A Grammarian’s View of Negation: Nāgeśa’s Paramalaghumañjūs.ā on Nañartha

The theory of negation developed in the grammatical-philosophical system of later Vyākaraṇa remains almost entirely unstudied, despite its close links with the (widely studied) approaches to negation found in other philosophical schools such as Nyāya and Mīmāṃsā, and despite its consequent importance for a comprehensive understanding of the theory of negation in ancient India. In this paper we present an edition, translation and commentary of the relevant sections of Nāgeśa’s Paramalaghumañjūṣā, a concise presentation by the final authority of the Pāṇinian tradition, together with an explanatory introduction outlining the grammarians’ theory of negation and its relations particularly with the Nyāya theory of negation.

However, the later vyākaraṅa tradition addressed the theory of the meaning of negation in much more extensive and sophisticated terms than found in Patañjali, and is therefore worthy of detailed analysis. In the work of the later grammarians, particularly Bhat˙ṫojidīkṡita, Kauṅḋabhat˙t˙a, and Nāgeśabhat˙ṫa, Vyākaraṅa developed into a sophisticated linguistically-oriented philosophy, standing alongside, and in many respects in opposition to, the other major philosophical schools of early modern India, in particular Mīmāṁ sā and Nyāya. 2 In their treatment of negation, the situation is no different. The grammarians explore the fundamentals of the working of negation, always with a particular view to correct (i.e. Pāṅinian) linguistic analysis, but in so doing, they explicitly engage with, and attempt to refute, aspects of the theory of negation in other philosophical schools. In doing this, they develop their own unique theory of negation.
Numerous works by Bhaṫṫoji, Kauṅḋabhat˙t˙a and Nāgeśa include discussions of nañartha 'the meaning of nañ' (nañ = the negative marker, na/a(n)-), including Bhat˙ṫoji's Śabdakaustubha, Siddhāntakaumudī, Prauḍhamanoramā and Vaiyākaraṇasiddhāntakārikā, Kauṅḋabhat˙ṫa's Vaiyākaraṇabhūṣaṇa and Vaiyākaraṇabhūṣaṇasāra, and Nāgeśa's Bṛhacchabdenuśekhara, Laghuśabdenduśekhara, Laghuśabdaratna, Vaiyākaraṇasiddhāntamañjūṣā, Laghumañjūṣā and Paramalaghumañjūṣā. For the most part these discussions cover similar ground, treating varying subsets of an apparently established set of 'problematic' cases, and starting out with similar assumptions. Yet the treatments, and conclusions drawn, differ in numerous ways not only between the three authors, but even within the works of each individual author.
A comprehensive treatment of the full range of the theory of negation in the later tradition of Vyākaraṅa would therefore be a significant undertaking, which cannot be attempted here. In this paper, as a first foray into the field, we present a detailed analysis, together with translation and commentary, of just one of these works: Nāgeśa's treatment of the meaning of negation in his Paramalaghumañjūṣā (PLM). This particular treatment is distinguished in being unusually both succinct and accessible, and in addition in presenting particularly clear and distinct conclusions.
1 See e.g. the short summary in Rahlwes (2022), and for detail on Patañjali's treatment see Joshi and Roodbergen (1973, pp. 70-117). 2 Evidence for the understanding of Vyākaraṅa as an independent philosophical school is established by its appearance as one of the sixteen darśanas in Mādhavāchārya's Sarvadarśanasaṃgraha (14th century). The treatment of the 'Pāṅinīya' darśana in the Sarvadarśanasaṃgraha focuses on the concept of sphoṭa, and is mostly based on Helārāja's treatment of this topic in his commentary on Bhartṙhari's Vākyapadīya. The grammarians' theory of sphoṫa was already an object of attack from the Mīmāṁ saka Kumārila Bhaṫṫa in the second half of the first millennium, suggesting that the appearance of the 'Pāṅinīya' darśana in the Sarvadarśanasaṃgraha reflects a tradition of understanding Vyākaraṅa as a philosophical school which was already several centuries old in Mādhava's time.
As we will see, Nāgeśa draws a clear semantic distinction between the two types of negation, paryudāsa and prasajyapratiṣedha. This semantic distinction underlies the debate in all the texts mentioned in the previous paragraph, but it is not presented so conclusively in any other work. Nāgeśa's treatment of negation in the PLM also contains one of the most extensive critiques of the Nyāya theory of negation found in this body of work.
Of all the works of the later grammatical tradition mentioned above, the Paramalaghumañjūṣā has a reasonable claim to representing the final authoritative account of the philosophy of the grammarians. Nāgeśa himself is generally considered the final authority in the Pāṅinian tradition of vyākaraṅa, and of his three major works on the semantics and philosophy of grammar, the Vaiyākaraṇasiddhāntamañjūṣā (or just Mañjūṣā), the Laghumañjūṣā (or Laghusiddhāntamañjūṣā), and the PLM, it is the latter which is likely his final composition, and thus the final presentation of his linguistic philosophy, being not merely an abridgement of the Laghumañjūṣā (itself theoretically an abridgement of the Mañjūṣā, although it is much longer), but also differing in some of the conclusions drawn. 3 A summary of the content and arguments of the PLM as a whole is provided in Raja (1990).
In the section "Nāgeśa's Theory of Negation in the PLM" we provide an overview analysis of Nāgeśa's theory of negation as presented in the PLM. In the section "Text with Translation and Commentary" we provide the text of the PLM itself, in transliteration, translation, and with explanatory commentary. In the final "Conclusion" section we conclude.

Nāgeśa's Theory of Negation in the PLM
The vyākaraṅa theory of negation shares several basic features with corresponding theories in other philosophical schools. Perhaps the most important notion is abhāva 'non-existence, absence', which is necessarily a non-existence, or absence, of something, namely its pratiyogin 'counterpositive'. 4 The notion of the anuyogin 'substratum' of negation, which is so prominent in the Nyāya theory of negation, is largely lacking in the vyākaraṅa treatments.
The PLM, like all the treatments of negation by the later vaiyākaraṅas, begins with the paryudāsa negation. This is because the grammatical tradition enters into 3 The traditional view that the three texts are simply abridgements one of another is presented in Coward and Raja (1990, p. 324). The reality cannot be this simple, not least because the Laghumañjūṣā is considerably longer than the Mañjūṣā, and differs in the order of presentation. The latter is likely an earlier work of Nāgeśa's, appearing more beholden to the views of Kauṅḋabhaṫṫa, while the Laghumañjūṣā can best be seen as the full presentation of Nāgeśa's mature philosophy of language. The PLM cannot be a mere abridgement of the Laghumañjūṣā, since it does not maintain all the same conclusions; there may be elements of pedagogical simplification at work. A full understanding of the relations between the three texts requires further research. the debate on the meaning of negation through the introduction of the negative particle, nañ, in Pāṅini's Aṣṭādhyāyī (2.2.6), to license negative compounds. Since the primary locus of paryudāsa negation is in nominal compounds, while the primary locus of prasajyapratiṣedha is (non-compounded) sentential negation, which Pāṅini does not explicitly treat, the grammatical texts begin their discussion with the paryudāsa negation.
However, as discussed below, the paryudāsa negation is problematic for the grammarians in relation to the assumption that the negative particle denotes abhāva. In terms of outlining the vyākaraṅa theory of negation, particularly as presented in the PLM, it is therefore more helpful to begin with the prasajyapratiṣedha negation.

