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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).
ཚད་མ། (Wyl. tshad ma) n. Pron.: tsema; Buddhist Logic
valid cognition; verifying cognition [ Logic) [ Epistemology] ▷RTH
logic and epistemology; Logic; Epistemology
རང་སྟོབས་ཀྱིས་མི་བསླུ་བའི་རིག་པ། [ Definition ] ▷KPH
Skt. प्रमाणम्, pramāṇa, Pron.: pramana.
From Sanskrit: measure, scale, standard | measure of any kind (as size, extent, circumference, length, distance, weight, multitude, quantity, duration) | 'on an average' | prosodical length (of a vowel) | measure in music | accordance of the movements in dancing with music and song | measure of physical strength | below | the first term in a rule of three sum | the measure of a square | a side of it | principal, capital (•opp. to interest) | right measure, standard, authority | 'your ladyship is the authority or must judge' | in this sense also | and | and | 'the Vedas are authorities' | 'they whose authority is a woman' | a means of acquiring Pramā or certain knowledge (6 in the Vedānta, viz. | perception by the senses | inference | analogy or comparison | or | verbal authority, revelation | or | non-perception or negative proof | inference from circumstances | the Nyāya admits only 4, excluding the last two | the Sāṃkhya only 3, viz. | and | other schools increase the number to 9 by adding | equivalence | tradition or fallible testimony | and | gesture | any proof or testimony or evidence | a correct notion, right perception | oneness, unity | N. of a large fig-tree on the bank of the Ganges
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.
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.
‘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.
Vidyabhusana (1921), Randle (1930) and Stcherbatsky (1930) employed terms such as “Indian Logic” and “Buddhist Logic” which established this terminology, though a key difference between Western Logic and Indian Logic is that certain epistemological issues are included within Indian Logic, whereas in modern Western Logic they are deliberately excluded. Indian Logic includes general questions regarding the ‘nature of the derivation of knowledge’, epistemology, from information supplied by evidence, evidence which in turn may be another item of knowledge
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'.
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.
A 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 the Prajñāpradīpa.
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.
......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 of ahimsa 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.
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 (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) and Dharmakīrti (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. lotsawa) Ngok Lekpei Sherap (1059–1109)—was "the great academy for the study of logic in Tibet."
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.
佛家因明的理性思考 蔡禮德 Hetu－Vidyā Of Rational Thinking. by Choy L.T.
逻辑学（Logic）及简单枚举归纳法 （Induction by Simple Enumeration）
科学方法 （Scientific Method） 及假设演绎法 （Hypothetico-Deductive Method）
佛家因明的理性思考再探 蔡禮德 Hetu－Vidyā Of Rational Thinking (II). by Choy L.T.
因明的辨义理 （Meaning & Argument Analysis） 方法，具有语理分析 （Linguistic - conceptual Analysis） 及谬误剖析 （Fallacy Analysis） 的元素。
佛家因明的理性思考三探 蔡禮德 Hetu－Vidyā Of Rational Thinking(III). by Choy L.T.
「因明逻辑真值的量化公式」与贝尔斯学派统计学 蔡禮德 Quantification Formula Of Hetu－Vidyā Logical Truth－Value And Bayesian School Statistics by Choy L.T.
(ca. 7th century) was an Indian 'scholar' (pandita) and Buddhist who contributed significantly to the Buddhist development and application of Indian philosophical logic. He was one of the primary theorists of Buddhist atomism, according to which the only items considered to exist are momentary atoms (in the Buddhist sense) and states of consciousness. The following exposition of Dharmakirti's theory of inference was drawn from Prasad (2002).
Apoha is negative abhavatmaka in nature. Apohas are different due to the diversity in apohyas (things to be excluded). The word apoha, which is the abridged form of anyapoha, means the 'exclusion of negation of others (ataddvyavrtti)'.
For example, the word 'cow' gives its own meaning only by the exclusion of all those things which are other than cow. Dingnaga declares that a word can express its own meaning only by repudiating opposite meanings, just as words like 'krtaka' (i.e. that which has origin) designate their meanings only through the exclusion of their opposite like 'akraka' (i.e. that which does not have origin).
