Dinnaga and Metal Modes-A Reconstruction

Philosophy East & West Volume 60, Number 3 July 2010 315–340 315© 2010 by University of Hawai‘i Press

DIṄNĀGA AND MENTAL MODELS: A RECONSTRUCTION

Amita ChatterjeeProfessor at the Department of Philosophy and Coordinator at the Centre for Cognitive Science, Jadavpur University

Smita SirkerLecturer at the Department of Philosophy and Researcher at the Centre for Cognitive Science, Jadavpur University

It is platitudinous to say that whenever we try to read some ancient text or interpret some theory distant in space and/or time, we employ contemporary tools of analysis, contemporary techniques of modeling. Even while building theories, theoreticians (philosophers and scientists alike) are found to take help from the technology of the time. Aristotle, for example, had a wax-tablet view of memory. Leibniz used the model of a clock to explain the harmonious universe. Freud used a hydraulic model of the flow of libido, and the telephone switchboard model guided psychologists while they were theorizing on intelligence. Nearer to our time, we have seen physicists explaining the structure of an atom by the model of the solar system and cognitive scientists explaining the working of the human mind by the analogy of a computer. In this essay, we would like to borrow the tool of mental models from the famous cogni-tive psychologist P. N. Johnson-Laird and his team, to offer an alternative picture of the Buddhist ‘logical’ scenario, which we think will enable us to understand some perplexing issues in the given area and offer some solutions to them.

I

Theory of inference, which is the core of any logical theory, belongs to the pramāṇa theory in Indian philosophy. Stalwarts of Indian philosophy have attempted to glean logical insights from the pramāṇa theory by interpreting it in their own way. Conse-quently, we have come across all sorts of views regarding Indian logic. For example, (a) inferences are syllogistic in nature, hence Indian logic is deductive;1 (b) infer-ence always depends on a vyāptivākya, a generalization based on observations, and therefore Indian logic is inductive;2 (c) inference is both deductive and inductive;3 (d) inference is neither inductive nor deductive;4 (e) Indian theory of inference can be re-constructed within the first-order logic,5 in spite of its explicit intentional language;6 and (f ) inferences cannot be understood at all within the framework of monotonic reasoning—these are instances of non-monotonic reasoning,7 especially of default reasoning.8

Indian theories of inference definitely form the core of Indian logic. But be-cause of its epistemological origin and motivations, the contour of Indian logic does not nicely fit the outline of Western logic, which moves around the consequence relation and its formal properties. Though these theories of inference tell us how to

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distinguish good arguments from bad arguments, people hesitate to admit it as logic wholeheartedly. Scholars are often found to be very apologetic in the face of com-ments such as that Indians did not have any sense of logic at all because they did not have the concepts of formal system, entailment, validity, or tautology. We grant that Indians did not develop any axiomatic/formal system, nor did they have the notion of tautology. However, we needn’t be unduly defensive because of that. For, (a) the ap-proach of the Indian theorists was predominantly model-theoretic, and (b) they were interested in tracing the psycho-causal steps underlying the reasoning processes of ordinary people in their everyday life. Let us explain these points a bit.

Modern logicians distinguish between proof theory and model theory. While proof theory follows a rule-based axiomatic approach, model theory proceeds by developing models or systems of interpretations. A model theory is supposed to tell us how values associated with constituents determine the values of the compound they make up and how values associated with premises lead to the value of the con-clusion and the validity/invalidity of the argument. A model-theoretic approach does not necessarily presuppose a sterile, content-free environment and is often found to go beyond the formal properties of the entailment relation. Indian logicians, we have already mentioned, had no truck with pure formal logic. Besides, as epistemologists, the pramāṇavādins were interested to find out how inference results from a number of cognitive states and what conditions give rise to cognitive certainty. They were not primarily concerned with the question of how ideally rational human beings reason under ideal conditions.

The last point leads us to the ‘rationality debate’—a debate that has drawn a lot of attention due to cognitive psychologists for the last forty years. Previously it was supposed that people reason by following the laws of the traditional Aristotelian logic or the rules of the first-order predicate calculus. But several experiments on human reasoning have revealed that a majority of us, most of the time, do not use the rules of classical logic while reasoning. Hence the question how do people actually reason or what is the nature of mental logic, if there is any, has become very significant. P. N. Johnson-Laird conjectures that human beings actually reason by constructing mental models and not by following rules admitted in the Natural Deduction system.9 The rules of the Natural Deduction system are such that it is quite unlikely that these are innate. People cannot grasp these rules without their being taught explicitly. If logi-cal thinking depended on grasping these rules, then common people without logical training could never reach the right conclusion. But they do reason tolerably well, arrive at correct results, and by virtue of that survive in this world. The mental-model theory assumes that logically untrained reasoners are not equipped with formal rules of inference, but rather they rely on their ability to understand the premises. They build mental models of the relevant states of affairs based on this understanding and general knowledge. They can arrive at a conclusion that is true in these models and they can test the validity of an inference by establishing that no alternative models of the premises refute it. “In other words, a mental model is a representation of a pos-sibility, which itself may occur in many ways, and so its structure and content capture what is common to these.”10

Amita Chatterjee, Smita Sirker 317

Before we proceed further we must point out that the model theorists and the mental model theorists use the word ‘model’ in different though related senses. While model theory tells us under what interpretations a given proposition turns out to be true and an inference sound, a mental-model theory deals with how the premises of a sound inference is mentally represented to a reasoner. The former addresses a semantic issue while the latter forms part of the theory of mental representation. However, a theory of mental representation can also be viewed as a semantic the-ory. Mental model theorists emphasize the semantic interpretation of a given issue/problem/situation whose mental-model construction will vary accordingly. Formal logic—axiomatic or natural deductive—brackets the process of inference that goes on within us and focuses on a linguistically expressed product of that process. An argument or an argument form is always expressed through some symbol, and when an argument is evaluated, a logician needs to interpret that symbol and determine the truth conditions of the premises of the argument.

The mental model theorist, on the contrary, is interested in unraveling the pro‑cess of inference and hence in determining how the inferential situation is internally represented to a reasoner, which enables her to arrive at a conclusion that fits the happenings in the external world. Since the reasoner reaches the conclusion through a causal chain of contentful beliefs/cognitions, it becomes imperative to all who deal with inferential process to conjecture how our beliefs get their content and in what mode such contents are represented. The mental-model theorists hypothesize that the world is represented to the reasoner through some mental models and not through explicit propositional representations of logical rules. These models are said to have a structural and a relational similarity to the external elements of which they are a representation. With these models, the reasoner may construe one or many different possibilities of any given problem before arriving at her conclusion. Mental models are iconic and can be construed with pictures, images, directed graphs, diagrams, et cetera, depending on individual competence in handling them.

