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Alan Ross Anderson
Alan Ross Anderson (1925–1973) was an American logician and professor of philosophy at Yale University and the University of Pittsburgh. A frequent collaborator with Nuel Belnap, Anderson was instrumental in the development of relevance logic and deontic logic. Anderson died of cancer in 1973. Relevance logic Anderson believed that the conclusion of a valid inference ought to have something to do with (i.e. be ''relevant'' to) the premises. Formally, he captured this "relevance condition" with the principle that : ''A'' entails ''B'' only if ''A'' and ''B'' share at least one non-logical constant. As simple as this idea appears, implementing it in a formal system requires a radical departure from the semantics of classical logic. Anderson and Belnap (with contributions from J. Michael Dunn, Kit Fine, Alasdair Urquhart, Robert K. Meyer, Anil Gupta, and others) explored the formal consequences of the relevance condition in great detail in their influential ''Entail ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yale University
Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the world. It is a member of the Ivy League. Chartered by the Connecticut Colony, the Collegiate School was established in 1701 by clergy to educate Congregational ministers before moving to New Haven in 1716. Originally restricted to theology and sacred languages, the curriculum began to incorporate humanities and sciences by the time of the American Revolution. In the 19th century, the college expanded into graduate and professional instruction, awarding the first PhD in the United States in 1861 and organizing as a university in 1887. Yale's faculty and student populations grew after 1890 with rapid expansion of the physical campus and scientific research. Yale is organized into fourteen constituent schools: the original undergraduate col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Logic
Classical logic (or standard logic or Frege-Russell logic) is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy. Characteristics Each logical system in this class shares characteristic properties: Gabbay, Dov, (1994). 'Classical vs non-classical logic'. In D.M. Gabbay, C.J. Hogger, and J.A. Robinson, (Eds), ''Handbook of Logic in Artificial Intelligence and Logic Programming'', volume 2, chapter 2.6. Oxford University Press. # Law of excluded middle and double negation elimination # Law of noncontradiction, and the principle of explosion # Monotonicity of entailment and idempotency of entailment # Commutativity of conjunction # De Morgan duality: every logical operator is dual to another While not entailed by the preceding conditions, contemporary discussions of classical logic normally only include propositional and first-order logics. Shapiro, Stewart (2000). Classical Logic. In Stanford Encyclop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophical Realism
Philosophical realism is usually not treated as a position of its own but as a stance towards other subject matters. Realism about a certain kind of thing (like numbers or morality) is the thesis that this kind of thing has ''mind-independent existence'', i.e. that it is not just a mere appearance in the eye of the beholder. This includes a number of positions within epistemology and metaphysics which express that a given thing instead exists independently of knowledge, thought, or understanding. This can apply to items such as the physical world, the past and future, other minds, and the self, though may also apply less directly to things such as universals, mathematical truths, moral truths, and thought itself. However, realism may also include various positions which instead reject metaphysical treatments of reality entirely. Realism can also be a view about the properties of reality in general, holding that reality exists independent of the mind, as opposed to non-realist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Platonist
Platonism is the philosophy of Plato and school of thought, philosophical systems closely derived from it, though contemporary platonists do not necessarily accept all of the doctrines of Plato. Platonism had a profound effect on Western thought. Platonism at least affirms the existence of abstract objects, which are asserted to exist in a third realm distinct from both the sensible external world and from the internal world of consciousness, and is the opposite of nominalism." Philosophers who affirm the existence of abstract objects are sometimes called platonists; those who deny their existence are sometimes called nominalists. The terms "platonism" and "nominalism" have established senses in the history of philosophy, where they denote positions that have little to do with the modern notion of an abstract object. In this connection, it is essential to bear in mind that modern platonists (with a small 'p') need not accept any of the doctrines of Plato, just as modern nominalis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal Logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators \Diamond and \Box, representing possibility and necessity respectively. For instance the modal formula \Diamond P can be read as "possibly P" while \Box P can be read as "necessarily P". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When \Box is used to represent epistemic necessity, \Box P states that P is epistemically necessary, or in other words that it is known. When \Box is used to represent deontic necessity, \Box P states that P is a moral or legal obligation. In the standard relational semantics for modal logic, formulas are assigned truth values relative to a ''possible world''. A formula's truth value at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alethic Logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators \Diamond and \Box, representing possibility and necessity respectively. For instance the modal formula \Diamond P can be read as "possibly P" while \Box P can be read as "necessarily P". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When \Box is used to represent epistemic necessity, \Box P states that P is epistemically necessary, or in other words that it is known. When \Box is used to represent deontic necessity, \Box P states that P is a moral or legal obligation. In the standard relational semantics for modal logic, formulas are assigned truth values relative to a ''possible world''. A formula's truth value at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norm (philosophy)
