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81-610: The Udānavarga has around 1100 verses in 33 chapters. The chapter titles are: Comparatively, the most common version of the Dhammapada, in Pali , has 423 verses in 26 chapters. Comparing the Udānavarga , Pali Dhammapada and the Gandhari Dharmapada, Brough (2001) identifies that the texts have in common 330 to 340 verses, 16 chapter headings and an underlying structure. The Udānavarga

162-546: A Sanskrit Mahāvibhaṣa , compiled by the Kashmir Sarvāstivāda synod. The Jñānaprasthāna and its Mahāvibhaṣa, were then declared to be the new orthodoxy by Kashmiris, who called themselves Vaibhāṣikas. This new Vaibhāṣika orthodoxy, however, was not readily accepted by all Sarvāstivādins. Some "Western masters" from Gandhara and Bactria had divergent views which disagreed with the new Kashmiri orthodoxy. These disagreements can be seen in post- Mahāvibhaṣa works, such as

243-529: A calculus, a method of representing categorical statements (and statements that are not provided for in syllogism as well) by the use of quantifiers and variables. A noteworthy exception is the logic developed in Bernard Bolzano 's work Wissenschaftslehre ( Theory of Science , 1837), the principles of which were applied as a direct critique of Kant, in the posthumously published work New Anti-Kant (1850). The work of Bolzano had been largely overlooked until

324-619: A commonly used synonym for Mahāyāna. The Mahāvibhāṣā reads: What is the Vaipulya? It is said to be all the sūtras corresponding to elaborations on the meanings of the exceedingly profound dharmas. According to a number of scholars, Mahāyāna Buddhism flourished during the time of the Kuṣāṇa Empire, and this is illustrated in the form of Mahāyāna influence on the Mahāvibhāṣā Śāstra . The Mañjuśrīmūlakalpa also records that Kaniṣka presided over

405-555: A great deal of material with what appear to be strong affinities to Mahāyāna doctrines. The Mahāvibhāṣā is also said to illustrate the accommodations reached between the Hīnayāna and Mahāyāna traditions, as well as the means by which Mahāyāna doctrines would become accepted. The Mahāvibhāṣā also defines the Mahāyāna sūtras and the role in their Buddhist canon. Here they are described as Vaipulya doctrines, with "Vaipulya" being

486-649: A later date, the Śāriputraparipṛcchā , contains a very similar passage with nearly the same information. In the earlier source, the Sarvāstivāda are described as wearing dark red robes, while the Dharmaguptas are described as wearing black robes. However, in the corresponding passage found in the later Śāriputraparipṛcchā , the Sarvāstivāda are described as wearing black robes and the Dharmaguptas as wearing dark red robes. In traditions of Tibetan Buddhism , which follow

567-756: A method of valid logical reasoning, will always be useful in most circumstances, and for general-audience introductions to logic and clear-thinking. In antiquity, two rival syllogistic theories existed: Aristotelian syllogism and Stoic syllogism. Aristotle defines the syllogism as "a discourse in which certain (specific) things having been supposed, something different from the things supposed results of necessity because these things are so." Despite this very general definition, in Prior Analytics Aristotle limits himself to categorical syllogisms that consist of three categorical propositions , including categorical modal syllogisms. The use of syllogisms as

648-742: A more inductive approach to the observation of nature, which involves experimentation, and leads to discovering and building on axioms to create a more general conclusion. Yet, a full method of drawing conclusions in nature is not the scope of logic or syllogism, and the inductive method was covered in Aristotle's subsequent treatise, the Posterior Analytics . In the 19th century, modifications to syllogism were incorporated to deal with disjunctive ("A or B") and conditional ("if A then B") statements. Immanuel Kant famously claimed, in Logic (1800), that logic

729-436: A premise containing the modal words necessarily , possibly , or contingently . Aristotle's terminology in this aspect of his theory was deemed vague, and in many cases unclear, even contradicting some of his statements from On Interpretation . His original assertions on this specific component of the theory were left up to a considerable amount of conversation, resulting in a wide array of solutions put forth by commentators of