Prasajyapratis . edha
The majority context for prasajyapratiṣedha is uncompounded nañ functioning as a sentential negation, as for example in the sentence ghaṭo nāsti 'the pot does not exist', in comparison with ghaṭo 'sti 'the pot exists'. Following Patañjali, for Nāgeśa in prasajyapratiṣedha negation the negative particle takes as its pratiyogin a word denoting an action (kriyā) or a quality (guṇa), not a word denoting an entity (dravya), even in cases where the particle is compounded with a noun.
In the theory of negation presented in the PLM, an important feature of abhāva is that it cannot be a qualifier (viśeṣaṇa), but only a qualified element (viśeṣya); the implications of this are discussed further below. In the context of prasajyapratiṣedha negation, this means that the meaning abhāva 'non-existence, absence' of the negative particle is always the semantic head of its clause. In the semantic theory of the vaiyākaraṅas, the semantic head of a positive verbal clause is the meaning of the verbal root itself; for example, the meaning of the sentence ghaṭo 'sti 'the pot exists' is: 5 (1) ghaṭa-kartṛkā sattā 'An action of existing of which the agent is the pot.' The grammatical and semantic head of this gloss is sattā 'existing, existence', which is qualified by the adjective ghaṭakartṛkā 'whose agent (kartṛ) is pot', containing the meaning of the subordinate element ghaṭa 'pot'. In the negated version of this sentence, ghaṭo nāsti 'the pot does not exist', it is the meaning of the negative particle which is the grammatical and semantic head of the semantic paraphrase: (2) ghaṭakartṛka-sattā-pratiyogiko 'bhāvaḥ 'A non-existence/absence whose counterpositive is an action of existing of which the pot is the agent.' The meaning of the positive sentence is embedded under the meaning of the negation, mediated by the relation of being the pratiyogin 'counterpositive'. The PLM offers various examples of Sanskrit sentences, the correct interpretation of which supports (at least according to Nāgeśa) this understanding of prasajyapratiṣedha negation. These include the expressions nāsmākam ekaṃ priyam 'there is not one thing that is dear to us', na saṃdehaḥ 'no doubt', no 'palabdhiḥ 'no comprehension', anaci ca 'and when a vowel does not follow', and sentences like ahaṃ nāsmi 'I do not exist', where the agreement facts follow from the grammarians' interpretation. These examples are discussed in detail where they appear in the section "Text with Translation and Commentary" below. A challenge to this understanding of negation is provided by sentences in which the subject/ agent does not exist, similar to familiar examples from Western philosophy like The king of France is bald. Such sentences require special accounting for under Nāgeśa's approach; in the PLM, this is discussed in reference to the sentence vāyau rūpaṃ nāsti 'there is no colour in air', which appears in an apparently interpolated passage (text section 9 below). 6 There are, of course, four recognized types of abhāva: prāgabhāva 'prior nonexistence', dhvaṃsābhāva 'posterior non-existence, non-existence following destruction', atyantābhāva 'absolute non-existence', and anyonyābhāva 'mutual non-existence'. 7 Nāgeśa recognizes only the last two as possible meanings of nañ: prasajyapratiṣedha nañ can have either meaning when uncompounded, but when compounded it can only mean absolute non-existence. The example treated above, ghaṭo nāsti 'the pot does not exist', is an example of uncompounded nañ meaning atyantābhāva.
In compound examples like anaci ca 'and when a vowel does not follow', the meaning of nañ is likewise atyantābhāva. The example Nāgeśa gives for anyonyābhāva with uncompounded nañ is ghaṭo na paṭaḥ 'the pot is not a cloth'.

Paryudāsa
As noted above, the PLM begins its discussion of negation not with the prasajyapratiṣedha, but with the paryudāsa negation. The standard examples are aghaṭa 'non-pot' and abrāhmaṇa 'non-brāhmaṅa'. In paryudāsa negation, the negative particle modifies a noun, with which it is usually compounded, and the reference of the whole is to an entity which in some contextually relevant way (see below) lacks the relevant property introduced by the noun. So, abrāhmaṇa may refer to a person from a varṇa (social class) other than the brāhmaṅa varṇa, such as a kṡatriya, or it may refer, in a derogatory manner, to a brāhmaṅa whose conduct, for example, is not in keeping with his status.
Here, the grammarians encounter a difficulty with the intuition that nañ means abhāva. Since Nāgeśa holds to the assumption that abhāva is necessarily a viśeṣya element, and cannot be a viśeṣaṇa, if that is the meaning of nañ in a paryudāsa negation, then abhāva would be the semantic head of the construction; for example, aghaṭa would have to mean something like ghaṭa-pratiyogiko abhāvaḥ 'a nonexistence of the pot'.
For the grammarians, the semantically predominant element should also be the grammatically predominant element. But there is evidence that the second member of a negative compound is the grammatically predominant element. Crucial evidence for the grammarians is found in compounds of negative+pronoun, such as asarva 'notall', atad 'not-that'. These follow the morphological rules for pronouns (e.g. taking the pronoun-specific case endings, such as dative asarvasmai, atasmai), which in the grammarians' theory can only be the case if the second member of the compound, the pronoun, is the predominant element. A contrast is provided by pronouns compounded with some other indeclinables, e.g. atisarva 'all-surpassing', with dative atisarvāya.
Furthermore, nañ (like ati) is classified among the set of indeclinables, nipātas, 8 and nipātas are standardly assumed to be dyotaka 'manifesting' rather than vācaka 'denotative'. That is, while words such as nouns and verbs directly denote a particular meaning, or artha, by virtue of their particular śakti 'denotative power', dyotaka elements as it were indirectly manifest a particular meaning in, or in relation to, another (vācaka) word.
In a paryudāsa negation, then, Nāgeśa takes the negative particle not to denote abhāva but rather to manifest a particular property of the referent of the construction. That property is āropaviṣayatva, the property of being the range of a superimposition, āropa. By understanding the manifestation of this property in connection with the meaning of the modified noun, the hearer understands that the property denoted by the noun is applied to the object referred to as a superimposed (āropita) property. For example, the noun brāhmaṇa denotes the property of brāhmaṇatva 'brāhmaṅa-ness', which in an ordinary, unmodifed use of the noun, would be interpreted as holding of the referent of the noun. That is, the referent of any semantically-appropriate use of the noun brāhmaṇa has the property brāhmaṇatva, and it is this property which is the reason for the use (pravṛttinimitta) of the word in relation to its referent. But in the compound abrāhmaṇa, due to the meaning manifested by nañ, the property holding of the referent is understood to be āropitabrāhmaṇatva 'superimposed brāhmaṅa-ness'.
The terms āropa 'superimposition' and āropita 'superimposed' are familiar from philosophical discourse, where they are roughly equivalent to adhyāropa or adhyāsa. 9 In philosophical discourse āropa or adhyāropa is generally understood in terms of a cognitive error, such as mistaking mother-of-pearl for silver, or a rope for a snake. Here, though, the āropita nature of e.g. brāhmaṇatva in the use of the compound abrāhmaṇa is intended by the speaker, and intended to be understood as such by the hearer. The term Nāgeśa uses to describe the nature of āropa is āhārya 'adventitious, removable'. This is a term used in the older tradition for assertions made in counterfactual arguments, and its transfer to the context of paryudāsa negation by Nāgeśa is an insightful extension of this use. In the use of the word abrāhmaṇa, then, one understands a counterfactual, hypothetical, assignment of brāhmaṇatva to the referent of the noun.

