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'''''Catuskoti''''' (Sanskrit) is a form of argument in Buddhist logic first put forth by Nagarjuna and is of particular importance to the [[Madhyamaka]] school. It is usually rendered in English as 'tetralemma'
'''''Catuskoti''''' (Sanskrit) is a logical argument(s) of a 'suite of four discrete functions' or 'an indivisible quaternity' that has multiple applications and has been important in the [[Dharmic traditions]] of [[Indian logic]] and the [[Buddhist logic|Buddhadharma logico-epistemological traditions]], particularly those of the [[Madhyamaka]] school.


Robinson (1957: pp.302-303) states ([[negativism]] is employed in amplification of the Greek tradition of [[Philosophical skepticism]]):
Robinson (1957: pp.302-303) states ([[negativism]] is employed in amplification of the Greek tradition of [[Philosophical skepticism]]):

Revision as of 00:27, 22 March 2009

Catuskoti (Sanskrit) is a form of argument in Buddhist logic first put forth by Nagarjuna and is of particular importance to the Madhyamaka school. It is usually rendered in English as 'tetralemma'

Robinson (1957: pp.302-303) states (negativism is employed in amplification of the Greek tradition of Philosophical skepticism):

A typical piece of Buddhist dialectical apparatus is the ...(catuskoti). It consists of four members in a relation of exclusive disjunction ("one of, but not more than one of,'a,' 'b,' 'c,' 'd,' is true"). Buddhist dialecticians, from Gautama onward, have negated each of the alternatives, and thus have negated the entire proposition. As these alternatives were supposedly exhaustive, their exhaustive negation has been termed "pure negation" and has been taken as evidence for the claim that Madhyamika is negativism.[1]

Nomenclature, orthography and etymology

The Catuskoti in Western Discourse has often been glossed, Tetralemma, which is the nomenclature for the Greek form. Both of the variations have similarities but also differences and the traditions were mutually iterating.

Antecedents and pervasion

Antecedents of the Catuskoti have been charted to grammatical structures in the Vedas. The Nasadiya Sukta of the Rigveda (RV 10.129) contains ontological speculation in terms of various logical divisions that were later recast formally as the four circles of catuskoti: "A", "not A", "A and not A", and "not A and not not A".[2]

McEvilley (2002: p.495) maps an interesting 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.[3]

Gorgias

Gorgias (c 487-376 BCE), the author of a lost work: 'On Nature or the Non-Existent'.

Syādvāda

Jaina Dharma has a seven-fold logical architecture, the Syādvāda, which is a formulation to convey the insight of Anekantavada.

Literature review

Robinson (1957: p.294)[4] holds that Stcherbatsky (1927)[5], opened a productive period in Madhyamaka studies. Schayer (1933)[6] 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)[7] states that "Schayers criticisms of Stcherbatsky are incisive and just." Murti (1955)[8] makes no mention of the logical contribution of Schayer. According to Robinson (1957: p.294)[9], 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)[10] opines that Nakamura (1954)[11], 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.[12]

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.... Such extra-logical observations as emerge will be confined to the concluding paragraphs...[13]

Nargarjuna

The Catuskoti was employed particularly by Nagarjuna who developed it and engaged it as a 'learning, investigative, meditative'[14] 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)[15] 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][16]

Catuskoti post-Nargarjuna

The Catuskoti, 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...".[17] This noise may also have co-arisen with Nagarjuna, following the work of Jayatilleke (1967).

Catuskoti: a simple complex

The Catuskoti may be employed in different ways and often these are not clearly stated in the tradition. They 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 even four mercury switches where only certain functions or switches are employed at particular times. This difference in particular establishes a distinction with the Greek tradition of the Tetralemma. Also, predicate logic has been applied to the Dharmic Tradition, and though this in some quarters has established interesting correlates and extension of the logico-mathematical traditions of the Greeks, it has also obscured the logico-grammatical traditions of the Dharmic Traditions of Catuskoti within modern English discourse.

Four Extremes

The 'Four Extremes' (Wylie: mtha' bzhi; Sanskrit: caturanta) [18] is a particular application of the Catuskoti:

  • Being (Wylie: yod)
  • Non-being (Wylie: med)
  • Both being and non-being (Wylie: yod-med)
  • Neither being and non-being (Wylie: yod-med min)[19]

Robinson (1957: p.297) renders a verse 21.14 of the Mūlamadhyamakakārikā thus:

"He who posits an entity becomes entangled in eternalism and annihilism,
since that entity has to be either permanent or impermanent."[20]

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. If it exists, it must belong to an existent entity, which means that it must be conditioned, dependent on other entities, and possessed of causes. But a svabhava is by definition unconditioned, not dependent on other entities, and not caused. Thus the existence of a svabhava is impossible. [NB: typographical errors repaired] [21]

