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Sign (lakṣaṇa) and propositional logic in Pāṇini

– Sergiu Al-George –

In rule III, 3, 8 (loṭarthalakṣaṇe ca), Pāṇini refers to a conditional type of subordination, in which the protasis verb is in the present or future and the apodosis verb in the imperative, and considers the relation between the two clauses to be a relation of signification: the sense of the subordinate clause is the sign (lakṣaṇa) of the sense of the main clause. With the implied elements between brackets, the respective rule could be rendered thus:

[The endings of both the present and the two future tenses are valid] also for expressing the sign of the sense denoted by the verb in the imperative.

The examples provided by commentators to illustrate this rule are of the type: upādhyāyaś ced āgacchati / āgamiṣyati / āgantā / atha tvam chando ‘dhīṣva, “If the teacher comes / will come, learn the metrics!”

The logical importance of this rule, which qualifies the relation between the antecedent and the consequent clauses in conditional subordination as a relation between sign and signified, becomes evident when we compare it to the Stoic fragment II, 221:

The sign is an antecedent proposition in valid hypothetical major premiss, which serves to reveal the consequent[1].

Starting from the logical significance of the Stoic fragment (which refers to the logical consequence discovered by the Greeks in the 4th century B.C.), Pāṇini’s rule calls for a consideration in relation with propositional logic and for a detailed analysis of the conception of the sign (lakṣaṇa) in the system of the great Indian grammarian.

Leaving aside all the differences between the Indian and the Greek conceptions of the sign, we believe that for a better understanding of Pāṇini’s doctrine of the sign it is necessary to confront it first with the doctrine of the Greek shmeion. A consideration of the latter in the context of propositional logic can bring out the logical importance of Pāṇini’s doctrine of the sign more easily than could be achieved by a direct confrontation with Indian logic, where the sign also plays a very important role, namely in inference (anumāna).

The analysis of Pāṇini’s conception of the sign has not yet constituted a particular research topic and, with the exception of a short note by L. Renou which attempts to compare the acceptations of the term lakṣaṇa[2] in the Aṣṭādhyāyī, its importance seems to have been overlooked by those scholars who have dealt with Indian grammatical philosophy.

The word “sign” is one of the most generic terms that designates one of our modalities of cognition, i. e. the indirect, mediated one. In the act of cognition by means of the sign, or semiosis, the mind

takes account of something else mediately, i. e. by means of a third something. Semiosis is accordingly a mediated-taking-account-of[3].

The terms sign and semiosis appeared concomitantly with the dawns of human thinking, in magic divination and medical thinking. A concern with the concept of sign goes back to ancient times and is attested in Indian and Stoic logic. In our time, the problem of the sign is a common meeting ground of various disciplines, which approach it under various aspects. The elaboration of a general semiology is still a desideratum, given that the relation sign/signified is one of the most elementary and basic structures of thought.

As we have already said, the Stoic fragment II, 221 connects the problem of the relation sign/signified with the logical implication, a much disputed, yet equally important problem both in Megarian-Stoic and contemporary logic. In fact, it is the symbolic logic which has reconsidered and pointed out the contemporary relevance of Megarian-Stoic logic, long time disregarded by the historians of logic, like Prantl, for instance. The reason for this present interest is the fact that, unlike Aristotle’s and unlike classical logic, the Megarian-Stoic one was not a logic of terms (S – subject and P – predicate) but, like contemporary logic, a propositional logic.

Among propositional relations, the most disputed was the hypothetical one (“if p then q”); then, as today, it was considered that the implication was not of one type only. Thus, there were Philo’s and Diodorus’ implications which are thought to foreshadow the main types of symbolic logical implications: Bertrand Russell’s material implication, and C. I. Lewis’ strict implication. The major premiss of a Stoic reasoning consisted of a valid hypothetical judgment (to sunhmmenon), i. e. one built upon an implication. According to the Stoic fragment II, 221, in this valid hypothetical judgment, the antecedent is the sign of the consequent. Although Sextus Empiricus comments upon the respective fragment showing that the intended type of implication is Philo’s material implication, sufficient arguments can be adduced to refute this opinion. If it is difficult to superpose the sign/signified relation on the truth tables of Philo’s implication, a difficulty which provided Sextus Empiricus himself with arguments against the intelligible sign, there are, in exchange, enough arguments to convince us that the respective Stoic fragment refers to an implication akin to that of Diodorus, or to the formal one on which Chrysippus built his “indemonstrables”. The relation of signification is of an analytical or apodictic nature, which is missing in the material implication, but is present in Diodorus’ implication. An argument in favour of an overlap between the relation of signification and Diodorus’ implication comes from the fact that the Stoics looked upon proof as “an instance of sign”, as it “reveals the non-evident conclusion by means of agreed premisses”[4]. For the Stoics, the proof was a special type of reasoning in which, by means of agreed premisses, non-evident conclusions were reached deductively: if the validity of “if p, then q” and that of ‘p‘ is admitted, then the truth of ‘q‘ is proved. Thus, for the Stoics, the sign is both the relation between the two atomic propositions of the hypothetical molecular judgment (which is the valid major premiss) and the relation between the two premisses and the conclusion. Therefore, the relation of signification in Stoic logic includes the principle of logical consequence, what mathematical logic calls entailment. As entailment falls outside the study of the functions of truth, it is not a logical calculus, and belongs to metalogic. In the Stoics’ conception, the sign appears thus rather as a metalogical relation.

Concerned with problems of language, Pāṇini only incidentally, though substantially enough, refers to the relation of signification. His interest in the sign, as well as the Stoics’, partakes of the speculative ambiency in which their thinking was developing. Just as Stoic logic has speculative affinities with medical semiologic science[5], Indian grammar developed as an auxiliary of magical and ritualistic thinking, dominated by the sign and the symbol[6].

A very subtle and complex semiologic doctrine could be reconstructed on the basis of the Aṣṭādhyāyī; here, we shall insist on its logical aspects only. The term lakṣaṇa, “characteristic sign”, the topic of the present study, is only one of the numerous terms, in the sanskrit vocabulary, that connote the idea of sign. The widely employed term liṅga, meaning “sign” in Indian logical terminology, is used by Pāṇini with the derived sense of grammatical gender. The terms liṅga and lakṣaṇa, considered to be interchangeable, seem to offer, however, a distinction pertaining to the domain of the extension. The term liṅga seems to have a wider acceptation, denoting all types of sign, while lakṣaṇa rather indicates the sign as a characteristic mark, by which one object is marked off from another object. Unlike liṅga, which designates both temporal-causal relations (from effect to cause and from cause to effect) and non‑temporal, co-occurrence relations (the coinherence of two qualities, or the part/whole relation), lakṣaṇa, as characteristic mark, covers only the latter type of formal relations. Pāṇini’s preference for the term lakṣaṇa, instead of liṅga, could be justified by the capacity of this term to denote more abstract, synchronic relations. There are two rules (VI, 2, 112 and VI, 3, 115) where the term lakṣaṇa is not used technically, but taken in its primary, current acceptation, namely a mark of ownership applied on the ears of the cattle.