Norms are concepts (Sentence (linguistics), sentences) of practical import, oriented to affecting an action, rather than conceptual abstractions that describe, explain, and express. Normative sentences imply "ought-to" types of statements and assertions, in distinction to sentences that provide "is" types of statements and assertions. Common normative sentences include Imperative mood, commands, permissions, and prohibitions; common normative abstract concepts include ''sincerity'', ''justification'', and ''honesty''. A popular account of norms describes them as Reason (argument), reasons to take action (philosophy), action, to belief, believe, and to emotion, feel. Types of norms Orders and permissions express norms. Such norm sentences do not describe how the world is, they rather prescribe how the world should be. Imperative mood, Imperative sentences are the most obvious way to express norms, but declarative sentences also may be norms, as is the case with laws or 'principles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Explosion
In classical logic, intuitionistic logic and similar logical systems, the principle of explosion (, 'from falsehood, anything ollows; or ), or the principle of Pseudo-Scotus, is the law according to which any statement can be proven from a contradiction. That is, once a contradiction has been asserted, any proposition (including their negations) can be inferred from it; this is known as deductive explosion. The proof of this principle was first given by 12th-century French philosopher William of Soissons. Priest, Graham. 2011. "What's so bad about contradictions?" In ''The Law of Non-Contradicton'', edited by Priest, Beal, and Armour-Garb. Oxford: Clarendon Press. p. 25. Due to the principle of explosion, the existence of a contradiction ( inconsistency) in a formal axiomatic system is disastrous; since any statement can be proven, it trivializes the concepts of truth and falsity. Around the turn of the 20th century, the discovery of contradictions such as Russell's parado ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Boole
George Boole (; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher, and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland. He worked in the fields of differential equations and algebraic logic, and is best known as the author of ''The Laws of Thought'' (1854) which contains Boolean algebra. Boolean logic is credited with laying the foundations for the Information Age. Early life Boole was born in 1815 in Lincoln, Lincolnshire, England, the son of John Boole senior (1779–1848), a shoemaker and Mary Ann Joyce. He had a primary school education, and received lessons from his father, but due to a serious decline in business, he had little further formal and academic teaching. William Brooke, a bookseller in Lincoln, may have helped him with Latin, which he may also have learned at the school of Thomas Bainbridge. He was self-taught in modern languages.H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gottlob Frege
Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever. His contributions include the development of modern logic in the ''Begriffsschrift'' and work in the foundations of mathematics. His book the ''Foundations of Arithmetic'' is the seminal text of the logicist project, and is cited by Michael Dummett as where to pinpoint the linguistic turn. His philosophical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of philosophy within the Lyceum and the wider Aristotelian tradition. His writings cover many subjects including physics, biology, zoology, metaphysics, logic, ethics, aesthetics, poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics, meteorology, geology, and government. Aristotle provided a complex synthesis of the various philosophies existing prior to him. It was above all from his teachings that the West inherited its intellectual lexicon, as well as problems and methods of inquiry. As a result, his philosophy has exerted a unique influence on almost every form of knowledge in the West and it continues to be a subject of contemporary philosophical discussion. Little is known about his life. Aristotle was born in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anil Gupta (philosopher)
Anil K. Gupta (; born 1949) is an Indian-American philosopher who works primarily in logic, epistemology, philosophy of language, and metaphysics. Gupta is the Alan Ross Anderson Distinguished Professor of Philosophy at the University of Pittsburgh. He is also a Fellow of the American Academy of Arts and Sciences. His most recent book, ''Conscious Experience: A Logical Inquiry'', was published by Harvard University Press in 2019. Biography Gupta earned his B.Sc. with first class honours from the University of London in 1969. He then attended the University of Pittsburgh where he received his M.A. (1973) and Ph.D. (1977). Gupta has taught at several universities: McGill University (1975-1982), University of Illinois at Chicago (1982-1989), Indiana University (1989-2000). In 2001 Gupta joined the Department of Philosophy at the University of Pittsburgh where he served as Distinguished Professor of Philosophy and, since 2013, as Alan Ross Anderson Chair. Revision theory Gup ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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