Philosophy East and West

Volume 60, Number 3, July 2010

Amita ChatterjeeSmita SirkerDiṅnāga and Mental Models: A ReconstructionPhilosophy East and West - Volume 60, Number 3, July 2010, pp. 315-340

University of Hawai'i Press

Abstract:

In the fifth century c.e., Diṇnāga introduced a distinction between inference for-oneself (svarthānumāna) and inference-for-others (parārthānumāna), which was adopted by all later pramāṇa theorists. A reevaluation of this well-known distinction has led us to some philosophically significant theses, which we propose to discuss here. Many scholars have already pointed out that (a) the aim of the Buddhists in developing a theory of inference was different from that of a formal logician; (b) svarthānumāna falls in the domain of psychology of reasoning, while parārthānumāna falls in the domain of logic proper; and (c) parārthānumāna should be considered a model-theoretic as opposed to a proof theoretic enterprise. In consonance with these views, it is aimed to show that (1) Diṇnāga's account of good inferential process leading to sound inference as laid down in the Hetucakaraḍamaru is very similar to the Mental Model Theory proposed by P. N. Johnson-Laird and others, and (2) although Jonardon Ganeri's reinterpretation of the early Nyāya inference as a type of case-based reasoning may be extended to the Buddhist parārthānumāna, the most plausible reinterpretation of svārthānumāna can be given in terms of mental models.

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Philosophy East & West Volume 60, Number 3 July 2010 315–340315© 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 forCognitive Science, Jadavpur University

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

It is platitudinous to say that whenever we try to read some ancient text or interpretsome 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 thetime. Aristotle, for example, had a wax-tablet view of memory. Leibniz used themodel of a clock to explain the harmonious universe. Freud used a hydraulic model ofthe flow of libido, and the telephone switchboard model guided psychologists whilethey were theorizing on intelligence. Nearer to our time, we have seen physicistsexplaining the structure of an atom by the model of the solar system and cognitivescientists explaining the working of the human mind by the analogy of a computer. Inthis 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 ofthe Buddhist ‘logical’ scenario, which we think will enable us to understand someperplexing issues in the given area and offer some solutions to them.ITheory of inference, which is the core of any logical theory, belongs to the pramāṇatheory in Indian philosophy. Stalwarts of Indian philosophy have attempted to gleanlogical 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;6and (f ) inferences cannot be understood at all within the framework of monotonicreasoning—these are instances of non-monotonic reasoning,7 especially of defaultreasoning.8Indian theories of inference definitely form the core of Indian logic. But be-cause of its epistemological origin and motivations, the contour of Indian logic doesnot nicely fit the outline of Western logic, which moves around the consequencerelation and its formal properties. Though these theories of inference tell us how to

Page 2316Philosophy East & Westdistinguish good arguments from bad arguments, people hesitate to admit it as logicwholeheartedly. 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 nothave the concepts of formal system, entailment, validity, or tautology. We grant thatIndians did not develop any axiomatic/formal system, nor did they have the notion oftautology. 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 wereinterested in tracing the psycho-causal steps underlying the reasoning processes ofordinary people in their everyday life. Let us explain these points a bit.Modern logicians distinguish between proof theory and model theory. Whileproof theory follows a rule-based axiomatic approach, model theory proceeds bydeveloping models or systems of interpretations. A model theory is supposed to tellus 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 doesnot necessarily presuppose a sterile, content-free environment and is often found togo beyond the formal properties of the entailment relation. Indian logicians, we havealready mentioned, had no truck with pure formal logic. Besides, as epistemologists,the pramāṇavādins were interested to find out how inference results from a numberof cognitive states and what conditions give rise to cognitive certainty. They were notprimarily concerned with the question of how ideally rational human beings reasonunder ideal conditions.The last point leads us to the ‘rationality debate’—a debate that has drawn a lotof attention due to cognitive psychologists for the last forty years. Previously it wassupposed that people reason by following the laws of the traditional Aristotelian logicor the rules of the first-order predicate calculus. But several experiments on humanreasoning have revealed that a majority of us, most of the time, do not use the rules ofclassical logic while reasoning. Hence the question how do people actually reasonor 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 mentalmodels and not by following rules admitted in the Natural Deduction system.9 Therules of the Natural Deduction system are such that it is quite unlikely that these areinnate. People cannot grasp these rules without their being taught explicitly. If logi-cal thinking depended on grasping these rules, then common people without logicaltraining 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 rulesof inference, but rather they rely on their ability to understand the premises. Theybuild mental models of the relevant states of affairs based on this understanding andgeneral knowledge. They can arrive at a conclusion that is true in these models andthey can test the validity of an inference by establishing that no alternative models ofthe 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 capturewhat is common to these.”10