Context
This understanding of a superimposed property is only the penultimate stage in understanding the meaning of a paryudāsa negation. The final understanding involves moving beyond the literal or purely linguistic (śābda) aspect of meaning to meaning based on context (ārtha). The understanding of a relevant contextual meaning blocks the literal meaning.
Nāgeśa's PLM quotes a well-known verse which lists six contextually possible meanings for nañ: (3) tatsādṛśyam abhāvaś ca tadanyatvaṃ tadalpatā / aprāśastyaṃ virodhaś ca nañarthā ṣaṭ prakīrtitāḥ // '(1) Similarity to that, and (2) non-existence, (3) the property of being other than that, (4) the property of being a small amount of that, (5) the property of being non-praiseworthy, and (6) opposition are declared to be the six meanings of ñan.' For example, if abrāhmaṇa were used in reference to a member of the kṡatriya varṇa, we could understand from the literal meaning āropitabrāhmaṇatva that the intended meaning is e.g. brāhmaṇasādṛśya 'the property of being similar to a brāhmaṅa', or perhaps brāhmaṇānyatva 'the property of being other than a brāhmaṅa'. If, on the other hand, it were used in reference to a brāhmaṅa, we could understand from the literal meaning āropitabrāhmaṇatva that the intended meaning is brāhmaṇāprāśastya 'the property of being non-praiseworthy in a brāhmaṅa'.

The Argument with Nyāya
The final sections of the PLM are devoted to a refutation of various aspects of the Nyāya theory of the meaning of nañ, and a defence of the vaiyākaraṅa view against certain specific objections raised by the Naiyāyika theorists. The Nyāya theory of negation is presented in detail by Matilal (1968) and cannot be recapitulated in full here. There are two key differences between the Vyākaraṅa and Nyāya approaches, one of which goes beyond simply the treatment of negation. For the Naiyāyikas, the semantically predominant element in a positive sentence is not the verb, as the grammarians hold, but the noun which appears in the nominative case, that is in Western terms the grammatical subject. 10 Furthermore, in contrast to Nāgeśa, the Nyāya theory of negation has no problem with the idea of abhāva being a viśeṣaṇa element. Nyāya paraphrases of the sentences ghaṭo 'sti 'the pot exists' and ghaṭo nāsti 'the pot does not exist' would be, respectively: 11 (4) a. sattānukūla-kṛtimān ghaṭaḥ 'The pot qualified by / possessing activity conducive to existence.' b. sattānukūla-kṛti-pratiyogika-abhāvavān ghaṭaḥ 'The pot qualified by / possessing non-existence whose counterpositive is activity conducive to existence.' The Nyāya assumption that the nominative case argument is the predominant element in a sentence is attacked by the later grammarians in various contexts. Here, the criticism is that the grammatical agreement of verb with subject cannot be derived on this Nyāya analysis of prasajyapratiṣedha negation. The grammarians note that even in the presence of sentential negation, there is still agreement between verb and (in our terms) subject, so ahaṃ nāsmi 'I do not exist', tvaṃ nāsi 'you do not exist', etc., with respectively 1sg. and 2sg. agreement on the verb. This falls out unproblematically on the grammarians' approach to the meaning of negation, because the relation between the meaning of the verb and the meaning of the noun does not change when the negation is incorporated, for example: (5) a. mad-kartṛkā sattā 'An action of existing of which the agent is me.' b. mad-kartṛka-sattā-pratiyogiko 'bhāvaḥ 'A non-existence the counterpositive of which is an action of existing of which the agent is me.' (5a) represents the semantic gloss of aham asmi 'I exist', fully parallel to (1), while (5b) represents the semantic gloss of aham nāsmi 'I do not exist', fully parallel to (2). Crucially, in both glosses the relation between mad 'me' and sattā, which represents the meaning of the verb, is identical. 12 On the Naiyāyika view, on the other hand, the relation does change, such that in the negative sentence, there is no direct relation between the meaning of the verb and the meaning of its subject. If the meaning of ahaṃ nāsmi 'I do not exist' is structurally equivalent to (4b), that is (6) sattā-pratiyogika-abhāvavān aham 'Me, qualified by non-existence whose counterpositive is an action of existing.' then the relation between aham 'I' and sattā 'existing' is mediated by the property of abhāva and the relation of counterpositiveness, and there is no way to directly account for the verbal agreement. In this context, Nāgeśa offers the example of the semantically equivalent sentence madabhāvo 'sti lit. 'there exists a non-existence of me' (i.e. 'I do not exist'), where, just as in the semantic paraphrase of the Naiyāyikas, the relation between the verb and the first person pronoun is mediated by the abhāva, and where, quite correctly, the verb does not agree with the first person.
In at least one case, however, the Nyāya theory of sentence meaning and the meaning of negation has an apparent advantage over that of the vaiyākaraṅas. This is the sentence vāyau rūpaṃ nāsti 'there is no colour in air'. This sentence is problematic granted the assumption that the counterpositive of an abhāva cannot be unknown or impossible, and on the ontological assumption that colour cannot reside in air, i.e. that colour in air is impossible, the grammarians' paraphrase, roughly (7) vāyvadhikaraṇaka-rūpakartṛka-sattā-pratiyogiko 'bhāvaḥ 'A non-existence whose counterpositive is an action of existing of which the agent is colour and whose locus is air.' would involve an impossible counterpositive. On the other hand, the Nyāya analysis would not have this problem: vāyuvṛttitvapratiyogikābhāvavad rūpam 'colour, possessing the property of non-existence whose counterpositive is occurrence in air'. The discussion of this example appears to be a later interpolation into the text of the PLM, but it appears in other texts, and has evidently found its way into the text as part of the refutation of the Nyāya theory. 13 Following this is another refutation of a Naiyāyika criticism of the grammarians' theory of negation. The issue is the obvious truth that the existence of existing things cannot be denied or simply cancelled. In particular, the meanings denoted by words cannot simply be cancelled: if the word ghaṭa denotes a pot, or more specifically denotes ghaṭatva 'the condition of being a pot', then we face a problem if our analysis of a negated sentence such as ghaṭo nāsti does not include the denotation of ghaṭatva. 14 Nāgeśa's solution involves drawing a distinction between mental meaning, bauddhārtha, and external reference, bāhyārtha. Words denote mental meanings and do not directly denote external referents. Negation, therefore, does not cancel the given mental meanings, but denies the external referent. So the sentence ghaṭo nāsti does include ghaṭatva as part of the bauddhārtha it expresses (we may picture a pot when we say/hear it), but crucially it makes a claim which involves the non-existence of a pot in the real world.
The final engagement with the Naiyāyikas comes in the concluding paragraph of the text. After presenting his own analysis of the sentence ghaṭo na paṭaḥ 'the pot is not a cloth', Nāgeśa contrasts the corresponding Naiyāyika analysis, and finds it wanting in several respects. The details are presented in the final text section below.

