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Boolos, George
George Stephen Boolos (; September 4, 1940 – May 27, 1996) was an American philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology. Life Boolos was of Greek-Jewish descent. He graduated with an A.B. in mathematics from Princeton University after completing a senior thesis, titled "A simple proof of Gödel's first incompleteness theorem", under the supervision of Raymond Smullyan. Oxford University awarded him the B.Phil. in 1963. In 1966, he obtained the first PhD in philosophy ever awarded by the Massachusetts Institute of Technology, under the direction of Hilary Putnam. After teaching three years at Columbia University, he returned to MIT in 1969, where he spent the rest of his career. A charismatic speaker well known for his clarity and wit, he once delivered a lecture (1994b) giving an account of Gödel's second incompleteness theorem, employing only words of one syllable. At the end of his viva, Hilary Putnam asked him, "And ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Western Philosophy
Western philosophy refers to the Philosophy, philosophical thought, traditions and works of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the Pre-Socratic philosophy, pre-Socratics. The word ''philosophy'' itself originated from the Ancient Greek (φιλοσοφία), literally, "the love of wisdom" , "to love" and σοφία ''Sophia (wisdom), sophía'', "wisdom". History Ancient The scope of ancient Western philosophy included the problems of philosophy as they are understood today; but it also included many other disciplines, such as pure mathematics and natural sciences such as physics, astronomy, and biology (Aristotle, for example, wrote on all of these topics). Pre-Socratics The pre-Socratic philosophers were interested in cosmology (the nature and origin of the universe), while rejecting unargued fables in place for argued theory, i.e., dogma superseded reason, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosopher
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational and critical inquiry that reflects on its methods and assumptions. Historically, many of the individual sciences, such as physics and psychology, formed part of philosophy. However, they are considered separate academic disciplines in the modern sense of the term. Influential traditions in the history of philosophy include Western philosophy, Western, Islamic philosophy, Arabic–Persian, Indian philosophy, Indian, and Chinese philosophy. Western philosophy originated in Ancient Greece and covers a wide area of philosophical subfields. A central topic in Arabic–Persian philosophy is the relation between reason and revelation. Indian philosophy combines the Spirituality, spiritual problem of how to reach Enlightenment in Buddhism, enlighten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Jeffrey
Richard Carl Jeffrey (August 5, 1926 – November 9, 2002) was an American philosopher, logician, and probability theorist. He is best known for developing and championing the philosophy of radical probabilism and the associated heuristic of probability kinematics, also known as Jeffrey conditioning. Life and career Born in Boston, Massachusetts, Jeffrey served in the U.S. Navy during World War II. As a graduate student he studied under Rudolf Carnap and Carl Hempel. He received his M.A. from the University of Chicago in 1952 and his Ph.D. from Princeton in 1957. After holding academic positions at MIT, City College of New York, Stanford University, and the University of Pennsylvania, he joined the faculty of Princeton in 1974 and became a professor emeritus there in 1999. He was also a visiting professor at the University of California, Irvine. Jeffrey, who died of lung cancer at the age of 76, was known for his sense of humor, which often came through in his breezy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pancreatic Cancer
Pancreatic cancer arises when cell (biology), cells in the pancreas, a glandular organ behind the stomach, begin to multiply out of control and form a Neoplasm, mass. These cancerous cells have the malignant, ability to invade other parts of the body. A number of types of pancreatic cancer are known. The most common, pancreatic adenocarcinoma, accounts for about 90% of cases, and the term "pancreatic cancer" is sometimes used to refer only to that type. These adenocarcinomas start within the part of the pancreas that makes digestive enzymes. Several other types of cancer, which collectively represent the majority of the non-adenocarcinomas, can also arise from these cells. About 1–2% of cases of pancreatic cancer are neuroendocrine tumors, which arise from the hormone-producing neuroendocrine cell, cells of the pancreas. These are generally less aggressive than pancreatic adenocarcinoma. Signs and symptoms of the most-common form of pancreatic cancer may include jaundice, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crossword
A crossword (or crossword puzzle) is a word game consisting of a grid of black and white squares, into which solvers enter words or phrases ("entries") crossing each other horizontally ("across") and vertically ("down") according to a set of clues. Each white square is typically filled with one letter, while the black squares are used to separate entries. The first white square in each entry is typically numbered to correspond to its clue. Crosswords commonly appear in newspapers and magazines. The earliest crosswords that resemble their modern form were popularized by the ''New York World'' in the 1910s. Many variants of crosswords are popular around the world, including cryptic crosswords and many language-specific variants. Crossword construction in modern times usually involves the use of software. Constructors choose a theme (except for themeless puzzles), place the theme answers in a grid which is usually symmetric, fill in the rest of the grid, and then write clues. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Times