Page 3Amita Chatterjee, Smita Sirker317Before we proceed further we must point out that the model theorists and themental model theorists use the word ‘model’ in different though related senses. Whilemodel theory tells us under what interpretations a given proposition turns out to betrue and an inference sound, a mental-model theory deals with how the premisesof a sound inference is mentally represented to a reasoner. The former addressesa 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. Formallogic—axiomatic or natural deductive—brackets the process of inference that goeson within us and focuses on a linguistically expressed product of that process. Anargument or an argument form is always expressed through some symbol, and whenan argument is evaluated, a logician needs to interpret that symbol and determine thetruth 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 internallyrepresented to a reasoner, which enables her to arrive at a conclusion that fits thehappenings in the external world. Since the reasoner reaches the conclusion througha causal chain of contentful beliefs/cognitions, it becomes imperative to all who dealwith inferential process to conjecture how our beliefs get their content and in whatmode such contents are represented. The mental-model theorists hypothesize that theworld is represented to the reasoner through some mental models and not throughexplicit propositional representations of logical rules. These models are said to havea structural and a relational similarity to the external elements of which they are arepresentation. With these models, the reasoner may construe one or many differentpossibilities of any given problem before arriving at her conclusion. Mental modelsare iconic and can be construed with pictures, images, directed graphs, diagrams, etcetera, depending on individual competence in handling them.In Indian theories of inference and in Buddhist theory in particular, the primaryemphasis has always been on the process of inferential representation and not onlogical, rule-governed symbol manipulation. We would, therefore, like to argue thatsvārthānumāna (SA) or inference-for-oneself of the Buddhists provides us with themental 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 tobe viewed from the proof-theoretic perspective as formal rule-governed demonstra-tions but as models of reasoning that guide one to sound conclusions. To convincereaders 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’sPramāṇasamuccaya11 and Dharmakīrti’s Pramāṇavārtikka12 and Nyāyabindu.13IIThe 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-

Page 4318Philosophy East & Westfuted an earlier Vaiśeṣika view on this distinction, which leads us to think that theremight 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, followingFrauwallner, maintained that Diṅnāga probably borrowed this important distinctionfrom the Sāṃkhya logicians.15 Though this distinction has been admitted in almostall systems of classical Indian philosophy, no one except Diṅnāga has attached somuch significance to it. Dharmakīrti did not always see eye to eye with Diṅnāga, yethis exposition of this distinction in the Pramāṇavārttika and Nyāyabindu is in keep-ing with Diṅnāga’s understanding, according to many Buddhist scholars. Diṅnāgaand Dharmakīrti desisted from giving a general definition of inference simply be-cause they considered these two kinds of inference so different from each other thatthey could not bring them under the same defining characteristics. They, therefore,explained the nature of each kind of inference separately, and, as there are onlytwo kinds of inference, to explain the nature of each one of them is to explain thenature of inference. The Naiyāyikas (post-Diṅnāga), on the other hand, first gave adefinition of inference and then classified inference into SA and PA, thus somewhat

undermining the sharpness of the distinction. In spite of their different nature, boththese means of knowledge are called anumāna because both SA and PA produceknowledge of objects that cannot be obtained perceptually (parokṣārtha-pratipatti).Before giving the standard definition of SA and PA we first need to describe theminimum 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) thesignified (sādhya-dharma), and (c) the subject-locus (pakṣa). When, for example, oneinfers fire on a hill—seeing smoke coming out of the hilltop—smoke is generallytaken 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) havingthree characteristics.16 PA is defined as the expression or statement of the logical signhaving 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 experiencedby the person making an inference (parārthānumānaṁ svaḍṛstārthaprakāśanam). Thefirst clause is related to the soundness of inference and the second clause emphasizesthe inadequacy of mere hearsay evidence. The word ‘artha’ mentioned here has aspecial significance for our theory that we will discuss later.The major difference between SA and PA lies in the fact that while SA dealswith psychological conditions, that is, causally connected cognitive states leading toone’s own inferential knowledge (jńānātmakam), PA essentially deals with the properlinguistic 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 beconvinced? 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 theNaiyāyikas and almost all modern interpreters of Indian logic have concentrated onPA. Again, as SA contributes to one’s own knowledge, here one’s private knowledgebase enables one to infer. PA, on the other hand, is meant for public demonstrationand hence must draw upon resources from a third person / public point of view.

Page 5Amita Chatterjee, Smita Sirker319According 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 twomembers; in PA the thesis need not be stated because having heard the premises thehearer can arrive at the conclusion without any difficulty. Let us consider here oneexample 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 isno fire there is no smoke as in a lake (dṛṣṭānta-vacanam).In the example of SA, the intermediate steps have not been stated, though Diṅnāgahas 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 itis obvious. Another point that becomes evident from the examples above is that theBuddhist inferences are of the form ‘Q because P’ and not of the form ‘P thereforeQ.’19One infers for oneself in order to have a certain awareness of some object, whichone cannot directly apprehend through sense perception. So the SA theory specifiesconditions 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 acaveat: Diṅnāga’s specification of a sign leading to a sound inference should not betaken as a normative enterprise; it should rather be looked upon as a description orreporting of the steps usually followed by a competent reasoner. A property P1 canbe a sign for another property P2, says Diṅnāga, provided (a) the first property P1 isobserved at least once along with the second property P2 and (b) if no instance hasbeen 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) orheterologues.The significance of the theory of the sign with three characters will be clear if weapply it to the case of an actual inference. Consider the condensed inference: soundis 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 beingproduced by human effort is the logical sign. A similar location or a homologueis similar to the subject-locus with respect to the presence of the signified, but isdifferent from the subject-locus. So, in this case, a homologue is any locationother than sound where the property of being non-eternal is present—say, a pot. A

