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William Of Soissons
William of Soissons; French: Guillaume de Soissons; was a French logician who lived in Paris in the 12th century. He belonged to a school of logicians, called the Parvipontians.Graham Priest, 'What's so bad about contradictions?' in Priest, Beall and Armour-Garb, ''The Law of Non-Contradiction'', p. 25, Clarendon Press, Oxford, 2011. William of Soissons fundamental logical problem and solution William of Soissons seems to have been the first one to answer the question, "Why is a contradiction not accepted in logic reasoning?" by the Principle of explosion. Exposing a contradiction was already in the ancient days of Plato a way of showing that some reasoning was wrong, but there was no explicit argument as to why contradictions were incorrect. William of Soissons gave a proof in which he showed that from a contradiction any assertion can be inferred as true. In example from: ''It is raining (P) and it is not raining (¬P)'' you may infer ''that there are trees on the moon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logician
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually und ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paris
Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. Since the 17th century, Paris has been one of the world's major centres of finance, diplomacy, commerce, fashion, gastronomy, and science. For its leading role in the arts and sciences, as well as its very early system of street lighting, in the 19th century it became known as "the City of Light". Like London, prior to the Second World War, it was also sometimes called the capital of the world. The City of Paris is the centre of the Île-de-France region, or Paris Region, with an estimated population of 12,262,544 in 2019, or about 19% of the population of France, making the region France's primate city. The Paris Region had a GDP of €739 billion ($743 billion) in 2019, which is the highest in Europe. According to the Economist Intelli ... [...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] |
Plato
Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution of higher learning on the European continent. Along with his teacher, Socrates, and his student, Aristotle, Plato is a central figure in the history of Ancient Greek philosophy and the Western and Middle Eastern philosophies descended from it. He has also shaped religion and spirituality. The so-called neoplatonism of his interpreter Plotinus greatly influenced both Christianity (through Church Fathers such as Augustine) and Islamic philosophy (through e.g. Al-Farabi). In modern times, Friedrich Nietzsche diagnosed Western culture as growing in the shadow of Plato (famously calling Christianity "Platonism for the masses"), while Alfred North Whitehead famously said: "the safest general characterization of the European philosophical tra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clarence Irving Lewis
Clarence Irving Lewis (April 12, 1883 – February 3, 1964), usually cited as C. I. Lewis, was an American academic philosopher. He is considered the progenitor of modern modal logic and the founder of conceptual pragmatism. First a noted logician, he later branched into epistemology, and during the last 20 years of his life, he wrote much on ethics. ''The New York Times'' memorialized him as "a leading authority on symbolic logic and on the philosophic concepts of knowledge and value." He was the first to coin the term "Qualia" as it is used today in philosophy, linguistics, and cognitive sciences.Lewis, Clarence Irving (1929). ''Mind and the world-order: Outline of a theory of knowledge''. New York: Charles Scribner's Sons. p. 121 Biography Lewis was born in Stoneham, Massachusetts. His father was a skilled worker in a shoe factory, and Lewis grew up in relatively humble circumstances. He discovered philosophy at age 13, when reading about the Greek pre-Socratics, Anaxagoras ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cologne
Cologne ( ; german: Köln ; ksh, Kölle ) is the largest city of the German western States of Germany, state of North Rhine-Westphalia (NRW) and the List of cities in Germany by population, fourth-most populous city of Germany with 1.1 million inhabitants in the city proper and 3.6 million people in the Cologne Bonn Region, urban region. Centered on the left bank of the Rhine, left (west) bank of the Rhine, Cologne is about southeast of NRW's state capital Düsseldorf and northwest of Bonn, the former capital of West Germany. The city's medieval Catholic Cologne Cathedral (), the third-tallest church and tallest cathedral in the world, constructed to house the Shrine of the Three Kings, is a globally recognized landmark and one of the most visited sights and pilgrimage destinations in Europe. The cityscape is further shaped by the Twelve Romanesque churches of Cologne, and Cologne is famous for Eau de Cologne, that has been produced in the city since 1709, and "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] |
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] |
Logicians
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually und ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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