From the syntactic point of view, Pāṇini, unlike the Stoics, does not restrict the relation of signification to conditional subordination only, but applies it to other subordinations with conditional value, and to the terms of some apparently simple propositions which could in fact be considered syntactic equivalents of conditional subordination.

Going back to rule III, 3, 8, we should add several specifications. First: the following rule, III, 3, 9, further specifies that the conditional subordinate clause – the sign of the main clause – is constructed with the optative, instead of the two future forms, when the action expressed takes place in the near future, “in an hour from now” (muhūrta). From a logical point of view, we should notice that the presence of the imperative in the main clause makes the action, i. e. the content of this clause, neither false nor true.

Upon closer examination, Pāṇini’s construction appears as a conditional imperative, not a categorical one. Because of the conditional subordinate, the imperative no longer expresses an affective reality, an order or an act of volition on the part of the speaker; being linked to a conditional subordinate, and justified by it, the imperative rather expresses the idea of necessity as opportunity. In its turn, the presence of the imperative enables the protasis no longer to appear as a groundless assumption, an assertion about which it is not known whether it is false or true, or even possible. In the enunciation of a conditional imperative, Pāṇini established the form of a valid conditional judgment. As a matter of fact, Pāṇini (III, 3, 163) surveyed a varied range of meanings of the imperative, among which that of opportunity (praptakala). The complex sentence: “If the teacher comes / will come, learn the metrics!” is the result of the general sentence: “If the teacher comes, the pupil must learn”. The sentence expresses the idea of necessity, not absolute, of course, but circumstantial, not that of an order. The idea of necessity belongs to modal logic which deals with possibility, impossibility, necessity, not with truth and false. In Pāṇini’s rule, the apodosis appears as necessary if it is related to the protasis, which might correspond to relative necessity in modal logic. Relative necessity, be it logical or physical (the latter including the former), is defined as derivability: in the metalanguage, the fact that ‘q‘ is necessary with respect to ‘p‘ is defined as “’q‘ is derivable from ‘p‘”[7], which is one and the same with Pāṇini’s implicit statement “’p‘ is the sign of ‘q‘”.

It is important to emphasize that Pāṇini does not identify the derivability of the signified from the sign with the syntactic “if / then” form; for him, the deduction of the signified from the sign is only one of the relations that can be expressed by hypothetical–conditional subordination. The value of the syntactic construction varies according to the tense and mood of the verbs in it. According to rules III, 3, 132 and III, 3, 134, the hypothetical–conditional subordination can express a hope (aśamsa), which the commentators Katyayana and Patañjali include within the more general idea of “possibility” (sambhavana)[8]. Due to the interference of the present, future or aorist (instead of the imperative), the example illustrating the relation of signification thus becomes: upadhyayaś ced agacchati / agamisyati / agamat, ete chando ‘dhimahe / adhyesyamahe / adhyagismahi, “If the teacher is to come, we should learn the metrics”. This represents a possible hypothetical relation.

The unreal, impossible hypothetical relation is stipulated in rules III, 3, 139-141, and is called kriyatipatti, “non-performance of an action” (lit. “going beyond action”); it is constructed with the conditional. The illustrative examples are of the following kind: yadi varsasahasram ajivisyam tada putraśatam ajanayisyam, “If I had lived a hundred years, I should have given birth to a hundred children”. The content of the protasis, an imminent reality when it expresses lakṣaṇa, a possible one when it expresses hope, is here rejected, being considered a matter of impossibility. Rule III, 3, 139 (liṅnimitte lrṅ kriyatipattau) actually presents a causal relation driven to absurdity, referring directly to rule III, 3, 156 (hetuhetumator liṅ): “The potential [is valid] for expressing the cause/effect relation”. This last rule also hints at a conditional subordination illustrated by such examples as: dakṣinam ced yayan na śakatam paryabhavet / paryabhavisyati, “If the car went to the right side, it would not overturn”. As Pāṇini shows in rule III, 3, 139, the difference between kriyatipatti and hetuhetumant lies in the use of the conditional (lrṅ) instead of the optative (liṅ).

Having reviewed these relations analysed by Pāṇini within the “if / then” syntactic construction, we should emphasize the importance of the distinction he establishes between the sign/signified consequence and the cause/effect consequence. The causal relation is of an empirical nature, expressing temporal consequence, while the significative one expresses a logical consequence between two cognitions, therefore between two propositions. There is no temporal consequence between the subordinate clause in the present or future and the main clause in the imperative expressing a relation of signification; on the contrary, the teacher’s coming (the sign) occurs after the act of learning the metrics (the signified). As we shall see, the opposition between sign (lakṣaṇa) and cause (hetu) is preserved by Pāṇini when he takes into consideration other syntactic structures capable of expressing both of them.

In fact, if Pāṇini does not identify the relation of signification with the syntactic structure of conditional subordination, he nevertheless points to its existence in other grammatical structures as well. Among the structures with the value of a subordinate clause, he mentions the absolute constructions with the locative and the genitive, as well as the present participle; moreover, within the framework of a coherent conception of syntactic equivalences, he extends his analysis to propositions, establishing the signification value of some prepositions (karmapravacanīya) as well as that of the instrumental case.

In rule II, 3, 37 (yasya ca bhavena bhavalakṣaṇam): “[The seventh suffix (= the locative) is valid] also for expressing that by the action of which another action is signified”, he shows that the locative absolute expresses a process which is the sign of another process. In Sanskrit, the locative absolute can express the most varied types of subordination: conditional, concessive, causal, temporal or adversative. The ascription of a sign value to the locative absolute concerns the first two values only. Katyayana very judiciously considers that the locative absolute is used in other circumstances than the sign/signified relation, and that to the respective rule it should be added: “also when it is not a signified action”[9]. He further indicates that the rule is valid when the manifestation of a process coincides with the beginning of another process[10]. In his turn, Patañjali explains that “the rule referring to the locative should be formulated when, at the manifestation of a process, a second process is initiated”[11]. He illustrates the non-significative relation of the locative absolute by examples with temporal values, such as: gosu duhyamanasu prasthito dugdhasv agatah, “Gone while the cows were being milked, he returned when they were milked”. He states that this consequence has an incidental character, contrary to the constant relation sign/signified[12]. And yet, after Katyayana and Patañjali, the entire exegetical tradition, starting with Candra, illustrates the respective rule by this and other similar examples which express a temporal consequence. Böhtlingk and Renou also cite them. However, the examples that would adequately illustrate this rule should express the idea of non-temporal consequence from the antecedent to the consequent, where the antecedent represents a valid condition; unlike conditional subordination, the idea in the subordinate clause constructed with the locative absolute is no longer a groundless assumption. Rule II, 3, 37 can be illustrated by numerous examples where the locative absolute is a sign with respect to the idea in the main clause; these examples can be taken from abstract texts among which we should first quote the Aṣṭādhyāyī itself.

