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Georg Kreisel
Georg Kreisel FRS (September 15, 1923 – March 1, 2015) was an Austrian-born mathematical logician who studied and worked in the United Kingdom and America. Biography Kreisel was born in Graz and came from a Jewish background; his family sent him to the United Kingdom before the Anschluss in 1938. He studied mathematics at Trinity College, Cambridge, and then, during World War II, worked on military subjects. Kreisel never took a Ph.D., though much later, in 1962, he was awarded the Cambridge degree of Sc.D., a `higher doctorate' given on the basis of published research. He taught at the University of Reading from 1949 until 1954 and then worked at the Institute for Advanced Study from 1955 to 1957. He returned to Reading in 1957, but then taught at Stanford University from 1958-1959. Then back at Reading for the year 1959-1960, and then the University of Paris 1960-1962. Kreisel was appointed a professor at Stanford University in 1962 and remained on the faculty t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United Kingdom
The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Europe, off the north-western coast of the continental mainland. It comprises England, Scotland, Wales and Northern Ireland. The United Kingdom includes the island of Great Britain, the north-eastern part of the island of Ireland, and many smaller islands within the British Isles. Northern Ireland shares a land border with the Republic of Ireland; otherwise, the United Kingdom is surrounded by the Atlantic Ocean, the North Sea, the English Channel, the Celtic Sea and the Irish Sea. The total area of the United Kingdom is , with an estimated 2020 population of more than 67 million people. The United Kingdom has evolved from a series of annexations, unions and separations of constituent countries over several hundred years. The Treaty of Union between the Kingdom of England (which included Wales, annexed in 1542) and the Kingdom of Scotland in 170 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is considered by some to be the greatest philosopher of the 20th century. From 1929 to 1947, Wittgenstein taught at the University of Cambridge. In spite of his position, during his entire life only one book of his philosophy was published, the 75-page ''Logisch-Philosophische Abhandlung'' (''Logical-Philosophical Treatise'', 1921), which appeared, together with an English translation, in 1922 under the Latin title ''Tractatus Logico-Philosophicus''. His only other published works were an article, "Some Remarks on Logical Form" (1929); a book review; and a children's dictionary. His voluminous manuscripts were edited and published posthumously. The first and best-known of this posthumous series is the 1953 book ''Philosophical Investigations''. A su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basic Books
Basic Books is a book publisher founded in 1950 and located in New York, now an imprint of Hachette Book Group. It publishes books in the fields of psychology, philosophy, economics, science, politics, sociology, current affairs, and history. History Basic Books originated as a small Greenwich Village-based book club marketed to psychoanalysts. Arthur Rosenthal took over the book club in 1950, and under his ownership it soon began producing original books, mostly in the behavioral sciences. Early successes included Ernest Jones's ''The Life and Work of Sigmund Freud'', as well as works by Claude Lévi-Strauss, Jean Piaget and Erik Erikson. Irving Kristol joined Basic Books in 1960, and helped Basic to expand into the social sciences. Harper & Row purchased the company in 1969. In 1997, HarperCollins announced that it would merge Basic Books into its trade publishing program, effectively closing the imprint and ending its publishing of serious academic books. That same year, Bas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francis Crick
Francis Harry Compton Crick (8 June 1916 – 28 July 2004) was an English molecular biologist, biophysicist, and neuroscientist. He, James Watson, Rosalind Franklin, and Maurice Wilkins played crucial roles in deciphering the helical structure of the DNA molecule. Crick and Watson's paper in ''Nature'' in 1953 laid the groundwork for understanding DNA structure and functions. Together with Maurice Wilkins, they were jointly awarded the 1962 Nobel Prize in Physiology or Medicine "for their discoveries concerning the molecular structure of nucleic acids and its significance for information transfer in living material". Crick was an important theoretical molecular biologist and played a crucial role in research related to revealing the helical structure of DNA. He is widely known for the use of the term " central dogma" to summarise the idea that once information is transferred from nucleic acids (DNA or RNA) to proteins, it cannot flow back to nucleic acids. In other words ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proof
A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in ''all'' possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructivism (mathematics)