Page 6320Philosophy East & Westdissimilar 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 eternalthing.Diṅnāga’s formulation of the three characters highlights not only the subjectivenature 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 toquantify pakṣa, sapakṣa, and vipakṣa. He was severely criticized by Uddyotakara forthat. Dharmakīrti, therefore, presents the final formulation of the three characters ofthe 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 astatement 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 thegenuine 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 thatthe linguistic expression of the statement containing an adequate sign together withthe example is called an anumāna only in a secondary sense (kāraṇe kāryopacārāt).These statements cause an inferential cognition in a listener indirectly and hence arecalled an inference (anumāna). The object of inferential theory in the primary senseis 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 cognitionthrough a causal sequence, mentioned above. She then expresses it in the standardform 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 betweenthe 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, theentire drama, might be silently, or sub-vocally enacted, but certainly not withoutinvolving any use of language.”21 Nor does a PA cease to be knowledge-producingsimply because it has been expressed in language. It is true that in the example of SAthe 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 theother hand, in the example of PA, knowledge resulting from the ascertainment of thetriple-character sign has been explicitly stated in the form of a positive or negativestatement of universal concomitance, thus making the structure of the inference per-spicuous. Still, that does not amount to any logical difference between two kinds ofinference. For, as has been pointed out by Rajendra Prasad, “the set of conditions ofthe validity of inference, whether it is in the SA form, or in the PA form is the same.”22

Page 7Amita Chatterjee, Smita Sirker321Only 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 whichlegitimize drawing its conclusion from its premises is not wholly identical with the set ofrules which legitimize drawing the latter’s conclusion from its premises. Since this is nottrue 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 tworepresent the two basic and broadest types, or forms, of inference.23

We think we can justify the proposed distinction between SA and PA by rememberingthat SA belongs to the realm of mental reasoning and PA to the realm that is acceptedas logic proper. In logic proper, the connection obtaining between the premise(s) andthe conclusion needs to be shown explicitly; mere seeing of the connection is notenough. We hope to explain the distinction better by using the tool of mental model.IIIJohnson-Laird developed Kenneth Craik’s intuitive idea of an inner mental replicathat 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 ofthem, react to future situations before they arise, utilize the knowledge of past event[s] indealing 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.24Johnson-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 hypothesisabout mental models yields a descriptively adequate account of reasoning. The the-ory of mental models postulates that human reasoning depends on understanding themeaning of the given premises and then uses this meaning and general knowledgeto construct mental models of the possibilities under description. There are five mainassumptions of the mental-model theory, and these make it different from the othertheories of human reasoning. The first assumption is that a mental model representsa possibility. A model captures what is common to the different ways in which thepossibility 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 evenabstract ideas. They can represent discourse about real, hypothetical, or imaginarycases, and they reside in long-term memory as a representation of knowledge.The second assumption is the principle of truth; that is, mental models representwhat 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, andif they retain the footnotes then they can construct explicit mental models, in which

Page 8322Philosophy East & Westclauses are represented when they are false. The principle also postulates that peoplenormally do not represent what is false. This helps in reducing the volume of thingsthat 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 rationalprinciple that a conclusion is valid if it holds in all the models of the premises, thatis, it has no counterexample, and so it is necessary, given the premises. Johnson-Lairdand Ruth Byrne25 claim that this theory has theoretical advantages. It dovetails withother 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 tohave empirical advantages. Reasoners are faster and make fewer errors with deduc-tions that require them to construct only one model than with deductions that requirethem to construct multiple models.

The fourth assumption is that mental models are iconic. So reasoners can use amodel to draw a conclusion that does not correspond to any of the representationsused to construct a model.The fifth assumption holds that while reasoning using mental models one neednot 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 theoryof inference let us see how Johnson-Laird explains syllogistic reasoning. According tohis analysis, all sixty-four kinds of syllogism are variations of the following example:All artists are beekeepersAll beekeepers are chemistsHe says that to arrive at a true conclusion from these two premises, we need notknow rules of syllogistic inference or a sophisticated system of notation. All we needto do is to construct adequate mental models. He asks us to pretend that we havethe power to conjure up individuals who fulfill one or more of the roles stated in thepremises. We can think of individuals who fulfill all the roles at one time, and theseindividuals may be represented in the form of arrays in a mental model as:artist – beekeeper – chemistartist – beekeeper – chemistartist – beekeeper – chemistWe are also aware of those persons who are beekeepers and chemists but not artists,for whom the representing array is:beekeeper – chemistbeekeeper – chemistbeekeeper – chemist

