Definition
It states that with reference to any a logical proposition X, there are four possibilities:
- (affirmation)
- (negation)
- (both)
- (neither)
The tetralemma is a figure that features prominently in the logic of India.
It states that with reference to any a logical proposition X, there are four possibilities:
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 of logic before Buddhism. [1]
In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is true. It is one of the three laws of thought, along with the law of noncontradiction, and the law of identity; however, no system of logic is built on just these laws, and none of these laws provides inference rules, such as modus ponens or De Morgan's laws. The law is also known as the law / principleof the excluded third, in Latin principium tertii exclusi. Another Latin designation for this law is tertium non datur or "no third [possibility] is given". In classical logic, the law is a tautology.
In logic, mathematics and linguistics, and is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as or or (prefix) or or in which is the most modern and widely used.
In logic, a logical connective is a logical constant. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective can be used to join the two atomic formulas and , rendering the complex formula .
The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India, China, and Greece. Greek methods, particularly Aristotelian logic as found in the Organon, found wide application and acceptance in Western science and mathematics for millennia. The Stoics, especially Chrysippus, began the development of predicate logic.
Chandrakirti or "Chandra" was a Buddhist scholar of the Madhyamaka school and a noted commentator on the works of Nagarjuna and those of his main disciple, Aryadeva. He wrote two influential works on madhyamaka, the Prasannapadā and the Madhyamakāvatāra.
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition to another proposition "not ", standing for " is not true", written , or . It is interpreted intuitively as being true when is false, and false when is true. Negation is thus a unary logical connective. It may be applied as an operation on notions, propositions, truth values, or semantic values more generally. In classical logic, negation is normally identified with the truth function that takes truth to falsity. In intuitionistic logic, according to the Brouwer–Heyting–Kolmogorov interpretation, the negation of a proposition is the proposition whose proofs are the refutations of .
Mādhyamaka, otherwise known as Śūnyavāda and Niḥsvabhāvavāda, refers to a tradition of Buddhist philosophy and practice founded by the Indian Buddhist monk and philosopher Nāgārjuna. The foundational text of the Mādhyamaka tradition is Nāgārjuna's Mūlamadhyamakakārikā. More broadly, Mādhyamaka also refers to the ultimate nature of phenomena as well as the non-conceptual realization of ultimate reality that is experienced in meditation.
Dialetheism 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.
Tsongkhapa was an influential Tibetan Buddhist monk, philosopher and tantric yogi, whose activities led to the formation of the Gelug school of Tibetan Buddhism. He is also known by his ordained name Losang Drakpa or simply as "Je Rinpoche". He is also known by Chinese as Zongkapa Lobsang Zhaba or just Zōngkābā (宗喀巴).
The development of Indian logic dates back to the Chandahsutra of Pingala and anviksiki of Medhatithi Gautama ; the Sanskrit grammar rules of Pāṇini ; the Vaisheshika school's analysis of atomism ; the analysis of inference by Gotama, founder of the Nyaya school of Hindu philosophy; and the tetralemma of Nagarjuna.
The Svātantrika–Prāsaṅgika distinction is a doctrinal distinction made within Tibetan Buddhism between two stances regarding the use of logic and the meaning of conventional truth within the presentation of Madhyamaka.
Śāntarakṣita, whose name translates into English as "protected by the One who is at peace" was an important and influential Indian Buddhist philosopher, particularly for the Tibetan Buddhist tradition. Śāntarakṣita was a philosopher of the Madhyamaka school who studied at Nalanda monastery under Jñānagarbha, and became the founder of Samye, the first Buddhist monastery in Tibet.
Bhāviveka, also called Bhāvaviveka, and Bhavya was a sixth-century madhyamaka Buddhist philosopher. Alternative names for this figure also include Bhavyaviveka, Bhāvin, Bhāviviveka, Bhagavadviveka and Bhavya. Bhāviveka is the author of the Madhyamakahrdaya, its auto-commentary the Tarkajvālā and the Prajñāpradīpa.
Buddhapālita was an Indian Mahayana Buddhist commentator on the works of Nagarjuna and Aryadeva. His Mūlamadhyamaka-vṛtti is an influential commentary to the Mūlamadhyamakakarikā.
Āryadeva, was a Mahayana Buddhist monk, a disciple of Nagarjuna and a Madhyamaka philosopher. Most sources agree that he was from "Siṃhala", which some scholars identify with Sri Lanka. After Nagarjuna, he is considered to be the next most important figure of the Indian Madhyamaka school.
The Nāsadīya Sūkta, also known as the Hymn of Creation, is the 129th hymn of the 10th mandala of the Rigveda (10:129). It is concerned with cosmology and the origin of the universe. The Nāsadīya Sūkta has been the subject of extensive scholarly attention.
Buddhist logico-epistemology is a term used in Western scholarship to describe Buddhist systems of pramāṇa and hetu-vidya. 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", i.e. the school of 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 India.
Gorampa Sonam Senge was an important philosopher in the Sakya school of Tibetan Buddhism. He was the author of a vast collection of commentaries on sutra and tantra whose work was influential throughout Tibetan Buddhism. Gorampa is particularly known for his writings on madhyamaka philosophy, especially his critique of the madhyamaka views of Tsongkhapa and Dolpopa. Gorampa defended the mainly anti-realist interpretation of madhyamaka held by the Sakya school.
The Madhyamakālaṃkāra is an 8th-century Buddhist text, believed to have been originally composed in Sanskrit by Śāntarakṣita (725–788), which is extant in Tibetan. The Tibetan text was translated from the Sanskrit by Surendrabodhi and Jñānasūtra.
Catuṣkoṭi 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.