810-439: A rectangle is a square that is a quadrangle." A categorical syllogism consists of three parts: Each part is a categorical proposition , and each categorical proposition contains two categorical terms. In Aristotle, each of the premises is in the form "All S are P," "Some S are P", "No S are P" or "Some S are not P", where "S" is the subject-term and "P" is the predicate-term: More modern logicians allow some variation. Each of

891-409: A tool for understanding can be dated back to the logical reasoning discussions of Aristotle . Before the mid-12th century, medieval logicians were only familiar with a portion of Aristotle's works, including such titles as Categories and On Interpretation , works that contributed heavily to the prevailing Old Logic, or logica vetus . The onset of a New Logic, or logica nova , arose alongside

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972-628: Is a great deal of mystery surrounding the rise and early development of the Sarvāstivādin school." According to Dhammajoti, "its presence, as well as that of its rival — the Vibhajyavāda lineage — in the time of Emperor Aśoka is beyond doubt. Since Aśoka's reign is around 268–232 B.C.E., this means that at least by the middle of the 3rd century B.C.E., it had already developed into a distinct school." In Central Asia, several Buddhist monastic groups were historically prevalent. According to some accounts,

1053-498: Is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (defined by Aristotle in his 350 BC book Prior Analytics ), a deductive syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across. For example, knowing that all men are mortal (major premise), and that Socrates

1134-498: Is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: All men are mortal. Socrates is a man. Therefore, Socrates is mortal. In antiquity, two rival syllogistic theories existed: Aristotelian syllogism and Stoic syllogism . From the Middle Ages onwards, categorical syllogism and syllogism were usually used interchangeably. This article

1215-438: Is about drawing valid conclusions from assumptions ( axioms ), rather than about verifying the assumptions. However, people over time focused on the logic aspect, forgetting the importance of verifying the assumptions. In the 17th century, Francis Bacon emphasized that experimental verification of axioms must be carried out rigorously, and cannot take syllogism itself as the best way to draw conclusions in nature. Bacon proposed

1296-727: Is attributed by Brough to the Sarvāstivādins . Hinüber suggests that a text similar to the Pali Canon's Udāna formed the original core of the Sanskrit Udānavarga , to which verses from the Dhammapada were added. Brough allows for the hypothesis that the Udānavarga , the Pali Dhammapada and the Gandhari Dharmapada all have a "common ancestor" but underlines that there is no evidence that any one of these three texts might have been

1377-480: Is concerned only with this historical use. The syllogism was at the core of historical deductive reasoning, whereby facts are determined by combining existing statements, in contrast to inductive reasoning , in which facts are predicted by repeated observations. Within some academic contexts, syllogism has been superseded by first-order predicate logic following the work of Gottlob Frege , in particular his Begriffsschrift ( Concept Script ; 1879). Syllogism, being

1458-521: Is emphasized by the historian of logic John Corcoran in an accessible introduction to Laws of Thought . Corcoran also wrote a point-by-point comparison of Prior Analytics and Laws of Thought . According to Corcoran, Boole fully accepted and endorsed Aristotle's logic. Boole's goals were "to go under, over, and beyond" Aristotle's logic by: More specifically, Boole agreed with what Aristotle said; Boole's 'disagreements', if they might be called that, concern what Aristotle did not say. First, in

1539-737: Is explicated in modern fora of academia primarily in introductory material and historical study. One notable exception to this modern relegation is the continued application of Aristotelian logic by officials of the Congregation for the Doctrine of the Faith , and the Apostolic Tribunal of the Roman Rota , which still requires that any arguments crafted by Advocates be presented in syllogistic format. George Boole 's unwavering acceptance of Aristotle's logic

1620-666: Is famous for being the author of the Abhidharmakośa (4–5th century CE), a very influential Abhidharma work, with an auto-commentary that defends the Sautrāntika views. He famously later converted to the Yogācāra school of Mahāyāna Buddhism , a tradition that itself developed out of the Sarvāstivāda Abhidharma. Vasubandhu's Kośa led to a vigorous reaction from his contemporary, the brilliant Vaibhāṣika master Saṃghabhadra, who

