THE INDIAN APPROACH TO FORMAL LOGIC AND THE METHODOLOGY OF THEORY CONSTRUCTION : A PRELIMINARY VIEW

I. Logical and Methodological Foundations of Indian Sciences

There seems to be a generally prevalent opinion, both among the scholars and the lay-educated, that the indian tradition in sciences had no sound logical or methodological basis1. While we know that the Western tradition in abstract or theoretical sciences is founded on the logic of Aristotle and the deductive and axiomatic method of theory construction as evidenced in Euclid’s Elements (both of which have been further refined in the course of the work of last hundred years in logic and mathematics), we seem to have no clear idea of the foundational methodologies which were employed in the Indian scientific tradition. This, to a large extent, has hampered our understanding of the Indian tradition in sciences, especially as regards their foundations and as regards their links both amongst themselves as well as with the Indian tradition in philosophy.

The traditional Indian view, as it appears from the popular saying Kanadam Paniniyanca sarvasastropakarakam, is that the sastras expounded by Kanada and Panini are the basis for all other sastras. Here the sastras expounded by Kanada refers to the entire corpus of Nyaya-Vaisesika Darsanas, ie. the ‘Physics and Metaphysics’ as expounded mainly in the Vaisesika Darsana, and the epistemology and logic as expounded chiefly in the Nyaya-Darsana. The sastra of Panini is the entire science of language (sabda sastra). In Indian view these appear to be the foundational disciplines whose mastery is a pre-requisite for a serious study of all other sastras, meaning all sciences, theoretical as well as practical, natural as well as social and also philosophy. So in order to have a reasonable idea of the logical and methodological foundations of Indian Sciences, we should have an in-depth understanding of the methodologies, theories and techniques developed in the Nyaya and Vaisesika works as also the work on sabdasastra.

In this article we attempt to present an outline of the Indian approach to just one particular logical and methodological issue2, viz. the question of how the Indian tradition handles various foundational problems which involve the use of what are generally known as ‘formal methodologies’ or ‘formal techniques’ in the Western tradition. The foundational disciplines of logic and mathematics in the Western tradition are considered rigorous mainly because they are sought to be formulated in a content-independent, purely symbolic or ‘formal’ language and the aim of many a theoretical science in the Western tradition is to attain standards of rigour comparable to logic or mathematics, by being formulated as a ‘formal system’. Such attempts have repeatedly been made in the West in various domains of natural sciences, some social sciences and much more so in linguistics, the science of language.

In this article we present an outline of some of the methodologies and techniques developed in the Indian tradition of logic and linguistics and compare them with the formal methodologies and techniques developed in the Western tradition. Firstly we discuss the distinctive features of Indian logic as compared with the Western tradition of formal logic. We explain how the Indian logicians provide a logical analysis of every cognition in terms of a technical language and use it to explicate logical relations between cognitions. We also discuss how the Indian logicians achieve a precise and unambiguous formulation of universal statements in terms of their technical language, without taking recourse to quantification over unspecified universal domains. Then we consider the Indian tradition in linguistics especially the grammatical treatise of Panini, Astadhyayi, as a model or a paradigm example of theory construction in India. We indicate the manner of systematic exposition as also the techniques employed in Astadhyayi, which appear to be common to the entire corpus of classical sastric literature wherein the sutra technique of systematisation has been employed. We also explain how the Paninian grammar serves not only as a ‘generative device’ for deriving all the correct forms of utterances but also as a ‘parser’ for arriving at a precise and unambiguous ‘knowledge representation’ (in terms of a technical language) of any correct utterance of Sanskrit language. Further, it is this systematic analysis of the Sanskrit language, which seems to have enabled the Indian Sastrakaras to develop a precise and technical language, suited for logical discourse.

In fact, the basic feature that emerges from our discussion of the Indian approach is that the Indian tradition did not go in for the development of purely symbolic and content-independent formal languages, but achieved logical rigour and systematisation by developing a precise and technical language of discourse founded on the ordinary Sanskrit language - a technical language which is so constructed as to easily reveal the logical structures which are not so transparent and often ambiguous in a natural language, but at the same time has a rich structure and interpretability which it inherits from the natural language Sanskrit from which it is constructed. Indian approach is thus free from many a philosophical and foundational problem faced by the formal methodologies developed in the Western tradition. More importantly, it seems to provide us an alternative, logically rigorous and systematic foundational methodology for natural sciences and philosophy.

II. The Indian Approach to Formal Logic

 Indian Logic and Western Logic

To understand the basic, foundational differences between Indian logic and Western logic, let us first note the essential features of logic in the Western tradition, which are well captured in the following extract from the article on logic by a famous mathematical logician in the XIV Edition of Encyclopaedia Britannica³

‘Logic is the systematic study of the structure of propositions and of the general conditions of valid inference by a method which abstracts from the content or matter of the propositions and deals only with their logical form. This distinction between form and matter is made whenever we distinguish between the logical soundness or validity of a piece of reasoning and the truth of the premises from which it proceeds and in this sense is familiar from everyday usage. However, a precise statement of the distinction must be made with reference to a particular language or system of notation, a formalised language, which shall avoid the inexactness and systematically misleading irregularities of structure and expression that are found in ordinary (colloquial or literary) English and other natural languages and shall follow or reproduce the logical form’.

In other words, the following appear to be the basic features of Western logic : It deals with a study of ‘propositions’, specially their ‘logical form’ as abstracted from their ‘content’ or ‘matter’. It deals with ‘general conditions of valid inference’, wherein the truth or otherwise of the premises have no bearing on the ‘logical soundness of validity’ of an inference. It seeks to achieve this by taking recourse to a symbolic language which apparently has nothing to do with natural languages. All this. is understandable, as the main concern of Western logic, in its entire course of development, has been one of systematising patterns of mathematical reasoning and that too in a tradition where mathematical objects have often been thought of as existing either in an independent ideal world or as a formal domain.

In what follows, we shall attempt to contrast the above features of Western logic with the basic features of Indian logic. The main point of this contrast is that Indian logic does not purport to deal with ideal entities such as propositions, logical truth as distinguished from material truth, or with purely symbolic languages which apparently have nothing to do with natural languages. As is well known, a central concern of Indian logic as expounded mainly by Nyaya Darsana has been epistemology or the theory of knowledge. Thus the kind of logic which developed here, is not in any sense confined to the limited objective of making arguments in mathematics rigorous and precise, but attends to the much larger issue of providing rigour to the various kinds of arguments encountered in natural sciences (including mathematics, which in Indian tradition has more the attributes of natural science than that of a collection of context-free abstract truths) and in philosophical or even natural discourse.

Further, inference in Indian logic is both ‘deductive and inductive’, ‘formal as well as material’. In essence, it is the method of scientific enquiry. In fact one of the main characteristics of Indian ‘formal logic’ is that it is not ‘formal’ at all, in the sense generally understood, as Indian logic refuses to totally detatch form from content. In takes great care to exclude from logical discourse terms which have no referential content. It refuses to admit as a premise in an argument any statement which is known to be false. For instance the ‘method of indirect proof’ (reductio ad absurdum) is not acceptable to most Indian schools of philosophy, as a valid method for proving the existence of an entity, which existence is not demonstrable (even in principle) by other (direct) means of proof⁴. In fact, the Indian logicians grant tarka (roughly translatable as the method of indirect proof) only the status of a subsidiary means of verification, helping us to argue for something which can be separately established (though often only in principle) by other (direct) means of knowledge⁵. 