"Nature" (a gloss of prakrti which in this context equals svabhava) does not entail an alter-entity:

The term "nature" (prakrti equals svabhava) has no complement. (36) "If (anythings) existence is due to its nature, its non-existence will not occur, since the alter-entity (complement) of a nature never occurs." (Mūlamadhyamakakārikā, 15.8)

That is, a nature is the class of properties attributed to a class of terms Since they are necessarily present throughout the range of the subject or class of subjects, cases of their absence do not occur.[22]

Karunadasa (1999, 2000: p.1) holds that Early Buddhism and early Buddhist discourse "often refer to the mutual opposition between two views":

  • 'permanence' or 'eternalism' (Pali: sassatavada) also sometimes referred to as 'the belief in being' (Pali: bhava-ditti); and
  • 'annihilation' or 'nihilism' (Pali: ucchadevada) also sometimes referred to as 'the belief in non-being' (Pali: vibhava-ditti).[23]

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).[24]

Karunadasa (1999, 2000: p.1) states that:

...it is within the framework of the Buddhist critique of sassatavada and ucchadavada that the Buddhist doctrines seem to assume their significance. For it is through the demolition of these two world-views that Buddhism seeks to construct its own world-view. The conclusion is that it was as a critical response to the mutual opposition between these two views that Buddhism emerged as a new faith amidst many other faiths.[25]

Notes

  1. ^ 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: [1] (accessed: Saturday March 21, 2009), pp.302-303
  2. ^ S. Kak (2004). The Architecture of Knowledge. CSC, Delhi.
  3. ^ McEvilley, Thomas (2002). The Shape of Ancient Thought. Allworth Communications. ISBN 1581152035., p.495
  4. ^ 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: [2] (accessed: Saturday March 21, 2009)
  5. ^ Stcherbatsky, Th. (1927). The Conception of Buddhist Nirvana. Leningrad: Publishing Office of the Academy of Sciences of the USSR.
  6. ^ Schayer, Stanislaw (1933). "Altindische Antizipationen der Aussagenlogik." Bulletin international de l'Academie Polonaise des Sciences et philologie, 1933, pp. 99-96.
  7. ^ 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: [3] (accessed: Saturday March 21, 2009)
  8. ^ Murti, T. R. V., 1955. The Central Philosophy of Buddhism. George Allen and Unwin, London. 2nd edition: 1960.
  9. ^ 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: [4] (accessed: Saturday March 21, 2009)
  10. ^ 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: [5] (accessed: Saturday March 21, 2009)
  11. ^ 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.
  12. ^ 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: [6] (accessed: Saturday March 21, 2009), p,293
  13. ^ 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: [7] (accessed: Saturday March 21, 2009), p.296
  14. ^ Rendering of the Three prajnas.
  15. ^ Liebenthal, Walter (1948). The Book of Chao. Peking: Gatholic University Press of Peking, 1948, p.3O.
  16. ^ 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: [8] (accessed: Saturday March 21, 2009), p.294
  17. ^ 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: [9] (accessed: Saturday March 21, 2009), p.294
  18. ^ 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. ISBN 0-86171-199-9, p.129.
  19. ^ 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. ISBN 0-86171-199-9, p.129.
  20. ^ 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: [10] (accessed: Saturday March 21, 2009), p.297
  21. ^ 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: [11] (accessed: Saturday March 21, 2009), p.300
  22. ^ 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: [12] (accessed: Saturday March 21, 2009), p.300
  23. ^ Karunadasa, Y. (1999, 2000). "The Buddhist Critique of Sassatavada and Ucchedavada: The Key to a proper Understanding of the Origin and the Doctrines of early Buddhism." from: Karunadasa, Y. (1999, 2000). The Middle Way, U.K., vol. 74 & 75.
  24. ^ Myanmar Piṭaka Association Editorial Committee (1993). Nidāna Saṃyutta: Group of Related Discourses on Causal Factors from Nidānavagga Saṃyutta: Division Containing Groups of Discourses on Causal Factors. Shakti Nagar, Delhi, India: Sri Satguru Publications. ISBN 81-7030-367-2. p.35
  25. ^ Karunadasa, Y. (1999, 2000). "The Buddhist Critique of Sassatavada and Ucchedavada: The Key to a proper Understanding of the Origin and the Doctrines of early Buddhism." from: Karunadasa, Y. (1999, 2000). The Middle Way, U.K., vol. 74 & 75.

See also

References

  • Jayatilleke, K.N. (1967). 'The Logic of Four Alternatives'. Philosophy East and West. Vol.17:1–4. Hawai'i, USA: University of Hawai'i Press. Source: [] (accessed:)
  • Wayman, Alex (1977). 'Who Understands the Four Alternatives of the Buddhist Texts?'. Philosophy East and West. Vol.27: no.1, Jan., 1977. Hawai'i, USA: University of Hawai'i Press.
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