Text with Translation and Commentary
In this section we present the text, translation, and commentary on the section on nañartha in Nāgeśa's Paramalaghumañjūṣā. Our text is based on the published edition of Shukla (1961, pp. 122-131), in comparison with the unpublished but superior edition of Cardona (forthcoming, pp. 57-61); we note some differences of reading below. We divide our presentation of the text into sections which 13 The Naiyāyikas maintain the claim that the counterpositive of an abhāva cannot be unknown or impossible (see Wada 2020, pp. 73-105). As pointed out to us by an anonymous reviewer, the image theory of meaning adopted by the grammarians (see text section 11 below) does, at least in theory, permit impossible counterpositives to be expressed, insofar as they can be mentally constructed. The discussion in our text aims to show that even granted the relevant Nyāya assumption, it is still possible to produce a valid analysis of the sentence in question within the grammarian's approach. 14 This is similar to a claim for monotonicity in linguistic analysis. correspond as far as possible to logical units, but which do not correspond to either Shukla 's or Cardona 's paragraph divisions.

Translation
Nañ is of two sorts, paryudāsa and prasajyapratiṣedha. Of these two, the condition of being the range of a superimposition (āropa) is to be made manifest by the nañ paryudāsa. And the condition of being something that manifests the condition of being the range of superimposition is the condition in nañ of being something that causes the comprehension of the intended meaning, that words like ghaṭa ('pot'), which are spoken together with it [i.e. in aghaṭaḥ 'non-pot'], bring about the knowledge of the cause for application (pravṛttinimitta) that has been superimposed.
The cause for application is the condition of being a pot (ghaṭatva), the condition of being a brāhmaṅa (brāhmaṇatva) etc. Therefore, from 'abrāhmaṇa' (nonbrāhmaṅa) etc. there is knowledge of a kṡatriya etc. that possesses the superimposed condition of being a brāhmaṅa.

Commentary
Our text begins by distinguishing the two varieties of nañ, and immediately enters into the complexities of the paryudāsa. In a paryudāsa, nañ manifests āropaviṣayatva, the condition of being the range of a superimposition. This function is further defined as causing the comprehension of the intended (literal) meaning, specifically that the property which is the cause for application, the reason for use, of a word is to be understood as being superimposed.
So ordinarily, ghaṭatva is the cause for application of the word ghaṭa: the use of the word ghaṭa causes knowledge of ghaṭatva as applied to a particular referent. This is the sense of pravṛttinimitta 'cause for application'. But the intention behind using the word aghaṭa is that the knowledge of ghaṭatva should be understood as superimposed in relation to its referent, and this intention is manifested by nañ.
Note that at this point we are discussing the literal, śābda, meaning that derives from a paryudāsa compound. We have not yet reached the point of contextual inference which gets us to our final, ārtha, understanding.

Translation
For this reason the common claim that in a nañ tatpuruṣa the meaning of the following word is predominant makes sense. And for this reason, in 'atasmai brāhmaṇāya', 'asaḥ śivaḥ' ('to a brāhmaṅa that is not-that (one)', 'Ś iva, who is notthat (one)') etc., an operation concerning a pronoun applies. Otherwise, because it is subordinate, it would not. And the superimposition of the cause for application takes place only in reference to something that is similar, and so the common view, 'a paryudāsa causes the comprehension of something similar' (holds true). And in a paryudāsa (the understanding of) prohibition is based on context (circumstance). And the superimposition of one thing's (anya) feature on another (anya) item has the form of āhārya knowledge. 15 According to the older tradition, it is just knowledge that is produced in accord with a desire at the time of a blocking that is āhārya. Similarity etc. are the limiting conditions for usage, and in a paryudāsa they are meanings based on context (artha).

Commentary
As discussed in the section "Paryudāsa", Nāgeśa's analysis of paryudāsa negation in terms of āropa is related to the grammatical concern that the second member of a nañ compound must be the grammatically and semantically predominant member. This follows Patañjali, who states (Mahābhāṣya 1.87.7-9) that the name pronoun (sarvanāman) is not applied to a form, which would otherwise get this name, when it is 'subordinate' (upasarjana). However, Aṣṭādhyāyī 6.1.132 makes direct reference to pronouns in compound with the negative particle, which makes sense only if e.g. saḥ in asaḥ is still considered to be a pronoun. 16 The statement that 'the superimposition of the cause for application takes place only in something that is similar' must be understood relatively loosely, or else in 15 Cf. Laghumañjūṡā, pp. 677-78, and Kalā commentary, p. 682. 16 Aṣṭādhyāyī 6.1.132 teaches the deletion of the nominative singular ending -s on the pronouns tad and etad before consonants, except in certain contexts, including when compounded with nañ. It is for this reason that the example given in the text, asaḥ śivaḥ, is both grammatically correct and an appropriate example for illustrating the pronominal nature of the negative compound. reference to the most common case, given the subsequent mention of at least four other possible contexts for the use of nañ below.
As discussed above, āhārya has the sense 'to be removed, adventitious', and refers to an intentional attempt to assert something which is factually wrong, such as assertions made in counterfactual arguments. As Nāgeśa explains here, the āhārya nature of the āropita knowledge in a negative compound becomes apparent specifically at the moment where that knowledge is blocked, presumably contextually. Shukla 's (1961, p. 125) commentary states: "Even at the time of a certain judgment of blocking, i.e., that 'the cloth possesses absence of the condition of being a pot', it is just the knowledge that arises through a desire (willfully) in the form, 'this is a pot', that is 'āhārya'." 17 The 'limiting conditions for usage' (prayogopādhi) are additional, here contextual, properties which limit the circumstances for use of a word, beyond the basic cause for application of a word, the pravṛttinimitta.

Translation
That has been stated by Hari, Similarity to that (1), and non-existence (2), the condition of being other than that (3), the condition of being small amount of that (4), the condition of being nonpraiseworthy (5), and opposition (6) are declared to be the six meanings of ñan.
Similarity to that occurs in 'this is a non-horse (anaśva)' in reference to an ass etc. (1). And non-existence will be discussed under the topic of the prasajyapratiṣedha (2). The condition of being other than that occurs in 'bring a living being that is a non-human (amanuṣya)' etc. (3). The condition of being a small amount of that occurs in 'a waistless girl' (anudara) where, on the basis of artha, 18 the smallness of the waist is understood through the denial of thickness (4). The condition of being non-praiseworthy occurs in the usage 'this is a bad brāhmaṅa' (abrāhmaṇa) in reference to a brāhmaṅa (5). Opposition occurs in the usage (s) 'opponent of the gods' (asura) and 'opposition to dharma' (adharma) (6). [p. 125]

Commentary
Although attributed here to Bhartṙhari, this verse seems to be absent from the Vākyapadīya. Nevertheless it is a well-known verse, found in a number of earlier authors. The examples given are relatively self-explanatory, though it should be noted that in different texts the same examples are given as examples of different meanings of nañ; this reflects the contextual nature of these meanings. So abrāhmaṇa, which is here given as an example of the 'non-praiseworthy' usage, is elsewhere given as an example of similarity (1) or the condition of being other than (3). Anaśva 'non-horse' is likewise elsewhere sometimes given as an example of (3).
It is interesting that Nāgeśa here does not give a paryudāsa example of sense (2), non-existence, but instead appears to restrict this sense of nañ to prasajyapratiṣedha. Other texts do offer the example of apāpa 'lack of sin' for sense (2), but without clearly assigning it to either paryudāsa or prasajyapratiṣedha.