The most distinguishing feature of the ‘non-formal’ approach of Indian logic is that it does not make any attempt to develop a purely symbolic and content independent or ‘formal language’ as the vehicle of logical analysis. Instead what Indian logic (especially in its later phase of Navya nyaya, say starting with the work of Gangesa Upadhyaya (14th century), has developed is a technical language which, by its very design, is based on the natural language Sanskrit but avoids ‘inexactness’ and ‘misleading irregularities’ by various technical devices. Thus the Indian tradition in logic has sought to develop a technical language which, being based on the natural language Sanskrit, inherits a certain natural structure and interpretation, and a sensitivity to the context of enquiry. On the other hand the symbolic formal systems of Western logic, though considerably influenced in their structure (say in quantification, etc.) by the basic patterns discernable in European languages, are professedly purely symbolic, carrying no interpretation what-so-ever — such interpretations are supposed to be supplied separately in the specific context of the particular field of enquiry ‘employing’ the symbolic formal system. 

Logical Analysis of Cognition (Jnana) in Indian Logic

It has become more and more clear from various recent investigations that Indian logic deals with entities and facts directly. It is a logic of Jnana (variously translated as knowledge, cognition, awareness, etc.) as constrasted with the Western logic of terms or sentences or propositions. While Indian thought does distinguish a sentence from its meaning, and also admits that sentences in different languages could have the same meaning (which are some of the arguments used in the West in favour of introduction of the notion of proposition), there appears to be a total disinclination amongst all Indian philosophers to posit or utilise ideal entities such as propositions in their investigations. On the other hand, what Indian logic deals with are the jnanas. Though philologically the Sanskrit word jnana is supposed to be cognate with the English word ‘knowledge’, a more preferred translation of jnana appears to be ‘cognition’ or ‘awareness’ as jnana unlike ‘knowledge’ can be either yathartha (‘true’) or ayathartha (‘false’).

Further, jnana is of two types savikalpa (often translated as ‘determinate’ or ‘propositional but not a proposition’) and nirvikalpa (‘indeterminate’ ‘nonrelational’ or nonpropositional’). But what is important to realise is that even the savikalpa or ‘propositional’ jnana is not to be identified with a sentence or proposition. As has been emphasised by a modern Indian philosopher . ‘The jnana, if it is not a nirvikalpa perception, is expressed in language, if it is sabda, it is essentially linguistic. But it is neither the sentence which expressed it, nor the meaning of the sentence, the proposition; for there is in. the (Indian) philosophies no such abstract entity, a sense as distinguished from reference, proposition as distinguished from fact’.

In what follows we will give a brief outline of Indian logical analysis of jnana, as brought out in some of the recent investigations.⁸ The main point that emerges is that though jnana is a concrete occurent in Indian philosophy (a guna or kriya of the jiva in some systems, a modification or vrtti of the inner senses the antahkarana in some other systems of Indian philosophy), it does have a logical structure of its own, a structure that becomes evident after reflective analysis. This logical structure of a jnana is different from the structure of the sentence with expresses it in ordinary discourse. There always remain logical constituents in a jnana which are not expressed in the usual sentential structure. For instance in the jnana usually expressed by the sentence ‘Ayam ghatah’ (‘this (is) a pot’), the feature that the pot is being comprehended as a pot, that is as qualified by potness (ghatatva) is not expressed in the sentential structure. Thus the logical structure of a jnana is what becomes evident after reflective analysis, and the sentential structure of ordinary discourse only provides a clue to eliciting this epistemic structure of a cognition.

According to Indian logic every cognition (jnana) has a contentness (visayata). For the case of a savikalpaka jnana this visayata is of three types: qualificandumness (visesyata), qualifierness (prakarata or visesanata) and relationness (samsargata). For instance, in the jnana expressed by Ghatavad-bhutalam (Earth is pot-possessing) the prakara is ghata, the pot (not the word ‘ghata’ or ‘pot’) the visesya is bhutala, the earth (not the word ‘bhutala‘ or ‘earth’) and since the pot is cognised as being related to the earth by contact, the samsarga is samyoga, the relation of contact. Thus the prakarata of the jnana, 'Ghatavad-bhutalam’ lies in ghata, the visesyata in bhutala and samsargata in samyoga. Thus in Indian logic, any simple cognition can be represented in the form a-Rb where ‘a’ denotes the Visesya, ‘b’ the prakara and ‘R' the samsarga, or the relation by which a is related to b. This analysis of a simple cognition as given by the Indian logicians is much more general than the analysis of the traditional subject - predicate judgement in Aristotelian logic or that of an elementary proposition in modern logic (say in the system of first order predicate calculus), as the Indian logicians always incorporate a samsarga or relation which relates the predicate to the subject.

Having identified the visesya, prakara and samarga of a jnana is not sufficient to fully characterise the jnana. According to the Naiyayika one has to clearly specify the modes under which these ontological entities become evident in the jnana, For instance while observing a pot on the ground one may cognise it merely as a substance (dravya). Then the qualifier (prakara) of this jnana, which is still the ontological entity pot, is said to be dravyatvavacchinna (limited by substanceness) and not ghatatvavacchinna (limited by pot-ness) which would have been the case had the pot been cognised as a pot. The Indian logician insists that the logical analysis of a jnana should reveal not only the ontological entities which constitute the visesya, prakara and samsarga of the jnana, but also the mode under which these entities present themselves, which are specified by the so called ‘limitors’ (avacchedakas) of the visesyata, prakarata and samsargata. The argument that is provided by Indian logicians in demanding that the avaechedakas should be specified in providing a complete logical characterisation of a jnana is essentially the following. Each entity which is a prakara or visesya or samsarga of a jnana by itself possesses innumerable attributes or characteristics. In the particular jnana any entity may present itself as a possessor of certain attributes or characteristics only, which will then constitute the limitors (avacchedakas) of the prakarata etc. (of the jnana) lying in the entity concerned. 

The Naiyayika therefore sets up a technical language to unambiguously characterise the logical structure of a jnana which is often different from the way this jnana might get expressed in the language of ordinary discourse. For instance,the jnana that the earth is pot-possessing which is ordinarily expressed by the sentence Ghatavad bhutalam, would be expressed by tha logician in the form : Samyoga sambandhavacchinna ghatatvavacchinna ghatanishtha prakarata nirupita-bhutalatvavacchinna bhutalanistha visesyatasali jnanam. A cognition whose visesyata present in bhutala (earth) which is limited by bhutalatva (earthness) and is described (nirupita) by a prakarata present in ghata (pot) and limited by ghatatva (pot-ness) and samyoga sambandha (relation of contact).

The Naiyayika’s analysis of more complex cognitions can now be briefly summarised. Each cognition reveals various relations (samsarga) between various entities (padarthas). Thus a (complex) cognition has several constituent simple cognitions each of which relate some two padarthas (one of which will be the prakara and other visesya) by a samsarga. The visesyata and prakarata present in any pair of padarthas are said to be described (nirupita) by each other. Thus the various entities (padarthas) revealed in a complex cognition have in general several visesyatas and prakaratas which are further characterised as being limited (avacchinna) by the various modes in which these entities present themselves. Further a detailed theory is worked out (with there being two dominant schools of opinion associated with the Navadwipa logicians of 17-18 century, Jagadisa Tarkalamkara and Gadadhara Bhattacharya) as to how the different visesyatas and prakaratas present in the same entity (padartha) are related to each other. In this way a detailed theory has been evolved by the Indian logicians to unambiguously characterise the logical structure of any complex jnana in a technical language. For instance the Naiyayika would characterise ithe cognition that the earth possesses a blue-pot, which is ordinarily expressed by the sentence Nilaghatavad-bhutalam as follows :

Tadatmya sambandhavacchinna-nilatvavacchina-nilanishtha prakatata niruputa ghatatvavacchina - ghatanishtha - visesyatvavaechinna - samyoga sambandhavacchinna ghatatavavachinna ghatanishtha prakarata nirupita bhutalatvavacchinna bhutala nishtha visesyatasali jnanam : A cognition whose visesyata present in bhutala is limited by bhutalatva and is described by prakarata present in ghata which prakarata is limited by ghatatva and samyoga sambandha and by the visesyatva in ghata which in turn is limited by ghatatva and is described by prakarata present in nila (blue) and limited by tadatmya sambandha (relation of essential identify) and nilatva (blueness).