For a better understanding of the structure of Pāṇini’s rules with the locative absolute, we shall reconsider them after having examined the function of the locative absolute in the syntax of logical texts. We shall begin with the unilateral dependence sign/signified as we find it expressed in the anumāna, the Indian inferential reasoning. The unilateral dependence conceived positively (anvayavyapti) – where from the existence of smoke recognized as sign (liṅga in logic) is deduced the existence of fire as signified – is expressed by a subordination of the type: yatra dhūmas tatragnih, “Whenever there is smoke, there is fire”. The same dependence conceived negatively (vyatirekavyapti) is expressed by the same type of subordination: yatra vahnir nasti tatra dhūmo ‘pi nasti, “Whenever there is no fire, there is no smoke”. In both examples, the unilateral dependence is expressed by a relative subordination (equivalent to a valid conditional subordination) where the logical antecedent belongs to the subordinate clause. The unilateral dependence in its negative form can also be expressed by means of the locative absolute, which can replace the relative protasis without changing the content of the sentence: agnyabhave dhūmo ‘pi nasti.

The locative absolute can likewise help to formulate definitions, where it expresses the definiens. In Indian logic, the relation between the two terms of the definition – the definiens and the definiendum – is considered an implication between sign and signified; the definition itself – by extension from the definiens – is called lakṣaṇa, “characteristic mark”. The stylistic value of the locative in formulating definitions has been noticed by the Indian logicians themselves. The Nyāyabodhini commentary on Tarkasamgraha 13 (definition of air) is formulated thus: “Lack of colour existing, possessing touch is the definition of air”[13]; it further explains: “Since the locative absolute has a qualifying meaning, possessing touch, qualified by lack of colour, is the definition of air”[14]. Thus, it becomes obvious that, in formulating a definition, the locative absolute may express lakṣaṇa, the characteristic mark of the definiens, which once again illustrates Pāṇini’s rule.

The use of the locative absolute in formulating a definition does not occur only in logical texts; it can be encountered in grammatical definitions, like the one given by Patañjali to anta, “end”: saty anyasmin yasmat param nasti pūrvam asti so ‘nta ity ucyate, “End is called that which, while is accompanied by something else, is not followed by anything but is preceded by something”[15].

The locative absolute can express both the sign on which the inference is based and the one which constitutes the defining element, because, in both cases, it expresses the relation between the antecedent and the consequent. The unilateral dependence or “pervasion” (vyapti) is the general relation that in Indian thought is considered to lie at the basis of both inference and definition. In Indian logic, the definition is an “abridged” or “defective” inference[16], and this is also confirmed by D. H. H. Ingalls’ observation that the three fallacies of the definition in Nyāya (ativyapti, “overpervasion”, avyapti, “nonpervasion”, and asambhava, “impossibility”) “are essentially the same as the traditional hetvabhasa‘s or fallacies of the hetu[17], the reason, also called sign, in the anumāna. Both definition and inference are incorporated in the relation of the sign, called respectively lakṣaṇa for definition, and liṅga for inference.

If we start from considering the locative absolute in logical texts, we shall be in a position to understand better the function of the locative in the formulation of some rules in Pāṇini’s own grammar, as well as the nature of these rules. The presence of the locative in the formulation of Pāṇini’s rules is very frequent and, more often than not, it has the value of an absolute construction. Because of the abridged style of the treatise, this absolute construction does not appear in its standard form – the participle accompanying the noun – but under an incomplete form: either the noun is missing and only the participle is present[18], or the noun alone is present, and sati, the present participle in the locative of the verb AS-, “to be”, is implicit[19]; at other times, the two terms of the locative absolute construction are fused into one, the latter only being in the locative[20].

In his account of the value of the locative in the nominal style of technical texts – without referring to Pāṇini, who in fact provided the first model in this sense, but to later texts instead – H. Jacobi noticed that “die Verwendung des Lokativus zur Umschreibung von Konditional- und Konzessivsätzen von dem Gebrauche des Lok[ativus] absol[utus] ausgegangen ist”[21]. In his turn, speaking about the use of some cases in pregnant constructions in technical texts, L. Renou[22] noticed that these cases play the role of a causal, conditional, etc. clause, illustrating them by the locative construction: nirdiste pūrvasya, which is actually drawn from Pāṇini’s rule I, 1, 66. Renou also admitted that some uses of the locative at the end of the compound are actually a locative absolute[23]. The absolute value of the locative in Pāṇini is self-evident when the noun is an abstract term; when concrete terms are used however, as for instance: chandasi, “in Vedic texts”[24], the nuance is ambiguous; it can be equally interpreted as an in-case expressing location and as an absolute locative, where sati is implicit.

This construction with the value of a locative absolute, used like a cliché in Pāṇini’s rules, is called by Patañjali visayasaptami, “field locative” or “locative of the range [of validity]”, in opposition with parasaptami, “locative of the following one”. The technical function of the latter is stipulated in metarule I, 1, 66 (tasminn iti nirdiste pūrvasya): in a rule, the word in the locative is placed after the one which is substituted; it refers therefore to the succession (paurvaparya) of the terms of a rule. Patañjali opposes the visayasaptami to the parasaptami, on account of the former expressing generality (samanya), unlike the latter[25]. The former does not refer to a physical succession, but to the consequence relation between the range of validity of an operation and the operation itself. The range of validity is marked by the locative, and represents the antecedent, while the operation to be carried through is the consequent. The visayasaptami generally refers to two types of operations: grammatical and metagrammatical. The first type, that of grammatical operations, is the most used, and is instantiated by the operation which generates expression forms, as the transition from the abstract plane to the concrete one: the locative with an absolute value marks units of the content or abstract grammatical functions, “terms of the higher strata”[26] for the expression of which concrete units in the expression chain are indicated. These rules have the general form: “When there is A to be expressed, then A’ is valid (or indicated)”. However, the function of the locative absolute is more comprehensive than the juxtaposition of two different levels; thus, it is sometimes used to express relations between terms of the same level[27].

