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Buddhist Logic


Buddhist Logic, the categorical nomenclature modern Western discourse has extended to Buddhadharma traditions of 'Hetuvidya' (Sanskrit) and 'Pramanavada' (Sanskrit), which arose circa 500CE, is a particular development, application and lineage of continuity of 'Indian Logic', from which it seceded. Indian logic, and Buddhist Logic—in main heralded by Dignāga  (c 480-540 CE)—are both primarily studies of 'inference'-patterns, where ‘inference’ is a gloss of anumāna (Sanskrit).
Sadhukhan, et al. (1994: p. 7) frames the centrality of 'syllogism' to Buddhist Logic and foregrounds its indivisibility as an investigative, authenticating and proofing tool instituted to establish the valid cognitive insights of the Buddhadharma:
Buddhist logic obviously contains the forms and nature of syllogism, the essence of judgement, etc. for which it deserves the name of logic. But that logic is not only logic it also establishes the doctrines of the Buddhists. Thus the philosophical tenets were the fulcrum and the logic developed as tools to establish those. 
Following the work of Tucci (1929) and the critique of Anacker (2005, rev.ed.) upon the collation of Frauwallner (1957),  it is now understood that Vasubandhu's Vāda-vidhi ("A Method for Argumentation") refined the five argument logic of the Nyāya-sūtra to a three argument form and not his pupil Dignāga.  In addition to pruning the two redundant arguments from the syllogism, Vasubandhu tendered a further qualification: he posited that a sound relationship, a 'logical pervasion' (vyāpti) needs to be defined between the first and second arguments, a relationship between the 'Demonstrandum' (pratijna) and the 'Justification' (hetu) that is assumed in the Nyāya-sūtra and other literature of the Nyāya school. This logical pervasion is required to fashion sound arguments. Vasubandhu's Vāda-vidhi was reconstructed by Frauwallner from embedded quotations harvested from the works of Dignāga, amongst others. Dignāga as the oft-cited wellspring of the logical triune in the Buddhadharma is now invalidated. 


Qualifications of what is signified by the lexical signifier 'Logic' in the Dharmic context

Logic (Dharmic traditions)   Logic (Classical logic)
‘Indian Logic’ should not be understood as logic in the sense of ‘Aristotelian syllogism’ (Greek or Classical Logic) or ‘modern predicate calculus’ (modern Western Logic), but as anumāna-theory, a system in its own right. ‘Indian Logic’ was influenced by the study of grammar, whereas Greek or Classical Logic which principally informed modern Western Logic was influenced by the study of mathematics. 
Nomenclature, orthography and etymology


 'Buddhist logic  


'Hetuvidya' (Sanskrit)


'Pramanavada' (Sanskrit)


'Anumana' (Sanskrit)
Etymology: anu ("subsequent") + manas ("perception, mind") is identified as a ‘source of knowledge’, a pramāṇa. Though not the founders of 'Indian logic', the Nyaya school first codified and established a 'system of logic'. The Nyāya recognized four 'sources of knowledge' (pramana): perception, inference, comparison and testimony.
Antecedents and secession
'Nyāya' (Skt. "recursion", with the semantic amplification of 'syllogism, inference') is the name given to one of the six 'orthodox' (astika) schools of Sanatana Dharma, which may be understood as "the school of logic." The Nyaya is founded in the Nyaya Sutras, attributed to Gotama (2nd century CE). Buddhist logic inherited much of the architecture of Nyaya's methodology, but where the Nyaya recognised a set of four pramanas—perception, inference, comparison and testimony—the logic of Buddhadharma only recognized two: perception and inference.
Syllogism
syllogism is a form of inference. Ames (1993: p. 210), holds that Bhāvaviveka (c.500-c.578) appears to be the first Buddhist logician to employ the 'formal syllogism' (Wylie: sbyor ba'i tshig; Sanskrit: prayoga-vākya) of Indian Logic in expounding the Mādhyamaka, which he employed to considerable effect in his commentary to Nagarjuna's Mūlamadhyamakakārikā entitled thePrajñāpradīpa.  Though due to the work of Anacker (2005, rev.ed.) and those upon whom his work is founded, we know that the first Buddhist to refine the syllogism to its three-line form is Vasubhandu. 
Dharmic logic in Western discourse & literature review
Vidyabhusana (1921), Randle (1930) and Stcherbatsky (1930)
Lineage
Dr S.C. Vidyabhusana, Mahapandit Rahul Sankrityayan, Dr M. K. Ganguli, A. Vostrikov, Prof. Giuseppe Tucci, B. Baradiin, V. Vassiliev (1818—1900), E. E. Obermiller (1901–1935), Prof. Gerhard Oberhammer, Prof. E. Franwallner, F. Th. Stcherbatsky, E. Steikellner.
Robinson (1957: p. 295) holds that, building upon the methodology of Schayer [1933], Nakamura (1954) 
...presents the case for the superiority of modern scientific, notational logic as an instrument for investigating Indian logic. Notational statement avoids the pitfalls and awkwardness of linguistic statement and rhetorical logic. It does not necessitate conversion of Indian forms into the standard forms of traditional Western logic, but clarifies the traditional Indian structure without requiring reformulation. To Nakamura's points I may add that modern logic asks a greater range of questions and hence sharpens the observation of the investigator.
Pramana sets as determining traditions of Dharma
Decisive in distinguishing Buddhadharma from what is generally understood as Sanatana Dharma is the issue of epistemological justification. All schools of Indian logic recognize various sets of 'valid justifications for knowledge' or pramana. The Buddhadharma recognizes a pramana set that is smaller than the other Dharmic Traditions. Most pramanavada of Dharmic Traditions accept 'perception' (Sanskrit: pratyakṣa) and 'inference' (Sanskrit: anumāna), for example, but for some schools of Sanatana Dharma and Buddhadharma the 'received textual tradition' (Sanskrit: āgamāḥ) is an epistemological category equal to perception and inference (although this is not necessarily true for some other schools). The Buddhadharma accepts 'received textual tradition' or āgamāḥ, including Buddhavacana, only if it accords with pratyakṣa and anumāna. Historically, Shakyamuni Buddha was qualifying the unquestionable authority of the Vedas on grounds ofahimsa as according to the Vedic Tradition of Sanatana Dharma, the Vedas are apauruṣeya "not of human agency,"  are supposed to have been directly revealed, and thus are called śruti("what is heard").  Vedic injunctions required sacrifices, Śrauta (an etymon of the English 'slaughter'), particularly 'animal sacrifices' (Pashu-Yajna, Ashvamedha) and which the compassionate Shakyamuni Buddha countered.