Translation
A paryudāsa is only compounded with the word used together with it, on the basis of sāmarthya (connection of meaning). [But sometimes it occurs in a non-compound as well, as in 'He says (the formula) 'ye yajāmahe' at the sacrifices, and not at the after-sacrifices' (yajatiṣu yeyajāmahaṃ karoti nānuyājeṣu) 20 etc., and in 'the pot is not a cloth' (ghaṭo na paṭaḥ), when the meaning is 'the pot is a non-cloth' (ghaṭaḥ apaṭo bhavati), etc., because of the (general) option in regard to compounding. Here 'mutual non-existence' (anyonyābhāva) results.]

Commentary
The text from kvacit tu through phalito bhavati ('But sometimes... results (phalitaḥ)') is absent from the manuscripts consulted by Cardona (forthcoming) 19 Shukla (1961) reads prāyaḥ 'for the most part' in parentheses at the end of this sentence with a note that it is absent from many manuscripts. Presumably the intention is that prāyaḥ should be substituted for eva 'only'. Cardona (forthcoming,p. 58) notes no variants in the manuscripts, reading only eva. 20 Cf. Śābarabhāṣya on JS 10.8.1. and appears only in printed editions. That it is an interpolation explains the fact that the analysis of ghaṭo na paṭaḥ given here contradicts the analysis given below. The discussion of nānuyājeṣu is also problematic, since it contradicts Nāgeśa's treatment of this example in the Laghumañjūṣā and Vaiyākaraṇasiddhāntamañjūṣā.
The nānuyājeṣu example is a well-known example from Mīmāṁ saka literature. It is a potential problem for the Mīmāṁ sakas, because under a prasajyapratiṣedha analysis-the natural analysis given that the negative is not compounded-they would end up with a vikalpa, an option: the sacrificer would be instructed both to say the ye yajāmahe formula at sacrifices in general (including the after-sacrifices), and not to say it at the after-sacrifices. They resolve the problem by treating this as an example of an uncompounded paryudāsa, in which case nānuyājeṣu modifies yajatiṣu, and the whole thing means 'He says (the formula) 'ye yajāmahe' at the sacrifices which are not the after-sacrifices.' This is the analysis adopted without comment by the interpolated text here.
The '(general) option in regard to compounding' follows Aṣṭādhyāyī 2.1.11 vibhāṣā 'optionally', which governs most of the rules specifying compounding in the Aṣṭādhyāyī. Sāmarthya 'connection of meaning' as the basis for compounding follows Aṣṭādhyāyī 2.1.1 samarthaḥ padavidhiḥ.

Translation
A prasajyapratiṣedha is of two types, compounded and not compounded. There, even though it (i.e., nañ) is restricted, as being the qualificand, to a connection with an action, and so there is no connection in meaning (sāmarthya) with a word in a case suffix, (still) on the basis of the indication (made) in rules such as asūryalalāṭayoḥ etc. there is a compound.

Commentary
Nāgeśa recognizes both compounded and uncompounded prasajyapratiṣedha negation. The standard type is, of course, the uncompounded. Nāgeśa's point is that since in a prasajyapratiṣedha nañ means abhāva, and must therefore be the qualificand (viśeṣya), its primary semantic relation must be with the action which is the meaning of the finite verb. This means there is no direct connection between the meaning of prasajyapratiṣedha nañ and a word that ends in a case suffix (i.e. a noun or adjective), and so ordinarily, compounding (which can occur with a noun or adjective) should not be possible. Nevertheless, Aṣṭādhyāyī 3.2.36 (asūryalalāṭayoḥ dṛśitapoḥ) licenses the compound asūryaṃpaśya 'one who does not see the sun'. The accepted meaning of this compound involves prasajyapratiṣedha, so this is taken as an indication that Pāṅini does license compounded prasajyapratiṣedha negation.

Translation
That has been stated, This is a prasajyapratiṣedha, where nañ occurs with a (word denoting an) action. 21 [p. 126] Here the word 'action' (kriyā) indicates (as included in its range) a quality (guṇa) as well, according to many. It is for this reason that in the (Mahā) Bhāṣya on the rule nañ (Aṣṭādhyāyī 2.2.6), it is declared, 'he supposes (prasajya) an action or a quality, and then, subsequently, cancels it' (MBh. 1.412.3-4). For example: 'there is not one thing that is dear to us' (nāsmākam ekaṃ priyam). In the prohibition of one dear thing there is an understanding of many dear things.