The second type of operations whose condition of validity is marked by the visayasaptami is that of interpreting and applying grammatical rules. These metarules called paribhasa, “the highest grammatical generalisations”, some of them with extragrammatical value[28], represent an axiomatic network of the grammatical system. Some of them are of older date than Pāṇini’s grammar; others are explicitly mentioned by him but, more often than not, they are deduced by scholiastic tradition, as being implicit in the master’s text. Out of the list of paribhasas we have chosen here one, explicitly stated by Pāṇini (I, 4, 2): vipratisedhe param karyam, “When there is mutual prohibition [between two rules having the same force], the latter is to be applied”. The use of the locative absolute in the formulation of the paribhasas is very frequent. Running through Nagojibhatta’s list of the paribhasas, we observe that out of a total of 122 metarules, more than one third resort to this syntactic form, in order to express an indication of a general character. On the other hand, relative subordination by yatra / tatra (“wherever / there”) is used only once (paribhasa 13), although it has the same logical value. The locative, therefore, seems to belong to the oldest axiomatic syntax. It seems that the value of sign ascribed by Pāṇini to the locative refers to the logical structure of some grammatical and metagrammatical rules: the antecedent/consequent relation is, in this case, the relation between the indication of an operation and the operation itself. The indication, representing the range of validity in a general rule, can be assimilated to the logical sign; grammatical rules, all the more metagrammatical rules, can be integrated into a logic of the sign.

Another argument in favour of our thesis, that rule II, 3, 37 illustrates the style of grammatical rules and metarules itself, seems to be provided by the next rule, II, 3, 38 (sasthi canadare). This rule implicitly extends the relation of signification to the concessive subordination by the locative and genitive absolute: “The endings of the sixth case (= the genitive) as well [as those of the locative are valid for expressing that by the action of which another action is signified] for expressing [the additional sense of] «indifference towards»”. (The elements between brackets are supplied according to the Benares Commentary[29], the respective rule not being commented in the Mahabhasya.)

At first sight, this rule is puzzling because it establishes a significative dependence between two clauses in concessive subordination, which precisely underlines the independence of the main clause content with respect to the content of the subordinate. The examples supplied by traditional exegesis (and cited by O. Böhtlingk and L. Renou) – for instance rudatah / rudati pravrajit, “Although [the other] was crying, he left the house to become a wandering ascetic” – do not disclose the deep meaning of this rule.

Starting from the opinion that Pāṇini’s terms should be taken in the same acceptation, we believe that lakṣaṇa must be translated in rules II, 3, 37-38 by “signified” or “indicated”, not by “characterized”[30] or “determined”[31], which are more or less ambiguous translations; only thus the respective rule can be adequately illustrated in the syntactic structures expressing the rules and metarules. The concessive construction is instantiated in the formula of restrictive rules (apavada). The exception from a general prescriptive rule (utsarga) is a rule in itself, and the same goes for the general descriptive rule. The particle api with concessive value is associated with absolute constructions in the expression of restrictive rules[32]; in tra I, 4, 96 Pāṇini assigns it a concessive (anvavasarga) value. The same concessive structure is found in the formulation of metarules. Thus, even the metarule which stipulates the possibility (sambhava) of applying a general prescriptive rule (utsarga) and a restrictive one (apavada) is expressed by means of the locative absolute with api, having a concessive value: saty api sambhave badhanam bhavati, “Even if the possibility exists [for the general prescriptive rule to be simultaneously applied with the restrictive rule], the negation [of the general prescriptive rule by the restrictive one] is valid”[33].

The fact that concessive subordination expresses the autonomy of the idea in the main clause with respect to the subordinate clause coincides with the unilateral nature of the sign/signified relation, with the fact that the non-perceiving or absence of the sign does not entail the negation or absence of the signified. In the temporal-causal consequence, on the contrary, the absence of the cause entails the absence of the effect. Remark that the locative and the genitive in concessive constructions, incapable of expressing causative consequence[34], represent a means of making less ambiguous syntactic constructions expressing both causal and logical consequence. Concessive subordination is semantically related to conditional subordination, because it reveals the non-causal dependence expressed by it. The concessive clause shows the unilateral nature of the dependence, the contingent character of the antecedent. We cannot pass over this rule, which assigns a value of signification to the concessive construction, without underlining that Pāṇini is the first and perhaps the only linguist to have noticed the logical import of the concessive construction.

We believe that the logical value of the locative absolute was suggested to Pāṇini by the syntactic structure of the ancient metarules (paribhasa) elaborated by his predecessors, a structure which he adopted in his own grammar. The pre-Pāṇinian system of metarules had developed basic ideas underlying Indian logic and, as J. F. Staal lucidly remarked, the status of a paribhasa corresponds “to the status of a metatheorem in modern logic”[35].

Nowadays, the transformational grammar claims to have contributed an important discovery to linguistic theory, namely that “linguistic «structure» is always relative not just to the data or corpus but also to the grammatical theory describing the data”[36]. Pāṇini’s anticipations of this “contribution” can be explained by the fact that in his time, just as today (according to transformational grammar), grammar was a grammar of rules, language and the language of rules being one.

Pāṇini considered that the constructions with the relative present participle are likewise capable of expressing both significative and causal consequence. Rule III, 2, 126 (lakṣaṇahetvoh kriyayah): “[The suffixes of the present active and medium participles can replace the endings of the present] in expressing the sign or the cause of the action”, completes the previous rule, III, 2, 124, which states that the suffixes of the present active (śatr) and medium (śanac) participles can be substituted for the present tense suffixes (lat). Katyayana and Patañjali submit the respective rule to various interpretations and illustrations; let us only retain the statement that the present active and medium participles are employed for expressing the essence (tattva) of an action. Patañjali gives the following two examples: “The rva grass grows standing recumbent” and “The lotus stalk grows sitting upright”[37]. Although this use is assigned as a supplement (upasamkhyana) to the uses mentioned in the Pāṇinian rule, it is very difficult to distinguish it from that of the lakṣaṇa: the definiens function ascribed to lakṣaṇa by Indian logicians derives precisely from its “quality to be a distinguisher of the essence (tattva) of the defined thing”[38]. In fact, Patañjali’s examples may be looked upon as providing defining elements related to the manner of growing of the respective plants. Thus we encounter here the same intimacy between sign and definition, as was discussed above in connexion with the locative absolute. However, it seems that the main employments of the respective participles, justifying their incorporation in the sign relation, are absent from traditional exegesis.

The co-occurrence in this rule of the ideas of cause (hetu) and sign (lakṣaṇa) suggests semantic affinities with the syntactic constructions capable of expressing them both. In Sanskrit, the present participle can play the role of subordinate clause with conditional, concessive, causal or temporal sense. As J. S. Speijer noticed, the participle can express “the protasis of a conditional or hypothetical sentence”[39]. In this way the present participle functions as an antecedent, like the absolute constructions with the locative or the genitive, and it is Pāṇini’s merit to have emphasized their logical value, alongside with that of the conditional subordinates proper.

