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Jaina Seven-valued Logic
Jaina seven-valued logic is system of argumentation developed by Jaina philosophers and thinkers in ancient India to support and substantiate their theory of pluralism. This argumentation system has seven distinct semantic predicates which may be thought of as seven different truth values. Traditionally, in the Jaina and other Indian literature dealing with topics in Jain philosophy, this system of argumentation is referred to as ''Saptabhangivada'' or ''Syadvada''. The earliest reference to ''Syadvada'' occurs is the writings of Bhadrabahu (c. 433–357 BCE). There is mention of ''Syadvada'' in the ''Nyayavatara'' of Siddhasena Divakara (about 480–550 CE). Samantabhadra (about 600 CE) gave a full exposition of the seven parts of ''Syadvada'' or ''Saptabhanginyaya'' in his ''Aptamimamsa''. The ''Syadvadamanjari'' of Mallisena (1292 CE) is a separate treatise on the same theory. There are, of course, still later works and a large number of modern commentaries. (Dialectica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Argumentation
Argumentation theory, or argumentation, is the interdisciplinary study of how conclusions can be supported or undermined by premises through logical reasoning. With historical origins in logic, dialectic, and rhetoric, argumentation theory, includes the arts and sciences of civil debate, dialogue, conversation, and persuasion. It studies rules of inference, logic, and procedural rules in both artificial and real-world settings. Argumentation includes various forms of dialogue such as deliberation and negotiation which are concerned with collaborative decision-making procedures. It also encompasses eristic dialog, the branch of social debate in which victory over an opponent is the primary goal, and didactic dialogue used for teaching. This discipline also studies the means by which people can express and rationally resolve or at least manage their disagreements. Argumentation is a daily occurrence, such as in public debate, science, and law. For example in law, in courts by the ju ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher learning in the United States and one of the most prestigious and highly ranked universities in the world. The university is composed of ten academic faculties plus Harvard Radcliffe Institute. The Faculty of Arts and Sciences offers study in a wide range of undergraduate and graduate academic disciplines, and other faculties offer only graduate degrees, including professional degrees. Harvard has three main campuses: the Cambridge campus centered on Harvard Yard; an adjoining campus immediately across Charles River in the Allston neighborhood of Boston; and the medical campus in Boston's Longwood Medical Area. Harvard's endowment is valued at $50.9 billion, making it the wealthiest academic institution in the world. Endowment inco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aristotelian Logic
In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, the Peripatetics. It was revived after the third century CE by Porphyry's Isagoge. Term logic revived in medieval times, first in Islamic logic by Alpharabius in the tenth century, and later in Christian Europe in the twelfth century with the advent of new logic, remaining dominant until the advent of predicate logic in the late nineteenth century. However, even if eclipsed by newer logical systems, term logic still plays a significant role in the study of logic. Rather than radically breaking with term logic, modern logics typically expand it, so to understand the newer systems, one must be acquainted with the earlier one. Aristotle's system Aristotle's logical work is collected in the six texts that are collectively known as the ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Catuṣkoṭi
''Catuṣkoṭi'' (Sanskrit; Devanagari: चतुष्कोटि, , Sinhalese:චතුස්කෝටිකය) 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, the Buddhist logico-epistemological traditions, particularly those of the Madhyamaka school, and in the skeptical Greek philosophy of Pyrrhonism. In particular, the catuṣkoṭi is a "four-cornered" system of argumentation that involves the systematic examination of each of the 4 possibilities of a proposition, ''P'': # ''P''; that is being. # not ''P''; that is not being. # ''P'' and not ''P''; that is being and that is not being. # not (''P'' or not ''P''); that is neither not being nor is that being. These four statements hold the following properties: (1) each alternative is mutually exclusive (that is, one of, but no more than one of, the four statements ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saptabhangi
( hi, wikt:अनेकान्तवाद, अनेकान्तवाद, "many-sidedness") is the Jainism, Jain doctrine about metaphysical truths that emerged in ancient India. It states that the ultimate truth and reality is complex and has multiple aspects. According to Jainism, no single, specific statement can describe the nature of existence and the Absolute (philosophy), absolute truth. This knowledge (''Kevala Jnana''), it adds, is comprehended only by the Arihant (Jainism), Arihants. Other beings and their statements about absolute truth are incomplete, and at best a partial truth. All knowledge claims, according to the ''anekāntavāda'' doctrine must be qualified in many ways, including being affirmed and denied. Anekāntavāda is a fundamental doctrine of Jainism. The origins of ''anekāntavāda '' can be traced back to the teachings of Mahavira, Mahāvīra (599–527 BCE), the 24th Jain . The dialectical concepts of ''syādvāda'' "conditioned viewpoints" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three-valued Logic