Dingnaga admits that apoha can also possess some characteristics of the realists' universals such as oneness, eternity, complete subsistence in each individual, etc. He apprehends the concept of universal through the negation of its non-self.
He explains that if the non-self of a universal is absent in a locus, then its presence in that locus can be inferred. For example, a cow is qualified by the deniability of the non-cow. This concept of Dingnaga's is similar to that Hegel who also believes that the universality of a concept is posited through its negativity.
The words blue and non-blue negate each other, simply because they are opposite to each other. According to Dingnaga, a similar exclusion of others is due to the non-apprehension of the meaning of a particular word in other words.
A particular word excludes the other particular words because its own meaning is not apprehended in the other ones. For example, the word simsapa-tree excludes the word palasa-tree because its own meaning is not available in the latter one.
Argument: vada, rtsod pa
Characteristic: laksana, mtshan nid
Condition: pratyaya, rkyen
Demonstrandum: sadhya, bsgrub par bya ba
Demonstrator: sadhaka, grub byed
Dialectician: tartika, rtog ge ba
Dialectics: tarka, rtog ge
Direct perception: pratyaksa, mnon sum
Event: dharma, chos
Event-associate: dharmin, chos can
Exemplification: drstanta, dpe
Inference: anumana, rjes su dpag pa
Interference: vyavakirana, hdres pa
Invariable concomitance: avinabhava, med na mi hbyun ba
Judgment: prajnanana, shes-rab
Justification: hetu, gtan-tshigs
Means of cognition: pramana, tshad pa
Means ofevidence: linga, rtags
Pervading/pervasion/logical pervasion: vyapti, khyab pa
This article presents the "formal background" to Buddhist logic which started at about 500 CE in ancient India and still has a living tradition in the Tibetan Gelug order. Like the logic of Aristotle, ancient Indian logic is a highly formal system although it has not been developed in a context of a symbolic language.
The Indian Syllogism
A cognition (C) is Right-Knowledge (samyak-jnana (RK)) when
1) C is not contradicted by experience (avisamvadi) and
2) C’s object of cognition was unknown to the cognizer prior to having C.
From 1), it follows that C could be ascertained to be RK only a-posteriori.
From 2), it follows that only the first cognition of an object could count as RK.
Also, 2) could be ascertained only after 1) is ascertained to be true.
From 1) and 2), it follows that RK is essentially empirical.
Objects of Desire and Their Acquisition
n [[object-of-desire (purushartha (P)) is either an object-wanted (upadeya, an [[object of pro-desire), or an object-not-wanted (heya, an object of con-desire). An object-of-indifference (upekshaniya) is an object neither wanted nor not wanted. It is not a P.
RK (jnapaka, an information supplying cause of P) and/or non-empirical knowledge are necessary for P’s attainment.
(RK and/or non-empirical knowledge) and karaka, an effectuating cause of P, are sufficient for P’s attainment.
Right Knowledge is desirable for its own sake too, that is, for its intrinsic value.
To attain a certain P; its RK is desired. RK itself can be viewed as an object-of-desire (P’).
To attain P’; its (RK)’ is desired.
(RK)’ is yet another object-of-desire (P’’), attainment of which it’s (RK)’’ is desired, so on ad infinitum.
Thus P cannot be attained.
But, for practical purposes, P’ need only be common sense knowledge of P, which one is already assumed to know.
Thus the aforementioned infinite regress is avoided and P could be attained.
Perception (pratyaksha) is the only mode (pramana) of RK. Perception is not a means to RK. Rather, to perceive is to know. Perception of an object is a direct cognition of it, unmediated by, or independent of, any other cognition. Definition of a perceivable object (DI): x is perceived at a place S (Px) iff 1) x exists at S (existential condition (Ex)) 2) there must be a perceiver who is sufficiently motivated to perceive x, is properly located wrt to x to perceive it, has healthy eyes, has adequate time at his disposal, is provided with sufficient light in the place, etc.( other necessary conditions (Ox))
DI assumes that x by its very nature is not unperceivable. For example, if x is an atom, Ex and Ox maybe be true yet Px would be false since an atom cannot be perceived by the naked eye. Thus an atom is not a valid x, given the above definition of DI.