 We now consider the question as to how the above logical analysis worked out by the indian logician does serve the purpose of providing a representation of a jnana which is free from the various ambiguities which arise in the sentences of ordinary discourse, and also makes explicit the logical structure of each jnana and its logical relations with other jnanas. To start with let us discuss how the Naiyayikas formulate a sophisticated form of the law of contradiction via their notion of the pratibadhya (contradicted) and pratibandhaka (contradictory) jnanas. For this purpose we need to briefly outline the theory of negation in Indian logic as enshrined in their notion of abhava (absence).

 ‘Negation’ (Abhava) in Indian Logic 

Abhava is perhaps the most distinctive as also the most important technical notion of Indian logic. Compared to the Indian doctrine of negation, the notion of negation in Western logic is a rather naive or simplistic truth functional notion in which all the varieties of negation are reduced to the placing of ‘not’ or “it is not the case that’’ before some proposition or proposition-like expression. This latter notion does not for instance allow a subject term to be negated in a sentence and infact most cases of ‘internal negation’ in a complex sentence seem to be entirely outside the purview of Western formal logic⁹. 

The essential features of the notion of of abhava are summarised in the following extracts from a recent study :¹⁰ 

The concept of absence (abhava) plays larger part in Navya-nyaya (new-Nyaya) literature than comparable concepts of negation play in non-Indian systems of logic. Its importance is apparent from a consideration of only one of its typical applications. Navya-nyaya, instead of using universal quantifiers like ‘‘all’’ or “every”, is accustomed to express such a proposition as ‘all men are mortal’ by using notions of absence and locus. Thus we have “Humanity is ‘absent’ from a locus in which there is absence of mortality” (in place of “All humans are mortal”)... 

Absence was accepted as a separate category (‘padartha’) in the earlier Nyaya-Vaisesika school. The philosophers of that school tried always to construe properties or attributes (to use their own terms : guna ‘quality’, Karma ‘movement’ samanya ‘generic property’, Visesa ‘differentia’, etc.) as separate entities over and above the substrate or loci, i.e. -, the things that possess them. They also exhibited this tendency in their interpretation of negative cognitions or denials. Thus they conceived of absence as a property by a hypostasis of denial. The negative cognition “There is no pot on the ground” or “A pot is absent from the ground” was interpreted as “There is an ‘absence of pot’ on the ground”. It was then easy to construe such an absence as the object of negative cognitions — and hence as a separate entity. Moreover, cognitions like “A cloth is not a pot”... were also treated and explained as “A cloth has a mutual absence of pot, ie., difference from pot’’. And a mutual absence was regarded as merely another kind of absence... 

In speaking of an absence, Nyaya asserts, we implicity stand committed to the following concepts. Whenever we assert that an absence of an object ‘a’ (say a pot) occurs in some locus (say, the ground), it is implied that ‘a’ could have occured in, or, more generally, could have been related to, that locus by some definite retation. Thus, in speaking of absence of ‘a’ we should always be prepared to specify this such-and-such relation, that is, we should be able to state by which relation, ‘a’ is said to be absent from the locus. (This relation should not be confused with the relation by which the absence itself, as an independent property, occurs in the locus. The latter relation is called... a svarupa relation) The first relation is described in the technical language of Navya-nyaya as the “limiting or delimiting relation of the relational abstract, counterpasitiveness, involved in the instance of absence in question’’ (pratiyogitavacchedakasambandha). Thus, a pot usually occurs on a ground by samyoga or conjunction relation, When it is absent there, we say that a pot does not occur on the ground by conjunction or that pot is not conjoined to the ground. By this simple statement we actually imply, according to Nyaya, that there is an absence on the ground, an absence the counterpositive (pratiyogin) of which is a pot, and the delimiting relation of ‘‘being the counterpositive” (i.e., counterpositiveness -.pratiyogita) of which is conjunction. While giving the identity condition of an instance of absence, Nyaya demands that we should be able to specify this delimiting relation whenever necessary. The following inequality statements will indicate the importance of considering such a relation: 

1) “Absence of pot ≠ absence of cloth”.

2) “An absence of pot by the relation of conjunction ≠ an absence of pot by the relation of inherence”. 

Thus for the indian logician, absence is always the absence of some definite property (dharma) in a locus (dharmi) and characterised by a relation — technically, either an occurence—exacting realation (vrttiniyamaka sambandha) or identity (tadatmya) by which the entity could have occured in the locus, but is now cognised to be absent. Thus each abhava is characterised by its pratiyogi (the absentee or the entity absent, sometimes called the ‘counter positive’) as limited (i) by its pratiyogitavacchedakadharma (the limiting attribute(s) limiting its counter positiveness) as also (ii) by the pratiyogitavacchedaka sambandha (the limiting relation limiting its counterpositiveness). Thus in the cognition ghatabhavavad bhutalam (The ground possesses potabsence), the pratiyogi of ghatabhava (pot-absence) is ghata (pot) whose pratiyogita is ghatatvavacchinna and a samyoga - samhandhavacchina, as what is being denied is the occurrence of pot as characterised by potness in relation of contact with the ground. 

Further, it is always stipulated in indian logic that abhava of some property (dharma) is meaningful only if that property is not a universal property (Kevalanvayi dharma, which occurs in all loci) or an empty property (aprasiddha dharma, which occurs nowhere)¹¹. Thus ‘empty’ or ‘universal’ terms cannot be negated in Indian logic and many sophisticated techniques are developed in order that one does not nave to employ such negations in logical discourse. 

The sophistication of the Indian logicians concept of abhava (as compared to the notion of negation in Western logic) can be easily seen by the formulation of the “law of contradiction” in Indian logic. Instead of considering trivial truth- functional or linguistic tautologies of the form ‘either “p’’ or “not-p’” the Indian logician formulates the notion of pratibandhakatva (contradictorinesss) of one jnana (cognition) with respect to another. Further, this relation of pratibandhakatva can be ascertained only when the appropriate logical structures of each cognition are clearly set forth and can thus be stated precisely only in the technical ‘language formulated by the Indian logician for this purpose. For instance, it would clearly not do to state that the cognitions ghatavad bhutalam (The ground possesses pot) and ghatabhavavadbhutalam (The ground possesses pot-absence) are contradictory, because in the first cognition the pot could be cognised to be present in the ground by the relation of contact (samyoga) while in the second the pot could be assumed to have been cognised as being absent in the ground by the relation of inherence’ (samavaya).¹² These two cognitions do not contradict each other at all and in fact they can both be valid. The law of contradiction can be correctly formulated only when the logical structure of both the cognitions are clearly set forth with all the vésesyata, prakarata and samsargatas and their limitors (avacchedakas) being fully specified and it is seen from their logical structures that certainty (niscayatva) of one cognition prevents (pratibadhnati) the possibility of the other cognition arising (in the same person). Consider the case when for instance the cognition that the ground possesses pot (ghatavad bhutalam) actually has the logical structure : samyoga sambandhavacchinna ghatatvavacchinna prakarata nirupita bhutalatvavacchinna visesyataka jnanam. This cognition is prevented by the cognition that the ground possesses pot-absence (ghatabha- vavad bhutelam) only if the latter has the logical structure: Svarupasambandha- vacchinna samyoga sambandhavacchinna ghatatvavacchinna pratiyogitaka abhavatva- vacchinna prakaratanirupita bhutalatvavacchinna visesyataka jnanam. This prevented- preventor (pratibadhya-pratibandhaka) relation between these two cognitions is formulated. in the following form by the Indian logician : 

