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Tetralemma
The tetralemma is a figure that features prominently in the logic of India. Definition It states that with reference to any a logical proposition (or axiom) X, there are four possibilities: : X (affirmation) : \neg X (negation) : X \land\neg X (both) : \neg (X \lor \neg X) (neither) Catuskoti The history of fourfold negation, the Catuskoti (Sanskrit), is evident in the logico-epistemological tradition of India, given the categorical nomenclature Indian logic in Western discourse. Subsumed within the auspice of Indian logic, 'Buddhist logic' has been particularly focused in its employment of the fourfold negation, as evidenced by the traditions of Nagarjuna and the Madhyamaka, particularly the school of Madhyamaka given the retroactive nomenclature of Prasangika by the Tibetan Buddhist logico-epistemological tradition. Though tetralemma was also used as a form inquiry rather than logic in the Nasadiya Sukta of Rigveda (creation hymn) though seems to be rarely used as a tool o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indian Logic
The development of Indian logic dates back to the Chandahsutra of Pingala and '' anviksiki'' of Medhatithi Gautama (c. 6th century BCE); the Sanskrit grammar rules of Pāṇini (c. 5th century BCE); the Vaisheshika school's analysis of atomism (c. 6th century BCE to 2nd century BCE); the analysis of inference by Gotama (c. 6th century BC to 2nd century CE), founder of the Nyaya school of Hindu philosophy; and the tetralemma of Nagarjuna (c. 2nd century CE). Indian logic stands as one of the three original traditions of logic, alongside the Greek and the Chinese logic. The Indian tradition continued to develop through early to modern times, in the form of the Navya-Nyāya school of logic. Origins 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". Medhatithi Gautama (c. 6th cen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Catuṣkoṭi
''Catuṣkoṭi'' (Sanskrit; Devanagari: चतुष्कोटि, , Sinhalese:චතුස්කෝටිකය) refers to logical argument(s) of a 'suite of four discrete functions' or 'an indivisible quaternity' that has multiple applications and has been important in the Indian logic and the Buddhist logico-epistemological traditions, particularly those of the Madhyamaka school. 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 is true) and (2) that all the alternatives are together exhaustiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-truths Doctrine
The Buddhist doctrine of the two truths (Sanskrit: '','' ) differentiates between two levels of ''satya'' (Sanskrit; Pāli: ''sacca''; meaning "truth" or "reality") in the teaching of Śākyamuni Buddha: the "conventional" or "provisional" (''saṁvṛti'') truth, and the "absolute" or "ultimate" (''paramārtha'') truth. The exact meaning varies between the various Buddhist schools and traditions. The best known interpretation is from the Mādhyamaka school of Mahāyāna Buddhism, whose founder was the 3rd-century Indian Buddhist monk and philosopher Nāgārjuna. For Nāgārjuna, the two truths are ''epistemological truths''. The phenomenal world is accorded a provisional existence. The character of the phenomenal world is declared to be neither real nor unreal, but logically indeterminable. Ultimately, all phenomena are empty (''śūnyatā'') of an inherent self or essence due to the non-existence of the self (''anātman''), but temporarily exist depending on other phenome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Connective
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective \lor can be used to join the two atomic formulas P and Q, rendering the complex formula P \lor Q . Common connectives include negation, disjunction, conjunction, implication, and equivalence. In standard systems of classical logic, these connectives are interpreted as truth functions, though they receive a variety of alternative interpretations in nonclassical logics. Their classical interpretations are similar to the meanings of natural language expressions such as English "not", "or", "and", and "if", but not identical. Discrepancies between natural language connectives and those of classical logic have motivated nonclassical approaches to natural language meaning as well as approaches which pair a classi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dialetheism
Dialetheism (; from Greek 'twice' and 'truth') is the view that there are statements that are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called "true contradictions", ''dialetheia'', or nondualisms. Dialetheism is not a system of formal logic; instead, it is a thesis about truth that influences the construction of a formal logic, often based on pre-existing systems. Introducing dialetheism has various consequences, depending on the theory into which it is introduced. A common mistake resulting from this is to reject dialetheism on the basis that, in traditional systems of logic (e.g., classical logic and intuitionistic logic), every statement becomes a theorem if a contradiction is true, trivialising such systems when dialetheism is included as an axiom.Ben Burgis, Visiting Professor of Philosophy at the University of Ulsan in South Korea, iBlog&~Blog Other logical systems, however ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buddhist Logic