Anumana is a formally valid deductive inference with true premises. Anumana is a valid, indirect cognition of the object inferred(OI) since it is mediated by, or dependent on, another cognition, that is the cognition of another object called linga, hetu, sadhana (sign, logical reason, mark) with which the sadhya (OI) is invariably, unexceptionally, universally, related.
Therefore, anumana is not a mode of RK. An inductive inference might say something which is not already known, but not with certainty. Thus it may be contradicted by experience. Therefore, inductive inference too isn’t a mode of RK.
• All inferences are linguistic.
• An inference’s validity has nothing to do with the intention associated with the inference.
• PA does not yield RK to the demonstrator, but only to the demonstratee.
• There is no logical difference between SA and PA.
• Either the demonstrator demonstrating the truth of a proposition P has acquired knowledge of P’s truth by SA or it has been demonstrated to him/her by someone else by a PA. Thus, each PA has a SA as its basis.
Paksha Vakya (PV): It is an existential proposition that asserts that the locus of logical reason (paksha) has a logical mark/sign (hetu). Hetu has three characteristics:
1) It is necessarily present in the paksha.
2) It is present only in things similar (wrt sadhya) to the paksha (sapaksha).
3) It is not present in things dissimilar (wrt sadhya) to the paksha (vipaksha)
All of 1), 2) & 3) are not necessary for all forms of inference.
Three Types of Hetu
1) Anupalabdhi hetu (AH): Px is not true.
2) Svabhava hetu (SH): Identity as logical reason
3) Karya hetu : Effect as logical reason
The universal proposition which states the invariable concomitance, both positive and negative, between a logical mark/sign (hetu) and the object inferred or to be inferred (anumeya or sadhya).
Vyapati includes an example (udaharana or drstanta) which exemplifies the relation, both positive and negative, between hetu and sadhya, and also states that the subject of the universal proposition does not denote an empty class.
PV and V together are called as the HetuVakya (HV). HV is necessary and PV must be cognized in anumana.
Nigamana (N): It asserts that the locus of reason (paksha) has the sadhya.
Anuplabdhi Hetu inference (AHI) and its types
HV: DI, Ox are true ie. x is uplabdhi-lakshana-prapta(ULP) and AH is true.
N: Ex is false.
Example:There is no jar there (Ex is false),
the jar is, by its very nature, perceivable and
other necessary conditions for its perception are satisfied (Ox is true),
yet the jar is not perceived there (Px is false).
Non perception of the effect is the hetu for the non existence of its cause having unobstructed capability to produce it.
Non existence of a light source is inferred from no visual perception by a perceiver capable of visual perception.
Let a thing x (vyapya) be included in a thing y (vyapaka). The non existence of x is inferred from the non perception of y.
Watermelon seeds do not exist there
Watermelon was not perceived there.
4) Svabhava- virudhh-opalabhdhi
Non existence of x is inferred from the perception of y, when x and y cannot exist simultaneously.
There is no fire on the glacier
iced water are perceived to be present in the glacier
wherever there is iced water there can be no fire.
Non existence of z is inferred from the perception of x, where x is the effect of y and y is the effect of not-z. (Thus x implies y and y implies not-z.)
Non existence of depression is inferred from the perception of euphoria
The perception of euphoria is an effect of increased serotonin levels in the brain
Increased serotonin levels in the brain causes the non existence of depression
A is not-x is inferred from A’s dependence on y and y being pervaded by not-x.
A hurricane is non empty
A hurricane depends on the earth’s atmosphere
The earth’s atmosphere is pervaded by non-emptiness
Not-x is inferred from the perception of y, which is antagonistic of z, and z is an effect of x.
Non starving is inferred from the perception of satiety
perception of satiety is antagonistic of the perception of hunger
the perception of hunger is caused by starving.
