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Nāgārjuna’s Negation


The logical analysis of Nāgārjuna’s (c. 200 CE) catuṣkoṭi (tetralemma or four-corners) has remained a heated topic for logicians in Western academia for nearly a century. At the heart of the catuṣkoṭi, the four corners’ formalization typically appears as: A, Not A (¬A), Both (A &¬A), and Neither (¬[A∨¬A]). The pulse of the controversy is the repetition of negations (¬) in the catuṣkoṭi. Westerhoff argues that Nāgārjuna in the Mūlamadhyamakakārikā uses two different negations: paryudāsa (nominal or implicative negation) and prasajya-pratiṣedha (verbal or non-implicative negation). This paper builds off Westerhoff’s account and presents some subtleties of Nāgārjuna’s use of these negations regarding their scope. This is achieved through an analysis of the Sanskrit and Tibetan Madhyamaka commentarial tradition and through a grammatical analysis of Nāgārjuna’s use of na (not) and a(n)- (non-) within a diverse variety of the catuṣkoṭi within the Mūlamadhyamakakārikā.

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  1. Schayer (1933) appears to be the first scholar that attempts a formalization of Nāgārjuna’s catuṣkoṭi.

  2. See Robinson (1967), pp. 57–58, and Westerhoff (2006, 2009, 2018).

  3. See Chi (1969), pp. 156–163; Staal (1975), pp. 36–46.

  4. See Priest and Garfield (2002), Garfield and Priest (2009), Tillemans (2009), and Priest (2010, 2015, 2018).

  5. This may be attested to some degree. Russell (1906) argued for this ambiguity. Horn (2001/1989) argues the wide scope negation reading is that of a metalinguistic negation and not an ambiguity due to semantic negations. This debate hinges on a semantic/pragmatic division between the two.

  6. It could also establish that the denotatum is a brahmin in name only. They may be in the brāhmaṇa caste, but they fail to live up to the standards of being a brahmin.

  7. It remains unclear to me how a speech act embeds under a negation. Embedding is a syntactical notion. Speech-acts and other pragmatic phenomena are not typical understood as being applicable to the domain of syntax.

  8. Matilal (1986), Matilal (2005), and Chakravarti and Chakrabarti (1980) make a similar appeal to Searle’s illocutionary (de)negation to explain Nāgārjuna’s use of the prasajya.

  9. Russell (1906) himself didn’t see this as problematic. Strawson (1950) and the following literature construe the problematic nature of Russell’s example.

  10. Searle notes that the illocutionary (de)negation does not follow double negation elimination. See Vanderveken and Searle (1985), pp. 153–4.

  11. Nāgārjuna does not use the word prasaṅga in the MMK, but later commentators use this word to refer to his argumentative structure.

  12. The Tibetan tradition separated what they saw as Bhāviveka’s philosophy from what they saw as Buddhapālita’s and Candrakīrti’s philosophy. They titled the former Svātantrika (Rang rgyud pa) and the later Prāsaṅgika (Thal ‘gyur pa). These titles would be unfamiliar to Buddhapālita, Bhāviveka, and Candrakīrti and each would likely reject such a division of Madhyamaka.

  13. See previous note.

  14. Candrakīrti also includes opponent acknowledge inference (tatprasiddha anumāna) as an acceptable argument for a Mādhyamika. See MacDonald (2015), pp. 130-133.

  15. It is possible that this account may provide a route to a constructive skepticism that establishes a positive element which is beyond discourse and conceptualization. See Garfield (2002), pp. 66–67.

  16. Tillemans (1999, p. 197) notes this as well.

  17. Lhas byin (or Lhejin per Samten and Garfield’s translation) is Tsongkhapa’s translation of Devadatta.

  18. Arthāpatti deals with the background knowledge surrounding the claim. In the example of Lhejin, there is an assumption that he must eat. If he must eat and doesn’t eat during the daytime, he necessarily must be eating during the nighttime. This example deals with pragmatic concerns since the speaker is not outright stating “Fat Lhejin eats during the nighttime”. As such, the speaker violates the Gricean Maxim of Quality.

  19. The author of the Jñānasārasamuccaya does not appear to be the Āryadeva (c. 200 CE) of the Catuḥśataka but, instead, is the much later Tantric Āryadevapāda. See Ruegg (1981, p. 54 and pp. 105–106).

  20. This has a similar structure to Dignāga’s theory of apoha, but Tsongkhapa makes no reference to it.

  21. Further, the Tibetan tradition had difficulties in parsing out the internal negations of the fourth corner. See Tillemans (2015).

  22. One possible reading of ahetu is that a(n)- indicates something deficient. As such, it should be read as ‘a bad cause’. This reading is quickly rejected by Candrakīrti, see Macdonald (2015), p. 155.

  23. This is especially due to the typical reading of the third corner as A & ¬A and the fourth corner as ¬ (A ∨ ¬A). These two corners would be logically equivalent through the application of De Morgan’s and double negation elimination. This has been widely noted by the literature.

  24. Siderits and Katsura (2013, p. 199) suggest that the fourth corner could be a distinctively Mahāyāna view (potentially Yogācāra) which could be due to its similarity with passages from the Vajracchedikā Prajñāpāramitā Sūtra and other Prajñāpāramitā Sūtras.

  25. This form of ‘not not’ (na na) for the fourth corner appears frequently in Pāḷi within the various catuṣkoṭi of the Anuradha Sutta, Sabhiya Sutta, Cūḷamāluṅkhya Sutta, and throughout the Sutta Piṭaka.

  26. Grice (1989) argues that conversations follow four main maxims: Quantity, Quality, Relation, and Manner. The Maxim of Quantity holds that the speaker should be as informative as needed. When the reader provides less information than needed, a conversational implicature may occur which communicates the needed information.

  27. Tsongkhapa (2002, pp. 312-315) holds that if something has a cause then it must be from itself, another, or both. Tsongkhapa provides the example of the creation of a clay pot which is production of itself (as its clay) and from another (the potter’s spinning and molding). While I’ve provided the example of a rock to make the issue of a category mistake clear, Tsongkhapa and likely Nāgārjuna are focused on the idea of spontaneous creation which is postulated by the Lokāyata school. Spontaneous creation still indicates a category mistake since it makes it explicit that there is a type of creation that falls outside of the category of being caused. Thus, there are four explanations for the arising of beings where three belong to the category of causes and one outside of this category.


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I thank Jay Garfield, Ethan Mills, Richard Hayes, Alexus McLeod, Mitchell Green, and two anomyous peer reviewers for their comments, which greatly improved the clarity and focus of this article.

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Rahlwes, C. Nāgārjuna’s Negation. J Indian Philos 50, 307–344 (2022).

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  • Catuṣkoṭi
  • Negation
  • Nāgārjuna
  • Paryudāsa
  • Prasajya
  • Denial