In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating ''true'', ''false'' and some indeterminate third value. This is contrasted with the more commonly known bivalent logics (such as classical sentential or Boolean logic) which provide only for ''true'' and ''false''. Emil Leon Post is credited with first introducing additional logical truth degrees in his 1921 theory of elementary propositions. The conceptual form and basic ideas of three-valued logic were initially published by Jan Łukasiewicz and Clarence Irving Lewis. These were then re-formulated by Grigore Constantin Moisil in an axiomatic algebraic form, and also extended to ''n''-valued logics in 1945. Pre-discovery Around 1910, Charles Sanders Peirce defined a many-valued logic system. He never published it. In fact, he did not even number the three pages of notes where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prasanta Chandra Mahalanobis
Prasanta Chandra Mahalanobis OBE, FNA, FASc, FRS (29 June 1893– 28 June 1972) was an Indian scientist and statistician. He is best remembered for the Mahalanobis distance, a statistical measure, and for being one of the members of the first Planning Commission of free India. He made pioneering studies in anthropometry in India. He founded the Indian Statistical Institute, and contributed to the design of large-scale sample surveys. For his contributions, Mahalanobis has been considered the father of modern statistics in India. Early life Mahalanobis belonged to a family of Bengali landed gentry who lived in Bikrampur (now in Bangladesh). His grandfather Gurucharan (1833–1916) moved to Calcutta in 1854 and built up a business, starting a chemist shop in 1860. Gurucharan was influenced by Debendranath Tagore (1817–1905), father of the Nobel Prize-winning poet, Rabindranath Tagore. Gurucharan was actively involved in social movements such as the Brahmo Samaj, acting as i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Many-valued Logic
Many-valued logic (also multi- or multiple-valued logic) refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false") for any proposition. Classical two-valued logic may be extended to ''n''-valued logic for ''n'' greater than 2. Those most popular in the literature are three-valued (e.g., Łukasiewicz's and Kleene's, which accept the values "true", "false", and "unknown"), four-valued, nine-valued, the finite-valued (finitely-many valued) with more than three values, and the infinite-valued (infinitely-many-valued), such as fuzzy logic and probability logic. History It is wrong that the first known classical logician who did not fully accept the law of excluded middle was Aristotle (who, ironically, is also generally considered to be the first classical logician and the "father of wo-valuedlogic"). In fact, Aristotle did not contest the univer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jainism
Jainism ( ), also known as Jain Dharma, is an Indian religions, Indian religion. Jainism traces its spiritual ideas and history through the succession of twenty-four tirthankaras (supreme preachers of ''Dharma''), with the first in the current time cycle being Rishabhadeva, whom the tradition holds to have lived millions of years ago, the twenty-third ''tirthankara'' Parshvanatha, whom historians date to the 9th century BCE, and the twenty-fourth ''tirthankara'' Mahāvīra, Mahavira, around 600 BCE. Jainism is considered to be an eternal ''dharma'' with the ''tirthankaras'' guiding every time cycle of the Jain cosmology, cosmology. The three main pillars of Jainism are ''Ahimsa in Jainism, ahiṃsā'' (non-violence), ''anekāntavāda'' (non-absolutism), and ''aparigraha'' (asceticism). Jain monks, after positioning themselves in the sublime state of soul consciousness, take five main vows: ''ahiṃsā'' (non-violence), ''satya'' (truth), ''Achourya, asteya'' (not stealing), ''b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bhadrabahu
Ācārya Bhadrabāhu (c. 367 - c. 298 BC) was, according to the ''Digambara'' sect of Jainism, the last '' Shruta Kevalin'' (all knowing by hearsay, that is indirectly) in Jainism . He was the last ''acharya'' of the undivided Jain ''sangha''. He was the spiritual teacher of Chandragupta Maurya, the founder of Maurya Empire. According to the ''Digambara'' sect of Jainism, there were five ''Shruta Kevalins'' in Jainism - Govarddhana Mahamuni, Vishnu, Nandimitra, Aparajita and Bhadrabahu. Early life Bhadrabahu was born in Pundravardhana (The region mainly consisted of parts of the Northern West Bengal and North-Western Bangladesh, i.e., parts of North Bengal) to a Brahmin family during which time the secondary capital of the Mauryas was Ujjain. When he was seven, Govarddhana Mahamuni predicted that he will be the last ''Shruta Kevali'' and took him along for his initial education. According to ''Śvētāmbara'' tradition, he lived from 433 BC to 357 BC. ''Digambara'' tradition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syadvada
( hi, अनेकान्तवाद, "many-sidedness") is the Jain doctrine about metaphysical truths that emerged in ancient India. It states that the ultimate truth and reality is complex and has multiple aspects. According to Jainism, no single, specific statement can describe the nature of existence and the absolute truth. This knowledge ('' Kevala Jnana''), it adds, is comprehended only by the Arihants. Other beings and their statements about absolute truth are incomplete, and at best a partial truth. All knowledge claims, according to the ''anekāntavāda'' doctrine must be qualified in many ways, including being affirmed and denied. Anekāntavāda is a fundamental doctrine of Jainism. The origins of ''anekāntavāda '' can be traced back to the teachings of Mahāvīra (599–527 BCE), the 24th Jain . The dialectical concepts of ''syādvāda'' "conditioned viewpoints" and ''nayavāda'' "partial viewpoints" arose from ''anekāntavāda'' in the medieval era, providin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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