Page 9Amita Chatterjee, Smita Sirker323We also know from common sense and careful consideration of the problem thatthere can be chemists who are not beekeepers. So we also have the following array

at our disposal:chemistschemistschemistsOnce we have created a mental model that arrays all the information that can betaken 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 simplylook at the tableaux and reach a positive conclusion. On the other hand, if we wantto answer the question whether all chemists are beekeepers, we would answer inthe 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 ofthe premises that is inconsistent with the model. An inference is sound if and onlyif there is no way of interpreting the premises that is consistent with a denial of theconclusion. The benefit of this model-based approach lies in the prospect of creatingan ‘integrated picture’ of the models built out of the given problem. This integrationenables the reasoner to look for both the confirming/positive cases as well as thedisconfirming/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 isimpermanent because it is produced by human effort. Diṅnāga wants us to considera few (at least one) object(s) possessing the property of being produced by humaneffort 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 penimpermanent object – [not produced by human effort] – object lightningimpermanent object – [not produced by human effort] – object thunderpermanent object – [not produced by human effort] – object ākāśapermanent object – [not produced by human effort] – object atom

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

Page 10324Philosophy East & Westis, no counterexample of the thesis is known to be present—we can safely concludethat 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 considerationalready established information. Let us analyze two such inferences mentioned inDiṅnāga’s table.1. Sound is permanent because it is knowableFollowing Diṅnāga, the possibilities related to this inference may be tabulated asfollows:permanent object – knowable object – object ākāśapermanent object – knowable object – object atompermanent object – [but not knowable] – nilimpermanent object – knowable object – object potimpermanent object – knowable object – object clothimpermanent object – knowable object – object bookimpermanent object – knowable object – object penimpermanent object – [but not knowable] – nilSince there are objects, which are knowable but impermanent, sound may not bepermanent because it is knowable. In this case, the third condition of the sign withthree characters has been violated. Whenever a given frame shows that the sign ispresent in the heterologue, no conclusion is warranted. In case someone draws aconclusion in contravention of the third condition, the inference is vitiated by thefallacy 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 atomimpermanent object – produced object – object potimpermanent object – produced object – object clothimpermanent object – produced object – object bookimpermanent object – [but not produced] – object lightningimpermanent object – [but not produced] – object thunder

Page 11Amita Chatterjee, Smita Sirker325The sign ‘being produced’ is absent in the homologue (any permanent object) butpresent in the heterologues. So the inference is doubly erroneous. This frame isgiven 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 isnot 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 withthe sādhya; that is, one is just taking stock of the information available from the dataat hand. It may be asked: how many models does an individual need to constructto arrive at the conclusion? Definitely, the number is finite. But if there is essentialidentity between the sign and the signified, or a causal connection, then one singlemodel may suffice.When, however, one uses a PA, one needs to make the connection explicit andexpress 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 premisesmerely by virtue of the form of the argument, but because the background modelsprovide 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 thesoundness 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 certainrules. Without keeping these rules in mind one cannot possibly design suitable mod-els corresponding to different inferences. But that is not true. One first constructsall possible alterative models depending on the information given, integrates thesemodels, and then formulates a rule. Besides, the rules that one is supposedly usingare all related to the ascertainment of the relation of pervasion (vyāpti) between thesign and the signified. The rule of ascertainment of pervasion, we must point out, isagain 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 determinedby constructing models of co-occurrence and non-occurrence of these propertiesin some locations on the basis of observation, as is evident from examples of arrayslike pot-ākāśa, lightning-ākāśa-pot, et cetera, in the Hetucakraḍamaru. FollowingDiṅnāga, Hayes also has explained pervasion with the help of models.26 To explainthe notion of pervasion, Hayes wants us to imagine a small universe that is made upof four loci (a, b, c, d) and four properties (W, X, Y, Z). Let us also imagine that thesefour properties are distributed in the four loci as follows:aW, X, Y, ZbW, X, , ZcW, X, YdW, XFrom 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