With this rule we have concluded our considerations on the logical value of some subordinations in Sanskrit. We may  now pass on to another chapter dealing with the logical value Pāṇini ascribes to some constituents of the simple sentence, for instance certain prepositions and the instrumental case.

*

Pāṇini also ascribes a role in expressing the sign/signified relation to certain invariable words from the group called karmapravacanīya, and to some invariable compounds (avyayibhava) into which some of these may enter. The term karmapravacanīya was translated as “governing preposition” (or postposition) by scholars who have dealt with Pāṇini’s vocabulary. The etymology of the word shows, however, that Pāṇini did not assign to the respective technical term the same function that European traditional grammar and linguistics assign to the term “preposition”, or “prothesis”, first introduced by Dionysius Thrax. Unlike prepositions, which express relations between sentence constituents with different morphological and syntactical functions – e. g. the relation between a noun (object) and a verb (predicate governing it) –, the term karmapravacanīya, by its semantic content, indicates that the relation it denotes is different from that existing between the respective morphological and syntactical categories. Pāṇini is well aware of the case-regime of prepositions, as shown by the fact that he states the case required by a certain karmapravacanīya, for instance the accusative in rule II, 3, 8. We have to point out, however, that the governed nouns are meant to represent a certain verbal expression. This technical term is translated by Renou as “qui communique l’acte”[40], on the basis of Patañjali (on I, 4, 83) who glosses it as: karma proktavantah, “[words] which have revealed an action”. Starting from the same gloss, Faddegon observes that the respective action is not directly expressed, but given to understand. According to Faddegon this “means that any karma-pravacanīya can be paraphrased or explained with the help of a verb”[41]. Actually it is not in isolation that a karmapravacanīya can be paraphrased with the help of a verb, but together with the noun it governs. In traditional linguistic terminology, we could say that the karmapravacanīya, together with the noun it governs, is the syntactic synonym of a subordinate clause. In transformational language, this is to say that the karmapravacanīya marks a nominalized verbal structure, referring therefore to a deep verbal structure which lies beyond the surface nominal structure.

The traditional concept of preposition refers exclusively to a surface structure; karmapravacanīya is therefore a transformational concept, much more complex than the traditional term “preposition”, and the translation by “preposition” obscures its linguistic value. It finds an equivalent in contemporary conceptions only.

Among the Sanskrit prepositions which mark an implied subordination, a deep structure capable of expressing the sign/signified consequence, Pāṇini explicitely indicates anu (I, 4, 84; I, 4, 90), prati and pari (I, 4, 90) and abhi (I, 4, 91).

In the beginning of the chapter dedicated to the karmapravacanīyas, Pāṇini refers to the function of the preposition anu in expressing the sign/signified relation. The respective rule I, 4, 84 (anur lakṣaṇe): “anu [is valid] for expressing the sign”, should be understood in the sense that the noun governed by anu, which is in the accusative (II, 3, 8), actually expresses an action representing the sign of the action expressed by the verb. Or, more explicitly, two verbal ideas in a sign/signified relation occur in a single sentence in which the noun governed by anu has the value of a subordinate clause, although apparently it is an object. The preposition anu has the following meanings: “after”, “along”, “towards”, “in consequence of”, “according to”, “being indicated by”. Most of these meanings point to the idea of consequence, and the last (“being indicated by”) to that of significative consequence. The connexion made by Pāṇini between the relation of signification and the preposition anu, taken in itself, seems important to us because it throws into relief the logical idea of consequence. As Ch. Serrus has remarked,

l’inférence primitive est la consécution. Le donc est une transformation presque insensible de l’apres, et c’est de lui cependant qu’est née la logique[42].

It is interesting to note that, without exception, Pāṇinian exegesis illustrates rule I, 4, 84 by examples in which the consequence is established between a magical act and its projection. The first example of this kind can be found in the Mahabhasya (ad I, 4, 84, init.): Śakalyasya samhitam anu pravarsat, “It rained according to Śakalya’s samhita”. Patañjali himself is not at ease with the analysis of this example. He wonders whether Śakalya’s samhita is hetu or lakṣaṇa in relation to the rain, in other words, if the relation between the magic act and the rain is a sign/signified or a cause/effect consequence. He concludes that “the hetu is included in the lakṣaṇa[43]. Patañjali’s embarrassment communicated itself to the European translators of this rule. L. Renou rendered the rule as follows: “Le mot anu (porte le nom de préposition pour suggérer le sens de) signe (dont tel phénomene est l’effet, = «en conséquence de»)”[44]; inspired by Patañjali, he identifies the sign with the cause, thus running counter to the distinction between sign (lakṣaṇa) and cause (hetu), to which Pāṇini himself was faithful throughout. In translating Patañjali’s commentary on the same rule, H. Scharfe renders the word hetu by “logical reason” (Grund)[45], which is not justified by the above-mentioned example. We consider it to be inadequate to speak of a logical or even causal relation in this example, which illustrates a magical relation between a rite and the phenomenon it brings about. For the archaic mentality, what is obtained by a magic act is not an effect strictly speaking, but a replica, a projection onto the phenomenal world of a magic reality. In a rain-making rite, the rain has already been symbolically performed in the magic act which simulates it, when the operator proclaims as fulfilled the result he is pursuing[46]. Between the magic act and its projection onto the phenomenal world, there is a relation of conformity or analogy. In all the examples illustrating the relation between the magic act of bringing the rain and the rain itself, anu expresses the consequence as an analogical conformity of the real to the symbolic model of the rite, and it should therefore be translated by “according to”, “in accordance with”. The qualification lakṣaṇa which applies to the magic act is justified by the ambiguity between sign and symbol in the archaic mentality (cf. Lat. signum)[47].

Pāṇini resumes the relation anu/lakṣaṇa more explicitly in rule I, 4, 90 (lakṣaṇettham-bhūtakhyanabhagavipsasu pratiparyanavah): “The words prati, pari and anu [are valid] for expressing the ideas of «sign», «being thus», «having a part» and «distributiveness»”. For the idea of sign we are concerned with, commentators give the example: vr̥kṣam prati / pari / anu vidyotate, “The lightening is flashing in the direction indicated by the tree”. The noun governed by anu (i.e. vr̥kṣa, “the tree”) fully  maintains its sign value, like in the preceding rules, and there is no reason to translate it by “Richtung”, as Böhtlingk does. Renou captures the exact translation of lakṣaṇa by “signe (manifestant la direction du proces = «vers»)”[48]. This interpretation is confirmed by rule II, 1, 14 where, dealing with invariable compounds (avyayibhava) having an adverbial value, Pāṇini stipulates that, together with the noun they govern, abhi and prati can make up an invariable compound with the same value as the analytical expression. The respective rule (lakṣaṇenabhiprati abhimukhye) clearly distinguishes the sign (lakṣaṇa) from the direction (abhimukhya) it indicates: “The words abhi and prati, together with the sign, [form an undeclinable compound] for expressing the direction”. Thus agnim abhi is interchangeable with abhyagni.

