubt in the hearer about the topic (*prakaraṇasama*); (6) where the *h* needs proof as much as the *s* (*sādhyasama*); and (7) where the *h* is mistimed (*kālātīta*). But his explanations of some of these notions are not at all precise.

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Vātsyāyana helps us a bit in understanding (1) and (7). The contradictoriness of (1), he says, occurs when one puts forth as *h* a term which contradicts something he himself holds—either the hypothesis itself or something else which the speaker holds to be true along with the hypothesis. As for (7), Vātsyāyana rejects the notion that it merely means the case where one member is spoken today and the others a year from now; actually, he says, what is meant under (7) is fallacies of equivocation generally.

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Now we come to Praśastapāda. True to Vaiśeṣika tradition, he accepts (1)—(3) of Kaṇāda, but then adds one of his own, (8) uncertain (anadhyavasita). His explanations take us farther; (2) the "unproved" hetu, may be subdivided into 4 sorts, accordingas the h is not recognized as existing by either party, not recognized by one of the two parties, is mischaracterized, or is not recognized by one or both parties. (This last, which looks like a confusion, is viewed by Śrīdhara as actually referring to the status of the term p.) As for (3), the "doubtful" h, this occurs when what is offered as h turns out to reside in both sp and vp. And (8), has added "uncertain" variety, is glossed as that putative hetu which is too specific (asādhāraṇa) so that the p and h terms are identical, as in "this hill is possessed of fire, because it is this hill."

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Uddyotakara tells us that (6) is the same kind of fault as (2), since if h needs proof as much as s then it is safe to say that h is unproved. And he provides some subvarieties of (2): (a) where the very nature (svarūpa) of the proposed h is unproved; (b) where the locus of the proposed h is unknown; (c) where the proposed reason (the second member of the argument) can be analyzed differently so that the h turns out not to prove s. Uddyotakara has also achieved some notoriety for his apparent belief that it might, after all, be possible to specify an exhaustive list of fallacies and thus get a decision procedure for validity, albeit a very complicated one.²³

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This brings us to Bhāsarvajña, whose treatment of fallacies, by comparison with the time spent in Nyāyasāra on other topics, is remarkably comprehensive. He lists 6 main varieties of hetvābhāsa, namely (1) contradictory, (2) unproved, (4) indecisive, (8) uncertain, (5) the h which produces doubt, and (7) the "mistimed." His explanation of (1) is that it is the fallacy which occurs when h turns out to reside in both sp and vp: we just saw that this mistake was classified by Praśastapāda under (3) doubtful. As for (2) the unproved h, Bhāsarvajña says that this covers all cases where it is doubtful that h occurs in p, and he subdivides it into 12 varieties, a couple of which had been classified by Uddyotakara under (6). The other 5 main varieties are elaborately subdivided as well, and in many cases it is apparent that these subvarieties are related with subvarieties of other main classes in such a way that if an argument commits one kind of mistake it must commit another. Bhāsarvajña recognizes this aspect of his classification and is unperturbed by it. For example, (4) indecisive turns out to occur whenever the supposed h occurs in p, sp and vp; it would appear that whenever this happens the h will also be (1) contradictory. And (8), the uncertain h, is explained as in Praśastapāda. But when he comes to (5) his explanation diverges in an interesting way. In (5) the “mistimed” occurs, says Bhāsarvajña, whenever *h*’s occurrence in *p* is sublated by a valid instrument; thus Bhāsarvajña incorporates into his list of fallacies one of the added positive requirements of validity that Jayanta had insisted on, indeed both, since others among his fallacies, notably (8), rule out the possibility that one *h* can prove both *s* and its complement.

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Vyomaśiva’s treatment is also elaborate. It is apparent that he has read others on the topic, and his list of fallacies is not limited to the 4 given by Praśastapāda, on whose text he is commenting. In addition to Praśastapāda’s (1), (2), (3) and (8) he specifically admits a fallacy he calls “mistimed,” and he also discusses the (4) indecisive sort. He mentions in passing that Kaṇāda presumably included these last 2 under (1), contradictory, but is not very impressed with this notion, for he suggests that we should accept these additional types of fallacy on the authority of Nyāya authors (not Vaiśeṣika ones!) regardless of Kaṇāda’s intentions.

First 74 of 133 passages. Read on

Cites (13)