Page 12326Philosophy East & WestY are in a relation of non-reciprocal pervasion because though X pervades Y, Y doesnot pervade X; that is, X is erratic with respect to Y though Y uniformly co-occurswith X. It therefore appears from the Hetucakraḍamaru and Hayes’ explanation thatDiṅnāga’s system agrees with the fifth assumption of the mental model theory, whichis: models first, rules later.Adoption of the mental model theory enables us to answer another puzzle aswell. 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, whatis the need to state that the sign must also be absent in heterologues? Isn’t the secondimplied 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 nototherwise. In order to show this, both characters have been mentioned. . . . And sincethey must not allow any exception, only one of them should actually be expressed, notboth of them together.27Dharmakīrti’s view accords well with the Nyāya position. Besides, strictly from alogical standpoint, where the interpretation of negation is standard, (II) and (III) areequivalent 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 thisquestion. Diṅnāga was concerned with building a complete frame, which will en-able one to infer correctly even without the knowledge of any logical rule. Withoutconsidering 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 besound. The logical equivalence of (II) and (III) may follow from the available set ofinformation but is not in any way operative in the actual process of reasoning; hencehis insistence on all three conditions.A mental model, we have seen, expresses a possibility. Diṅnāga, in hisHetucakraḍamaru, has constructed all possible models that we need to consider inany inferential situation. As a sign may be present in all, some, or no similar locationsand 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 ofa sign’s residing in the subject locus constant.28In a syllogism the location of the middle term in the premises changes the formof the argument. But in neither an SA nor a PA does the location of occurrence of thesign in the premise(s) have any logical significance. For the basic unit here is of theform ‘a has f-ness’ or ‘f-ness-in-a.’ Whichever way the sign may be considered, theinformation content as well as the logical significance remains the same in a locus-located frame.29 Hence, when translated into language, sound inferences may takeonly two different logical forms, BARBARA and CESARE, depending on the nature

Page 13Amita Chatterjee, Smita Sirker327of 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 orof syllogism. We wholeheartedly concur with Daye that meta-theories of PA and ofpropositional and predicate logic are neither fully isomorphic nor fully compatible.IVSo far we have shown the similarity between Diṅnāga’s Wheel of Reason andJohnson-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 tobelieve in her piece of cognition. Thus SA needs to be translated linguistically into PAthat may be interpreted according to more than one model. Jonardon Ganeri (2003),following the Nyāyasūtra with Nyāyabhāṣya, has shown how a pańcāvayavi-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) didnot draw any distinction between SA and PA.30 They spoke of no such classificationof inference. They had shown how good arguments must be presented in a structuredfive-step inference. Ganeri contends that the logic of ancient India is an informallogic of case-based reasoning.31 He writes:I would like to argue that the Nyāya-sūtra presages a transformation in Indian thinkingabout logic. And this in two inter-related respects: in the beginnings of a shift of interestaway from the place of argumentation within dialectic and debate and towards a greaterconcern with the more formal properties of sound inference, and in a parallel correlatedshift from case-based to rule-governed accounts of logical reasoning. The logic of ancientIndia, 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 showsa strong tendency towards formalisations, the logic of ancient India tried to modelinformal patterns of case-based reasoning, patterns that are increasingly becomingrecognised as widespread and representative of the way much actual reasoning takesplace.”34CBR refers to a style of designing a system so that thought and action in a givensituation are guided by a single distinctive prior case (precedent, prototype, exem-plar, or episode).35 According to the CBR theorists, human reasoning, memory, andlearning 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 processof 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, forexample, solves new problems by retrieving traces of relevant prior problems from

Page 14328Philosophy East & Westmemory, 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 thatsome new object belongs to the same category on the grounds that it resembles insome appropriate and context determined manner . . . one of the exemplars.”36Ganeri 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 ofa similarity with an example (udāharaṇa). For instance, one infers the existence ofunseen 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 associatedin other places like the kitchen (udāharaṇa). Here an object is inferred to have anunobserved property on the grounds that it has another, observed one. The citationof 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 understandGaneri’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-stepinference pattern will be:(i) The hill possesses fire – pratijńā (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-presentwith 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 theother on a dissimilar one.37 In the following schematic representation of the five-stepproof-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 perceptionof a plume of smoke, just as the two have been found associated in other places, likethe 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 formatin which parārthānumāna would be made following the typical five-step proof. Thecitation of an example (either a similar instance—sādharmya dṛṣṭānta—or a dissimi-

Page 15Amita Chatterjee, Smita Sirker329lar instance—vaidharmya dṛṣṭānta) and its application in the case at hand helps notonly 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 andconvincing them as well. As stated earlier, a case-based reasoning pattern typicallyinvolves 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 decisionor 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 toprove 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 smokyproves Ga, because b is similar to a.[example]bWhatever is smoky is fiery, like the kitchen stovehas the ‘character of a’ because it issimilar to a[application]a

The hill is like thatis the same as b with respect to G[conclusion]Ga∴ The hill is fieryG = fiery; F = smoky; a = hill; b = kitchen stoveTable 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 lakedoes not have the ‘character of a’because it is dissimilar to a[application]aThe hill is not likeis not the same as b with respect to G[conclusion]Ga∴ The hill is fieryG = fiery; F = non-smoky; a = hill; b = lake

Page 16330Philosophy East & Westlectical 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, canbe 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’sthree-member PA can also be presented in the CBR schema. Let us show an examplewhere one infers fire on a hill (see table 3).PA