Samyoga sambandhavacchinna - ghatatvavacchinna prakarata nirupita bhutalatvaechinna visesyataka jnanatvavacchinnam prati svarupa sambandhavacchinna samyoga sambandhavacchinna ghatatvavacchinna pratiyogitaka abhavatvavachinna prakarata nirupita bhutalatvavacchinna visesyataka niscayatvena pratibandhakatvam : “In regard to the knowledge having its qualificandness limited by groundness and described by the qualifierness limited by potness and the relation of contact, the knowledge having its qualificandness limited by groundness and described by qualifierness limited by constant absenceness and the relation svarupa (absential self-linking relation) the counter-positiveness (pratiyogita) of which absence is limited by potness and the relation of contact is the contradictory definite knowledge, contradictoriness resident in it being limited by the property of niscayatva (definite knowledgeness)’¹³ 

‘Quantification’ in Indian Logic 

As another instance of the Indian approach of making the logical structure of a cognition clear and unambiguous by reformulating it in a technical language, we consider here the method developed in Indian logic for formulating universal statements, ie. statements involving the so-called universal quantifier ‘all’. Such statements arise in the basic scheme of inference considered in Indian logic where one concludes from the cognition ‘the mountain is smokey’ (Parvato dhumavan) that ‘the mountain is fiery’ (Parvato vahniman), whenever one happens to know that ‘wherever there is smoke there is fire’ (Yatra yatra dhumah tatra vahnih). A careful formulation’ of this last statement which is said to express the knowledge of pervasion (vyapti jnana) of fire by smoke has been a major concern of Indian logicians, who have developed many of their sophisticated techniques mainly in the course of arriving at a precise formulation of vyapti. 

According to the Indian logicians a statement such as ‘All that possesses swoke posseses fire’ is unsatisfactory as an expression of vyapti jnana. Firstly we have the problem that the statement as formulated above is beset with ambiguities (nowadays referred to as the ‘confusion in binders’ or ‘ambiguity in the scope of quantifiers’). For instance there is a. way of misinterpreting the above statement using the so-called calani nyaya — by arguing that if all that possesses smoke possesses fire, what prevents mountain-fire from occurring in the kitchen where one sights smoke, or vice versa. The Greeks also discussed some of these ambiguities in formulating universal statements. In the Western tradition some sort of a solution to this problem was arrived at only in late 19th century via the method of quantification. In this procedure, the statement “All that possesses smoke possesses fire’ is rendered into the form ‘For all x, if x possesses smoke then x possesses fire’, before formalisation. 

The approach of the Indian logician is very different from the above method of quantification. The Naiyayika insists that the formulation of vyapti jnana, apart from being unambiguous, should be phrased in accordance with the way such a cognition actually arises. Hence an expression such as ‘‘For all x, if x is smokey then x is fiery’’ involving a variable x, universally quantified over an (unspecified) universal domain, would be totally unacceptable to the Indian logicians¹⁴. What they do instead is to employ a technique which involves use of two abhavas (use of two negatives) which are appropriately characterised by their pratiyogita - vacchedaka dharmas and sambandhas. The steps involved may be briefly illustrated as follows¹⁵. 

The statement ‘All that possesses smoke possesses fire’ can be converted into the form ‘All that possesses fire-absence, possesses smoke-absence’. Here fire- absence (vahnyabhava) should be precisely phrased as an absence which describes a counterpositiveness limited by fireness and the relation of contact (samyoga sambandhavacchinna vahnitvavacchinna pratiyogita nirupaka abhavah). Now the statement that smoke is absent by relation of contact from every locus which possesses such a fire-absence is formulated in the following precise manner: ‘Smokeness is not a limitor of occurentness limited by relation of contact and described by locus of absence of fire which absence describes a counterpositiveness limited by fireness and contact’ (Samayoga sambandhavacchinna vahnitvavacchinna pratiyogita nirupaka abhavadhikarana nirupita samyoga sambandhevacchinna vrittita-anavacehe-dakata dhumatve).¹⁶ In the above statement we may note that the ‘locus of absence of fire’ (vahnyabhavadhikarana) is not the locus of absence of this or that case of fire, but indeed of any absentee limited by fireness, as also by the relation of contact (samyoga sambandhavacchinna vahnitvavacchinna pratiyogita nirupaka abhavadhikarana). This is what Indian logic employs instead of notions such as ‘all the loci of absence of fire’ or ‘every locus of absence of fire’. In the same way, the phrase that ‘smokeness is not the limitor of an occurrentness limited by relation of contact and described by locus of...’ (... adhikarananirupita samyoga sambandhavacchinna vrittita anavacchedakata dhumatve) serves to clearly and unambiguously set forth that no case of smoke occurs in such a locus (of absence of fire) by relation of contact. 

We now make a few brief remarks on the Indian logicians’ way of formulating statements of vyapti such as ‘All that possesses smoke possesses fire’, as compared with the method of quantification employed in modern Western logic. Firstly, the Indian formulation of vyapti always takes into account the relations by which fire and smoke occur in their loci. But even more important is the fact that the Indian logician completely avoids quantification over (unspecified) universal domains which is what is employed in modern Western logic. The statement that ‘All that possesses smoke possesses fire’ is intended to say something only about the loci of smoke—that they have the property that they possess fire also. But the corresponding ‘quantified’ statement, ‘For all x, if x possesses smoke then x possesses fire’, seems to be a statement as regards ‘all x’ where the variable ‘x’ ranges over some universal domain of ‘individuals’ (or other sort of entities in more sophisticated theories such as the ‘theory of types’). The Indian logicians’ formulation of vyapti completely avoids this sort of universalisation and strictly restricts its consideration to the loci of absence of fire (as in the above formulation, known as purvapaksha vyapti) or to the loci of smoke (in the more exact formulation known as siddhanta vyapti, which formulation is also valid for statements involving the unnegatable kevalanvayi, or universally present, properties) .¹⁷ 

Another important feature of the Naiyayika method of formulating vyapti is that it does not employ quantification over some ‘set’ of individuals viewed in a purely ‘extensional’ sense. It does not talk of the ‘set of all loci of absence of fire’, but only of ‘a locus which possesses an absence the counterpositive of which absence is limited by fireness and relation of contact’. In this sense, the Indian method of formulating universal statements does take into account the ‘intensions’ of all the properties concerned and not merely their ‘extensions’. As one scholar has noted ¹⁸. 

‘The universal statements of Aristotelian or mathematical logic are quantified statements, that is, they are statements about all entities (individuals, classes or statements) of a given sort. On the otherhand, Navya-nyaya regularly expresses its universal statements and knowledges not by quantification but by means of abstract properties. A statement about causeness to pot differs in meaning from a statement about all causes of pots just as “manness” differs in meaning from “all men....’ 