Not-x is inferred from the perception of y, which is antagonistic of z, and z includes/subsumes x.
Non-attachment is inferred from the perception of indifference, which is antagonistic of desire, and desire subsumes attachment.
Non-existence of x is inferred from the non perception of its cause y. It is assumed that the y invariably results in x and y alone results in x.
Non-existence of appeal is inferred from non perception of beauty.
Assume that y causes x, then the non-existence of x is inferred from the perception of not-y. It is assumed y invariably causes x and y alone causes x.
Non existence of vibration, in a medium capable of vibration, is inferred from the perception of no sound, in a perceiver capable of aural perception.
Assume that y causes x, then the non-existence of x is inferred from the perception of z, which is the effect of not-y.
Absence of the perception of danger is inferred from the perception of security.
Absence of fear is inferred from the absence of the perception of danger.
Absence of fear is inferred from the perception of security.
Svabhava Hetu Inference (SHI)
A has/is s is inferred from A has/is h, where being h, in a way, is identical to being s. The vyapati in SHI is obvious and is often unstated.
A is a musical instrument
A is a sarod
Karya Hetu Inference (KHI)
The existence of a cause is inferred from the cognition of its effect.
PV: There is smoke (hetu) on the hill (paksha).
V: Wherever there is smoke, there is fire (sadhya) as in a kitchen (sapaksha), and wherever there is no smoke, there is no fire, as in a pond (vipaksha).
N: Therefore there is fire on the hill.
In the above example the existence of fire (cause) is inferred from the perception of smoke (effect)
AHI, SHI and KHI do not form an exhaustive set of inferences. Thus Dharmakirti’s Theory of Inference is incomplete.
"Apoha" is negative "abhavatmaka" in nature. Apohas are different due to the diversity in apohyas (things to be excluded). The word "apoha" which is the abridged form of anyapoha means the 'exclusion of negation of others (ataddvyavrtti)'.
The word 'cow' gives its own meaning only by the exclusion of all those things which are other than cow. Dingnaga declares : word can express its own meaning only by repudiating opposite meanings, just as the words like 'krtaka'(i.e. that which has origin) designate their meanings only through the exclusion of their opposite like 'akraka'(i.e. that which does not have origin).Dingnaga admits apoha can also possess some characteristics of the realists' universals such as oneness, enternity, complete subsistence in each individual etc. Dingnaga apprehends concept of universal through the negation of its non-self.
This concept of Dingnaga similar to that Hegel,he also believes that universality of a concept is posited through its negativity."Apoha" is not the object of sense perception ("pratyaksa")Itis apprehensible only through word or inference.In essence, Dingnaga uses "anyyapoha"as a substitute for universal.The concept of "apoha" depends upon the law of contradiction.
The words blue and non-blue negate each other just because they are opposite to each other. According to Dingnaga,similar exclusion of others is due to the non-apprehension of the meaning of a particular word in other words. A particular word excludes the other particular words because its own meaning is not apprehends in the other ones.For example, the word "simsapa-tree excludes the word "palasa"-tree because its own meaning is not available in the latter one.
2. 'Six Buddhist Nyaya Tracts', p.3, line7 edited by M.M. Har Prasad Shastri, Bibliotheca Indica,Calcutta,1910 ,3. 'Apohasiddhi', ( p.3) RatnakÏrti, Bib..Indica. See also Buddhist Doctrine of Universal Flux (p. 132-133) by Satkari Mukerjee.4. "...Hegel was quite right when he said that Negativity is the soul of the world. Buddhist logic: part -I (1930) page no.498 : F. Th. Stcherbatsky. [Insert footnote text here] 21. arthasya bahudharmasca sarve lingannakalpitam. yo'nubandho'nyasmat vyatireka'dhigamyate.: 'Pramanasamuccaya' : 2:1322. bhedo bhedantarartham tu virodhitvad apohate, samanyantara bhedartha svasamanya virodhinah . : 'Pramanasamuccaya' 5:28