1. Here is fire2. Because here is smoke3. Wherever there is smoke, there is fire, for example in a kitchen, and whereverthere 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 ornot (pakṣa), and‘b’, ‘c ’ = the cited example (udāharaṇa)39Having discussed Ganeri’s proposal and demonstrated how Diṅnāga’s PA mayalso be interpreted in a CBR model, what is left to be addressed is why we think thatthe mental-model theory is better suited for interpreting Diṅnāga’s SA than CBR. Itmay appear that there is not much difference between the mental model theory andthe 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 acollection of different individual cases, and given a new problem situation or prob-Table 3 Ga = The Hill Has Fire —Three-step ProofSādhyaGaHere is fireHetuFaBecause here is smokeproves Ga, because b is similar to a.Pakṣa:sapakṣa(an object other than athat possesses G )bWherever there is smoke, there isfire, for example, in a kitchenhas the ‘character of a’ because it issimilar to avipakṣa(an object other than athat does not possess G )cWherever there is no fire there is

no smoke, as in a lakedoes not have ‘character of a’because it is dissimilar to aG = fire; F = smoke; a = hill; b = kitchen; c = lake

Page 17Amita Chatterjee, Smita Sirker331lem case, there is a relevant retrieval from the source case base. The distinguishingfeature of such a system is that the cases that are stored in the case base are notgeneralized versions of different cases. Rather each individual case is stored with itsdistinctive features. When presented with a new case, it is matched with each caseavailable in the case base, and the closest relevant match is recalled. Taking a cluefrom the recalled case provides the solution to the new one. Case-based reasoningshave been used for medical diagnostics and legal reasoning40 and also in artificial-intelligence models. Mental model reasoning involves constructing models on thebasis of the given information. These models, we have seen, have the same structureas that of their corresponding counterparts in the real world. Each model representsa possibility, capturing what is common to the different ways in which the possibilitycould occur. These models, we have seen, are said to be iconic; that is, the parts ofthe 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 toJohnson-Laird the advantage of such an iconic nature of the mental model is that onecan build a model with some given assertions and then use the model to come to aconclusion 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 representationscloser to language than to reality. This characteristic of CBR makes it a better modelfor PA, which is śabdātmakam, than for SA, which is jńānātmakam. Johnson-Lairdsays that the two theories appear to be compatible in principle, yet the particularmechanisms and representations invoked by the two theories may be different.In CBR, to prove a thesis (a case), a single relevant similar or dissimilar exemplaris sufficient. We do not play around with different alternatives or possibilities. A singlematching case with respect to either the presence of a property (hetu) or the absenceof a property (refer back to the previous example of proof by similarity and proof bydissimilarity) is good enough. In the mental-model approach, one builds differentpossibilities 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 mentalmodel typically searches for the presence of counterexamples, and a model is saidto 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-specificgeneralization. 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. SoCBR is usually seen as a postponement of induction. CBR talks about the usefulnessof general knowledge, but that only relates to domain-specific general knowledge. Inmental models, on the other hand, general knowledge plays a very important role. Itacts as background knowledge for constructing models. This background knowledgeis 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

Page 18332Philosophy East & Westreasoning, our beliefs and knowledge influence reasoning. They certainly influencethe 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 casebase. And the greater the number of cases available under a single case-category, theeasier it is to find the target case with greater efficiency. The larger the case base, thegreater the efficiency of the case-based reasoner. But in mental models, one of thepredictions is that inferences (cases/problems) that call for just one mental modelshould be easier than those that call for multiple models. They should take less timeand be less prone to error. The greater the number of models, the harder it is for thereasoner 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 similaritiesor dissimilarities between the case at hand and a past referent case will not workwithout an explicit argumentation form (a typical case shown by Ganeri with a five-membered inference form). Mental models, being iconic in representation, work finewithout explicit linguistic representation, as shown, which is ideal for Diṅnāga’s SA.To avoid misconception, we must mention here that the lack of explicit linguisticrepresentation of a particular type does not imply that the process of inference is anon-conceptual one. Inference definitely involves concepts, which need not always

have explicit internal linguistic representation. But, to possess a concept is to be in acertain sort of epistemic state, having the potential for articulation.Second, CBR works with a single exemplar. On the other hand, mental modelshelp 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 alsohelp the cognizer to test n number of conclusions that can be generated or madeavailable 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. Buteven in this two-term argument form, the sign (hetu) leading to a sound inference isadequate only if it has the triple character that the cognizer must be aware of. Thatis, even while inferring for oneself, the cognizer must know the presence of the triplecharacter of the hetu. A mental model would ideally help the cognizer to constructpossibilities or models of pakṣa, sapakṣa, and vipakṣa. The models will representmultiple 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)