1701-645: Is important to realize that not all of them necessarily subscribed to each and every view sanctioned by the MVŚ compilers. Moreover, the evolving nature of the Vaibhāṣika views must be recognized as well." The Vaibhāśika-Sarvāstivādins are sometimes referred to in the MVŚ as "the Ābhidharmikas", "the Sarvāstivāda theoreticians" and "the masters of Kāśmīra." In various texts, they also referred to their tradition as Yuktavāda (the doctrine of logic), as well as Hetuvāda (the doctrine of causes). The Vaibhāṣika school saw itself as

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1782-427: Is known as the middle term ; in this example, humans . Both of the premises are universal, as is the conclusion. Here, the major term is die , the minor term is men , and the middle term is mortals . Again, both premises are universal, hence so is the conclusion. A polysyllogism, or a sorites , is a form of argument in which a series of incomplete syllogisms is so arranged that the predicate of each premise forms

1863-610: Is much uncertainty as to the relationship of the Mūlasarvāstivāda (meaning root or original Sarvāstivāda) school and the others. They were certainly influential in spreading their Mūlasarvāstivāda Vinaya, as it remains the monastic rule used in Indo-Tibetan Buddhism today. Also, they seem to have been influential in Indonesia by the 7th century, as noted by Yijing . A number of theories have been posited by academics as to how

1944-512: Is said to have spent 12 years composing the Nyāyānusāra , a commentary to Vasubandhu's verses to refute his views and those of other Sautrāntika monks, such as Sthavira Śrīlāta and his pupil Rāma. The Kośa was so influential that it became the Abhidharma text par excellence in both Indo - Tibetan Buddhism and East Asian Buddhism , and remains the primary source for Abhidharma studies. There

2025-414: Is the principle of 'all exists' that is the axial doctrine holding the larger movement together when the precise details of other doctrines are at stake. In order to explain how it is possible for a dharma to remain the same and yet also undergo change as it moves through the three times, the Vaibhāṣika held that dharmas have a constant essence ( svabhāva ) which persists through the three times. The term

2106-430: Is the subject of the conclusion, P is the predicate of the conclusion, and M is the middle term. The major premise links M with P and the minor premise links M with S. However, the middle term can be either the subject or the predicate of each premise where it appears. The differing positions of the major, minor, and middle terms gives rise to another classification of syllogisms known as the figure . Given that in each case

2187-404: Is traditional to use is rather than are as the copula , hence All A is B rather than All As are Bs . It is traditional and convenient practice to use a, e, i, o as infix operators so the categorical statements can be written succinctly. The following table shows the longer form, the succinct shorthand, and equivalent expressions in predicate logic: The convention here is that the letter S

2268-760: The Dharmaguptaka Vinaya. In the 7th century, Yijing wrote that in eastern China, most people followed the Dharmaguptaka Vinaya, while the Mahāsāṃghika Vinaya was used in earlier times in Guanzhong (the region around Chang'an ), and that the Sarvāstivāda Vinaya was prominent in the Yangzi River area and further south. In the 7th century, the existence of multiple Vinaya lineages throughout China

2349-618: The Dīrgha Āgama in Sanskrit. The Madhyama Āgama (T26, Chinese trans. Gotama Saṅghadeva) and Saṃyukta Āgama (T99, Chinese trans. Guṇabhadra) have long been available in Chinese translation. The Sarvāstivāda is therefore the only early school besides the Theravada for which we have a roughly complete sutra collection, although unlike the Theravada it has not all been preserved in the original language. During

2430-621: The Little Vehicle of the school of the Sarvāstivādas (Shwo-yih-tsai-yu-po). Their doctrine (teaching of Sūtras) and their rules of discipline (principles of the Vinaya) are like those of India, and those who read them use the same (originals). Sarvāstivāda was a widespread group, and there were different sub-schools or sects throughout its history, the most influential ones being the Vaibhāṣika and

2511-857: The Mahāsāṃghikas used Prākrit, the Sarvāstivādins used Sanskrit, the Sthavira nikāya used Paiśācī , and the Saṃmitīya used Apabhraṃśa . The Sarvāstivādins of Kāśmīra held the Mahāvibhāṣā Śāstra as authoritative, and thus were given the moniker of being Vaibhāṣikas. The Mahāvibhāṣā is thought to have been authored around 150 CE, around the time of Kaniṣka (127–151) of the Kushan Empire . This massive treatise of Abhidharma (200 fascicles in Chinese) contains