In Indian theories of inference and in Buddhist theory in particular, the primary emphasis has always been on the process of inferential representation and not on logical, rule-governed symbol manipulation. We would, therefore, like to argue that svārthānumāna (SA) or inference‑for‑oneself of the Buddhists provides us with the mental representation in the form of mental models and that parārthānumāna (PA) or inference‑for‑others is the externalization of mental models. Hence PAs are not to be viewed from the proof-theoretic perspective as formal rule-governed demonstra-tions but as models of reasoning that guide one to sound conclusions. To convince readers that our reading of the Buddhist inference is not anachronistic, we would like them to look closely at the svārtha‑parārtha distinction as expounded in Diṅnāga’s Pramāṇasamuccaya11 and Dharmakīrti’s Pramāṇavārtikka12 and Nyāyabindu.13

II

The distinction between SA and PA was first introduced by Diṅnāga (400–480 c.e.) and was adopted by all later pramāṇa theorists. Diṅnāga in Pramāṇasamuccaya re-

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futed an earlier Vaiśeṣika view on this distinction, which leads us to think that there might have been some Vaiśeṣika thinkers of the ‘dark period’ who made this distinc-tion but that it was unacceptable to Diṅnāga.14 Richard P. Hayes, however, following Frauwallner, maintained that Diṅnāga probably borrowed this important distinction from the Sāṃkhya logicians.15 Though this distinction has been admitted in almost all systems of classical Indian philosophy, no one except Diṅnāga has attached so much significance to it. Dharmakīrti did not always see eye to eye with Diṅnāga, yet his exposition of this distinction in the Pramāṇavārttika and Nyāyabindu is in keep-ing with Diṅnāga’s understanding, according to many Buddhist scholars. Diṅnāga and Dharmakīrti desisted from giving a general definition of inference simply be-cause they considered these two kinds of inference so different from each other that they could not bring them under the same defining characteristics. They, therefore, explained the nature of each kind of inference separately, and, as there are only two kinds of inference, to explain the nature of each one of them is to explain the nature of inference. The Naiyāyikas (post-Diṅnāga), on the other hand, first gave a definition of inference and then classified inference into SA and PA, thus somewhat undermining the sharpness of the distinction. In spite of their different nature, both these means of knowledge are called anumāna because both SA and PA produce knowledge of objects that cannot be obtained perceptually (parokṣārtha‑pratipatti).

Before giving the standard definition of SA and PA we first need to describe the minimum structure of an inference and clarify some technical terms. All inferences, according to the Buddhists, must possess three terms: (a) a logical sign (hetu), (b) the signified (sādhya‑dharma), and (c) the subject-locus (pakṣa). When, for example, one infers fire on a hill—seeing smoke coming out of the hilltop—smoke is generally taken as the logical sign, the hill as the subject-locus, and fire as the signified.

Dharmakīrti, following Diṅnāga, defines SA as knowledge of the signifier (sādhya) in the subject-locus (pakṣa) originating from a logical sign (hetu) having three characteristics.16 PA is defined as the expression or statement of the logical sign having three characteristics.17 Diṅnāga’s definition of PA had two additional clauses, namely that the logical sign must express reality and that it must be experienced by the person making an inference (parārthānumānaṁ svaḍṛstārthaprakāśanam). The first clause is related to the soundness of inference and the second clause emphasizes the inadequacy of mere hearsay evidence. The word ‘artha’ mentioned here has a special significance for our theory that we will discuss later.

The major difference between SA and PA lies in the fact that while SA deals with psychological conditions, that is, causally connected cognitive states leading to one’s own inferential knowledge (jñānātmakam), PA essentially deals with the proper linguistic expression (śabdātmakam) of this inference with a view to convincing oth-ers. If the grounds of an inference are not expressed in language, how can others be convinced? So, if one is interested in the logical form of an inference, one must con-centrate on PA. That is why we find that most Indian philosophers starting from the Naiyāyikas and almost all modern interpreters of Indian logic have concentrated on PA. Again, as SA contributes to one’s own knowledge, here one’s private knowledge base enables one to infer. PA, on the other hand, is meant for public demonstration and hence must draw upon resources from a third person / public point of view.


According to Diṅnāga, SA comprises two members—thesis (pakṣa) and reason (hetu)—and PA consists of three members—thesis (pakṣa18), reason (hetu), and ex-ample (dṛṣṭānta). Dharmakīrti, however, maintains that both SA and PA have two members; in PA the thesis need not be stated because having heard the premises the hearer can arrive at the conclusion without any difficulty. Let us consider here one example of each type of inference, following Dharmakīrti:

SA: Here is fire (pakṣa); because here is smoke (hetu).

PA: Here is smoke (hetu‑vacanam). Wherever there is smoke, there is fire, for example in a kitchen; wherever there is no fire there is no smoke as in a lake (dṛṣṭānta‑vacanam).

In the example of SA, the intermediate steps have not been stated, though Diṅnāga has meticulously formulated the implicit intermediate steps in the Hetucakraḍamaru. In PA, on the other hand, the conclusion ‘Here is fire’ has not been mentioned, as it is obvious. Another point that becomes evident from the examples above is that the Buddhist inferences are of the form ‘Q because P’ and not of the form ‘P therefore Q.’19

One infers for oneself in order to have a certain awareness of some object, which one cannot directly apprehend through sense perception. So the SA theory specifies conditions that yield certainty whenever one infers something (sādhya) on the basis of an adequate sign (hetu) in a particular subject-locus (pakṣa). Here we must enter a caveat: Diṅnāga’s specification of a sign leading to a sound inference should not be taken as a normative enterprise; it should rather be looked upon as a description or reporting of the steps usually followed by a competent reasoner. A property P1 can be a sign for another property P2, says Diṅnāga, provided (a) the first property P1 is observed at least once along with the second property P2 and (b) if no instance has been observed where P1 is present but P2 is absent. An adequate sign, therefore, pos-sesses the following three characteristics.

(i) The inferential sign must be known to be present in the subject-locus (pakṣa) where the signified would be inferred.

(ii) It should be known to occur in similar locations (sapakṣa) or homologues. (iii) It should not be known to occur in dissimilar locations (asapakṣa/vipakṣa) or

heterologues.

The significance of the theory of the sign with three characters will be clear if we apply it to the case of an actual inference. Consider the condensed inference: sound is non‑eternal because it is produced by human effort. Here sound is the subject-locus, the property of being non-eternal is the signified, and the property of being produced by human effort is the logical sign. A similar location or a homologue is similar to the subject-locus with respect to the presence of the signified, but is different from the subject-locus. So, in this case, a homologue is any location other than sound where the property of being non-eternal is present—say, a pot. A


dissimilar location or a heterologue here would be any eternal entity—for example, an atom—because a dissimilar location has been defined as that in which the prop-erty to be proved is absent,20 and the absence of anything non-eternal is an eternal thing.

