Catuṣkoṭi (Sanskrit; Devanagari: चतुष्कोटि, , Sinhalese:චතුස්කෝටිකය) refers to logical argument(s) of a 'suite of four discrete functions' or 'an indivisible quaternity' that has multiple applications and has been important in the Indian logic and the Buddhist logico-epistemological traditions, particularly those of the Madhyamaka school.
In particular, the catuṣkoṭi is a "four-cornered" system of argumentation that involves the systematic examination of each of the 4 possibilities of a proposition, P : P ; that is being. not P ; that is not being. P and not P ; that is being and that is not being. not (P or not P); that is neither not being nor is that being.
These four statements hold the following properties: (1) each alternative is mutually exclusive (that is, one of, but no more than one of, the four statements is true) and (2) that all the alternatives are together exhaustive (that is, at least one of them must necessarily be true). This system of logic not only provides a novel method of classifying propositions into logical alternatives, but also because it does so in such a manner that the alternatives are not dependent on the number of truth-values assumed in the system of logic.
An example of a Catuṣkoṭi using the arbitrary proposition, "Animals understand love" as P would be: Animals understand love Animals do not understand love Animals both do and do not understand love Animals neither do nor do not understand love
Origins The catuṣkoṭi probably originated in an earlier Indian sceptical tradition rather than in Buddhism. Its similarity to Pyrrho’s fourfold antinomies suggests that both Pyrrho and Buddhism were influenced by this earlier Indian scepticism. The method was later prominently used in Mādhyamika Buddhism.
History Nasadiya Sukta Statements similar to the tetra lemma seems to appear in the Nasadiya Sukta (famous creation hymn), trying to inquire on the question of creation but was not used as a significant tool of logic before Buddhism.
Early Buddhism Śākyamuni, as remembered by Ānanda and codified in the Brahmajala Sutta 2.27, when expounding the sixteenth wrong view, or the fourth wrong view of the 'Eel-Wrigglers' (Pali: amarā-vikheppikā), the non-committal equivocators who adhered to Ajñana, the sceptical philosophy, though the grammatical structure is identical to the Catuṣkoṭi (and there are numerous other analogues of this fourfold grammatical structure within this Sutta), the intentionality of the architecture employed by Nagarjuna is not evident, as rendered into English by Walshe (1987, 1995: p. 81): 'What is the fourth way? Here, an ascetic or Brahmin is dull and stupid. Because of his dullness and stupidity, when he is questioned he resorts to evasive statements and wriggles like an eel: "If you ask me whether there is another world. But I don't say so. And I don't say otherwise. And I don't say it is not, and I don't not say it is not." "Is there no other world?..." "Is there both another world and no other world?..."Is there neither another world nor no other world?..." "Are there spontaneously-born beings?..." "Are there not...?" "Both...? "Neither...?" "Does the Tathagata exist after death? Does he not exist after death? Does he both exist and not exist after death? Does he neither exist nor not exist after death?..." "If I thought so, I would say so...I don't say so...I don't say it is not." This is the fourth case.'Walshe, Maurice (1987, 1995). The Long Discourses of the Buddha: A Translation of the Digha Nikaya. Boston: Wisdom Publications. , p.81
Pyrrhonism
McEvilley (2002: p. 495) makes a case for mutual iteration and pervasion between Pyrrhonism and Madhyamika: An extraordinary similarity, that has long been noticed, between Pyrrhonism and Mādhyamika is the formula known in connection with Buddhism as the fourfold negation (catuṣkoṭi) and which in Pyrrhonic form might be called the fourfold indeterminacy., p.495
Nagarjuna The Catuṣkoṭi was employed particularly by Nagarjuna who developed it and engaged it as a 'learning, investigative, meditative'Rendering of the Three prajnas. portal to realize the 'openness' (Sanskrit: Śūnyatā), of Shakyamuni's Second Turning of the Dharmacakra, as categorized by the Sandhinirmocana Sutra.
Robinson (1957: p. 294), building on the foundations of Liebenthal (1948)Liebenthal, Walter (1948). The Book of Chao. Peking: Gatholic University Press of Peking, 1948, p.3O. to whom he gives credit, states: What Nagarjuna wishes to prove is the irrationality of Existence, or the falsehood of reasoning which is built upon the logical principle that A equals A.... Because two answers, assertion and denial, are always possible to a given question, his arguments contain two refutations, one denying the presence, one the absence of the probandum. This double refutation is called the Middle Path. [emphasis evident in Robinson]Robinson, Richard H. (1957). 'Some Logical Aspects of Nagarjuna's System'. Philosophy East & West. Volume 6, no. 4 (October 1957). University of Hawaii Press. Source: (accessed: Saturday March 21, 2009), p.294
Śūnyatā is the ninth 'view' (Sanskrit: dṛṣṭi), the viewless view, a superposition of the eight possible arrays of proposition P [and its 'inseparable contradistinction' (Sanskrit: apoha)].