As explained by another scholar,¹⁹ 

The Naiyayayikas in their logical analysis use a language structure which is carefully framed so as to avoid explicit mention of quantification, class and class membership. Consequently their language structure shows a marked difference from that of the modern Western logicians... Naiyayikas instead of class use properties, and in lieu of the relation of membership, they speak in terms of occurrence (vrittitva) and its reciprocal, possession, moreover, instead of quantification, the Nalyayikas use “double negatives and abstract substantives’’ to accomplish the same result... Any noun substantive in Sanskrit... may bs freated as a dharma (property) occuring in some locus and also as a dharmi (aproperty-possessor) in which some dharma or property occurs.” 

Further, according to the same scholar,²⁰

(In Wastern logic) classess with the same members are identical... But a property or an attribute, in its non-extensional sense, cannot be held to be identical with another attribute even if they are present in all and only the same individuals. Properties are generally regarded by the Indian logicians as non-extensional, in as much as we see that they do not identify two properties like anityatva (non-eternalness) and kritakatva (the property of being caused.) although they occur in exactly the same things. In Udayana‘s system, however, such properties as are called jati (generic characters) are taken in extensional sense because Udayana identifies two jati properties if only they occur in the same individuals’. 

It should be added however, that according to Udayanacarya there are a whole lot of properties which cannot be considered as jati and are generally referred to as Upadhi. In fact Udayanacarya has provided a precise characterisation of all those properties which cannot be considered as jati or generic characters. Another point that should be noted is that the Indian logicians do consider the notion of a collection of entities, especially in the context of their discussion of number and the paryapti relation. But they refuse to base their entire theory on notions such as ‘class’ or ‘set’ viewed in purely extensional terms, and in this respect the Indian logicians’ approach (which does not seem to separate extensions from intensions) is very different from most of the approaches evolved in the Western tradition of philosophy and foundations of logic and mathematics. 

III.  Astadhyayi : The Paradigm Example of Theory Construction in India 

Just as the modern Western systems of axiomatised formal theories find their paradigm example in the exposition of geometry in Euclid’s Elements, the Indian method of theory construction finds its paradigm example in the Sanskrit grammar of Panini, the Astadhyayi. As one scholar has noted,²² 

‘Historically speaking, Panini's method has occupied a place comparable to that held by Euclid’s method in Western thought. Scientific developments have therefore taken different directions in India and the West .... In India Panini’s perfection and ingenuity have rarely been matched outside the realm of linguistics. In the West this corresponds to the belief that mathematics is the more perfect of the sciences’. 

Astadhyayi as a Generative Device 

Over the last two centuries, the Indian grammatical tradition (especially the Astadhyayi of Panini and other works of Paninian school) have proved to be a major fountainhead of ideas and techniques for the newly emerging discipline of linguistics both in its phase of historical and comparative linguistics in the 19th century and in the descriptivist and structuralist and generativist phases of 20th century. Inspite of such intensive study and considerable borrowals over a long period of time, the basic methodology and the technical intricacies of Panini’s grammar were very little understood till the advent and development of the modern theory of generative grammars in the last few decades. As a scholar has noted recently,²³

The algebraic formulation of Panini’s rules was not appreciated by the first Western students; they regarded the work as abstruse or artificial. This criticism was evidently not shared by most Indian grammarians because several of them tried to outdo him in concieness by “‘trimming the last fat’ from the great teachers’s formulations ... The Western critique was muted and eventually turned into praise when moden schools of linguistics developed sophisticated notation systems of their own. Grammars that derive words and sentences from basic elements by a string of rules are obviously in greater need of symbolic code than paradigmatic or direct method practical grammars ... 

It is a sad observation that we did not learn more from Panini than we did, that we recognized the value and the spirit of his “artificial” and “abstruse” formulations only when we had independently consstructed comparable systems, The Indian New Logic (navya nyaya) ‘had the same fate : only after Western mathematicians had developed a formal logic of their own and after this knowledge had reached a few Indologists, did the attitude towards the navya-nyaya school change from ridicule to respect’. 

The major proponent of the present day Generative and Transformational Grammars refers to Panini‘s grammar as ‘a much earlier tradition’ of generative grammar, though ‘long forgotten with a few exceptions’²⁴. For another modern expert, Panini’s Astadhyayi is ‘the most comprehensive generative grammar written so far’.²⁵ This feature of Panini’s grammar is explained in the’ following quotations : 

‘To Panini... grammar is not understood as a body of learning resulting from linguistic analysis but as a device which enables us to derive correct Sanskrit words. ‘The machinery consists of rules and technical elements, its inputs are word-elements, stems and suffixes, its output are any correct Sanskrit words. Thus the Astadhyayi is a generative device in the literal sense of the word. Since it is also a system of rules which allows us to decide the correctness of the words derived, and at the same time, provides them with a structural description, the Astadhyayi may be called a generative grammar’.²⁶

‘Panini’s Astadhyayi:...is a set of rules capable of formally deriving an infinite number of correct Sanskrit. utterances together. with their semantic interpretation,.. The entire grammar may be visualised as consisting of various domains. Each domain contains one or more interior domains. The domain(s) may likewise contain one or more interior domains. The first rule of a domain is called its governing rule. These rules assist one in scanning. Given an input string, one scans rules to determine which paths should be followed within domains. These paths are marked by interior domains, each one headed by a rule that specifies operational constraints and offers selection in accordance with the intent (a set of quasi-semantic notions related to what we know about what we say before we speak... (denoted by) the Sanskrit term (vivaksa). Where choices are varied in operation and there are innumerous items to select from, an interior domain is further responsible for sub-branching in tha path resulting in its division into interior domains’.²⁷                                   

Though various attempts havé been made to find parallels to notions such as ‘deep structure’ or even ‘transformations’ etc., in Paninian system, it is now becoming clear that, though it is operating with concepts and techniques of comparable sophistication, the Paninian system of linguistic description is very different from the various models which have been and are being developed in modern Western linguistics. 

In fact the differences between the Paninian approach and those of modern linguistic theories have to do with several methodological and foundational issues. For Instance while the Paninian system is viewed as a generative device, the inputs to this device are not formal objects such as symbols and strings which are to be later mapped onto appropriate ‘semantic’ and ‘phonological’ representatives. Further the vivaksa or the ‘intent of the speaker’ ‘seems to play a prominent role in the Paninian system and:as has been noted recently ‘Panini’ accounts for utterances and their components by means of a derivational system in which one begins with semantics and ends with utterances that are actually usable’.²⁸ 

Technical Features of Astadhyayi

We now turn to the various technical aspects of the Astadhyayi which reveal some of the basic features of theory-construction in the Indian tradition.

The technical terms of the theory (samjna), the meta-rules (paribhasha) which circumscribe how the rules (sutras) have to be used, the limitation of the general (utsarga) rules by special (apavada) rules, use of headings (adhikarasutra), the convention of recurrence (anuvrtti) whereby, parts of rules are considered to recur in subsequent rules, the various conventions on rule-ordering and other decision procedures as also the various so called ‘meta-linguistic’ devices such as the use of markers (anubandhas) and the use of different cases to indicate the context, input and change — al! these and many other technical devices employed in Astadhyayi,²⁹ are now coming to be more and more recognised as the technical components of an intricate but tightly knit logical system, as sophisticated as any conceivable formal system of modern logic, linguistics, mathematics or any other theoretical science. But there is one crucial feature in which the Paninian system (like perhaps all other theoretical systems constructed in Indian tradition) differs from the modern formal systems. While it employs countless symbols, technical terms and innumerable’ ‘meta-linguistic’ conventions and devices, the Paninian grammar is still a theoretical system formulated very much in the Sanskrit language, albeit of an extremely technical variety. It is not a formal system employing a purely symbolic language.