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2592-725: The Mūlasarvāstivāda Vinaya, red robes are regarded as characteristic of their tradition. During the first century BCE, in the Gandharan cultural area (consisting of Oddiyana , Gandhara and Bactria , Tokharistan , across the Khyber Pass ), the Sthaviriyas used the Gāndhārī language to write their literature using the Kharosthi . The Tibetan historian Buton Rinchen Drub wrote that

2673-458: The Mūlasarvāstivāda sect, although the relationship between these two groups has not yet been fully determined. According to Prebish, "this episode corresponds well with one Sarvāstivādin tradition stating that Madhyantika converted the city of Kasmir, which seems to have close ties with Gandhara." A third tradition says that a community of Sarvāstivādin monks was established at Mathura by

2754-553: The Samayabhedoparacanacakra state that the Mahīśāsaka emerged from the Sarvāstivāda. The Sarvāstivādins are believed to have given rise to the Mūlasarvāstivāda and Sautrāntika schools, although the relationship between these groups has not yet been fully determined. Sarvāstivāda is a Sanskrit term that can be glossed as: "the theory of all that exists". The Sarvāstivāda argued that all dharmas (phenomena) exist in

2835-849: The Sautrāntika schools. According to Cox, Willemen and Dessein: we have, basically, to differentiate the original Sarvāstivādins originating from Mathura , the Kaśmīri Vaibhāṣikas, the Western Masters of Gandhara and Bactria (the Dārṣṭāntika-Sautrāntika Masters) who were also referred to as Bahirdesaka, Aparāntaka and Pāścāttya, and the Mūlasarvāstivādins. As the various groups influenced one another, even these sub-schools do very often not form homogeneous groups. [REDACTED] Religion portal The Vaibhāṣika

2916-572: The Tarim Basin in 630 CE, he received the favours of Suvarṇadeva, the son and successor of Suvarṇapuṣpa , the non- Mahayana Buddhist king of Kucha. Xuanzang described in many details the characteristics of Kucha, and probably visited the Kizil Caves . Of the religion of the people of Kucha, he says that they were Sarvastivadins: There are about one hundred convents (saṅghārāmas) in this country, with five thousand and more disciples. These belong to

2997-665: The Tibetan tenets system as the two tenets of the Hinayana , ignoring other early Indian Buddhist schools, which were not known to the Tibetans. Sarvāstivādin meditation teachers also worked on the dhyāna sutras ( Chinese : 禪經 ), a group of early Buddhist meditation texts which were translated into Chinese and became influential in the development of Chinese Buddhist meditation methods. Syllogism A syllogism ( Ancient Greek : συλλογισμός , syllogismos , 'conclusion, inference')

3078-500: The "primitive Dharmapada" from which the other two evolved. The Tibetan Buddhist and Chinese Buddhist canons' recensions are traditionally said to have been compiled by Dharmatrāta . Sarvastivada The Sarvāstivāda ( Sanskrit : 𑀲𑀭𑁆𑀯𑀸𑀲𑁆𑀢𑀺𑀯𑀸𑀤 ; Pali : 𑀲𑀩𑁆𑀩𑀢𑁆𑀣𑀺𑀯𑀸𑀤 , romanized:  Sabbatthivāda Chinese : 說一切有部 ; pinyin : Shuōyīqièyǒu Bù ; Japanese : せついっさいうぶ ; Korean : 설일체유부 ; Thai : สรวาสติวาท )

3159-486: The * Tattvasiddhi-Śāstra (成實論), the * Abhidharmahṛday a (T no. 1550) and its commentaries (T no. 1551, no. 1552), the Abhidharmakośakārikā of Vasubandhu and its commentaries (who critiqued some orthodox views), and the * Nyāyānusāra (Ny) of master Saṃghabhadra (ca fifth century CE) who formulated the most robust Vaibhāṣika response to the new criticisms. When the Chinese pilgrim Xuanzang visited Kucha in