In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a specific example of a mathematical object in order to prove that an example exists. Contrastingly, in classical mathematics, one can prove the existence of a mathematical object without "finding" that object explicitly, by assuming its non-existence and then deriving a contradiction from that assumption. Such a proof by contradiction might be called non-constructive, and a constructivist might reject it. The constructive viewpoint involves a verificational interpretation of the existential quantifier, which is at odds with its classical interpretation. There are many forms of constructivism. These include the program of intuitionism founded by Brouwer, the finitism of Hilbert and Bernays, the constructive recursive mathematics of Shanin and Markov, and Bishop's program of constructive analysis. Constructivism also includes the study of constructive set theories such as CZ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Theory
Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Jon Barwise, Barwise (1978) consists of four corresponding parts, with part D being about "Proof Theory and Constructive Mathematics". of mathematical logic that represents Mathematical proof, proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as Recursive data type, inductively-defined data structures such as list (computer science), lists, boxed lists, or Tree (data structure), trees, which are constructed according to the axioms and rule of inference, rules of inference of the logical system. Consequently, proof theory is syntax (logic), syntactic in nature, in contrast to model theory, which is Formal semantics (logic), semantic in nature. Some of the major areas of proof theory include structural proof theory, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Paris
, image_name = Coat of arms of the University of Paris.svg , image_size = 150px , caption = Coat of Arms , latin_name = Universitas magistrorum et scholarium Parisiensis , motto = ''Hic et ubique terrarum'' (Latin) , mottoeng = Here and anywhere on Earth , established = Founded: c. 1150Suppressed: 1793Faculties reestablished: 1806University reestablished: 1896Divided: 1970 , type = Corporative then public university , city = Paris , country = France , campus = Urban The University of Paris (french: link=no, Université de Paris), metonymically known as the Sorbonne (), was the leading university in Paris, France, active from 1150 to 1970, with the exception between 1793 and 1806 under the French Revolution. Emerging around 1150 as a corporation associated with the cathedral school of Notre Dame de Paris, it was considered the second-oldest university in Europe. Haskins, C. H.: ''The Rise of Universities'', Henry Holt and Company, 1923, p. 292. Officially chartered i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctor Of Science
Doctor of Science ( la, links=no, Scientiae Doctor), usually abbreviated Sc.D., D.Sc., S.D., or D.S., is an academic research degree awarded in a number of countries throughout the world. In some countries, "Doctor of Science" is the degree used for the standard doctorate in the sciences; elsewhere the Sc.D. is a "higher doctorate" awarded in recognition of a substantial and sustained contribution to scientific knowledge beyond that required for a Doctor of Philosophy (PhD). Africa Algeria and Morocco In Algeria, Morocco, Libya and Tunisia, all universities accredited by the state award a "Doctorate" in all fields of science and humanities, equivalent to a PhD in the United Kingdom or United States. Some universities in these four Arab countries award a "Doctorate of the State" in some fields of study and science. A "Doctorate of the State" is slightly higher in esteem than a regular doctorate, and is awarded after performing additional in-depth post-doctorate research or ach ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Military
A military, also known collectively as armed forces, is a heavily armed, highly organized force primarily intended for warfare. It is typically authorized and maintained by a sovereign state, with its members identifiable by their distinct military uniform. It may consist of one or more military branches such as an army, navy, air force, space force, marines, or coast guard. The main task of the military is usually defined as defence of the state and its interests against external armed threats. In broad usage, the terms ''armed forces'' and ''military'' are often treated as synonymous, although in technical usage a distinction is sometimes made in which a country's armed forces may include both its military and other paramilitary forces. There are various forms of irregular military forces, not belonging to a recognized state; though they share many attributes with regular military forces, they are less often referred to as simply ''military''. A nation's military may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing military alliances: the Allies and the Axis powers. World War II was a total war that directly involved more than 100 million personnel from more than 30 countries. The major participants in the war threw their entire economic, industrial, and scientific capabilities behind the war effort, blurring the distinction between civilian and military resources. Aircraft played a major role in the conflict, enabling the strategic bombing of population centres and deploying the only two nuclear weapons ever used in war. World War II was by far the deadliest conflict in human history; it resulted in 70 to 85 million fatalities, mostly among civilians. Tens of millions died due to genocides (including the Holocaust), starvation, ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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