Page 19Amita Chatterjee, Smita Sirker333Let 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]43pot – 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 effortGiven this mental-model-based representation of the case—is sound, a product ofhuman effort, impermanent?—a reasoner can construct an integrated picture whereinstances of both sapakṣa and vipakṣa are incorporated. An integrated model con-sisting of both the sapakṣa model and the vipakṣa model give enough evidence tosolve the case at hand—whether sound, a product of human effort, is permanent orimpermanent. Such integration benefits the reasoner as it contains both positive andnegative instances in a single place or in a singular model.The mental-model theorists distinguish among three different mental operationsor phases: the construction phase, the inspection phase, and the variation phase.44In the construction phase, a reasoner reflects on the given set of information andattempts to build the mental model accordingly. In the inspection phase, the con-structed model is inspected and the reasoner searches for new information that maynot 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 putativeconclusion is considered to be true. In the construction phase of Diṅnāga’s model areasoner attempts to build the model depending on prima facie information, and inthe inspection phase she inspects sapakṣa and vipakṣa cases. In the variation phaseshe 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. Itis a fiction useful for analysis and understanding, but it does not correspond to anyrealities in the world as it stands independent of our awareness of it.45 One must becautious while reading the ‘realities of the world.’ The world that we are consideringis the world of experience, which is empirically real (saṁvṛti sat) and not ultimatelyreal (pāramārthika sat).46 However, the conceptual constructs correspond to reali-

Page 20334Philosophy East & Westties as experienced by the cognizer, and this leaves room for sufficient freedom andflexibility in how we go about accounting for our experiences. So our SA involvesnothing 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, representationof which within the cognizer can be of different types. The mental-model theory hereseems 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 withdifferent intentions. Inference-for-oneself falls within the domain of psychology ofreasoning, whereas inference-for-others calls for more explicit logical structure, asit 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 andcase-based reasoning (CBR) on the other. In spite of their differences, the inferentialcontent 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 thatthe mental-model approach and the case-based approach are mutually compa-tible. This lends plausibility to the suggested reconstruction of the Buddhist theory ofinference.NotesThe first draft of this essay was presented as a paper at a conference organized tocelebrate the birth centenary of T.R.V. Murti in 2002. It was also presented at aninternational seminar, Language, Consciousness and Culture: East West Perspective,organized by the Society of Indian Philosophy and Religion, U.S.A., in 2004. We aregrateful to Roy Perrett of the University of Hawai‘i for comments on an earlier draftof 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 versionof 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 ofrhetorical exposition.

Page 21Amita Chatterjee, Smita Sirker3355 – 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 offragments 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 jńānaṁ tad anumānam (Nyāyabindu2.3). 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 yaḥsādhayitum iṣṭah—while in PA it means pakṣavacanam, namely the statementof the thesis (Pramāṇasamuccaya III.2). Previously we have seen that pakṣa alsomeans one of the constituents of inference, that is, the subject locus where thesignified 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 beingmentioned here for the convenience of the reader.

Page 22336Philosophy East & WestD1: 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 ofbeing produced is the sign, sound is the subject-locus, and impermanence isthe 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 beingproduced 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 thesignified.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 thesign 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, theproperty 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 Diṅnāga1933; 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

Page 23Amita Chatterjee, Smita Sirker33729 – 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 propertyor a concrete object, residing in a locus. So a surrogate proposition in Indianlogic is of the locus-locatee model, namely a has f-ness.30 – However, later Naiyāyikas did make a distinction between svārthānumāna andparārthānumāna. 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 (pratijńā); (2) citation of a rea-son (hetu); (3) mention of an example (udāharaṇa); (4) application of reasonand 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 isreasoning from case to case. It is a three-step process described by the doctrineof precedent in which a proposition descriptive of the first case is made intoa 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 isannounced; then the rule of law is made applicable to the second case” (quotedGaneri 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 theconclusion.44 – M. Knauff 2007, p. 27.45 – R. P. Hayes 1988, p. 154.

Page 24338Philosophy East & West46 – According to Vijńānavāda, all our phenomenal knowledge is without any es-sence or truth (niḥsvabhāva) and is a creation of avidyā. There is nothing thatmay 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 deludedas if it exists by itself (nirmmitapratimohi).References

Ballantyne, J. R. 1849. “On the Argumentative Portion of the Nyāya Philosophy.”Benares Magazine 1 (July).Bochenski, I. M. 1961. A History of Formal Logic. Translated by I. Thomas. NotreDame: University of Notre Dame Press.Colebrook, H. T. 1824/1873. “On the Philosophy of the Hindus: Part II—On theNyāya and Vaiśeṣika Systems.” Transactions of the Royal Asiatic Society 1.Reprinted in Miscellaneous Essays, edited by H. T. Colebrook, vol. 2. London:Trubner and Co.Craik, K. 1943. The Nature of Explanation. Cambridge: Cambridge University Press.Daye, D. D. 1986. “Metalogical Remarks on the Procrustean Translation of the Bud-dhist Parārthānumāna into the Anglo-European Predicate Calculus.” In BuddhistLogic and Epistemology, edited by B. K. Matilal and R. D. Evans. Dordrecht: D.Reidel Publishing Company.Dharmakīrti. 1955. Nyāyabindu with Dharmottara’s Nyāyabindutīkā and DurvekaMiśra’s Pradīpa. Edited by V. Malvania. Patna: K. P. Jayasawal Research Institute.———. 1968. Pramāṇavārttika with Manorathanandin’s Vrtti. Edited by SwamiDwarikadas Shastri. Varanasi: Bauddha Bharati.Diṅnāga. 1933. Hetucakraḍamaru. Sanskrit reconstruction in D. C. Chatterji,Hetucakranirṇaya. Indian Historical Quarterly 9.Diṅnāga. 1961. Pramāṇasamuccaya (Tib.). Partly “reconstructed” in Sanskrit by MuniSri Jambuvijayji in Vaiśeṣika sūtra of Kanada. With commentary of Candrananda,Appendix 7. Baorda: Oriental Institute, Gaekwad’s Oriental Series 136.Ganeri, Jonardon. 2003. “Ancient Indian Logic as a Theory of Case-Based Reason-ing.” Journal of Indian Philosophy 32(1–3): 33–45.Gautama, Akṣapāda. 1939. Nyāya-sūtra. Edited by G. Jha. Poona: Oriental Series.Hayes, R. P. 1988. Dignaga on the Interpretation of Signs. Dordrecht: Kluwer Aca-demic Publishers.Ingalls, D.H.H. 1951. Materials for the Study of Navya Nyāya Logic. Cambridge, MA:Harvard University Press.