3240-527: The Chinese term, Shuōyīqièyǒu bù ( Chinese : 說一切有部 ), which is literally "the sect that speaks of the existence of everything," as used by Xuanzang and other translators. The Sarvāstivāda was also known by other names, particularly hetuvada and yuktivada . Hetuvada comes from hetu – 'cause', which indicates their emphasis on causation and conditionality. Yuktivada comes from yukti – 'reason' or even 'logic', which echoes their use of rational argument and syllogism . According to Charles Prebish, "there

3321-574: The Sarvāstivāda school held a synod in Kashmir during the reign of Kanishka II (c. 158–176), the most important Sarvāstivāda Abhidharma text, the Astagrantha of Katyayaniputra was rewritten and revised in Sanskrit. This revised text was now known as Jñānaprasthāna ("Course of Knowledge"). Though the Gandharan Astagrantha had many vibhaṣas (commentaries), the new Kashmiri Jñānaprasthāna had

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3402-479: The Sarvāstivāda’: Dharmatrāta, Buddhadeva, Vasumitra and Ghoṣaka. The doctrines of Sarvāstivāda were not confined to 'all exists', but also include the theory of momentariness ( ksanika ), conjoining ( samprayukta ) and causal simultaneity ( sahabhu ), conditionality ( hetu and pratyaya ), a unique presentation of the spiritual path ( marga ), and others. These doctrines are all inter-connected and it

3483-521: The Sarvāstivādins emerged from the Sthavira nikāya , a small group of conservatives, who split from the reformist majority Mahāsāṃghikas at the Second Buddhist council. According to this account, they were expelled from Magadha, and moved to northwestern India where they developed into the Sarvāstivādin school. A number of scholars have identified three distinct major phases of missionary activity seen in

3564-561: The Venn diagrams, the black areas indicate no elements, and the red areas indicate at least one element. In the predicate logic expressions, a horizontal bar over an expression means to negate ("logical not") the result of that expression. It is also possible to use graphs (consisting of vertices and edges) to evaluate syllogisms. Similar: Cesare (EAE-2) Camestres is essentially like Celarent with S and P exchanged. Similar: Calemes (AEE-4) Similar: Datisi (AII-3) Disamis

3645-520: The categorical syllogism were central to expanding the syllogistic discussion. Rather than in any additions that he personally made to the field, Boethius' logical legacy lies in his effective transmission of prior theories to later logicians, as well as his clear and primarily accurate presentations of Aristotle's contributions. Another of medieval logic's first contributors from the Latin West, Peter Abelard (1079–1142), gave his own thorough evaluation of

3726-403: The concept over time. This theory of the syllogism would not enter the context of the more comprehensive logic of consequence until logic began to be reworked in general in the mid-14th century by the likes of John Buridan . Aristotle's Prior Analytics did not, however, incorporate such a comprehensive theory on the modal syllogism—a syllogism that has at least one modalized premise, that is,

3807-426: The conclusion can be of type A, E, I or O, and the syllogism can be any of the four figures. A syllogism can be described briefly by giving the letters for the premises and conclusion followed by the number for the figure. For example, the syllogism BARBARA below is AAA-1, or "A-A-A in the first figure". The vast majority of the 256 possible forms of syllogism are invalid (the conclusion does not follow logically from

3888-431: The conclusion is S-P, the four figures are: (Note, however, that, following Aristotle's treatment of the figures, some logicians—e.g., Peter Abelard and Jean Buridan —reject the fourth figure as a figure distinct from the first.) Putting it all together, there are 256 possible types of syllogisms (or 512 if the order of the major and minor premises is changed, though this makes no difference logically). Each premise and

3969-406: The day. The system for modal syllogisms laid forth by Aristotle would ultimately be deemed unfit for practical use, and would be replaced by new distinctions and new theories altogether. Boethius (c. 475–526) contributed an effort to make the ancient Aristotelian logic more accessible. While his Latin translation of Prior Analytics went primarily unused before the 12th century, his textbooks on

4050-570: The establishment of Prajñāpāramitā doctrines in the northwest of India. Étienne Lamotte has also pointed out that a Sarvāstivāda master is known to have stated that the Mahāyāna Prajñā sūtras were to be found amongst their Vaipulya sūtras. According to Paul Williams, the similarly massive Da zhidu lun also has a clear association with the Vaibhāṣika Sarvāstivādins. The Vaibhāṣika and Sautrāntika subschools are both classified in