Commentary
Given the Mahābhāṣya statement which notes both actions and qualities as being subject to prasañjana 'supposition' 22 in a prasajyapratiṣedha negation, the word kriyā in the quote given first is taken to include reference to qualities guṇa, as well.
An example is then given to illustrate negation involving prasañjana of a guṇa. The sentence nāsmākam ekaṃ priyam is a minor rewording of the example na na 21 This is a line from a pair of verses widely cited in grammatical and poetic literature, the origins of which can no longer be traced; see Matilal (1968, p. 57). 22 More precisely, the sense of pra-sañj found in the prasajya of prasajyapratiṣedha is of admitting something as an undesired or to-be-cancelled possibility. Joshi and Roodbergen (1973, p. 107) translate the sentence of the Mahābhāṣya quoted in this passage as "Having (first) allowed the possibility of an action or quality, then, subsequently, he removes (that)". ekaṃ priyam given in the Mahābhāṣya 1.412.7. 23 There, it appears alongside another example, na na ekaṃ sukham 'there is not (only) one thing that is pleasant to us'. While priya does not occur in the standard Naiyāyika-Vaiśeṡika inventory of guṇas, sukha does, and it is clear from the context in the Mahābhāṣya that in these examples it is priya and sukha respectively which are the guṇas in question. This is despite the fact that number is a guṇa in the Naiyāyika-Vaiśeṡika ontology, and that it is the singular number which is subject to the pratiṣedha of the negation. We are not aware of any acknowledgement of number as a guṇa within the vyākaraṅa tradition, and certainly not in any discussion of these examples.
The interpretation of nāsmākam ekaṃ priyam is derived in the following way. All actions and qualities must have a substratum (āśraya), and therefore bring with them an implication (ākṣepa) of that substratum. The negation here is directed to that substratum as delimited by singularity, but since the implication of a substratum remains, we understand a substratum delimited by some other number. 24 That is, we rule out the existence of only one thing which is dear, and therefore understand a different number, necessarily more than one, of things which are dear; the sentence is therefore equivalent to saying 'there are many things which are dear to us'.
The text from evam through gehe ghaṭo nāsti ityādi ("Similarly... 'in the house there is no pot' etc.") is absent in manuscripts and appears only in editions. It merely adds a number of unobjectionable examples, first of negation of qualities, and then of actions. Knowledge in all its forms, including e.g. doubt and comprehension, are understood to be qualities of the ātman, and so the negation directed to words like saṃdeha and upalabdhi involves negation of qualities. 25 Aṣṭādhyāyī 8.4.47, anaci ca 'and when a vowel does not follow', teaches doubling of any consonant other than h when these follow a vowel and are not followed by a vowel (anaci). Under a paryudāsa interpretation, the compound would mean 'when something follows which is (similar to but) not a vowel', i.e. when a consonant follows. The distinguishing context is before a pause or at the end of a sentence, i.e. when nothing follows; the grammatical tradition from Kātyāyana onwards accepts that doubling is possible at the end of a sentence. The grammarians therefore interpret anaci as an instance of compounded prasajyapratiṣedha, 23 The original form can be read either as equivalent to nāsmākam ekaṃ priyam, that is with the second word being naḥ 'to us', or as an instance of doubling of the negative particle used in the context of ābādha 'torment', following Aṣṭādhyāyī 8.1.10 ābādhe ca, in which case it is taken as an exclamation in the context of an enemy having many dear things. The two possible interpretations are first discussed by Kaiyaṫa, and by Nāgeśa in his Uddyota. 24 On MBh. 1.412.3-4, in the context of an analysis of anekam, which immediately precedes the example na na ekaṃ priyam and which is analysed by Patañjali in the same way, Kaiyaṫa comments: nirāśrayayoś ca tayor asaṃbhavād aniyatasaṃkhyadravyākṣepe saty ekapratiṣedhād bahūnāṃ pratītir ity arthaḥ "Because those two [i.e., an action and a quality] are impossible when they lack a substrate, there is an implication of substance (dravya) with a non-restricted number, and due to the prohibition of 'one' (eka) there comes about an understanding of (two or) many. That is the meaning." Pravartakopādhyāya, commenting on Kaiyaṫa's initial gloss here, says (Narasimhacharya 1986, p. 330), "Here [on anekaśabda], the prasañjana of an action and a quality is just a vidhāna, so he says 'vidhāya'. Because the prasañjana serves its purpose in the prohibition of the singular, how can there be an understanding of many (bahutva)? With this concern in mind he says, ('because those two...) when they lack a substrate'..." Cf. also Vākyapadīya 3.14.290. 25 The commentators state that the absolute non-existence of doubt is understood from na saṃdehaḥ. therefore meaning 'when not followed by a vowel', and meaning that Pāṅini's statement correctly licenses doubling in pausa. 26

Translation
And when that is compounded it is just absolute non-existence that is the meaning. But when it is uncompounded, absolute non-existence and mutual non-existence (are the meanings). Absolute non-existence is the non-existence of any relation other than identity. Mutual non-existence is the non-existence of the relation of identity, and its meaning is bheda (difference). 27 'The king's wives do not see the sun' (asūryaṃpaśyā rājadārāḥ), 'in the house there is no pot' (gehe ghaṭo nāsti), 'the pot is not a cloth' (ghaṭo na paṭaḥ) are examples.
But prior non-existence and destruction are not manifested by nañ.

Commentary
Specifically, the three examples given are respectively examples of prasajyapratiṣedha: 1. compounded, and expressing absolute non-existence; 2. uncompounded, 26 This question is first addressed in Kātyāyana's third Vārttika on this rule as discussed in the Mahābhāṣya, which proposes to augment the Pāṅinian rule with avasāne ca 'and before a pause'. Kātyāyana therefore appears to have interpreted anaci as a paryudāsa, and the rule as thus in need of augmentation. Patañjali rejects the proposed addition, saying: vākk vāk. tvakk tvak. srukk sruk. tat tarhi vaktavyam. na vaktavyam. na ayaṃ prasajyapratiṣedhaḥ. aci na iti. kiṃ tarhi. paryudāsa ayam. yat anyat acaḥ iti. '[examples of doubling in pausa] That (proposed addition avasāne ca) therefore should be stated. No, it need not be stated. This is not a prasajyapratiṣedha, (meaning) 'not before vowels'. What then? It is a paryudāsa, (meaning) 'something other than a vowel'.' However, as Kaiyaṫa observes, Patañjali's comments here do not make sense. Kaiyaṫa comments: pāṭho 'yaṃ lekhakapramādān naṣṭaḥ. paryudāse hy acsadṛśasya varṇāntarasya nimittatvenopādānād avasāne dvirvacanasyāprasaṅgāt. tasmāt "nāyaṃ paryudāso yad anyad aca iti kiṃ tarhi prasajyapratiṣedho 'ci na" ity ayaṃ pāṭhaḥ. 'This reading is corrupted due to scribal negligence. For if this were a paryudāsa, then due to the acceptance of another sound similar to a vowel as the cause, we would not get doubling in pausa. Therefore we should read, 'This is not a paryudāsa, (meaning) 'something other than a vowel'. What then? It is a prasajyapratiṣedha, (meaning) 'not before vowels'.' There appears to be no better way to resolve the logical inconsistency in the existing text of the Mahābhāṣya than this proposed emendation. We can therefore conclude that Patañjali was first to reject the paryudāsa interpretation of anaci in favour of the prasajyapratiṣedha interpretation, a move which eliminates the need to augment the Pāṅinian rule, and a move followed by all later grammarians. 27 Cf. Laghumañjūṣā, beginning of section 33. and expressing absolute non-existence; and 3. uncompounded, and expressing mutual non-existence. The first two are not significantly different from the examples discussed above (e.g. ex. 2, and anaci immediately above); the third will be discussed in more detail below. The absence of the fourth logical possibility, compounded prasajyapratiṣedha expressing mutual non-existence, is interesting, but Nāgeśa offers no explanation. It is possible that mutual non-existence expressed by a compound would approximate so closely to paryudāsa negation as to be indistinguishable. In the interpolated passage given in text section 4 above, an instance of an uncompounded paryudāsa, ghaṭo na paṭaḥ was explained as meaning ghaṭaḥ apaṭo bhavati.

Translation
Of these two, absolute non-existence is in fact connected, as something to be qualified, with an action that is the meaning of a finite verb. (This is) because with regard to knowledge in which the qualified item is the absolute non-existence that is the meaning of nañ, the presentment brought about by the root spoken together with the finite verb suffix is the cause. And in this way, at 'there is no pot' (ghaṭo nāsti) etc. there is knowledge of non-existence for which the counterpositive is existence (i.e., the act of existing) in which a pot is the agent. It is for this reason that in 'I do not exist', 'you do not exist' etc., and in 'two pots do not exist', 'multiple (three or more) pots do not exist' etc., the (correct) settlement of person and number comes about. Otherwise, because of the absence of agreement (sāmānādhikaraṇya) of 'you' etc. with the finite verb suffix, just as in 'the absence of me exists' (madabhāvo 'sti) etc. that (settlement) would not occur.