''The Times'' is a British Newspaper#Daily, daily Newspaper#National, national newspaper based in London. It began in 1785 under the title ''The Daily Universal Register'', adopting its modern name on 1 January 1788. ''The Times'' and its sister paper ''The Sunday Times'' (founded in 1821), are published by Times Media, since 1981 a subsidiary of News UK, in turn wholly owned by News Corp. ''The Times'' and ''The Sunday Times'' were founded independently and have had common ownership only since 1966. It is considered a newspaper of record in the UK. ''The Times'' was the first newspaper to bear that name, inspiring numerous other papers around the world. In countries where these other titles are popular, the newspaper is often referred to as or , although the newspaper is of national scope and distribution. ''The Times'' had an average daily circulation of 365,880 in March 2020; in the same period, ''The Sunday Times'' had an average weekly circulation of 647,622. The two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytical Hierarchy
Analytic or analytical may refer to: Chemistry * Analytical chemistry, the analysis of material samples to learn their chemical composition and structure * Analytical technique, a method that is used to determine the concentration of a chemical compound or chemical element * Analytical concentration Mathematics * Abstract analytic number theory, the application of ideas and techniques from analytic number theory to other mathematical fields * Analytic combinatorics, a branch of combinatorics that describes combinatorial classes using generating functions * Analytic element method, a numerical method used to solve partial differential equations * Analytic expression or analytic solution, a mathematical expression using well-known operations that lend themselves readily to calculation * Analytic geometry, the study of geometry based on numerical coordinates rather than axioms * Analytic number theory, a branch of number theory that uses methods from mathematical analysis M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Columbia University
Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church (Manhattan), Trinity Church in Manhattan, it is the oldest institution of higher education in New York (state), New York and the fifth-First university in the United States, oldest in the United States. Columbia was established as a Colonial colleges, colonial college by royal charter under George II of Great Britain. It was renamed Columbia College (New York), Columbia College in 1784 following the American Revolution, and in 1787 was placed under Trustees of Columbia University in the City of New York, a private board of trustees headed by former students Alexander Hamilton and John Jay. In 1896, the campus was moved to its current location in Morningside Heights and renamed Columbia University. Columbia is organized into twenty schoo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MIT School Of Humanities, Arts, And Social Sciences
The MIT School of Humanities, Arts, and Social Sciences (SHASS) is one of the five schools of the Massachusetts Institute of Technology, located in Cambridge, Massachusetts, US. The school includes 11 academic areas and works alongside six departments, labs, and programs. SHASS grants SB, SM, and PhD degrees. Major fields of study include anthropology, comparative media studies and writing, economics, history, linguistics, literature, music, philosophy, political science, science, technology, and society, and theater arts. Other programs include the Center for International Studies; Knight Science Journalism; Science, Technology, and Society; Security Studies; and HyperStudio (digital humanities). , the Dean of the School is Professor Agustín Rayo. With dozens of faculty members, hundreds of graduate students, 109 undergraduate majors, and 161 minors, the school is the fourth largest at MIT. All MIT undergraduates must take at least eight semesters of courses (approxi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raymond Smullyan
Raymond Merrill Smullyan (; May 25, 1919 – February 6, 2017) was an American mathematician, magician, concert pianist, logician, Taoist, and philosopher. Born in Far Rockaway, New York, Smullyan's first career choice was in stage magic. He earned a BSc from the University of Chicago in 1955 and his PhD from Princeton University in 1959. Smullyan is one of many logicians to have studied with Alonzo Church. Life Smullyan was born on May 25, 1919, in Far Rockaway, Queens, New York, to an Ashkenazi Jewish family. His father was Isidore Smullyan, a Russian-born businessman who emigrated to Belgium when young and graduated from the University of Antwerp, his native language being French. His mother was Rosina Smullyan (née Freeman), a painter and actress born and raised in London. Both parents were musical, his father playing the violin and his mother playing the piano. Smullyan was the youngest of three children. His eldest brother, Emile Benoit Smullyan, later became an econ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gödel's Incompleteness Theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. The first incompleteness theorem states that no consistency, consistent system of axioms whose theorems can be listed by an effective procedure (i.e. an algorithm) is capable of Mathematical proof, proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency. Employing a Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