4131-594: The first century, the Sarvāstivāda abhidharma primarily consisted of the Abhidharmahrdaya authored by Dharmashresthin, a native from Tokharistan , and the Ashtagrantha authored/compiled by Katyayaniputra. Both texts were translated by Samghadeva in 391 AD and in 183 AD. respectively, but they were not completed until 390 in Southern China. The Sarvāstivāda Abhidharma consists of seven texts: Following these, are

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4212-405: The foremost logician of the later Middle Ages, contributed two significant works: Treatise on Consequence and Summulae de Dialectica , in which he discussed the concept of the syllogism, its components and distinctions, and ways to use the tool to expand its logical capability. For 200 years after Buridan's discussions, little was said about syllogistic logic. Historians of logic have assessed that

4293-422: The form (note: M – Middle, S – subject, P – predicate.): The premises and conclusion of a syllogism can be any of four types, which are labeled by letters as follows. The meaning of the letters is given by the table: In Prior Analytics , Aristotle uses mostly the letters A, B, and C (Greek letters alpha , beta , and gamma ) as term place holders, rather than giving concrete examples. It

4374-512: The history of Buddhism in Central Asia , which are associated with respectively the Dharmaguptaka , Sarvāstivāda, and the Mūlasarvāstivāda, and the origins of the Sarvāstivāda have also been related to Ashoka sending Majjhantika (Sanskrit: Madhyāntika ) on a mission to Gandhara , which had an early presence of the Sarvāstivāda. The Sarvāstivādins in turn are believed to have given rise to

4455-605: The late 20th century, among other reasons, because of the intellectual environment at the time in Bohemia , which was then part of the Austrian Empire . In the last 20 years, Bolzano's work has resurfaced and become subject of both translation and contemporary study. This led to the rapid development of sentential logic and first-order predicate logic , subsuming syllogistic reasoning, which was, therefore, after 2000 years, suddenly considered obsolete by many. The Aristotelian system

4536-458: The orthodox Sarvāstivāda tradition, and they were united in their doctrinal defense of the theory of "all exists" ( sarvām asti ). This is the doctrine which held that dharmas , past present and future, all exist. This doctrine has been described as an eternalist theory of time . While the Vaibhāṣikas held that dharmas of the three times all exist, they held that only present dharmas have "efficacy" ( karitra ), thus they were able to explain how

4617-448: The orthodox Vaibhāṣika views or provided a defense of the orthodoxy. Dhammajoti provides the following list of such later abhidharma works that are extant in Chinese: 108 109 Between 148 and 170 CE, the Parthian monk An Shigao came to China and translated a work which described the color of monastic robes (Skt. kāṣāya ) utilized in five major Indian Buddhist sects, called Da Biqiu Sanqian Weiyi (大比丘三千威儀). Another text translated at

4698-489: The past, present and future, the "three times". Vasubandhu 's Abhidharmakośa-bhāsya states, "He who affirms the existence of the dharmas of the three time periods [past, present and future] is held to be a Sarvāstivādin." Although there is some dispute over how the word "Sarvāstivāda" is to be analyzed, the general consensus is that it is to be parsed into three parts: sarva "all" or "every" + asti "exist" + vada "speak", "say" or "theory". This equates perfectly with

4779-535: The patriarch Upagupta . In the Sarvāstivādin tradition Upagupta is said to have been the fifth patriarch after Mahākaśyapa, Ānanda, Madhyāntika, and Śāṇakavāsin, and in the Ch'an tradition he is regarded as the fourth. The Sarvāstivāda enjoyed the patronage of Kanishka (c. 127–150 CE) emperor of the Kushan Empire , during which time they were greatly strengthened, and became one of the dominant sects of Buddhism in north India for centuries, flourishing throughout Northwest India, North India, and Central Asia . When

4860-479: The premises has one term in common with the conclusion: in a major premise, this is the major term (i.e., the predicate of the conclusion); in a minor premise, this is the minor term (i.e., the subject of the conclusion). For example: Each of the three distinct terms represents a category. From the example above, humans , mortal , and Greeks : mortal is the major term, and Greeks the minor term. The premises also have one term in common with each other, which