Buddhist logico-epistemology is a term used in Western scholarship to describe Buddhism, Buddhist systems of ' (Epistemology, epistemic tool, valid cognition) and ' (reasoning, logic). While the term may refer to various Buddhist systems and views on reasoning and epistemology, it is most often used to refer to the work of the "Epistemological school" (Sanskrit: ), i.e. the school of Dignāga, Dignaga and Dharmakirti which developed from the 5th through 7th centuries and remained the main system of Buddhist reasoning until the Decline of Buddhism in the Indian subcontinent, decline of Buddhism in India. The early Buddhist texts show that the Gautama Buddha, historical Buddha was familiar with certain rules of reasoning used for debating purposes and made use of these against his opponents. He also seems to have held certain ideas about epistemology and reasoning, though he did not put forth a logico-epistemological system. The Theravada ''Kathāvatthu'' contains some rules on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Madhyamaka
Madhyamaka ("middle way" or "centrism"; ; ; Tibetic languages, Tibetan: དབུ་མ་པ་ ; ''dbu ma pa''), otherwise known as Śūnyavāda ("the Śūnyatā, emptiness doctrine") and Niḥsvabhāvavāda ("the no Svabhava, ''svabhāva'' doctrine"), refers to a tradition of Buddhist philosophy and practice founded by the History of Buddhism in India, Indian Buddhist monk and philosopher Nagarjuna, Nāgārjuna ().Wynne, Alexander (2015) ''Early Buddhist Teaching as Proto-śūnyavāda.'' Journal of the Oxford Centre for Buddhist Studies, 6. pp. 213-241. The foundational text of the Mādhyamaka tradition is Nagarjuna, Nāgārjuna's ''Mūlamadhyamakakārikā'' ("Root Verses on the Middle Way"). More broadly, Madhyamaka also refers to the ultimate nature of phenomena as well as the non-conceptual realization of ultimate reality that is experienced in Buddhist meditation, meditation. Since the 4th century CE onwards, Madhyamaka philosophy had a major influence on the subsequent d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Morgan's Laws
In propositional calculus, propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both Validity (logic), valid rule of inference, rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician. The rules allow the expression of Logical conjunction, conjunctions and Logical disjunction, disjunctions purely in terms of each other via logical negation, negation. The rules can be expressed in English as: * The negation of "A and B" is the same as "not A or not B". * The negation of "A or B" is the same as "not A and not B". or * The Complement (set theory), complement of the union of two sets is the same as the intersection of their complements * The complement of the intersection of two sets is the same as the union of their complements or * not (A or B) = (not A) and (not B) * not (A and B) = (not A) or (not B) where "A or B" is an "inclusive or" meaning ''at least' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nagarjuna
Nāgārjuna (Sanskrit: नागार्जुन, ''Nāgārjuna''; ) was an Indian monk and Mahayana, Mahāyāna Buddhist Philosophy, philosopher of the Madhyamaka (Centrism, Middle Way) school. He is widely considered one of the most important Buddhist philosophers.Garfield, Jay L. (1995), ''The Fundamental Wisdom of the Middle Way'', Oxford: Oxford University Press. Nāgārjuna is widely considered to be the founder of the Madhyamaka school of Buddhist philosophy and a defender of the Mahāyāna movement. His ''Mūlamadhyamakakārikā'' (''Root Verses on Madhyamaka'', MMK) is the most important text on the Madhyamaka philosophy of Śūnyatā, emptiness. The MMK inspired a large number of commentaries in Sanskrit, Chinese, Tibetan, Korean and Japanese and continues to be studied today. History Background India in the first and second centuries CE was politically divided into various states, including the Kushan Empire and the Satavahana dynasty, Satavahana Kingdom. At ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paraconsistent Logic
Paraconsistent logic is a type of non-classical logic that allows for the coexistence of contradictory statements without leading to a logical explosion where anything can be proven true. Specifically, paraconsistent logic is the subfield of logic that is concerned with studying and developing "inconsistency-tolerant" systems of logic, purposefully excluding the principle of explosion. Inconsistency-tolerant logics have been discussed since at least 1910 (and arguably much earlier, for example in the writings of Aristotle); however, the term ''paraconsistent'' ("beside the consistent") was first coined in 1976, by the Peruvian philosopher Francisco Miró Quesada Cantuarias. The study of paraconsistent logic has been dubbed paraconsistency, which encompasses the school of dialetheism. Definition In classical logic (as well as intuitionistic logic and most other logics), contradictions entail everything. This feature, known as the principle of explosion or ''ex contradiction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