Rules II, 1, 15 (anur yat samaya) and II, 1, 16 (yasya cayamah) further stipulate similar optional constructions of the avyayibhava type, where anu, compounded with a noun, indicates respectively “near to” (II, 1, 15) or “alongside of” (II, 1, 16). Rule II, 1, 15 is illustrated by examples like anuvanam aśanir gatah, “the thunder fell near the forest”, and rule II, 1, 16 by anugaṅgam varanasi, “The city of Varanasi extends alongside of the river Ganges”.

In all these constructions, referred to by rules I, 4, 84; I, 4, 90-91; II, 1, 14-16, the  value of sign is ascribed to a noun governed by a karmapravacanīya, since the latter, together with the noun it governs, represents a nominalised verbal expression. The sign/signified relation is conceived here as a relation between two sentences in subordination, the sign belonging to the subordinate.

The deep structure of the sentence represents the analysis of some space contiguities, and therefore two cognition processes are implied: from the knowing of the direction where the tree is situated, there derives the knowing of the direction where the lightening has flashed, or by knowing the direction along which the Ganges flows, there derives the knowledge of the direction along which the Varanasi town is situated.

The last rule dealing with the sign value of a noun is rule II, 3, 21 (itthambhūtalakṣaṇe): “[The endings of the third case (= the instrumental) are valid] for expressing the sign which makes known somebody as possessing such a nature”. The examples illustrating this rule are of the type: api bhavan kamandaluna chattram adrakṣit, “Have you recognised the disciple by [perceiving] his pitcher?”[49], or śikhaya parivrajakam apaśyat, “He recognised the wandering ascetic by [perceiving] the lock of hair left on the crown of his head”. In these examples, the ending of the instrumental has the same function of referring to an implicit verb (i.e. the verb “to perceive”), to a deep verbal structure, like the karmapravacanīya, together with the noun it governs. The similarity between the function of the instrumental and that of the preposition anu has been explicitly shown by Pāṇini in rule I, 4, 85 (tr̥tyarthe):

[The word anu is valid] for expressing the sense of the endings of the third case[50].

Thus, just as in the case of a noun governed by anu, the word in the instrumental (in the examples stipulated by rule II, 3, 21) can be paraphrased by a verbal form. Accordingly, the instrumental of the sign has the value of a subordinate clause functioning as an antecedent to the idea expressed by the verb.

Pāṇini knows that in most of the rules dealing with the sign, as well as in the case of the instrumental, the idea of consequence includes both causal and significative consequence; once again he marks the difference between them, explaining in a following rule, II, 3, 23 (hetau), that “[The endings of the third case are valid] for expressing the cause”.

*

The consideration of all the rules that refer to the syntactic devices for expressing the sign/signified relation has enabled us to understand that in all these cases we are dealing with the consequence between two cognitions. Without forcing their interpretation, we can assert that all these rules are compatible with a logical commentary which has been overlooked by the Indian and Western commentators of Pāṇini.

However, Pāṇini’s main concern is not that of a logician. In support of this statement, let us observe that he did not deal with all the syntactic constructions capable of expressing the idea of consequence; thus, relative subordination, as it occurs in the “illustrative” part (udaharana) of Indian inferential reasoning (anumāna) of the type: yatra yatra dhūmas tatragnih, or yo yo dhūmavan sa so ‘gniman, “Wherever there is smoke, there is fire”, is not mentioned in connection with the sign/signified consequence. His main concern was that of a grammarian, and the logic he uncovered derived from the analysis of the grammatical structures he surveyed, according to the desideratum of Leibniz.

Pāṇini used the term lakṣaṇa also to qualify the relation of a suffix (pratyaya) with respect to its function, in rule I, 1, 62 (pratyayalope pratyayalakṣaṇam): “When there is a suffix syncopation, what is indicated by the suffix  [retains its validity]”; commenting on this rule, Patañjali explains that “the suffix is a distinguishing sign (lakṣaṇa), whose effect subsists after its syncopation”[51]. The same idea is resumed in rule I, 2, 65 in connection to the function of patronymic suffixes, when they are syncopated in the case of a unified form (ekaśesa) in the dual[52]. From both rules it is obvious that Pāṇini ascribes logical validity to the unilateral dependence of the suffix on its function, considering this dependence to be isomorphous to the syntactic structures we have been dealing with. The establishment of this isomorphism represents not only an obliteration of the delimitation between morphology and syntax, but the establishment of a parallelism between logic and grammar.

In qualifying consequence as a sign/signified relation (just as Indian logicians have done), Pāṇini deserves the credit for having anticipated a fundamental concept of Indian logic.

The most important fact that needs emphasizing is that, on Pāṇini’s conception, the sign, as a logical antecedent, is expressed by a proposition or by its syntactical equivalents. Thus, the Stoic remark that the indicative sign is always a proposition holds for Pāṇini’s system too; yet, unlike the Greeks, he ascribed it not only to conditional subordination, but to other syntactic means as well.

The sign/signified relation is actually the relation of consequence between two cognitions, the indirect acquiring of a cognition by means of another. The sign is not an individual or a class, but a process. Only through a superficial estimation, smoke, as a sign of fire, can be considered an individual or a class. In itself, smoke is not a sign, but the existence of smoke or, more precisely, the act or perceiving the smoke makes it into the sign of another process – the existence of fire. As the Indian logicians themselves suggested, in the anumāna type of reasoning, the logical reason (hetu) of the existence of fire, formulated in earlier texts as dhūmat, “because of the smoke”, should be understood as dhūmatvat, “because of the existence of smoke”, the suffix –tva expressing the fact of existing. These two processes of the sign and the signified correspond to two  cognitions, hence to two statements: from the admittance of the sign, the admittance of the signified is derived.

By confronting Stoic logic with that of Pāṇini it follows that the logic of sign belongs to that of propositions, which enables us to draw some important conclusions concerning Indian logic, since it is well known that the latter is a logic of the sign.