4941-403: The premises). The table below shows the valid forms. Even some of these are sometimes considered to commit the existential fallacy , meaning they are invalid if they mention an empty category. These controversial patterns are marked in italics . All but four of the patterns in italics (felapton, darapti, fesapo and bamalip) are weakened moods, i.e. it is possible to draw a stronger conclusion from

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5022-407: The premises. The letters A, E, I, and O have been used since the medieval Schools to form mnemonic names for the forms as follows: 'Barbara' stands for AAA, 'Celarent' for EAE, etc. Next to each premise and conclusion is a shorthand description of the sentence. So in AAI-3, the premise "All squares are rectangles" becomes "MaP"; the symbols mean that the first term ("square") is the middle term,

5103-406: The present seems to function differently than the past or future. Among the different Sarvāstivāda thinkers, there were different ideas on how this theory was to be understood. These differences were accepted as long as they did not contradict the doctrine of "all exists" and can be seen in the MVŚ, which outlines the four different interpretations of this doctrine by the ‘four great Ābhidharmikas of

5184-425: The primary changes in the post-Middle Age era were changes in respect to the public's awareness of original sources, a lessening of appreciation for the logic's sophistication and complexity, and an increase in logical ignorance—so that logicians of the early 20th century came to view the whole system as ridiculous. The Aristotelian syllogism dominated Western philosophical thought for many centuries. Syllogism itself

5265-401: The realm of applications, Boole's system could handle multi-term propositions and arguments, whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, Aristotle's system could not deduce: "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is

5346-420: The realm of foundations, Boole reduced Aristotle's four propositional forms to one form, the form of equations, which by itself was a revolutionary idea. Second, in the realm of logic's problems, Boole's addition of equation solving to logic—another revolutionary idea—involved Boole's doctrine that Aristotle's rules of inference (the "perfect syllogisms") must be supplemented by rules for equation solving. Third, in

5427-447: The reappearance of Prior Analytics , the work in which Aristotle developed his theory of the syllogism. Prior Analytics , upon rediscovery, was instantly regarded by logicians as "a closed and complete body of doctrine", leaving very little for thinkers of the day to debate, and reorganize. Aristotle's theory on the syllogism for assertoric sentences was considered especially remarkable, with only small systematic changes occurring to

5508-402: The school composed the large and encyclopedic Abhidharma Mahāvibhāṣa Śāstra around the time of the reign of Kanishka (c. 127–150 CE). Because of this, orthodox Sarvāstivādins who upheld the doctrines in the Mahāvibhāṣa were called Vaibhāṣikas . According to the Theravādin Dīpavaṃsa , the Sarvāstivādins emerged from the older Mahīśāsaka school, but the Śāriputraparipṛcchā and

5589-418: The second term ("rectangle") is the predicate of the conclusion, and the relationship between the two terms is labeled "a" (All M are P). The following table shows all syllogisms that are essentially different. The similar syllogisms share the same premises, just written in a different way. For example "Some pets are kittens" (SiM in Darii ) could also be written as "Some kittens are pets" (MiS in Datisi). In

5670-471: The subject of the next until the subject of the first is joined with the predicate of the last in the conclusion. For example, one might argue that all lions are big cats, all big cats are predators, and all predators are carnivores. To conclude that therefore all lions are carnivores is to construct a sorites argument. There are infinitely many possible syllogisms, but only 256 logically distinct types and only 24 valid types (enumerated below). A syllogism takes

5751-521: The syllogism concept, and accompanying theory in the Dialectica —a discussion of logic based on Boethius' commentaries and monographs. His perspective on syllogisms can be found in other works as well, such as Logica Ingredientibus . With the help of Abelard's distinction between de dicto modal sentences and de re modal sentences, medieval logicians began to shape a more coherent concept of Aristotle's modal syllogism model. The French philosopher Jean Buridan (c. 1300 – 1361), whom some consider