Diṅnāga’s formulation of the three characters highlights not only the subjective nature of SA but also the psycho-cognitive steps that finally lead to a conclusion. However, in Diṅnāga’s original formulation, we do not get any hint regarding how to quantify pakṣa, sapakṣa, and vipakṣa. He was severely criticized by Uddyotakara for that. Dharmakīrti, therefore, presents the final formulation of the three characters of the inferential sign as follows.

I. A sign must be known to be present in the whole of the subject-locus. II. A sign must be known to be present in at least one similar location. III. A sign must never be known to be present in any dissimilar location.

If someone comes across such an adequate sign, she can infer correctly. Communi-cating such a triple-character sign to others in a structured way is called PA because a statement containing an adequate sign generates in the listener the inferential cogni-tion of its conclusion. There is a debate regarding the issue: which is to be called the genuine PA, the linguistic statement of an adequate sign or the process that is gener-ated in the mind of the listener? Diṅnaga as well as Dharmakīrti stated explicitly that the linguistic expression of the statement containing an adequate sign together with the example is called an anumāna only in a secondary sense (kāraṇe kāryopacārāt). These statements cause an inferential cognition in a listener indirectly and hence are called an inference (anumāna). The object of inferential theory in the primary sense is SA. That is why Hayes sometimes describes SA theory as the general theory of in-ference. In a discourse situation, the speaker arrives at a sound inferential cognition through a causal sequence, mentioned above. She then expresses it in the standard form PA, which would generate an inference in others if, and only if, the three mem-bers of PA are properly represented to them.

The way SA and PA have been described does not make the distinction between the two types of inference transparent—not, at least, from a logical, that is, proof-theoretic standpoint. A critique has pointed out that “in SA, the whole process, the entire drama, might be silently, or sub-vocally enacted, but certainly not without involving any use of language.”21 Nor does a PA cease to be knowledge-producing simply because it has been expressed in language. It is true that in the example of SA the sign with three characteristics has not been explicitly stated, but without ascer-taining the three characters of the sign one cannot arrive at the conclusion. On the other hand, in the example of PA, knowledge resulting from the ascertainment of the triple-character sign has been explicitly stated in the form of a positive or negative statement of universal concomitance, thus making the structure of the inference per-spicuous. Still, that does not amount to any logical difference between two kinds of inference. For, as has been pointed out by Rajendra Prasad, “the set of conditions of the validity of inference, whether it is in the SA form, or in the PA form is the same.”22


Only the order of the constituent propositions in two types of inference varies. How-ever, logically speaking, that does not make them sufficiently different:

An inference can be called logically different from another only if the set of rules which legitimize drawing its conclusion from its premises is not wholly identical with the set of rules which legitimize drawing the latter’s conclusion from its premises. Since this is not true of SA and PA, there is no logical reason for calling them two different types of infer-ence, or for dividing inference into SA and PA, claiming that these two and only these two represent the two basic and broadest types, or forms, of inference.23

We think we can justify the proposed distinction between SA and PA by remembering that SA belongs to the realm of mental reasoning and PA to the realm that is accepted as logic proper. In logic proper, the connection obtaining between the premise(s) and the conclusion needs to be shown explicitly; mere seeing of the connection is not enough. We hope to explain the distinction better by using the tool of mental model.

III

Johnson-Laird developed Kenneth Craik’s intuitive idea of an inner mental replica that has the same ‘relation-structure’ with the phenomena that it represents. Craik (1943) wrote:

If the organism carries a ‘small scale model’ of external reality and of its own possible ac-tions within its head, it is able to try out various alternatives, conclude which is the best of them, react to future situations before they arise, utilize the knowledge of past event[s] in dealing with the present and the future, and in every way to react in a much fuller, safer, and more competent manner to the emergencies which face it.24

Johnson-Laird applies this idea to the rich and revealing test cases of mental infer-ence, both formal and informal, in order to discover what kind of working hypothesis about mental models yields a descriptively adequate account of reasoning. The theory of mental models postulates that human reasoning depends on understanding the meaning of the given premises and then uses this meaning and general knowledge to construct mental models of the possibilities under description. There are five main assumptions of the mental-model theory, and these make it different from the other theories of human reasoning. The first assumption is that a mental model represents a possibility. A model captures what is common to the different ways in which the possibility might occur. The structure of a mental model corresponds to the structure of the real world. In general, mental models can represent three-dimensional entities, spatial relations, temporal relations, events, processes, complex systems, and even abstract ideas. They can represent discourse about real, hypothetical, or imaginary cases, and they reside in long-term memory as a representation of knowledge.

The second assumption is the principle of truth; that is, mental models represent what is true, but, by default, not what is false. Johnson-Laird says that there are ex-ceptions to this. Individuals make ‘mental footnotes’ about the falsity of clauses, and if they retain the footnotes then they can construct explicit mental models, in which


clauses are represented when they are false. The principle also postulates that people normally do not represent what is false. This helps in reducing the volume of things that one has to keep in mind while working out a problem. In other words, the prin-ciple of truth reduces the load on the working memory.

The third assumption is that human reasoning depends on mental models. Ac-cording to Johnson-Laird, models can be used for reasoning according to the rational principle that a conclusion is valid if it holds in all the models of the premises, that is, it has no counterexample, and so it is necessary, given the premises. Johnson-Laird and Ruth Byrne25 claim that this theory has theoretical advantages. It dovetails with other parts of mental life—perception delivers models of the world, and comprehen-sion of discourse delivers models of what is described. The account is also said to have empirical advantages. Reasoners are faster and make fewer errors with deduc-tions that require them to construct only one model than with deductions that require them to construct multiple models.

The fourth assumption is that mental models are iconic. So reasoners can use a model to draw a conclusion that does not correspond to any of the representations used to construct a model.

The fifth assumption holds that while reasoning using mental models one need not eschew all rules. Some may even use some formal rules of inference. However, this assumption says: models first, rules afterward.

To understand the relevance of this theory in the context of the Buddhist theory of inference let us see how Johnson-Laird explains syllogistic reasoning. According to his analysis, all sixty-four kinds of syllogism are variations of the following example:

All artists are beekeepersAll beekeepers are chemists

He says that to arrive at a true conclusion from these two premises, we need not know rules of syllogistic inference or a sophisticated system of notation. All we need to do is to construct adequate mental models. He asks us to pretend that we have the power to conjure up individuals who fulfill one or more of the roles stated in the premises. We can think of individuals who fulfill all the roles at one time, and these individuals may be represented in the form of arrays in a mental model as:

artist – beekeeper – chemistartist – beekeeper – chemistartist – beekeeper – chemist

We are also aware of those persons who are beekeepers and chemists but not artists, for whom the representing array is:

beekeeper – chemistbeekeeper – chemistbeekeeper – chemist


We also know from common sense and careful consideration of the problem that there can be chemists who are not beekeepers. So we also have the following array at our disposal:

chemistschemistschemists

Once we have created a mental model that arrays all the information that can be taken directly from the given premises, we can now read off from the arrays the cor-rect conclusion. If we want to answer whether all artists are chemists, we can simply look at the tableaux and reach a positive conclusion. On the other hand, if we want to answer the question whether all chemists are beekeepers, we would answer in the negative. Finally, after all of the mental pictures have been constructed, an inte-grated picture is submitted to a test: a search is undertaken for an interpretation of the premises that is inconsistent with the model. An inference is sound if and only if there is no way of interpreting the premises that is consistent with a denial of the conclusion. The benefit of this model-based approach lies in the prospect of creating an ‘integrated picture’ of the models built out of the given problem. This integration enables the reasoner to look for both the confirming/positive cases as well as the disconfirming/negative cases.