Positive configuration P Not-P Both P and Not-P Neither P nor Not-P
Negative configuration Not (P) Not (Not-P) Not (Both P and Not-P) Not (Neither P nor Not-P)
The eight arrays or octaves of the iconographic Dharmacakra represent drishti or traditional views that Shakyamuni countered. These eight arrays may be plotted as coordinates on a multidimensional field which may be rendered as a sphere, a mandala, a multidimensional shunya or zero where shunyata denotes zero-ness. The eight arrays are in a concordant relationship where they each constitute a chord to the sphere. The coordinates are equidistant from the epicentre of shunya where the array of the positive configuration (or hemisphere) and the array of the negative configuration (or hemisphere) constitute two polar radii or diametrical complements, a diameter in sum. These are the 'eight limits' (Wylie: mtha' brgyad; Sanskrit: aṣṭānta) of 'openness' (Sanskrit: śūnyatā),Dorje, Jikdrel Yeshe (Dudjom Rinpoche, author), & translated and edited: Gyurme Dorje and Matthew Kapstein (1991). The Nyingma School of Tibetan Buddhism: Its Fundamentals and History. Boston, USA: Wisdom Publications. , p.158 where śūnyatā is amplified by 'freedom from constructs' or 'simplicity' (Wylie: spros bral; Sanskrit: aprapañca).Dharma Dictionary (June, 2006). 'spros bral'. Source: (accessed: Tuesday March 24, 2009)Abhayadatta (author); Dowman, Keith (translator); Downs, Hugh R. (1985). Masters of Mahāmudrā (Sanskrit: Caturaśītisiddha-pravṛtti ). SUNY Press. , . Source: (accessed: Tuesday March 24, 2009), p.397 Karmay (1988: p. 118) conveys that 'spros bral' is a homologue of 'thig le' (Sanskrit: bindu), where 'spros bral' is literally "without amplification", understood as "that which cannot be displayed".Karmay, Samten Gyaltsen (1988). The Great Perfection (rDzogs Chen): A Philosophical and Meditative Teaching of Tibetan Buddhism. Illustrated Edition. Brill. . Source: (accessed: Tuesday March 24, 2009), p.118
P is true ``1 P is not true or Not P is true Not P is true ``2. Not (Not P) is true i.e. P is true Both P and Not P are true i.e. the universal set `` 3 Neither P nor not P are true i.e. it is a null set Neither P nor not P are true it is a null set `` 4. Not (neither p nor not P are true ) = both P and not P are true which is the universal set.
Thus, a four-fold configuration resurfaces, with positive and negative configurations being mere rewritten alternatives (ie. it makes no difference whether one works with the positive or negative catuskoti). For example, if one replaces P with Not P, then the positive configuration set for Not P will be functionally equivalent to the negative configuration of P.
Sanjaya Belatthiputta, a 6th century BCE Indian ascetic whose teachings are similar to that of Nagarjuna are compared to that of a "theory of eel-wrigglers" in the famous Samannaphala Sutta (DN 2).Jayatilleke, p. 122.Bhaskar (1972) Sanjaya is recorded as saying: 'If you ask me if there exists another world [after death], if I thought that there exists another world, would I declare that to you? I don't think so. I don't think in that way. I don't think otherwise. I don't think not. I don't think not not. If you asked me if there isn't another world... both is and isn't... neither is nor isn't... if there are beings who transmigrate... if there aren't... both are and aren't... neither are nor aren't... if the Tathagata exists after death... doesn't... both... neither exists nor exists after death, would I declare that to you? I don't think so. I don't think in that way. I don't think otherwise. I don't think not. I don't think not not.'Thanissaro (1997).
Catuṣkoṭi post-Nagarjuna The Catuṣkoṭi, following Nagarjuna, has had a profound impact upon the development of Buddhist logic and its dialectical refinement of Tibetan Buddhism.
Robinson (1957: p. 294) qualifies the import of Nagarjuna's work (which includes Nagarjuna's application of the Catuskoti) due to the embedded noise in the scholarly lineage: "Certainly some of Nagarjuna's ancient opponents were just as confused as his modern interpreters...". This noise may also have co-arisen with Nagarjuna, following the work of Jayatilleke (1967).
Modern interpretations Robinson (1957: p. 294)Robinson, Richard H. (1957). 'Some Logical Aspects of Nagarjuna's System'. Philosophy East & West. Volume 6, no. 4 (October 1957). University of Hawaii Press. Source: (accessed: Saturday March 21, 2009) holds that Stcherbatsky (1927),Stcherbatsky, Th. (1927). The Conception of Buddhist Nirvana. Leningrad: Publishing Office of the Academy of Sciences of the USSR. opened a productive period in Madhyamaka studies. Schayer (1933) made a departure into the rules of inference employed by early Buddhist dialecticians and examines the Catuskoti (Tetralemma) as an attribute of propositional logic and critiques Stcherbatsky. Robinson (1957: p. 294) states that "Schayers criticisms of Stcherbatsky are incisive and just." Murti (1955)Murti, T. R. V., 1955. The Central Philosophy of Buddhism. George Allen and Unwin, London. 2nd edition: 1960. makes no mention of the logical contribution of Schayer. According to Robinson (1957: p. 294), Murti furthered the work of Stcherbatsky amongst others, and brought what Robinson terms "the metaphysical phase of investigation" to its apogee though qualifies this with: "Murti has a lot to say about 'dialectic,' but practically nothing to say about formal logic." Robinson (1957: p. 294) opines that Nakamura (1954),Nakamura, Hajime (1954). "Kukao no kigo-ronrigaku-teki ketsumei, (English: 'Some Clarifications of the Concept of Voidness from the Standpoint of Symbolic Logic')" Indogaku-bukkyogaku Kenkyu, No. 5, Sept., 1954, pp. 219-231. developed Schayer's methodology and defended and progressed its application.
Robinson (1957: p. 293) opines that the 'metaphysical approach' evident foremost in Murti (1955) was not founded in a firm understanding of the 'logical structure of the system', i.e. catuskoti, for example: Several fundamental limitations of the metaphysical approach are now apparent. It has tried to find comprehensive answers without knowing the answers to the more restricted questions involved - such questions as those of the epistemological and logical structure of the system.Robinson, Richard H. (1957). 'Some Logical Aspects of Nagarjuna's System'. Philosophy East & West. Volume 6, no. 4 (October 1957). University of Hawaii Press. Source: (accessed: Saturday March 21, 2009), p,293