Page 25

Amita Chatterjee, Smita Sirker339Jha, G. 1984. The Nyāyasūtras of Gautama with the Bhāṣya of Vātsyāyana and theVārttika of Uddyotakara. Vol. 1–4. Delhi: Motilal Banarasidass.Johnson-Laird, P. N. 1983. Mental Models: Towards a Cognitive Science of Language,Inference and Consciousness. Cambridge, MA: Harvard University Press.———. 2004. “Mental Models and Reasoning.” In The Nature of Reasoning, editedby Jacqueline P. Leighton and Robert J. Sternberg. Cambridge: Cambridge Uni-versity Press.Johnson-Laird, P. N., and Ruth M. J. Byrne. 1999. “Mental Rule, OK? A Reply toFetzer.” Minds and Machines 9 (1): 111–118.Johnson-Laird, P. N., Vittorio Girotto, and Paolo Legrenzi. 1998. “Mental Models:A Gentle Guide for Outsiders.” http://www.si.umich.edu/ICOS.gentleintro.html.Knauff, Markus. 2007. “How Brains Reason Logically.” Topoi—An International Re-view of Philosophy 26 (1) (Spring).Levi, E. H. 1949. An Introduction to Legal Reasoning. Chicago: University of ChicagoPress.Matilal, B. K. 1968. The Navya-Nyaya Doctrine of Negation. Cambridge, MA: Har-vard University Press.———. 1977. “Nyāya-Vaiśesika.” In A History of Indian Literature, vol. 6. Wies-baden: Otto Harrassowitz.———. 1998. The Character of Logic in India. Edited by J. Ganeri and H. Tiwari.Albany: State University of New York Press.Mohanty, J. N. 1971. “Bimal Krishna Matilal’s The Navya-Nyaya Doctrine of Nega-tion.” Journal of Indian philosophy 1.Müller, Max. 1853. “Indian Logic.” In W. Thomson, An Outline of the NecessaryLaws of Thought. London: Longmans Green and Co.Oetke, Claus. 2003. “In What Sense Are Indian Theories of Inference Non-monotonic.” In Hōrin Comparative Studies in Japanese Culture, edited by TakaoAoyama et al. IUDICIUM Verlag GmbH.Pakṣilasvāmin, Vātsyāyana. 1967. Nyāya-bhāṣya. Edited by Anantalal Thakur. Darb-

hanga: Mithila Institute.Prasad, Rajendra. 2002. Dharmakīrti’s Theory of Inference. New Delhi: Oxford Uni-versity Press.Roer, E., ed. and trans. 1850. Division of the Categories of the Nyāya Philosophy(Bhāṣāpariccheda). Calcutta: Baptist Mission Press.Ronald, Loui. 1999. “Case Based Reasoning and Analogy.” In The MIT Encyclopediaof the Cognitive Sciences, edited by Robert A. Wilson and Frank C. Keil. Cam-bridge, MA: MIT Press.

Page 26340Philosophy East & WestSarkar, T. K. 1997. “Jaina Logic in Perspective.” In Essays in Indian Philosophy,edited by S. Saha. Calcutta: Allied Publishers Ltd. in collaboration with JadavpurUniversity.Schayer, Stanislaw. 2001. “Studies in Indian Logic.” Reprinted in Indian Logic—AReader, edited by Jonardon Ganeri. Surrey: Curzon Press.Seal, B. N. 1915/1985. The Positive Sciences of the Ancient Hindus. London: Long-mans. Reprint, New Delhi: Motilal Banarsidass.Stcherbatsky, F. Th. 1962. Buddhist Logic, vols. 1 and 2. Bibliotheca Buddhica, 26Leningrad. Reprint, New York: Dover Publications, Inc.Vidyabhusana, S. C. 1921. A History of Indian Logic: Ancient, Medieval and ModernSchools. Calcutta: Calcutta University.