In Diṅnāga’s Hetucakraḍamaru we find different frames or tableaux for determin-ing whether or not a conclusion is sound. Consider the following inference: Sound is impermanent because it is produced by human effort. Diṅnāga wants us to consider a few (at least one) object(s) possessing the property of being produced by human effort and being impermanent. The resulting array will be:

impermanent object – produced by human effort – object potimpermanent object – produced by human effort – object clothimpermanent object – produced by human effort – object bookimpermanent object – produced by human effort – object pen

impermanent object – [not produced by human effort] – object lightningimpermanent object – [not produced by human effort] – object thunder

permanent object – [not produced by human effort] – object ākāśapermanent object – [not produced by human effort] – object atom

permanent object – produced by human effort – nil

Once we have these arrays integrated in a mental frame we know what conclusion is to be drawn with respect to sound given that it is produced by human effort. Since our search has failed to yield any permanent object produced by human effort—that


is, no counterexample of the thesis is known to be present—we can safely conclude that sound is impermanent.

Diṅnāga has also specified different frames explaining what sort of errors or-dinary people may commit if they create arrays without taking into consideration already established information. Let us analyze two such inferences mentioned in Diṅnāga’s table.

1. Sound is permanent because it is knowableFollowing Diṅnāga, the possibilities related to this inference may be tabulated as follows:

permanent object – knowable object – object ākāśapermanent object – knowable object – object atom

permanent object – [but not knowable] – nil

impermanent object – knowable object – object potimpermanent object – knowable object – object clothimpermanent object – knowable object – object bookimpermanent object – knowable object – object pen

impermanent object – [but not knowable] – nil

Since there are objects, which are knowable but impermanent, sound may not be permanent because it is knowable. In this case, the third condition of the sign with three characters has been violated. Whenever a given frame shows that the sign is present in the heterologue, no conclusion is warranted. In case someone draws a conclusion in contravention of the third condition, the inference is vitiated by the fallacy known as inconclusive (aniścita).

2. Sound is permanent because it is producedThe mental model should make the following frame transparent thus:

permanent object – produced object – nil

permanent object – [but not produced] – object ākāśapermanent object – [but not produced] – object atom

impermanent object – produced object – object potimpermanent object – produced object – object clothimpermanent object – produced object – object book

impermanent object – [but not produced] – object lightningimpermanent object – [but not produced] – object thunder


The sign ‘being produced’ is absent in the homologue (any permanent object) but present in the heterologues. So the inference is doubly erroneous. This frame is given the name ‘hostile’ (viruddha) because it warrants the contradictory of thethesis, namely that sound is impermanent because it is produced.

It is evident that in Diṅnaga’s frame, too, while using the mental model, one is not performing pure formal symbol manipulation; one is not even employing any for-mal logical rule. One is just supposed to use some model connecting the hetu with the sādhya; that is, one is just taking stock of the information available from the data at hand. It may be asked: how many models does an individual need to construct to arrive at the conclusion? Definitely, the number is finite. But if there is essential identity between the sign and the signified, or a causal connection, then one single model may suffice.

When, however, one uses a PA, one needs to make the connection explicit and express it in accordance with the accepted ‘logical structure.’ But she must remem-ber that here, too, the conclusion does not follow from the explicitly stated premises merely by virtue of the form of the argument, but because the background models provide warrant for them. That is why we said earlier that what is known as an infer-ence in the Indian parlance is always to be evaluated model-theoretically. Of course, at the level of PA, it is possible to use some well-established logical rules, but the soundness of a PA does not hinge on them.

One may anticipate an objection at this stage. It may appear that while ascertain-ing the relation between the hetu and the sādhya one is actually following certain rules. Without keeping these rules in mind one cannot possibly design suitable mod-els corresponding to different inferences. But that is not true. One first constructs all possible alterative models depending on the information given, integrates these models, and then formulates a rule. Besides, the rules that one is supposedly using are all related to the ascertainment of the relation of pervasion (vyāpti) between the sign and the signified. The rule of ascertainment of pervasion, we must point out, is again established by constructing some mental models. In fact, whether in a given in-ference a particular property P1 can be the sign of another property P2 is determined by constructing models of co-occurrence and non-occurrence of these properties in some locations on the basis of observation, as is evident from examples of arrays like pot-ākāśa, lightning-ākāśa‑pot, et cetera, in the Hetucakraḍamaru. Following Diṅnāga, Hayes also has explained pervasion with the help of models.26 To explain the notion of pervasion, Hayes wants us to imagine a small universe that is made up of four loci (a, b, c, d) and four properties (W, X, Y, Z). Let us also imagine that these four properties are distributed in the four loci as follows:

a W, X, Y, Zb W, X, , Zc W, X, Yd W, X

From the arrays above, it becomes transparent that W and X are in a reciprocal per-vasion relation, since, wherever there is W there is X and vice versa, whereas X and


Y are in a relation of non-reciprocal pervasion because though X pervades Y, Y does not pervade X; that is, X is erratic with respect to Y though Y uniformly co-occurs with X. It therefore appears from the Hetucakraḍamaru and Hayes’ explanation that Diṅnāga’s system agrees with the fifth assumption of the mental model theory, which is: models first, rules later.