For a long time, the Western world has misunderstood the real nature of Indian inference (anumāna), because it has been dominated by the logic of terms. Thus, the anumāna has been assimilated to Aristotle’s syllogism, and this conception has gone so far as to claim that Indian logic is tributary to Greek logic[53]. P. Masson-Oursel was the first to show the difference between the anumāna and Aristotle’s syllogism[54]. Later, St. Schayer considered Indian reasoning to be an anticipation of propositional logic[55], and A. Foucher maintained with keen common sense that:

les éléments du syllogisme aristotélicien sont des concepts, tandis que ceux du syllogisme indien ne sont que des propositions[56].

Referring to Navya-Nyāya only, D.H.H. Ingalls said that it

has the superficial appearance of a nonpropositional system of logic, for the form of expression of any element of its discourse is usually that of a single term rather than that of a statement (proposition). However, many of these expressions actually refer to cognitions corresponding to statements rather than to individuals or classes[57].

Nevertheless, in I.M. Bocheñsky’s more recent book, Indian logic is qualified as a logic of terms[58]; this point of view has been questioned by Madeleine Biardeau who is inclined to detect in the anumāna a logic of terms and one of propositions at the same time[59].

We believe that in this controversy on the propositional or nonpropositional nature of the Indian reasoning based on sign, Pāṇini’s conception of the sign is revealing. In order to understand Indian logic, one cannot abstract from the interpretation given by the Indian grammarians themselves to the linguistic structures of classical Sanskrit, the more so since the Indian philosophical speculation in its entirety has, as a substructure, reasonings of a grammatical character[60]. This is because in India, unlike Europe, grammatical theory preceded logical theory and influenced some of its developments.

As far as Western symbolic logic is concerned, Pāṇini gives us the opportunity to see how, in the case of consequence, the difference is obliterated between the logic of terms and that of propositions, by reference to the syntactical equivalents or to the transformational relations of propositions. Pāṇini showed what the consequences for logic can be of an adequate linguistic doctrine which goes beyond the surface form of the expression.

In conclusion, we would like to point out the historical importance of the facts discussed in this paper. Starting from the analysis of language facts, Pāṇini approximated in his own way the idea of consequence, which is the fundamental concept of formal logic. This was happening around 500-400 B.C., according to all probabilities, previously to the development of Megarian and Stoic logic (400-200 B.C.).

At the same time, Pāṇini was the first to uncover the logical structure of a language. In R. Carnap’s words,

if for any language the term «consequence» is established, then everything that is to be said concerning the logical connections within this language is thereby determined[61].


 [1]. Apud Sextus Empiricus, Adversus mathematicos VIII, 245.

 [2]. L. Renou, “La théorie des temps du verbe d’apres les grammairiens sanskrits”, JA 248 (1960), 3, p. 333, n. 50.

 [3]. Ch. W. Morris, “Foundations of the theory of signs”, International encyclopedia of unified science I, 1-5, Chicago 1955, p. 82.

 [4]. Sextus Empiricus, Adversus mathematicos VIII, 299.

 [5]. G. Preti, “Sulla dottrina del shmeion nella logica stoica”, Rivista critica di storia della filosofia 11 (1956), 1, pp. 5-14.

 [6]. See supra, pp. 85-88.

 [7]. H. Reichenbach, Elements of symbolic logic, New York 51947, p. 396.

 [8]. MBh ad III, 3, 132, varttika 3: aśamsasambhavanayor aviśesat tadvidhanasyapraptih //

 [9]. MBh ad II, 3, 37, varttika 1: bhavalakṣaṇe saptamividhane ‘bhavalakṣaṇa upasamkhyanam //

 [10]. MBh ad II, 3, 37, varttika 2: siddham tu bhavapravrttau yasya bhavarambhavacanat //

 [11]. MBh ad II, 3, 37, after varttika 2: yasya bhavapravrttau dvitiyo bhava arabhyate tatra saptami vaktavya /

 [12]. MBh ad II, 3, 37, after varttika 1: lakṣaṇam hi nama tad bhavati yena punah punar lakṣyate sakrc casau kathamcidgosu duhyamanasu prasthito dugdhasv agatah //

 [13]. Nyāyabodhini 13: parahitatve sati sparśavattvam vayor lakṣaṇam (Tarka-sa8graha, ed. Y.V. Atalye, transl. M. R. Bodas, Poona 21974, p. 10).

 [14]. Ibid.: satisaptamya viśistarthakataya rūparahitatvaviśistasparśavattvam vayor lakṣaṇam /

 [15]. MBh ad I, 1, 21, after varttika 1.

 [16]. Th. Stcherbatsky, Buddhist logic I, Leningrad 1932, p. 146 and n. 5.

 [17]. D. H. H. Ingalls, Materials for the study of Navya-nyaya logic, Cambridge (Mass.) 1951, p. 81.

 [18]. E. g., Pan II, 3, 1: anabhihite //

 [19]. E. g., Pan I, 4, 23: karake //. O. Böhtlingk, Pânini’s acht Bücher grammatischer Regeln II, Bonn 1840, p. 66, commenting on this rule, says that “karake ist als ein locativus absolutus zu fassen.”

 [20]. E. g., Pan III, 3, 144: kimvrtte liṅlrtau //

 [21]. H. Jacobi, “Über den nominalen Stil des wissenschaftlichen Sanskrits”, Indogermanische Forschungen 14 (1903), p. 244.

 [22]. L. Renou, Grammaire sanscrite II, Paris 1930, p. 317.

 [23]. Ibid., p. 314.

 [24]. Pan III, 4, 117: chandasy ubhayatha //

 [25]. MBh ad II, 4, 35, after varttika 5: yad apy ucyate paurvaparyabhavac ca samanyenanupapattir iti / arthasiddhir evaisa yat samanyena paurvaparyam nasti / asati paurvaparye visayasaptami vij4asyate /

 [26]. V. N. Misra, The descriptive technique of Pāṇini. An introduction, The Hague-Paris 1966, p. 103.

 [27]. E. g., the rule quoted in n. 20.

 [28]. P. Ch. Chakravarti, The philosophy of Sanskrit grammar, Calcutta 1930, p. 71.

 [29]. KV. ad II, 3, 38: anadaradhike bhavalakṣaṇe bhavavatah sasthisaptamyau vibhakti bhavatah /

 [30]. L. Renou, La grammaire de Pāṇini, traduite du sanskrit avec des extraits des commentaires indigènes I, Paris 1947, p. 76; however, his last translation of this rule is less ambiguous: “ce par l’3tre de quoi il y a signe d’un [autre] 3tre” (“La théorie des temps du verbe”, p. 333, n. 50).

 [31]. F. de Saussure, “De l’emploi du génitif absolu en sanscrit”, Recueil des publications scientifiques de Ferdinand de Saussure, Genève 1922, p. 289.

 [32]. E.g., Pan III, 3, 145: anavaklptyamarsayor akimvrtte ‘pi //

 [33]. MBh ad I, 1, 47, after varttika 1.