It is sometimes remarked that the language employed in Panini’s Astadhyayi (sometimes referred to as Panini’s meta-language) differs from ordinary Sanskrit so ‘strongly that one must speak of a particular artificial language’.³⁰ This is a misunderstanding in the sense that though, the technical language of Panini’s Astadhyayi abounds in technical terms and devices, and does differ,considerably from ordinary Sanskrit found in non-technical-literature, it is all the same only a technical or sastric version of Sanskrit-ie. a technical language constructed on the foundation of ordinary Sanskrit. As has been noted recently, many a technical device of Panini is arrived at via ‘an abstraction and formalisation of a feature of ordinary language’.³¹ 

The relation between the technical language employed by Panini and ordinary Sanskrit can be made clear by considerrng an example. We discuss the so called ‘meta-linguistic’ use of cases in Paninian Sutras. For instance consider the rule Ikoyanaci (Sutra 6.1.77 of Astadhyayi). Here ik, yan and ac are symbols for groups of sounds, but at the same time treated as Sanskrit word-bases. The word-base ik occurs in the sutra with genitive ending (ikah), yan with nominative and ac with locative ending (aci). The sutra stipulates that the vowels i,u,r,l (denoted by ik) are substituends to be replaced by y,v,r,l (denoted by yan) before a vowel (ac). The information as to what should serve as input, output and context is ‘meta- linguistically’ marked with various case—endings taken by the Sanskrit word-bases ik, yan, and ac. For instance ik is used with the genitive ending (ikah) to indicate that it is the substituend or input, as per the meta-rule (paribhasa) Sasthi sthaneyoga (sutra 1.1.49). The main point is that while there are various possible meanings indicated by the genitive case - ending, Panini uses the meta-rule 1.1.49 to delimit the meaning of the genitive case-ending to indicate (wherever the meta-rule applies) only the substituend or the input of a grammatical operation. As one scholar has explained’.³² 

‘The rule 1.1.49 sasthi sthaneyoga.. assigns a meta-linguistic value to the sixth triplet (sasthi) endings. As noted.. (the sutra sasthi sese) 2.3.50, introduces genitive endings when there is to be denoted a non-verbal relation in general. There are of course many such relations, such as father-son, part-whole ...etc., ,.. (The rule 1.1.49) states a particular relation to be understood when the genetive is used : the relation of. being a substituend.

In other words, these ‘meta-linguistic’ case conventions are not arbitrary or artificial - they most often serve only to fix an unique meaning where several interpretations are possible in the ordinary use of the language.

In this context the oft-quoted criterion of laghava employed by the Sanskrit grammarians should also be properly understood. This has often been interpreted as brevity and is sometimes seen as the sole raison de etre of Panini’s exposition— meaning thereby that most of: the techniques employed by Panini are mere arbitrary devices to achieve brevity in exposition. Further the tendency of the Indian grammarians to achieve brevity is often linked with other speculations concerning learning in ancient India such as possible shortage of writing Materials³³ or the possible necessities of a purely oral tradition placing heavy demands on memory³⁴, etc. Now, it is of course true that the Indian Grammarians did indeed rejoice (as the saying goes) at the saving of even half of a mora (matra) in their expositions³⁵. But this saving of moras was not to be achieved by arbitrary devices. As has been noted recently, ‘hundreds of moras could have been saved by selecting the accusative instead of the genitive case as marking the input of a: rule’³⁶ — but that would have meant a drastic deviation from the ordinary usage of the accusative.

Thus a ‘meta-linguistic’ device like the use of cases to indicate context, input and output in a grammatical operation, is not an arbitrarily chosen convention for achieving mere brevity, but is actually a technical device founded on the basic structures available in the ordinary Sanskrit language and which serves mainly to render the language unambiguous, more precise etc. This, we could perhaps assert, is true of all the technical devices employed in the Paninian grammar. For instance, it has recently been argued that, the Paninian use of anuvritti is not an artificial device for merely achieving brevity, but in fact a systematic and technical use of ‘real, language ellipsis’³⁷. As regards the criterion of brevity itself, it has heen remarked that ‘the point is rather that the rules are strictly purged of all information that is predictabe from other information provided in the system. What Panini constantly tries to eliminate is not moras, but redundancy‘³⁸

Apart from developing a technical or precision language system for the formulation of grammatical rules, Panini’s Astadhyayi also reveals several sophiticated devices which delimit the nature and application of these rules. Most of these techniques appear to be common for the entire corpus of classical sastric literature wherein the sutra technique of systematisation has been employed. Here again we should take note of the generally prevalent opinion that the sutra style is employed in the indian tradition merely for the purpose of achieving brevity in exposition. While brevity is indeed a hall-mark of the sutra technique of systematisation, there are a whole lot of other equally or even more important criteria that a sutra should satisfy. For instance, the Vishnudharmottara Purana characterises a sutra as being ‘concise (employing minimum number of syllables), unambiguous, pithy, comprehensive, shorn of irrelevancies and blemishless’.³⁹ 

Though the Paninian (or other) sutras are often translated as ‘rules’, they differ substantially from what are generally understood as ‘rules in modern linguitic theory’. According to one scholar,⁴⁰ 

Rules in modern linguistics are treated as statements independent of one another. They are formulated in such a way that they seldom require any information from other rules. Panini’s rules by contrast are interdependent. That is, for the application of a given rule one may at times have to retrieve many rules, which may be very distant with respect to their placement in the grammar. This is what the tradition calls ekavakyata or “single context”. Secondly, when it comes to interpreting a rule in modern linguistics we find that each hardly needs any help from the others. By ‘contrast, a rule in Panini usually requires the carrying over of previous (or later) rule(s), or other element(s) for its correct interpretation. This makes Paninian rules interdependent in contrast with rules in modern linguistics... This interdependence in the interpretation and application of rules required Panini to arrange his rules into domains and subdomains’. 

There are indeed several technical aspects of the sutra method of systematisation-such as the use of paribhasa, adhikara, upadesa, asiddha, vipratisedha etc. These are extensively employed in Panini’s Astadhyayi, but are not defined explicitly in the text. As has been noted recently; these and similar technical terms are ‘meta-grammatical in the sense that they refer not to concepts about which grammatical analysis must theorize, but to the basic equipment which one brings to the very task of grammatical analysis. It should be noted that many of these terms are common property of the sutra technique as applied not only in grammar but also in ritual and elsewhere’.⁴¹ 

Lest the main achievement of Panini’s Astadhyayi be lost amidst all this analysis of its methodology and technical sophistication, we should restate what Astadhyayi achieves in about 4000 sutras : It provides a complete charactarisation of Sanskrit utterances (of more appropriately, a characterisation more thorough than what has been possible for any other language so far) by devising a system of description which enables one to generate and analyse all possible meaningful utterances. It also provides the paradigm example of ‘theory construction’ in the indian tradition.