Adoption of the mental model theory enables us to answer another puzzle as well. Diṅnāga thinks that the above-mentioned three conditions taken together con-stitute the necessary condition of a projectable sign. Dharmakīrti, on the contrary, thinks that either (I) and (II) or (I) and (III) should be sufficient for arriving at an accept-able conclusion. So Dharmottara elucidates, in the Nyāyabindutīkā:

When it has already been said that the sign should be present only in homologues, what is the need to state that the sign must also be absent in heterologues? Isn’t the second implied by the first? Why, then, have two different characters of the sign been mentioned? The answer is as follows. [To legitimately arrive at the signified] either agreement in pres-ence or agreement in absence should be used; both must be without exception and not otherwise. In order to show this, both characters have been mentioned. . . . And since they must not allow any exception, only one of them should actually be expressed, not both of them together.27

Dharmakīrti’s view accords well with the Nyāya position. Besides, strictly from a logical standpoint, where the interpretation of negation is standard, (II) and (III) are equivalent and should have the same meaning. Then (I) along with either (II) or (III) should suffice to make a sign adequate. Why, then, does Diṅnāga insist on taking (I), (II), and (III) jointly? The mental model theory offers a plausible answer to this question. Diṅnāga was concerned with building a complete frame, which will en-able one to infer correctly even without the knowledge of any logical rule. Without considering all of the three arrays corresponding to the three characters of the hetu, one cannot really read off from the tableau a conclusion that will turn out to be sound. The logical equivalence of (II) and (III) may follow from the available set of information but is not in any way operative in the actual process of reasoning; hence his insistence on all three conditions.

A mental model, we have seen, expresses a possibility. Diṅnāga, in his Hetucakraḍamaru, has constructed all possible models that we need to consider in any inferential situation. As a sign may be present in all, some, or no similar locations and may be absent in all dissimilar locations, some dissimilar locations, or in none, Diṅnāga has specified nine possible models. Justifiably he has kept the parameter of a sign’s residing in the subject locus constant.28

In a syllogism the location of the middle term in the premises changes the form of the argument. But in neither an SA nor a PA does the location of occurrence of the sign in the premise(s) have any logical significance. For the basic unit here is of the form ‘a has f‑ness’ or ‘f‑ness‑in‑a.’ Whichever way the sign may be considered, the information content as well as the logical significance remains the same in a locus-located frame.29 Hence, when translated into language, sound inferences may take only two different logical forms, BARBARA and CESARE, depending on the nature


of the universal premise, or there may be just one form, the Modus Ponens. But that does not in any way signify the poverty of logical sense of the Buddhist thinkers. Moreover, we are not claiming here that PA has an implicit form of modus ponens or of syllogism. We wholeheartedly concur with Daye that meta-theories of PA and of propositional and predicate logic are neither fully isomorphic nor fully compatible.

IV

So far we have shown the similarity between Diṅnāga’s Wheel of Reason and Johnson-Laird’s mental model theory. When a cognizer wants to communicate her ‘cognition of X’ (‘there is fire on the hill’) to any listener, then the cognizer has to pre-pare a good, sound argument in order to communicate and persuade her listener to believe in her piece of cognition. Thus SA needs to be translated linguistically into PA that may be interpreted according to more than one model. Jonardon Ganeri (2003), following the Nyāyasūtra with Nyāyabhāṣya, has shown how a pañcāvayavi‑nyāya (five-member syllogism) can be interpreted as an instance of case-based reasoning (henceforth CBR). Here one must bear in mind that Maharṣi Gautama and his com-mentator Vātsyāyana in the Nyāyasūtra and Nyāyabhāṣya (pre-Diṅnāga period) did not draw any distinction between SA and PA.30 They spoke of no such classification of inference. They had shown how good arguments must be presented in a structured five-step inference. Ganeri contends that the logic of ancient India is an informal logic of case-based reasoning.31 He writes:

I would like to argue that the Nyāya‑sūtra presages a transformation in Indian thinking about logic. And this in two inter-related respects: in the beginnings of a shift of interest away from the place of argumentation within dialectic and debate and towards a greater concern with the more formal properties of sound inference, and in a parallel correlated shift from case‑based to rule‑governed accounts of logical reasoning. The logic of ancient India, I contend, is an informal logic of case-based reasoning.32

He states that the early Nyāya model of argumentation, the five-step inference pat-tern,33 can be interpreted in the line of CBR: “while the history of logic in India shows a strong tendency towards formalisations, the logic of ancient India tried to model informal patterns of case-based reasoning, patterns that are increasingly becoming recognised as widespread and representative of the way much actual reasoning takes place.”34

CBR refers to a style of designing a system so that thought and action in a given situation are guided by a single distinctive prior case (precedent, prototype, exem-plar, or episode).35 According to the CBR theorists, human reasoning, memory, and learning are inextricably bound together. The key assumption of CBR is that reason-ing is primarily based on remembering a prior similar case and reapplying the les-sons of prior episodes to the present new case. In other words, it refers to a process of solving a new problem by remembering a previous similar situation and by re-using information and knowledge of that situation. A case-based problem solver, for example, solves new problems by retrieving traces of relevant prior problems from


memory, establishing correspondence between these problems and the new situa-tion, and adapting the prior solutions to fit the problem at hand. In other words, CBR “begins with one or more prototypical exemplars of a category, and reasons that some new object belongs to the same category on the grounds that it resembles in some appropriate and context determined manner . . . one of the exemplars.”36

Ganeri states that in the ancient system of Nyāya argumentation, probans (hetu) is that which proves what is to be proved, that is, probandum (sādhya), by virtue of a similarity with an example (udāharaṇa). For instance, one infers the existence of unseen fire (sādhya) on the mountain (pakṣa) by witnessing the presence of smoke (hetu) on the mountain; as the two (fire and smoke) have been found to be associated in other places like the kitchen (udāharaṇa). Here an object is inferred to have an unobserved property on the grounds that it has another, observed one. The citation of an example, a single case either similar or dissimilar to the present case at hand (application), is of fundamental importance to draw an inference. Let us understand Ganeri’s proposal with the help of an illustration. Consider the same inference—‘there is fire on the mountain because there is smoke there.’ The Nyāya five-step inference pattern will be:

(i) The hill possesses fire – pratijñā (thesis) (ii) because it possesses smoke – hetu (reason) (iii) whatever possesses smoke possesses fire, as does the kitchen stove –

udāharaṇa (example) (iv) the hill is like that (i.e., possesses smoke, which is universally co-present

with fire) – upanaya (application) (v) therefore, the hill is like that (i.e., possesses fire) – nigamana (conclusion)

Ganeri gives a pair of schematic inferences, one based on similar instance and the other on a dissimilar one.37 In the following schematic representation of the five-step proof-inference,

‘F’ denotes the property that serves as the reason (hetu),‘G’ is the property whose presence we are seeking to infer (sādhya),‘a’ is the new object about which we are trying to decide if it is G or not (pakṣa),

and‘b’ is the cited example (udāharaṇa)

Case: An unseen fire is inferred to be present on the hill, on the basis of perception of a plume of smoke, just as the two have been found associated in other places, like the kitchen.