 [34]. L. Tesnière, Éléments de syntaxe structurale, Paris 1959, p. 601: “la proposition concessive peut 3tre considérée comme le contraire de la proposition causale.”

 [35]. J. F. Staal, “The theory of definition in Indian logic”, JAOS 81 (1961), pp. 123-124. As to the affinities existing between logical and grammatical rule, cf. S. Abraham, “Au sujet des regles grammaticales et des regles logiques”, Cahiers de linguistique théorique et appliquée 2 (1965), pp. 7-18.

 [36]. E. Bach, An introduction to transformational grammars, New York-Chicago-San Francisco 1964, p. 29.

 [37]. MBh ad III, 2, 126 varttika 3: tattvanvakhyane ca // – tattvanvakhyane copasamkhyanam kartavyam / śayana vardhate dūrva / asinam vardhate bisam iti //

 [38]. Nyāyatrabhasya I, 1, 3 (introductory text): uddistasya tattvavyavacchedako dharmo lakṣaṇam (Nyāyatram, ed. G. Jha, Poona 1939, p. 10, ll. 3-4).

 [39]. J. S. Speijer, Sanskrit syntax, Leyden 1886, p. 282. Speijer delimitates the two functions of the Sanskrit participle, namely that of “simple attributive adjectives” (p. 281) and that of being “a concurrent idiom of subordinate sentences, of which, indeed, they may be said to exhibit the rudimentary form” (p. 282).

 [40]. L. Renou, Terminologie grammaticale du sanskrit, Paris 21957, p. 124 (s.v. karmapravacanīya).

 [41]. B. Faddegon, “Studies on Pāṇini’s grammar”, VKNAW 38 (1936), 1, p. 17. Patañjali (MBh ad I, 4, 83) further explains that the karmapravacanīyas reveal an action which is not denoted for the present time (ye samprati kriyam nahuh), adding that they denote the action of the unexpressed agent (ye ‘prayujyamanasya kriyam ahus te karmapravacanīyah). The controversy raised by the explanation of this technical term in the exegetic literature is summarised by P. Ch. Chakravarti, The philosophy of Sanskrit grammar, pp. 165-169.

 [42]. Ch. Serrus, La langue, le sens, la pensée, Paris 1941, pp. 30-31.

 [43]. MBh ad I, 4, 84, after varttika 2: lakṣaṇena hetur api vyaptah /

 [44]. L. Renou, La grammaire de PāṇiniI, p. 50.

 [45]. H. Scharfe, Die Logik im Mahabhasya, Berlin 1961, p. 32.

 [46]. Cf. V. Henry, La magie dans l’Inde antique, Paris 1904, p. 11.

 [47]. This affinity is supported by other common syntactic structures too. The syntactic devices for expressing significant and symbolic structures can be common in the case of conditional subordination. Studying conditional subordination with yadi in ŚB, A. Minard, La subordination dans la prose védique, Paris 1936, p. 159, established an exegetic value to yadi (“yádi exégétique: «la raison pour laquelle / c’est que»”). On this occasion (§ 576) he refers to ŚB V, 4, 1, 13: átha rukmáh śatávitrnno va bhavati / návavitrnno va sá yádi śatávitrnnah śatayur va ayám púrusah śatátejah śatáviryas tásmac chatávitrnnah, “il y a une (autre) plaque d’or  1 100 trous ou 1 9 trous. Si elle a 100 trous, c’est que l’homme a 100 ans <1 vivre>, 100 vigueurs, 100 virilités”. The French Sanskritist comments: “On voit clairement par quel biais se fait le passage 1 ce sens insolite: «dans le cas où / elle symbolise» > «s’il en est ainsi / c’est qu’alors».”

 [48]. L. Renou, La grammaire de Pāṇini I, p. 51.

 [49]. B. Liebich’s translation of this example, “hast du den Schüler mit seinem Wasserkrug gesehen?”, obscures its logical value (“Die Casuslehre der indischen Grammatiker verglichen mit dem Gebrauch der Casus im Aitareya-brahmana”, BB 10 (1886), p. 219). L. Renou translates with accuracy the similar typical illustration of this rule: jatabhis tapasah, “il est ascete (1 en juger) 1 la natte”. He calls this instrumental “l’instr[umental] du critere” in the logical sense of the word, as it results as well from another example he gives: anvamiyata śuddheti śantena vapusa (Raghuvamºa XV, 77), “1 la pureté de son corps, on inférait qu’elle était chaste” (Grammaire sanscrite II, p. 293; italics ours).

 [50]. Pāṇini establishes this assimilation between anu and the instrumental by referring to their common function of expressing the idea of connection on which logical consequence is based. The semantic affinity between the prepositions denoting the consecution on the one hand, and the instrument on the other, can be found in other languages too, especially in expressing the idea of conformity or the derivability between two cognitions. Even in the English translation of the typical illustration of the rule II, 3, 21, the preposition “after” may be substituted to “by”: “he recognized the wandering ascetic after (= by) his lack of hair.”

 [51]. MBh ad I, 1, 62, init.: pratyayo lakṣaṇam yasya karyasya tallupte ‘pi bhavatiti /

 [52]. See supra, p. 96, n. 46.

 [53]. S. Ch. Vidyabhusana, A history of Indian logic, Calcutta 1921, pp. 511-513.

 [54]. P. Masson-Oursel, Esquisse d’une histoire de la philosophie indienne, Paris 1923, p. 154.

 [55]. St. Schayer, “Studien zur indischen Logik: II. Altindische Antizipationen der Aussagenlogik”, Bulletin international de l’Académie polonaise des sciences et des lettres, Classe de philologie, Classe d’histoire et de philosophie, 1933, 1-6, pp. 90-96.

 [56]. A. Foucher, Le compendium des topiques (Tarka-samgraha) d’Annambhatta, Paris 1949, p. 118.

 [57]. D. H. H. Ingalls, Materials for the study of Navya-nyaya logic, p. 63. Cf. H. Jacobi, “Die indische Logik”, Nachrichten von der Königl. Gesellschaft der Wissenschaften zu Göttingen, Phil-hist. Kl., 1901, p. 461 and n. 1.

 [58]. I. M. Bocheñsky, Formale Logik, Freiburg-München 1956, p. 509.

 [59]. M. Biardeau, Théorie de la connaissance et philosophie de la parole dans le brahmanisme classique, Paris 1964, pp. 134, n. 1; 137, n. 1.

 [60]. L. Renou, “Les connexions entre le rituel et la grammaire en sanskrit”, JA 233 (1941-1942), p. 164.

 [61]. R. Carnap, The logical syntax of language, London 1971, p. 168.

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