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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 ... [...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 Northwestern Europe, off the coast of European mainland, the continental mainland. It comprises England, Scotland, Wales and Northern Ireland. The UK includes the island of Great Britain, the north-eastern part of the island of Ireland, and most of List of islands of the United Kingdom, the smaller islands within the British Isles, covering . Northern Ireland shares Republic of Ireland–United Kingdom border, a land border with the Republic of Ireland; otherwise, the UK is surrounded by the Atlantic Ocean, the North Sea, the English Channel, the Celtic Sea and the Irish Sea. It maintains sovereignty over the British Overseas Territories, which are located across various oceans and seas globally. The UK had an estimated population of over 68.2 million people in 2023. The capital and largest city of both England and the UK is London. The cities o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. From 1929 to 1947, Wittgenstein taught at the University of Cambridge. Despite his position, only one book of his philosophy was published during his entire life: 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. #Works, His voluminous manuscripts were edited and published posthumously. The first and best-known of this posthumous series is the 1953 book ''Philosophical Investigations''. A 1999 survey among American university and college teachers ranked the ''Investigations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basic Books
Basic Books is a book publisher founded in 1950 and located in New York City, 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 sam ... [...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 Nucleic acid double helix, helical structure of the DNA molecule. Crick and Watson's paper in ''Nature (journal), 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 geometry, 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 prot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proof
A mathematical proof is a deductive reasoning, deductive Argument-deduction-proof distinctions, argument for a Proposition, 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 that establish logical certainty, to be distinguished from empirical evidence, empirical arguments or non-exhaustive inductive reasoning that 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 ... [...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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Theory
Proof theory is a major branchAccording to , proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. consists of four corresponding parts, with part D being about "Proof Theory and Constructive Mathematics". of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. Some of the major areas of proof theory include structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity. Much research also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Paris
The University of Paris (), known Metonymy, metonymically as the Sorbonne (), was the leading university in Paris, France, from 1150 to 1970, except for 1793–1806 during the French Revolution. Emerging around 1150 as a corporation associated with the cathedral school of Paris, it was considered the List of medieval universities, second-oldest university in Europe.Charles Homer Haskins: ''The Rise of Universities'', Henry Holt and Company, 1923, p. 292. Officially chartered in 1200 by Philip II of France, King Philip II and recognised in 1215 by Pope Innocent III, it was nicknamed after its theological College of Sorbonne, founded by Robert de Sorbon and chartered by King Louis IX around 1257. Highly reputed internationally for its academic performance in the humanities ever since the Middle Ages – particularly in theology and philosophy – it introduced academic standards and traditions that have endured and spread, such as Doctor (title), doctoral degrees and student nations. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctor Of Science
A Doctor of Science (; most commonly abbreviated DSc or ScD) is a science doctorate awarded in a number of countries throughout the world. 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 North African 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 achievement. Asia Japan Similarly to in the US and most of Europe, Japanese universities offer both the PhD and the ScD as initial doctorates in science. India In India only a few prestigious universities offer ScD/DSc in science which is obtained in Graduate School after satisfactory evaluation of knowledge, research accomp ... [...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. Militaries are typically authorized and maintained by a sovereign state, with their members identifiable by a distinct military uniform. They 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 a military is usually defined as defence of their state and its interests against external armed threats. In broad usage, the terms "armed forces" and "military" are often synonymous, although in technical usage a distinction is sometimes made in which a country's armed forces may include other paramilitary forces such as armed police. Beyond warfare, the military may be employed in additional sanctioned and non-sanctioned functions within the state, including internal security threats, crowd control, promotion of political agendas, emergency services and reconstruct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World War II
World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the world's countries participated, with many nations mobilising all resources in pursuit of total war. Tanks in World War II, Tanks and Air warfare of World War II, aircraft played major roles, enabling the strategic bombing of cities and delivery of the Atomic bombings of Hiroshima and Nagasaki, first and only nuclear weapons ever used in war. World War II is the List of wars by death toll, deadliest conflict in history, causing World War II casualties, the death of 70 to 85 million people, more than half of whom were civilians. Millions died in genocides, including the Holocaust, and by massacres, starvation, and disease. After the Allied victory, Allied-occupied Germany, Germany, Allied-occupied Austria, Austria, Occupation of Japan, Japan, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