Tables 1 and 2 show Ganeri’s representation and tabulation of the five-step proof-inference.38 The schematic models in these tables present the general format in which parārthānumāna would be made following the typical five-step proof. The citation of an example (either a similar instance—sādharmya dṛṣṭānta—or a dissimi-


lar instance—vaidharmya dṛṣṭānta) and its application in the case at hand helps not only in the process of drawing an inference but also in the establishment of the hy-pothesis. This process is particularly helpful in our drawing inference‑for‑others and convincing them as well. As stated earlier, a case-based reasoning pattern typically involves the use of past cases, episodes, and events as referents to ascertain the cur-rent unproved case. The recalled case lends an evidential support for any decision or action taken in the present case. As in CBR, the nyāya form of argumentation (PA) also rests on either a similar or a dissimilar case/example or udāharaṇa either to prove the thesis or disprove the antithesis. Nyāya anumāna or the nyāya argumenta-tion without convincing and relevant exemplars fails to clinch any ground in the dia-

Table 1 Five-step Proof Based on Similarity

[thesis] GaThe hill is fiery

[reason] FaBecause it is smoky

proves Ga, because b is similar to a.

[example] bWhatever is smoky is fiery, like the kitchen stove

has the ‘character of a’ because it issimilar to a

[application] aThe hill is like that

is the same as b with respect to G

[conclusion] Ga\ The hill is fiery

G = fiery; F = smoky; a = hill; b = kitchen stove

Table 2 Five-step Proof Based on Dissimilarity

[thesis] GaThe hill is fiery

[reason] FaBecause the hill is notnon-smoky (i.e. smoky)

proves Ga, because b is dissimilar to a.

[example] bWhatever is not non-fiery is notnon-smoky, like the lake

does not have the ‘character of a’because it is dissimilar to a

[application] aThe hill is not like

is not the same as b with respect to G

[conclusion] Ga\ The hill is fiery

G = fiery; F = non-smoky; a = hill; b = lake


lectical debate, which is like a CBR mechanism where, without past relevant cases, present unsolved cases will not be conclusive.

We have said that PA, being an exercise of drawing an inference for others, can be expressed in more than one way. Though Ganeri, in his paper, shows the ap-plication of CBR on the Nyāya five-member syllogism, we assume that Diṅnāga’s three-member PA can also be presented in the CBR schema. Let us show an example where one infers fire on a hill (see table 3).

PA1. Here is fire2. Because here is smoke3. Wherever there is smoke, there is fire, for example in a kitchen, and wherever

there is no fire there is no smoke, as in a lake

‘F ’ = the property that serves as the reason (hetu),‘G ’ = the property whose presence we are seeking to infer (sādhya),‘a’ = the new object about which we are trying to decide if it is G or

not (pakṣa), and‘b’, ‘c ’ = the cited example (udāharaṇa)39

Having discussed Ganeri’s proposal and demonstrated how Diṅnāga’s PA may also be interpreted in a CBR model, what is left to be addressed is why we think that the mental-model theory is better suited for interpreting Diṅnāga’s SA than CBR. It may appear that there is not much difference between the mental model theory and the CBR theory. So let us first see how the two differ in their approaches. The founda-tion of CBR is based on a collection of cases. It constitutes a case base containing a collection of different individual cases, and given a new problem situation or prob-

Table 3 Ga = The Hill Has Fire —Three-step Proof

Sādhya GaHere is fire

Hetu FaBecause here is smoke

proves Ga, because b is similar to a.

Pakṣa: sapakṣa (an object other than a that possesses G )

b

Wherever there is smoke, there is fire, for example, in a kitchen

has the ‘character of a’ because it is similar to a

vipakṣa (an object other than a that does not possess G )

cWherever there is no fire there is no smoke, as in a lake

does not have ‘character of a’ because it is dissimilar to a

G = fire; F = smoke; a = hill; b = kitchen; c = lake


lem case, there is a relevant retrieval from the source case base. The distinguishing feature of such a system is that the cases that are stored in the case base are not generalized versions of different cases. Rather each individual case is stored with its distinctive features. When presented with a new case, it is matched with each case available in the case base, and the closest relevant match is recalled. Taking a clue from the recalled case provides the solution to the new one. Case-based reasonings have been used for medical diagnostics and legal reasoning40 and also in artificial-intelligence models. Mental model reasoning involves constructing models on the basis of the given information. These models, we have seen, have the same structure as that of their corresponding counterparts in the real world. Each model represents a possibility, capturing what is common to the different ways in which the possibility could occur. These models, we have seen, are said to be iconic; that is, the parts of the mental model correspond to the parts of what it represents.41 Iconic representa-tions can vary from pictures to images to directed graphs, et cetera. According to Johnson-Laird the advantage of such an iconic nature of the mental model is that one can build a model with some given assertions and then use the model to come to a conclusion that does not correspond to any of the given assertions.

According to Johnson-Laird, the main difference between the case-based reason-ing approach and the mental model theory approach lies in the format of knowledge representation.42 The mental model theory postulates that knowledge is itself rep-resented in the form of models of the world. CBR seems to invoke representations closer to language than to reality. This characteristic of CBR makes it a better model for PA, which is śabdātmakam, than for SA, which is jñānātmakam. Johnson-Laird says that the two theories appear to be compatible in principle, yet the particular mechanisms and representations invoked by the two theories may be different.

In CBR, to prove a thesis (a case), a single relevant similar or dissimilar exemplar is sufficient. We do not play around with different alternatives or possibilities. A single matching case with respect to either the presence of a property (hetu) or the absence of a property (refer back to the previous example of proof by similarity and proof by dissimilarity) is good enough. In the mental-model approach, one builds different possibilities for a given problem or case. Among the possibilities both true (positive) and negative matching may be present, though not what is false. An explicit mental model typically searches for the presence of counterexamples, and a model is said to be foolproof when no counterexample is found to contradict the present model. In CBR, a generalization of a case is usually not made unless it is a domain-specific generalization. Each case is stored individually, as it helps in finding the exact match-ing case with more accuracy. Generalizations lead to loss of details from cases. So CBR is usually seen as a postponement of induction. CBR talks about the usefulness of general knowledge, but that only relates to domain-specific general knowledge. In mental models, on the other hand, general knowledge plays a very important role. It acts as background knowledge for constructing models. This background knowledge is not domain-specific, unlike in case-based reasoning. Generalized models may be constructed from the possibilities that are built in different cases. In mental-model


reasoning, our beliefs and knowledge influence reasoning. They certainly influence the interpretation of premises as well as the process of reasoning.

In CBR, the presence of a greater number of cases marks the richness of the case base. And the greater the number of cases available under a single case-category, the easier it is to find the target case with greater efficiency. The larger the case base, the greater the efficiency of the case-based reasoner. But in mental models, one of the predictions is that inferences (cases/problems) that call for just one mental model should be easier than those that call for multiple models. They should take less time and be less prone to error. The greater the number of models, the harder it is for the reasoner to reason.