Sabdabodha and ‘Knowledge Representation’

We have already noted how the Astadhyayi serves as a generative device which enables us to derive correct Sanskrit utterances and at the same time provides us also with a structural description of these utterances. We shall now discuss how the Paninian analysis of Sanskrit utterances enabled the Indian linguists (sabdikas) to provide a full-fledged semantic analysis of meaningful Sanskrit utterances and formulate the cognition generated by an utterance (sabdabodha) in an unambiguous manner in a technical language. In other words, the Indian tradition of linguistics (sabdasastra) has endeavoured to fully systematise bath the generetion of the form of an utterance (sabda) starting from the intention of the speaker (vaktr vivaksha) as well as the analysis of the cognition generated by such an utterance (sabdabodha) in any hearer (srotr) conversant with the Sanskrit Language.

The semantic analysis of Sanskrit utterances is outlined in the great commentary Mahabhasya of Patanjali. A detailed exposition of the semantic theories of Indian linguists may be found in the Vakyapadiya of Bhartrhari (believed to be of 5th century AD), which is in fact a treatise on Vaiyakaranadarsana, dealing with all aspects of the Indian philosophy of language. Since, sabda pramana (the utterance of reliable person (apta) as a valid means of knowledge) was accepted by most schools (Darsanas) of Indian philosophy, the analysis of sabdabodha (cognition generated by an utterance) was a major subject of enquiry. The entire analysis was deeply influenced by the technique developed by the Indian logicians of the Navya-nyaya school. During 16-18th century the technique of sabdabodha was more or less perfected. There were however three schools of thought—represented by the Navya-Vaiyakaranas (such as Bhattoji Dikshita, Kaunda Bhatta, Nagesha Bhatta, etc), Navya-Naiyayikas (such as Raghunatha Siromani, Jagadisa Tarkalamkara, Gadadhara Bhatacharya, etc) and Navya-Mimamsakas (such as Gaga Bhatta, Khandadeva Misra and others). All of them gave systematic procedures as to how the sabdabodha of any utterance may be formulated in a precise and unambiguous manner in a technical language (based on ordinary Sanskrit), with the only difference that each of them had different views on : (a) what are the entities (padarthas) associated with the various words⁴² (padas) in an utterance (b) what are the relations between these entities as revealed by the utterance and (c) what is the chief qualifier (mukhya visesya) of the cognition generated by the utterance. 

The basic technique of sabdabodha is briefly summarised in the following extract from a recent study.⁴² 

‘A sentence is composed of words whether their existence is considered real as in the case of the Logician (Naiyayika), the Mimamsaka and others, or mythical as in the case of the Grammarian (Vaiyakarana) .. Sabdabodha is the cognition of the meaning of sentence. It has been defined as “the cognition effected by the efficicent instrumentality of the cognition of words” (padajnanakaranakam jnanam)... “the cognition resulting from the recalling of things derived from words” (padajanya padarthopasthiti janya bodhah)... “the knowledge referring to the relation between each of the substances recalled by the words in a sentence” (Eka padarthe aparapadartha samsarga visayakam jnanam).

In order to have a clear idea of this theory the various stages of verbal cognition (sabdabodha-krama) may be studied with advantage. While comprehending the meaning of any sentence, first of all, we cognise the word and then its (denotative) potentiality (sakti) and from both of these put together the recalling of meanings is effected and thus import is generated. For instance in the sentence... “(Caitra) worships Hari” (Chaitrah Harim bhajati) there is first of all, the cognition of the several words “Hari”, the (accusative) case affix “am”, the root “‘worship" (bhaj) and the verbal affix “tip”, Next their (denotative) potentialties are comprehended in the following way :  The word “Hari" by virtue of its denotative capacity (abhidhasakti) denotes Hari, “am’’ the case affix denotes objectness (karmatva), the root “bhaj” denotes activity favourable to love (prityanukula vyapara), “tip denotes activity (kriti), of course In addition to the meanings of number, tense, etc. This is the cognition of the potentiality of words, the second stage of verbal import (sabdabodha).... Subsequently as there exists among these several words (or among their meanings) mental expectancy (akanksa), compatibility (yogyata) and juxtaposition (sannidhi or asatti) a totality of comprehension is produced in the form “Caitra is the substratum of activity favourable to love which has Hari for its object” (Harikarmaka prityanukula kritiman Caitrah). 

To elucidate the technique of sabdabodha let us consider the same Naiyayika method of sabdabodha of the sentence ‘Chaitrah harim bhajati’ in some detail. Here there are six ‘words’ — Chaitra, sup, .Hari, am, bhaj, tip. In the Naiyayika method of sabdabodha, ‘Chaitra’ refers to the individual Chaitra (Chaitra vyakti) as qualified by the genus Chaitraness (Chajtratva) and form (jatyakriti visistah). The same is true of the word ‘Hari’. The case affix ‘sup’ refers to singular number (ekatva samkhya) and ‘am’ refers to. objectness (karmatva). The root ‘bhaj’ refers to the activity favourable to love (prityanukula vyapara). The verbal affix (akhyata) ‘tip’ refers to. “effort’ (kriti), singular number (samkhya) and present tense (vartamanakala). The Naiyayika theory of sabdabodha further specifies the various relations by which all the above entitiés (padarthas) are related to each other. This can be illustrated by way of a diagram (see page 51) where the directed arrows indicate the various relations anvaya sambandhas between the padarthas : 

The Naiyayikas would express the sabda bodha of the sentence ‘Chaitrah Harim bhajati’ in the form : Ekatva samaveta haritva samaveta harinirupita karmatvasraya prityanukula vyaparanukula vartamanakalika ya kritih tasyasrayah ekatvasamavetachaitratva-samavetah chaitrah: Chaitra as qualified by singulartiy and Chaitraness (via the relation of inherence) is the substratum of the effort which is favourable to ‘activity’ favourable to love residing in the objectness described by Hari, who is qualified by singularity and Hariness (via the relation of inherence). The above is only a simplified form of the more refined . (pariskrta) sabdabodha wherein one would state precisely the various qualificandness (visesyata) and qualifierness (prakarata) resident in all the above padarthas along with their

limitors (avcchedakas) — both the limiting attributes (avacchedaka dharmas) as also the limiting relations (avacchedaka sambandhas) which later are nothing but the various ‘syntactical relations’ (anvaya sambandhas) that have been indicated between the various padarthas in the above simplified sabdabodha, or in the diagram.

The Vaiyakarana and the Mimamsaka formulations of sabdabodha follow a similar scheme; but the various padarthas associated with different padas and their anvaya sambandhas are slightly different in each scheme. Further the chief qualifer (mukhya visesya), which was Chaitra in the above Naiyayika formulation, would be the activity (vyapara) part of the meaning attributed to the verb—root (dhatu) bhaj in the case of the Vaiyakaranas and the activity (bhavana) part of the meaning attributed to the verb—affix (akhyata) ‘tip’ in the case of the Mimamsakas. Each of the three schools have come up with detailed arguments to show how their formulation of sabdabodha is not only fully consistent but also superior to the formulations given by the other schools, from various fundamental considerations.