5832-671: The sūtras"), also known as Dārṣṭāntika (who may or may not have been a separate but related group), did not uphold the Mahāvibhāṣa Śāstra but rather emphasized the Buddhist sūtras as being authoritative. Already by the time of the MVŚ, the early Dārṣṭāntika monks such as Dharmatrāta and Buddhadeva, existed as a school of thought within the fold of the Sarvāstivāda who disagreed with the orthodox views. These groups were also called "the western masters" ( pāścātya ) or "the foreign masters" ( bahirdeśaka ; also called ‘the masters outside Kaśmīra’, and

5913-648: The sūtras"). However, the Sautrāntikas did not reject the Abhidharma method; in fact, they were the authors of several Abhidharma manuals, such as the Abhidharmahṛdaya . The later Buddhist tradition of pramāṇa , founded by the Buddhist monks Dignāga and Dharmakīrti , is also associated with the Sautrāntika school. The most important Sautrāntika was Vasubandhu (ca. 350–430), a native from Purusapura in Gandhara . He

5994-643: The texts that became the authority of the Vaibhāṣika: All of these works have been translated into Chinese, and are now part of the Chinese Buddhist canon . In the Chinese context, the word abhidharma refers to the Sarvāstivāda abhidharma, although at a minimum the Dharmaguptaka, Pudgalavada and Theravada also had abhidharmas. Various other Abhidharma works were written by Sarvāstivāda masters, some are more concise manuals of abhidharma, others critiqued

6075-519: The two are related including: The Dharmaguptaka are known to have rejected the authority of the Sarvāstivāda pratimokṣa rules on the grounds that the original teachings of the Buddha had been lost. The complete Sarvāstivāda Vinaya is extant in the Chinese Buddhist canon . In its early history, the Sarvāstivāda Vinaya was the most common vinaya tradition in China. However, Chinese Buddhism later settled on

6156-431: The ‘Gāndhārian masters’). They studied the same Abhidharma texts as the other Sarvāstivādins, but in a more critical way. According to K. L. Dhammajoti, they eventually came to repudiate the Sarvāstivāda doctrine that "all exists". It is this group, i.e. those who rejected the most important Sarvāstivāda doctrine (along with numerous other key Vaibhāṣika views), which came to be called the Sautrāntika ("those who rely on

6237-418: Was also identified as a unique mark or own characteristic ( svalaksana ) that differentiated a dharma and remained unchangeable throughout its existence. According to Vaibhāṣikas, svabhavas are those things that exist substantially ( dravyasat ) as opposed to those things which are made up of aggregations of dharmas and thus only have a nominal existence ( prajñaptisat ). The Sautrāntika ("those who uphold

6318-505: Was criticized by prominent Vinaya masters such as Yijing and Dao'an (654–717). In the early 8th century, Daoan gained the support of Emperor Zhongzong of Tang , and an imperial edict was issued that the saṃgha in China should use only the Dharmaguptaka Vinaya for ordination. Scholars at present have "a nearly complete collection of sūtras from the Sarvāstivāda school" thanks to a recent discovery in Afghanistan of roughly two-thirds of

6399-546: Was formed by adherents of the Mahāvibhāṣa Śāstra (MVŚ) during the council of Kashmir. Since then, it comprised the orthodox or mainstream branch of the Sarvāstivāda school based in Kāśmīra (though not exclusive to this region). The Vaibhāśika-Sarvāstivāda, which had by far the most "comprehensive edifice of doctrinal systematics" of the early Buddhist schools , was widely influential in India and beyond. As noted by KL Dhammajoti, "It

6480-432: Was one of the early Buddhist schools established around the reign of Ashoka (third century BCE). It was particularly known as an Abhidharma tradition, with a unique set of seven canonical Abhidharma texts. The Sarvāstivādins were one of the most influential Buddhist monastic groups, flourishing throughout North India , especially Kashmir and Central Asia , until the 7th century CE. The orthodox Kashmiri branch of

6561-456: Was the one completed science, and that Aristotelian logic more or less included everything about logic that there was to know. (This work is not necessarily representative of Kant's mature philosophy, which is often regarded as an innovation to logic itself.) Kant's opinion stood unchallenged in the West until 1879, when Gottlob Frege published his Begriffsschrift ( Concept Script ). This introduced

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