Now, how is mental model theory better suited for Diṅnāga’s SA? First, the for-mat of knowledge representation in both is similar. SA, like mental models, is epis-temic in essence, and it does not require explicit means of linguistic expression. CBR essentially invokes linguistic representation. In CBR, drawing on similarities or dissimilarities between the case at hand and a past referent case will not work without an explicit argumentation form (a typical case shown by Ganeri with a five-membered inference form). Mental models, being iconic in representation, work fine without explicit linguistic representation, as shown, which is ideal for Diṅnāga’s SA. To avoid misconception, we must mention here that the lack of explicit linguistic representation of a particular type does not imply that the process of inference is a non-conceptual one. Inference definitely involves concepts, which need not always have explicit internal linguistic representation. But, to possess a concept is to be in a certain sort of epistemic state, having the potential for articulation.

Second, CBR works with a single exemplar. On the other hand, mental models help the cognizer to construct the problem with possibilities, which is ideal for gen-erating and testing instances of sapakṣa and vipakṣa for SA. These possibilities also help the cognizer to test n number of conclusions that can be generated or made available for this particular model. The readers will recall that SA is a two-term argu-The readers will recall that SA is a two-term argu-ment, involving the adequate sign (hetu) and the signified (sādhya)—for example, ‘Here is fire, because here is smoke.’ One infers fire from the presence of smoke. But even in this two-term argument form, the sign (hetu) leading to a sound inference is adequate only if it has the triple character that the cognizer must be aware of. That is, even while inferring for oneself, the cognizer must know the presence of the triple character of the hetu. A mental model would ideally help the cognizer to construct possibilities or models of pakṣa, sapakṣa, and vipakṣa. The models will represent multiple possibilities like the following:

• the positive instance of presence of hetu in the pakṣa where the sādhya is in-ferred (pakṣa);

• the presence of hetu (positive information of presence of hetu in other in-stances) in similar locations (sapakṣa); and finally

• the absence of the hetu (negative information of hetu with respect to a particu-lar location, but not a false information) in dissimilar locations (vipakṣa)


Let the case be: is sound—a product of human effort—impermanent? A singlemental-model representation of the hetu with three characters can be:

[Model for pakṣa]sound – impermanent – produced by human effort

[Model for sapakṣa]43

pot – impermanent – produced by human effortpen – impermanent – produced by human effortbook – impermanent – produced by human effortstatue – impermanent – produced by human effort

[Model for vipakṣa]ākāśa – permanent – not produced by human effortatom – permanent – not produced by human effort

Given this mental-model-based representation of the case—is sound, a product of human effort, impermanent?—a reasoner can construct an integrated picture where instances of both sapakṣa and vipakṣa are incorporated. An integrated model con-sisting of both the sapakṣa model and the vipakṣa model give enough evidence to solve the case at hand—whether sound, a product of human effort, is permanent or impermanent. Such integration benefits the reasoner as it contains both positive and negative instances in a single place or in a singular model.

The mental-model theorists distinguish among three different mental operations or phases: the construction phase, the inspection phase, and the variation phase.44 In the construction phase, a reasoner reflects on the given set of information and attempts to build the mental model accordingly. In the inspection phase, the con-structed model is inspected and the reasoner searches for new information that may not have been explicitly given. In the variation phase, the reasoner tries to con-struct alternative models from the given assertions that refute the putative conclu-sion. When even one such alternative model cannot be constructed, the putative conclusion is considered to be true. In the construction phase of Diṅnāga’s model a reasoner attempts to build the model depending on prima facie information, and in the inspection phase she inspects sapakṣa and vipakṣa cases. In the variation phase she constructs alternative models based on sapakṣa and vipakṣa cases wherever pos- wherever pos-sible and thereafter integrates the models in a single frame.

In Diṅnāga’s system a ‘property locus’ (dharmin) is a conceptual construct. It is a fiction useful for analysis and understanding, but it does not correspond to any realities in the world as it stands independent of our awareness of it.45 One must be cautious while reading the ‘realities of the world.’ The world that we are considering is the world of experience, which is empirically real (saṁvṛti sat) and not ultimately real (pāramārthika sat).46 However, the conceptual constructs correspond to reali-


ties as experienced by the cognizer, and this leaves room for sufficient freedom and flexibility in how we go about accounting for our experiences. So our SA involves nothing but mental, conceptual constructs corresponding to the experienced world. Hence, svadṛṣṭārthaprākaśanam, as previously mentioned in the context of PA, means the expression of the reality cognized by that person himself, representation of which within the cognizer can be of different types. The mental-model theory here seems more naturally extendable to Diṅnāga’s theory, since it leaves open the pos-sibility of having different forms of representation of the experienced external world.

The aim of this essay has been to show that the theory of inference pro- pounded by the Buddhist logicians should not be viewed in the light of formal logic. Svārthānumāna and parārthānumāna reflect two different domains of reasoning with different intentions. Inference‑for‑oneself falls within the domain of psychology of reasoning, whereas inference‑for‑others calls for more explicit logical structure, as it is meant for convincing others. It has also been shown that there are interest-ing parallels between svārthānumāna as depicted in Diṅnāga’s Hetuchakraḍamaru and Johnson-Laird’s mental model theory on the one hand and parārthānumāna and case-based reasoning (CBR) on the other. In spite of their differences, the inferential content of SA and the corresponding PA being the same, these two processes can-not be incompatible with each other. Johnson-Laird himself has pointed out that the mental-model approach and the case-based approach are mutually compatible. This lends plausibility to the suggested reconstruction of the Buddhist theory of inference.

Notes

The first draft of this essay was presented as a paper at a conference organized to celebrate the birth centenary of T.R.V. Murti in 2002. It was also presented at an international seminar, Language, Consciousness and Culture: East West Perspective, organized by the Society of Indian Philosophy and Religion, U.S.A., in 2004. We are grateful to Roy Perrett of the University of Hawai‘i for comments on an earlier draft of this essay.

1 – H. T. Colebrook (1824/1873), S. C. Vidyabhusana (1921), and Stcherbatsky (1930) thought that the Nyāya and the Buddhist theory of inference is a version of Aristotelian syllogism. Max Müller (1853) disagreed with them, but he inter-preted the Nyāya inference as a rule-based deductive inference.

2 – E. Roer 1850.

3 – B. N. Seal (1985, p. 252) wrote: “Hindu inference is . . . a combined Formal-Material Deductive-Inductive process” (S. C. Chatterjee, D. M. Datta, Rad-hakrishnan, and M. Hiriyanna all endorsed this view).

4 – J. R. Ballantyne (1849) pointed out that the theory of inference is a theory of rhetorical exposition.


5 – S. Schayer (1932–1933) used the tools of Natural Deduction to explain in-ference. Ingalls (1951) and Bochenski (1961) also adopted this formal inter-pretation.

6 – B. K. Matilal 1968 and J. N. Mohanty 1971.

7 – C. Oetke 2003.

8 – T. K. Sarkar 1997.

9 – P. N. Johnson-Laird 1983.

10 – Johnson-Laird, Girotto, and Legrenzi 1998, pp. 4–5.

