Catuṣkoṭi (Sanskrit; Devanagari: चतुष्कोटि, Tibetan: མུ་བཞི, Wylie: mu bzhi, 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.
[2] 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?
[4] The Catuṣkoṭi was employed particularly by Nagarjuna who developed it and engaged it as a 'learning, investigative, meditative'[5] 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)[6] 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.
[12][13] Sanjaya is recorded as saying: The Catuṣkoṭi, following Nagarjuna, has had a profound impact upon the development of Buddhist logic and its dialectical refinement of Tibetan Buddhism.
Schayer (1933)[17] 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.
[20] Robinson (1957: p. 296) conveys his focus and states his methodology, clearly identifying the limitations in scope of this particular publication, which he testifies is principally built upon, though divergent from, the work of Nakamura: In considering the formal structure of Nagarjuna's argumentation, I exclude epistemology, psychology, and ontology from consideration....
Wayman (1977) holds that the Catuṣkoṭi may be applied in suite, that is all are applicable to a given topic forming a paradoxical matrix; or they may be applied like trains running on tracks (or employing another metaphor, four mercury switches where only certain functions or switches are employed at particular times).
The 'Four Extremes' (Tibetan: མཐའ་བཞི, Wylie: mtha' bzhi; Sanskrit: Caturanta; Devanagari: चतुरन्त) [24] is a particular application of the Catuṣkoṭi: Dumoulin et al.'s (1988, 2005: pp.
43–44), work on Zen models a particular formulation of the Catuṣkoṭi that approaches the Caturanta engaging the Buddhist notion of dharmas, and attribute the model to Nagarjuna: If we focus on the doctrinal agreement that exists between the Wisdom Sūtras[25] and the tracts of the Mādhyamika we note that both schools characteristically practice a didactic negation.
By setting up a series of self-contradictory oppositions, Nāgārjuna disproves all conceivable statements, which can be reduced to these four: With the aid of these four alternatives (catuṣkoṭika: affirmation, negation, double affirmation, double negation), Nāgārjuna rejects all firm standpoints and traces a middle path between being and nonbeing.
Most likely the eight negations, arranged in couplets in Chinese, can be traced back to Nāgārjuna: neither destruction nor production, neither annihilation nor permanence, neither unity nor difference, neither coming nor going.
Padmasambhava in his "Secret Instruction in a Garland of Vision" (Tibetan: མན་ངག་ལྟ་བའི་ཕྲེང་བ, Wylie: man ngag lta ba'i phreng ba) lists them as follows with the English rendering following Dowman (2003)[27] and Wylie following Norbu et al. (2001):[28] Within English Buddhist logico-epistemological discourse, there is and has been historically, much obstruction to an understanding of the Caturanta (as the Catuṣkoṭi) due to inherent negligence in terminology not being clearly defined from the outset.
That said, acquisition of terminology must be engaged and actualized though the sadhana of the 'mūla prajñā', as definitions are slippery and challenging to pinpoint that hold for all contexts.
Language usage in Buddhist logic is not intuitive but technical and must be learnt, acquired through the perfection and power of 'diligence' (Sanskrit: vīrya).
"[29] Robinson (1957: p. 300) in discussing the Buddhist logic of Nagarjuna, frames a view of 'svabhava': Svabhava is by defini[t]ion the subject of contradictory ascriptions.
[30] Y Karunadasa (1999, 2000: p. 1) holds that Early Buddhism and early Buddhist discourse "often refer to the mutual opposition between two views": As Shakyamuni relates in a 'thread' (Sanskrit: sūtra) of discourse to Kaccānagotta in the Kaccānagotta Sutta, rendered into English by Myanmar Piṭaka Association Editorial Committee (1993: p. 35): "For the most part, Kaccāna, sentient beings depend on two kinds of belief - belief that 'there is' (things exist) and belief that 'there is not' (things do not exist).