Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Schayer (1933) appears to be the first scholar that attempts a formalization of Nāgārjuna’s catuṣkoṭi.
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.
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.
Searle notes that the illocutionary (de)negation does not follow double negation elimination. See Vanderveken and Searle (1985), pp. 153–4.
Nāgārjuna does not use the word prasaṅga in the MMK, but later commentators use this word to refer to his argumentative structure.
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.
See previous note.
Candrakīrti also includes opponent acknowledge inference (tatprasiddha anumāna) as an acceptable argument for a Mādhyamika. See MacDonald (2015), pp. 130-133.
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.
Tillemans (1999, p. 197) notes this as well.
Lhas byin (or Lhejin per Samten and Garfield’s translation) is Tsongkhapa’s translation of Devadatta.
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.
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).
This has a similar structure to Dignāga’s theory of apoha, but Tsongkhapa makes no reference to it.
Further, the Tibetan tradition had difficulties in parsing out the internal negations of the fourth corner. See Tillemans (2015).
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.
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.
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.
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.
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.
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.
References
Abhyankar, K. V. (1986). A dictionary of Sanskrit grammar (3rd ed.). Oriental Institute.
Ames, W. L. (1993). Bhāviveka’s “Prajñāpradīpa”: A translation of chapter one: ‘Examination of the causal conditions’ (“Pratyaya”). Journal of Indian Philosophy, 21(3), 209–259.
Apte, V. S. (1957–9). The practical Sanskrit-English dictionary (P. K. Gode and C. G. Karve eds.). Poona: Prasad Prakashan.
Bilimoria, P. (2017). Thinking negation in early Hinduism and classical Indian philosophy. Logica Universalis, 11, 13–33.
Cardona, G. (1967). Negations in Pāṇinian rules. Language, 43(1), 34–56.
Chakravarti, S. S., & Chakrabarti, S. S. (1980). The Mādhyamika “Catuṣkoṭi” or Tetralemma. Journal of Indian Philosophy, 8(3), 303–306.
Chi, R. S. Y. (1969). Buddhist formal logic. Luzac and Co.
Dreyfus, G. (2011) Can a Madhyamaka be a Skeptic? The case of Patsab Nyimadrak. In: Cowherds (Eds.), Moonshadows. Conventional Truth in Buddhist Philosophy (pp. 89–113). Oxford University Press.
Garfield, J. (2002) Emptiness and positionlessness: Do the Mādhyamika Relinquish All Views? In: Garfield, J. (Ed.), Empty Words (pp. 46-48). Oxford University Press.
Garfield, J., & Priest, G. (2009). Mountains are just mountains. In M. D’Amato, J. Garfield, & T. J. F. Tillemans (Eds.), Pointing at the moon (pp. 71–82). Oxford University Press.
Grice, H. P. (1989). Studies in the way of words. Harvard University Press.
Horn, L. (2001/ 1989) A natural history of negation. CSLI Publication.
Incurvati, L., & Schlöder, J. J. (2017). Weak rejection. Australasian Journal of Philosophy., 95(4), 741–760.
Kassor, C. (2011). Gorampa Sonam Senge on the Refutation of the Four Extremes. Revue D’études Tibétaines, 22, 121–137.
Kassor, C. (2021) "Gorampa [go rams pa]", The Stanford encyclopedia of philosophy (Summer 2021 Edition). https://plato.stanford.edu/archives/sum2021/entries/gorampa/.
Kajiyama, Y. (1973). Three kinds of affirmation and two kinds of negation in Buddhist philosophy. Wiener Zeitschrift Für Die Kunde Südaisiens Und Archiv Für Indische Philosophie, 17, 161–174.
MacDonald, A. (2015). In clear words the Prasannapadā, chapter one (Vol. 2). Verlag der Österreichischen Akademie der Wissenschaften.
Matilal, B. K. (1986). Perception. Clarendon Press.
Matilal, B. K. (2005). Epistemology, logic, and grammar in Indian philosophical analysis (2nd ed.). Oxford: Oxford University Press.
Mohanta, D. (2010). The use of four-cornered negation and the denial of the law of excluded middle in Nāgārjuna’s logic. In A. Schumann’s (Ed.), Logic in religious discourse (pp. 44–53). Berlin: De Gruyter.
Priest, G. (2010). The logic of The Catuskoti. Comparative Philosophy, 1(2), 24–54.
Priest, G. (2015). None of the above: The Catuṣkoṭi in Indian Buddhist logic. In M. C. Jean-Yves Beziau, and Some Dutta (Eds.), New direction in paraconsistent logic (pp. 517–527). London: Springer.
Priest, G. (2018). The fifth corner of four. Oxford University Press.
Priest, G., & Garfield, J. (2002). Nāgārjuna and the limits of thought. In G. Priest (Ed.), Beyond the limits of thought (pp. 249–270). Clarendon Press.
Robinson, R. (1967). Early Mādhyamika in India and China. University of Wisconsin Press.
Ruegg, D. S. (1977). The uses of the four positions of the “Catuṣkoṭi” and the problem of the description of reality in Mahāyāna Buddhism. Journal of Indian Philosophy, 5(1/2), 1–71.
Ruegg, D. S. (1981). The literature of the Madhyamaka School of Philosophy in India. Harrassowitz.
Russell, B. (1906). On denoting. Mind, 14, 479–493.
Schayer, S. (1933). Altindische Antizipationene der Aussagenlogik. Bulletin International de ‘l Académie Polonaise des Sciences et Philologie (1–6), 90–96.
Searle, J. (1969). Speech Acts. Cambridge University Press.
Siderits, M., & Katsura, S. (2013). Nagarjuna’s middle way: Mūlamadhyamakakārikā. Wisdom Publications.
Staal, F. (1975). Exploring mysticism: A methodological essay. University of California Press.
Strawson, P. F. (1950). On referring. Mind, 59, 320–334.
Thakchoe, S. (2004). How many Truths? Are there two truths or one the Tibetan Prāsa[ndot]gika Madhyamaka? Contemporary Buddhism., 5(2), 121–141.
Thakchoe, S. (2008). Gorampa on the objects of negation: Arguments for negating conventional truths. Contemporary Buddhism, 9(2), 265–280.
Tillemans, T. (1999). Is buddhist logic non-classical or deviant? (pp. 187–208) In Scripture, logic, language. Boston: Wisdom Publications.
Tillemans, T. (2009). How do Mādhyamikas think? In M. D’Amato, J. Garfield, & T. J. F. Tillemans (Eds.), Pointing at the moon (pp. 83–100). Oxford University Press.
Tillemans, T. (2015). What happened to the third and fourth lemmas in tibet? Journal of Buddhist Philosophy, 1, 24–38.
Tsongkhapa (2002). The great treatise on the stage of the path to enlightenment. Vol. III. (The Larim Chenmo Translation Committee, trans.). Snow Lion Publications.
Tsongkhapa (2006). Ocean of reasoning (G. N. Samten and J. L. Garfield, trans.). Oxford University Press.
Vanderveken, D., & Searle, J. (1985). Foundations of illocutionary logic. Cambridge University Press.
Walser, J. (1998). On the formal arguments of the Akutobhayā. Journal of Indian Philosophy, 26(3), 189–232.
Westerhoff, J. (2006). Nāgārjuna’s Catuṣkoṭi. Journal of Indian Philosophy, 34, 367–395.
Westerhoff, J. (2009). Nāgārjuna’s Madhyamaka. Oxford University Press.
Westerhoff, J. (2018). The golden age of Indian Buddhist philosophy. Oxford University Press.
Acknowledgements
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.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author has no relevant financial or non-financial interests to disclose.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