Commentary
The commentary glosses tatra, which we have translated as 'of these two', as atyantābhāvānyonyābhāvayoḥ 'Of absolute non-existence and mutual nonexistence'.
The term upasthiti, seen here in the compound tiṅsamabhivyāhṛtadhātujanyopasthiteḥ, and translated as 'presentment', is commonly used by the later grammarians to refer to the immediate mental effect of hearing a word. The upasthiti here is tiṅsamabhivyāhṛtadhātujanya 'brought about (janya) by the root (dhātu) spoken together (samabhivyāhṛta) with the finite verb suffix (tiṅ)'.
The semantic interpretation of prasajyapratiṣedha negation presented here is described in detail in the section "Prasajyapratiṡedha"; the discussion of agreement in the second half of this paragraph is discussed in detail in the section "The Argument with Nyāya".
The following section is an interpolation in our text. Therefore the sentence which originally directly follows this section is the first sentence in our section 10, which makes explicit the fact that this section (8) is a direct refutation of the Nyāya theory. atyantābhāvas tu phalita eva. vāyau rūpaṁ nāstīty atra tu tātparyānupapattyā rūpapratiyogikātyantābhāve lakṡaṅā. tena vāyvadhikaraṅikā rūpābhāvakartṙkā satteti bodhaḣ. vastutas tu samaniyatābhāvaikyam āśritya phalitārtha evāyam. arūpam astītyarthakaṁ vā tat.]

Translation
[But in 'doubtless' (asaṃdeha) etc. there is a compound just with the nañ by which a meaning has been superimposed. 28 And (the meaning) absolute non-existence in fact results. And in 'there is no color in air' (vāyau rūpaṃ nāsti), due to the impossibility of the intention (being expressed) there is lakṣaṇā with regard to the absolute non-existence in which color is the counterpositive. Therefore there is knowledge (perception) of the action of existing that has the air as its substrate and the non-existence of color as its agent. But in reality, by relying on the identity (aikya) of equally restricted absences (samaniyata) 29 this 30 in fact has the resulting meaning. Or, that has the meaning, 'a non-color (arūpam) exists'. 31 ]
The point of the first example is apparently to contrast with ahaṃ nāsmi 'I do not exist' etc., that although in asaṃdeha we derive a meaning of absolute nonexistence (just as with ahaṃ nāsmi), in this case we are dealing with a compound not a phrase and there is specific reference to an understanding based on the working of āropa.
The sentence 'there is no colour in air' has been partially discussed above ("The Argument with Nyāya" section). What has not been explained is this text's solution to the problem that this sentence raises for the vyākaraṅa theory of negation. Two or three options appear to be put forward. The first solution is that, given the impossibility of the literal meaning of this sentence, lakṣaṇā steps in: that is, the primary literal meaning is blocked, and a secondary meaning is inferred, here stated to be a non-existence of which the counterpositive is merely colour (as opposed to colour in air).
The second solution relies on the notion of equally restricted (samaniyata) nonexistence. Two things which are samaniyata, i.e. which have identical extensions, can be treated as identical. Wherever there is non-existence of an action of existing of which colour is the agent, there is also the non-existence of colour, necessarily, meaning that these two non-existences are samaniyata and therefore possess identity (aikya). We can therefore move directly from the unacceptable interpretation to an acceptable interpretation in which the counterpositive of the non-existence is merely colour. Thus we make exactly the same move as on the first proposed solution, but we do so not on the basis of lakṣaṇā, but on the basis of logical equivalence. 32 The grammarians consider lakṣaṇā a costly process (cf. text section 13, below), which directly increases the complexity (gaurava) of any linguistic analysis; the recourse to samaniyatānām aikyam is therefore preferable.
The final sentence 'or that has the meaning, a non-colour exists', suggests the possibility of a paryudāsa interpretation of the negation in vāyau rūpaṃ nāsti. This would make it parallel to the solution proposed for the sequence nānuyājeṣu in the previous interpolated passage above (text section 4). This suggestion is not otherwise unpacked here, nor is it mentioned as a solution for this sentence in any other text we are aware of. 32 Shukla's commentary explains this in the following way (p. 129-130): "Surely, if absolute nonexistence, the meaning of nañ, has a counterpositive that is limited by the condition of being an action, then in 'there is no color in air', since color possessing the condition of being the superstrate described by air is unknown (aprasiddha), and since the action of existing, in which the agent is that, is unknown, (and so) because an non-existence in which the counterpositive is unknown is not accepted, absolute nonexistence, the meaning of nañ, cannot be connected as something to be qualified with action that is the meaning of a finite verb, and thus it is just the non-existence in which the counterpositive is color that is established by the experience of everyone... It is only the non-existence of color, as content of the knowledge, that is the content of the intention... Where there is the non-existence of color, just there there is also the non-existence of the action of existing (sattā) in which color is the agent, and so those two are samaniyata, and there is identity (aikya) of two things that are samaniyata, and therefore when the nonexistence of the action of existing in which color is the agent is established, the non-existence of color certainly is established. This is the point."
Surely, [in this way a meaning, in the form of the existence of a pot (i.e., the action of existing performed by the pot), that is previously perceived, cannot be cancelled by nañ,] because there is no possible denial of something that exists, and it is from the non-existence of something that does not exist that the (effect of) vanishing (disappearing) is accomplished, whereby the denial is pointless. That has been stated, There is no denial of existing things, and that is not found in non-existing things. By this principle the meaning of nañ has disappeared in the world.

Commentary
The text from evam through nañā nivartayitum aśakyaḥ ("Surely in this way... cannot be cancelled by nañ") is absent from manuscripts and appears only in the printed editions; the manuscripts have nanu in place of nanv.
As stated above, if we ignore the passages absent from the manuscripts, then the first sentence of this section directly follows the end of section 8, making clear that the arguments in that section are direct refutations of the Naiyāyika position.
What follows returns to the Naiyāyika pūrvapakṡa, representing their interpretation of the vyākaraṅa approach to negation and its apparent failings. The issue in question is the apparent 'cancellation', nivṛtti, of the meaning of a counterpositive. That is, if ghaṭa denotes a pot, and asti an action of existing (sattā), then it is problematic for a sentence ghaṭo nāsti, which contains both these words, to denote neither a pot nor an action of existing.
The argument goes further, undermining the very nature of negation as the grammarians understand it. Since an existing thing cannot be denied, and a nonexisting thing does not need to be denied-that is, since words cannot affect the existence or otherwise of any thing-the idea that nañ involves a cancellation or denial renders it pointless.
The verse cited is Buddhist in origin; it appears in Helārāja's commentary on Vākyapadīya 3.3.42, and also e.g. in the Pramāṇaviniścaya, 226. 33

Translation
If you say this, it is wrong. (This is) because it has been said that a mental (bauddha) word is denotative, and it is just a mental meaning that is denoted, (and) because in regard to a meaning, even when it exists in the mind (in a perception) (buddhi), there is a denial of its external existence by nañ. (And) because the meaning is that a pot, even if existing in the mind (a perception) (buddhi), does not exist externally.
And do not say that the knowledge (/perception, buddhi) of asti 'exists', whose range is a pot, and that has come about from the words 'pot' and 'exists', is cancelled by nañ, and so what is the point in accepting a mental (bauddha) meaning. 34 (This is) because knowledge (a perception) (buddhi) cannot be expressed by a word, and so it cannot be denied by nañ. For this reason the Tārkikas, who do not accept a mental meaning and construct a difficult assumption for understanding the meaning of nañ, are refuted.