Thus, in the Sanatana Dharma traditions, if a claim was made that could not be substantiated by appeal to the textual canon, it would be considered as ridiculous as a claim that the sky was green and, conversely, a claim which could not be substantiated via conventional means might still be justified through textual reference, differentiating this from the epistemology of hard science. Some schools of Buddhadharma, on the other hand, rejected an inflexible reverence of accepted doctrine. As the Buddhavacana Kalama Sutta III.65 states:
Do not accept anything by mere tradition ... Do not accept anything just because it accords with your scriptures ... Do not accept anything merely because it agrees with your pre-conceived notions ... But when you know for yourselves – these things are moral, these things are blameless, these things are praised by the wise, these things, when performed and undertaken, conduce to well-being and happiness – then do you live acting accordingly. 
This verse is however taken out of context. In the Kalama Sutta the Buddha was talking to non-Buddhists and those were not already Buddhist disciples. Dhammapala's commentary on theNettipakarana says "for there is no other criterion beyond a text." 
Hetuvidya
Hetu = conditionality, causation (hetu and pratyaya), contending with Buddhist agency...karma
Vidya = (Sanskrit: Vidya; Tibetan: Rigpa), Avidya
Pramanavada
Pramana vada
Early Buddhism and the rise of Nagarjuna
Early Buddhist philosophers and exegetes of one particular early school (as opposed to Mahayana), the Sarvastivadins, created a pluralist metaphysical and phenomenological system, in which all experiences of people, things and events can be broken down into smaller and smaller perceptual or perceptual-ontological units called dharmas. Other schools incorporated some parts of this theory and criticized others. The Sautrantikas, another early school, and the Theravadins, the only surviving early Buddhist school, criticized the realist standpoint of the Sarvastivadins.
The Mahayanist Nagarjuna, one of the most influential Buddhist thinkers, promoted classical Buddhist emphasis on phenomena and attacked Sarvastivada realism and Sautrantika nominalism in his magnum opus The Fundamental Verses on the Middle Way. 
Robinson (1957: p. 293) makes an opinion that builds upon the foundation of Stcherbatsky (1927):
The Madhyamaka denies the validity of logic, i.e., of discursive conceptual thought, to establish ultimate truth. On the charge that in doing so he himself resorts to some logic, he replies that the logic of common life is sufficient for showing that all systems contradict one another and that our fundamental conceptions do not resist scrutiny. 
Catuskoti
Catuskoti (Sanskrit), had antecedents in the Vedas and is also evident in a mutually iterating form known by the Greek term 'Tetralemma', where 'tetra' holds the semantic field of "four" and 'lemma' holds the semantic field "auxiliary proposition".
Indian Transmission lineages to Tibet and concomitant translations
Tom Tillemans (1998: p. 1), in discussing the Tibetan translation and assimilation of the Buddhadharma logico-epistemological traditions embodied by the legacy of Dignāga (c 480-540 CE) andDharmakīrti (ca. 7th century), identifies two currents and transmission streams:
  • first current, principally geographical located at Sangpu Neutok and grounded in the works of Ngok Lodzawa Loden Shayrap (1059–1109) and Chapa Chögyi Sengge (1109–69) and their disciples. Chapa’s Tshad ma’i bsdus pa (English: 'Summaries of Epistemology and Logic') became the groundwork for the ‘Collected Topics’ (Tibetan: Düra; Wylie: bsdus grwa) literature, which in large part furnished Gelugpa-based logical architecture and epistemology. 
  • second current of Sakya Pandita (1182–1251) who wrote the Tshad-ma rigs-gter (English: "Treasury of Logic on Valid Cognition"),  who vehemently redressed the logical architecture of the Gangpu Neutok positions. 
Sangpu Neutok (Wylie: gSang-phu Ne'u-thog)
Dudjom (1904–87) and others (1991: p. 577) hold that at the time of Longchenpa (1308–1364/1369) who studied there, Sangpu Neutok (Wylie: gSang-phu Ne'u-thog)—a seminary founded in 1073  by the translator (Tib. lotsawaNgok Lekpei Sherap (1059–1109)—was "the great academy for the study of logic in Tibet." 
Gelugpa
The Vajrayana tradition of the Tibetan Buddhist Gelugpa—with their penchant for dialectic and courtyard debate—instituted, developed and perpetuated the systems of Indian Logic and Buddhist Logic that they had inherited, significantly contributing to and extending the traditions of Hetuvidya and Pramanavada within the logico-epistemological traditions of the Buddhadharma. Particularly, post-Candrakirti (600–c. 650), the Gelugpa refined the Catuskoti and Shunyata into the Prasangika.
Vasubandhu: Avinābhāva
Vasubandhu (fl. 4th c.)
Doctrine of Trairūpya
Dignaga's (c 480-540 CE) 'Three Modes' (Sanskrit: Trairūpya; Wylie: tshul-gsum)