11 – Diṅnāga, Pramāṇasamuccaya (Tib.), in Diṅnāga 1961, and also translation of fragments in Hayes 1988.

12 – Dharmakīrti 1968.

13 – Dharmakīrti 1955.

14 – B. K. Matilal 1977, p. 78.

15 – R. P. Hayes 1988, p. 133.

16 – Svārthaṁ trirūpālliṅgād yad anumeye jñānaṁ tad anumānam (Nyāyabindu 2.3). See also Hayes’ translation of the Pramāṇasamuccaya in Hayes 1988, pp. 231–232.

17 – trirūpa—liṅgākhyānaṁ parārtham anumānam (Nyāyabindu 3.1).

18 – Pakṣa in SA means that which the proponent intends to prove—pakṣo yaḥ sādhayitum iṣṭah—while in PA it means pakṣavacanam, namely the statement of the thesis (Pramāṇasamuccaya III.2). Previously we have seen that pakṣa also means one of the constituents of inference, that is, the subject locus where the signified would be inferred and is therefore called ‘sādhya‑dharmī.’

19 – D. D. Daye (1986, pp. 117–131) has discussed this point.

20 – In Pramāṇasamuccaya III.20, Diṅnāga defines asapakṣa as nothing but the ab-sence of sapakṣa.

21 – R. Prasad 2002, p. 31.

22 – Ibid., p. 36.

23 – Ibid., pp. 36–37.

24 – Quoted in Johnson-Laird 2004, p. 170.

25 – Johnson-Laird and Byrne 1999.

26 – R. P. Hayes 1988, pp. 156–157.

27 – At II.8 (Dharmakīrti 1955).

28 – See table 4. The arguments corresponding to the signs in this table are being mentioned here for the convenience of the reader.


D1: Sound is permanent, because it is knowable. Here, knowability is the sign, sound is the subject-locus, and permanence is the signified.

D2: Sound is impermanent, because it is produced. Here, the property of being produced is the sign, sound is the subject-locus, and impermanence is the signified.

D3: Sound is produced by human effort, because it is impermanent. Here, impermanence is the sign, sound is the subject-locus, and the property of being produced by human effort is the signified.

D4: Sound is permanent, because it is produced. Here, the sign is the prop-erty of being produced, sound is the subject-locus, and permanence is the signified.

D5: Sound is permanent, because it is audible. Here, the sign is audibility, the subject-locus is sound, and permanence is the signified.

D6: Sound is permanent, because it is produced by human effort. Here the sign is the property of being produced by human effort, sound is the subject-locus, and permanence is the signified.

D7: Sound is non-produced by human effort, because it is impermanent. Here the sign is impermanence, sound is the subject-locus, and being non-produced by human effort is the signified.

D8: Sound is impermanent, because it is produced by human effort. Here, the property of being produced by human effort is the sign, sound is the subject-locus, and impermanence is the signified.

D9: Sound is permanent, because it is not amenable to touch. Here, the property of being not amenable to touch is the sign, sound is the subject-locus, and permanence is the signified.

See the Sanskrit reconstruction of Diṅnāga’s Hetucakraḍamaru in Diṅnāga 1933; also B. K. Matilal 1998.

Table 4 Diṅnāga’s Wheel of Reason: A Tabular Representation

+ vipakṣa (pot)+ sapakṣa (ākāśa)[Pseudo-sign: Inconclusive] D1

– vipakṣa (ākāśa)+ sapakṣa (pot)[Adequate sign]D2

+ vipakṣa (+ ākāśa, – lightning)+ sapakṣa (pot)[Pseudo-sign: Inconclusive] D3

+ vipakṣa (pot)– sapakṣa (ākāśa)[Pseudo-sign : Hostile]D4

– vipakṣa (pot)– sapakṣa (ākāśa)[Pseudo-sign: Inconclusive]D5

+ vipakṣa (+ pot, – lightning)– sapakṣa (ākāśa)[Pseudo-sign: Hostile]D6

+ vipakṣa (pot)+ sapakṣa (+ lightning, ākāśa)[Pseudo-sign: Inconclusive]D7

– vipakṣa (ākāśa)+ sapakṣa (+ pot, – lightning)[Adequate sign]D8

+ vipakṣa (+ pleasure, – pot)+ sapakṣa (+ ākāśa, – atom)[Pseudo-sign: Inconclusive]D9

+ = all, + = some, – = none


29 – Indian logic is said to be intentional (logic of properties). In this context, a ‘property’ would signify any locatee, which can be either an abstract property or a concrete object, residing in a locus. So a surrogate proposition in Indian logic is of the locus-locatee model, namely a has f‑ness.

30 – However, later Naiyāyikas did make a distinction between svārthānumāna and parārthānumāna. Gaṅgeśa, a Navya-Naiyāyika, has accepted this distinction.

31 – J. Ganeri 2003.

32 – Ibid., p. 33.

33 – The proper formulation of an argument is said to contain five limbs/avayavas: (1) tentative statement of the thesis to be proved (pratijñā); (2) citation of a rea-son (hetu); (3) mention of an example (udāharaṇa); (4) application of reason and example to the case at hand (upanaya); and (5) final assertion of the thesis (nigamana/siddhānta).

34 – J. Ganeri 2003, p. 43.

35 – L. Ronald 1999, p. 99.

36 – Ibid., p. 40.

37 – Ibid., pp. 35–36.

38 – Ibid., p. 36.

39 – We use the same set of symbols (F, G, a, b, c) used by Ganeri for readers’ con-venience in understanding.

40 – Levi says “The basic pattern of legal reasoning is reasoning by example. It is reasoning from case to case. It is a three-step process described by the doctrine of precedent in which a proposition descriptive of the first case is made into a rule of law and then applied to a next similar situation. The steps are these: similarity is seen between cases; next the rule of law inherent in the first case is announced; then the rule of law is made applicable to the second case” (quoted Ganeri 2003, p. 43 n. 9).

41 – Johnson-Laird 2004, p. 171.

42 – We are grateful to Johnson-Laird for offering his opinion on the differences be-tween the two theories in our correspondence with him in 2004.

43 – Diṅnāga mentions another alternative in the sapakṣa model (D8): lightning im‑permanent—not produced by human effort. This however, does not affect the conclusion.

44 – M. Knauff 2007, p. 27.

45 – R. P. Hayes 1988, p. 154.


46 – According to Vijñānavāda, all our phenomenal knowledge is without any es-sence or truth (niḥsvabhāva) and is a creation of avidyā. There is nothing that may be called external. Everything is the imaginary creation of the mind (svacit‑ta), which has been accustomed to create imaginary appearances from begin-ningless time. We construct the external world ourselves and are then deluded as if it exists by itself (nirmmitapratimohi).

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Dinnaga and Metal Modes-A Reconstruction

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