Commentary
The grammarians' answer to the objection set forth in the previous section is that there is a difference between mental meaning, bauddhārtha, and external reference, bāhyārtha. Words denote mental meanings, not external referents; nañ does not cancel the mental meaning, but it does deny the external existence. Thus the (mental) meanings denoted by ghaṭa and asti in ghaṭo nāsti are not cancelled but remain; what is denied is the external existence of the pot.
The second paragraph continues the refutation. The presentation is rather oblique, but we are first presented in outline with a Naiyāyika response to the proposed solution which distinguishes mental meaning from external reference. Even if we accept this, the Naiyāyika argument runs, we still end up with the cancellation of something that unarguably exists, namely the cancellation of the buddhi, the knowledge or perception brought about by the words used. Thus it was pointless to bring in the concept of bauddhārtha. Nāgeśa's reply is that knowledge, buddhi, which is derived from the meaning, artha, of words but is not the same as artha, cannot itself be expressed by a word, and so the negation cannot touch it.
Shukla's commentary glosses kaṣṭakalpanā (difficult assumption) as śaśaśṛṅgaṃ nāstī 'ty atra śṛṅge śaśīyabhramādirūpā 'having the form of something such as error about the hare-relatedness of a horn in the sentence, 'the horn of the hare does not exist'.' The reference here is to the problem of negating non-existent or impossible entities, such as a hare's horn. 35

Translation
In 'the pot is not a cloth' (ghaṭo na paṭaḥ), in the word pot (ghaṭaḥ), it is just the unestablished denotative power that refers to the substrate of a difference (bheda) whose counterpositive is a pot that is lakṣaṇā, and the word nañ causes the comprehension of the intention. It is said that the condition of being something that causes the comprehension of the intention is just the condition of being something that manifests. It is for this reason that the declaration of the elders, namely, that with regard to knowledge of mutual non-existence, the condition in the pratiyogin and the anuyogin of having the same case suffix serves as a (required) restriction (niyāmaka), makes sense. 36

Commentary
The analysis proposed here for the final type of negation, uncompounded prasajyapratiṣedha with the sense of bheda 'difference' = anyonyābhāva 'mutual non-existence', is rather abruptly presented. We are simply told that a word like ghaṭa 'pot' has as one of its possible meanings 'the substrate of a difference whose counterpositive is a pot', and that the function of nañ here is to indicate that this is the intended meaning. The final sentence of this paragraph explains that the agreement between paṭa and ghaṭa in ghaṭo na paṭaḥ constrains the final interpretation, which for Nāgeśa here is something like ghaṭapratiyogikabhedāśrayapaṭa 'a cloth which is the substratum of a bheda of which the 35 On this, see Wada (2020, pp. 73-105). 36 Cf. Matilal (1968, p. 156). counterpositive is a pot'. This proposal is rather unsatisfyingly non-explanatory, perhaps, but within Nāgeśa's system there is nothing inherently problematic about it, in contrast with the Naiyāyika's approach, to which he now turns. 37

Translation
But the Tārkikas say that [in the sentence ghaṭo na paṭaḥ 'the pot is not a cloth'] the word pot is secondarily denotative of something whose counterpositive is a pot, and the word nañ is (secondarily denotative) of something that has a difference (bhedavat), 38 and therefore the knowledge is, 'a cloth that possesses difference in which the counterpositive is a pot'. 39 This is wrong. If the meaning of nañ is something that has a difference, because the difference is a part (ekadeśa) there would be no connection with (of) the meaning of the pot there. (This is) because of the principle that the meaning of a word is connected with the meaning of a word, not with a part of the meaning of a word. And because there is complexity in accepting lakṣaṇā in two words. This is because in the opinion of the Bhāṣya there is no acceptance of lakṣaṇā or of the condition in nipātas of being denotative. This is an abbreviated account.

Commentary
Nāgeśa now contrasts the Naiyāyika analysis of ghaṭo na paṭaḥ. Crucially, this involves two instances of lakṣaṇā, which for the grammarians results in an unreasonably complex analysis. First, the Naiyāyikas assume that a word like ghaṭa can denote something whose counterpositive is a pot, but this denotation comes by lakṣaṇā, not as one of the possible primary meanings of the word. Secondly, for the Naiyāyikas nañ does not denote bheda here, but rather something that has bheda, bhedavat. The problem identified by Nāgeśa here is that we cannot directly combine the meanings of the pot and the negation to get the desired 37 In the Laghumañjūṣā, Nāgeśa presents a rather different approach in greater detail, and does not mention even as a possibility the approach presented here. The question of why the two texts differ so significantly on this point is related to the question of the precise relation between the two texts, and what the purpose of the PLM is, whether an abridgement and update of the LM, or a pedagogical simplification of it. As noted above, these questions require further research. 38 Bheda was offered as the sense of anyonyābhāva above. 39 Cf. Laghumañjūṣā, p. 668, section 36. ghaṭapratiyogikabhedavat, because this would require us to combine the meaning of the word ghaṭa directly with a part of the meaning of the word nañ, i.e. with bheda; we cannot directly combine ghaṭapratiyogika with bhedavat as a whole to get the desired outcome.
Altogether then, the Naiyāyika account of ghaṭo na paṭaḥ faces a multitude of problems, in Nāgeśa's eyes: the composition of the meanings is impossible, lakṣaṇā has to be invoked twice, and, according to his final note, nañ should not be considered denotative (vācaka) in any case. 40

Conclusion
In the Paramalaghumañjūṣā, Nāgeśa presents a relatively clear theory of negation which draws a firm semantic distinction between paryudāsa and prasajyapratiṣedha. In the former case, the semantic contribution of nañ is to manifest the āropita nature of the meaning denoted by the word which nañ modifies (so e.g. āropitabrāhmaṇatva); context then enables the intended meaning (such as brāhmaṇa-sādṛśya) to be understood. In the case of prasajyapratiṣedha, nañ means abhāva 'non-existence', more specifically either atyantābhāva 'absolute nonexistence' or anyonyābhāva/bheda 'mutual non-existence'/'difference'.
Although this appears to be a very clear and absolute presentation, which perhaps represents the final siddhānta of the final authority of the Pāṅinian tradition, it is worth noting that it obscures a history of debate among the later grammarians with respect to the meaning of negation. Nāgeśa's theory is tied in part to his assumption that nañ can only be viśeṣya; this assumption does appear to be part of the debate for Bhat˙ṫojidīkṡita, who refers to it in the second of his Kārikās on nañ, but Bhaṫt˙oji himself admits the possibility of abhāva being viśeṣaṇa, which opens the door to abhāva being the meaning of nañ even in the case of paryudāsa negation; this is the siddhānta for Kauṅḋabhat˙t˙a. In contrast, in the Laghumañjūṣā Nāgeśa goes in the other direction, suggesting that the meaning of nañ is āropa even in the case of prasajyapratiṣedha negation. A detailed account of these fine-grained differences in the approaches to negation in the different authors and texts of the later vyākaraṅa tradition awaits future research.