Whether it be the Naiyayika formulation, of sabdabodha or the Vaiyakarana or the Mimamsaka formulation, what is achieved is indeed very significant. All of them provide precise and unambiguous characterisation of the cognition generated by any particular utterance of Sanskrit language. If the utterance has ambiguities (be they due to the presence of polysemious words (nanarthakasabdas) or of pronouns (sarvanama) or due to the sentence structure, etc), then procedures are outlined as to how the actual import that is intended to be conveyed (vaktrvivaksa or tatparya) is to be arrived at and the sabdabodha done accordingly. The sabdabodha itself is formulated in a technical language which is unambiguous and clearly presents the full content (visayata) of the cognition (the various padarthas and their sambandhas as manifested by the cognition) as well as its logical structure. Indeed, as has been noted recently, the technique of sabdabodha seems to be a full-fledged scheme for arriving at what has been called a ‘knowledge representation’ of every utterance in the natural language Sanskrit.⁴⁴ What is significant is that while most of the techniques of ‘knowledge representation’ which are currently being investigated (in connection with natural language processing by computers) are mostly ad hoc schemes usually applicable to a particular class of sentences etc, the technique of sabdabodha is a systematic procedure based on a fundamental analysis of the nature of linguistic utterances, and the cognition they generate, which at the same time can be applied to obtain a “knowledge representation” of all conceivable utterances in the natural language Sanskrit.

IV. The Technical Language of indian Sastras vis a vis Formal Languages

In conclusion, the main point we wish to focus upon is the power and potentiality of the technical language that has been developed in the Indian tradition as the basic tool for logical analysis. Our discussion of Indian logic has perhaps indicated how the Indian logicians, instead of seeking to develop content-independent and purely symbolic formal languages as in the West, have sought to develop a technical or precision language founded on the natural language Sanskrit which avoids all possible inexactness and ambiguities. By means of the procedure of pariskara (refinement) the Indian logicians achieve precision, and also bring out clearly the logical structure of a cognition, which structure has an unambiguous representation in their technical or sastric language. Thus the technical language developed by the Indian logicians is indeed one of their major achievements—a fact which was not realised by the modern scholarship on Indian logic till recently⁴⁵, partly because many of the comparable techniques in Western logic are perhaps less than a century old. It is now generally recognised that the technical language developed by the Indian logicians allows them to achieve much of what is supposed to be achieved via the symbolic formal languages of modern mathematical logic. According to one scholar,⁴⁶

‘Navya-nyaya (the modern school of Indian logic started by Gangesa Upadhyaya in 14th century) never invented the use of symbols. It invented instead a wonderfully complex system of cliches by which it expresses a great deal that we would never think of expressing without symbols.’

According to another scholar⁴⁷.

The technical language of Navya-nyaya is not I suspect so much a language as the groping for a kind of picture of the universe of individuals in their relationships with one another... There seems to be a kind of continuity extending from vague, ambiguous, inaccurate ordinary languages through languages filled with technical terms, to clear unambiguous, accurate maps of the kind exemplified by the mathematical physicists’ formulas... Naiyayika style, it may be conjectured, is not intended for the purpose of communicating more easily, any more than the mathematicians’ is; it is intended rather to provide a simple accurate framework for the presentation of the world as it really is. In short, the Navya-nyaya aim js not so far away from the apparent aim of those contemporary philosophers of this day and age in the West, who wish by use of techniques of symbolic logic to find a simple and accurate way of setting forth the picture of the world presented by the natural sciences.

We should here emphasize that these estimates of the technical or precision language employed in Indian logic seem to altogether miss the basic methodologcal principles inherent in the Indian approach. It appears to us that Indian logicians (instead of landing up somewhere in the ‘continuum extending from vague... ordinary languages... to clear... mathematical physicists’ formulas’) deliberately avoided the purely symbolic and content-independent formal languages, just as they avoided postulation or use af ideal entities such as ‘proposition’, ‘sense’ as distinguished from ‘reference’, ‘logical truth’ as distinguished from ‘material truth’, etc. In striving to provide a logical analysis of cognitions, the Indian philosophers did not confine their analysis to a study of sentences or their meanings. However, at the same time, Indian tradition does not start with any pronounced comtempt for the ordinary or natural languages. While it surely recognises the imperfections in the natural languages as vehicles for logical discourse, the attempt in Indian tradition has been mainly to evolve a technical or precision language which is constructed on the basis of the natural language, Sanskrit, and which is free of whatever ambiguities, inaccuracies, vagueness etc., that the natural language might have. This technical language is so constructed as to easily reveal the logical structures which are not so transparent and often ambiguous in a natural language, but at the same time has a rich structure and interpretability which it inherits from the natural language from which it is constructed. Perhaps, to a large extent, it was the strong foundation laid by the Paninian analysis of Sanskrit language, which enabled the Indian scientists and philosophers to (i) achieve a knowledge representation of all natural language utterances in terms of a technical language (thereby systematising also the use of the natural language itself) and (ii) systematically refine the natural language itself into a technical language with a transparent logical structure which could serve as a suitable vehicle for all precise and technical discourse.

The Indian approach of converting the ordinary discourse by pariskara (refinement) into a technical discourse, suitable for systematisation and logical analysis of knowledge, indeed appears to be in conformity with the larger philosophical and methodological principles which have governed Indian thought althrough. Instead of looking for ‘ideal’, ‘context-free’, and purely symbolic or ‘formal languages’ which have no relation with natural languages, as possible tools for attaining ‘perfect’ logical rigour, the Indian tradition sets out to systematically refine the natural language Sanskrit to free it of all known ambiguities and inaccuracies and arrive at a technical language which can reveal the logical structure of a cognition as accurately as possible. In this sense, the process of pariskara is an evolving and even context - dependent process depending on the demands of a particular problem and the kind of ambiguities needed to be resolved. Our Sastrakaras always leave the options open for further pariskaras to be done as and when subtler problems need to be tackled. This is how, for instance the technique of insertion of paryapti got developed during 16th-19th centuries⁴⁸.

 The above features of the Indian approach need to be clearly contrasted with what has been sought to be achieved by the purely, symbolic or formal language systems developed in the Western tradition and to what extent they have been successful so far. We shall here merely quote a recent estimate⁴⁹.

‘Traditional propositional logic is limited by two factors. Only truth functional connectives have been studied and among these only those that are relevant mathematics have been studied systematically. Originally logic was conceived of as a tool to study the logical properties of natural language. By translating arguments in natural language into propositional calculus one hoped to obtain the arguments in a more perspicuous form, where it would be easier to see whether they were valid. However, the translation turned out to be difficult : natural language with its vagueness and ambiguity had to be transferred into a somewhat arbitrarily chosen unambiguous system of formal representation. Since such a system was considered a great advantage in other respects, logic became increasingly estranged from the study of natural language. We still have not discovered how best to study and formalize non-truth functional relations⁵⁰ between sentences’.

What estimates such as the above reveal is that while the modern Western formal logic might have some relevance for providing foundational rigour to arguments in modern mathematics, it has so far totally failed in explicating logical relations between sentences as used in ordinary language or in most of scientific and philosophical argumentation. When it comes to thefoundations of mathematics itself, it has now become common knowledge that the formal and logical approaches being developed from the turn of the last century have hardly helped in tendering them secure.

Formal methods, whatever be their philosophical shortcomings, got wide acceptance in the Western tradition as they professed to free the ordinary discourse of all vagueness and ambiguity and provide logical rigour. What the Indian tradition seems to show is that one need not sacrifice the richness or the content of natural languages in order to achieve clarity, precision or logical rigour. In fact, in developing a technical or precision language based on the natural language Sanskrit, the Indian sastrakaras seem to have evolved a very powerful tool for the formulation of scientific theories, a tool very different from the modern mathematical logic or the attendant formal systems, and which needs to be investigated in much greater detail for its power and potential. A clear comprehension of the basic methodologies as outlined in the sastras of Kanada and Panini, will also help us inrediscovering the foundations of all Indian sastras and restore the vitality and creativity that they seem to have displayed although in history. 

M. D. Srinivas

Department of Theoretical Physics

University of Madras