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George Boolos
George Stephen Boolos (; 4 September 1940 – 27 May 1996) was an American philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology. Life Boolos is 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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Western Philosophy
Western philosophy encompasses the philosophical thought and work of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the pre-Socratics. The word ''philosophy'' itself originated from the Ancient Greek (φιλοσοφία), literally, "the love of wisdom" grc, φιλεῖν , "to love" and σοφία '' 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 mythical answers to such questions. They were specifically interested in the (the cause or first principle) of the w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Massachusetts Institute Of Technology
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the most prestigious and highly ranked academic institutions in the world. Founded in response to the increasing industrialization of the United States, MIT adopted a European polytechnic university model and stressed laboratory instruction in applied science and engineering. MIT is one of three private land grant universities in the United States, the others being Cornell University and Tuskegee University. The institute has an urban campus that extends more than a mile (1.6 km) alongside the Charles River, and encompasses a number of major off-campus facilities such as the MIT Lincoln Laboratory, the Bates Center, and the Haystack Observatory, as well as affiliated laboratories such as the Broad and Whitehead Institutes. , 98 ... [...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 w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pancreatic Cancer
Pancreatic cancer arises when cells in the pancreas, a glandular organ behind the stomach, begin to multiply out of control and form a mass. These cancerous cells have the 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 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 yellow skin, abdominal or back pain, unexplained weight loss, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crossword
A crossword is a word puzzle that usually takes the form of a square or a rectangular grid of white- and black-shaded squares. The goal is to fill the white squares with letters, forming words or phrases, by solving clues which lead to the answers. In languages that are written left-to-right, the answer words and phrases are placed in the grid from left to right ("across") and from top to bottom ("down"). The shaded squares are used to separate the words or phrases. Types Crossword grids such as those appearing in most North American newspapers and magazines feature solid areas of white squares. Every letter is checked (i.e. is part of both an "across" word and a "down" word) and usually each answer must contain at least three letters. In such puzzles shaded squares are typically limited to about one-sixth of the total. Crossword grids elsewhere, such as in Britain, South Africa, India and Australia, have a lattice-like structure, with a higher percentage of shaded squar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Times
''The Times'' is a British daily national newspaper based in London. It began in 1785 under the title ''The Daily Universal Register'', adopting its current name on 1 January 1788. ''The Times'' and its sister paper '' The Sunday Times'' (founded in 1821) are published by Times Newspapers, since 1981 a subsidiary of News UK, in turn wholly owned by News Corp. ''The Times'' and ''The Sunday Times'', which do not share editorial staff, were founded independently and have only had common ownership since 1966. In general, the political position of ''The Times'' is considered to be centre-right. ''The Times'' is the first newspaper to have borne that name, lending it to numerous other papers around the world, such as '' The Times of India'', ''The New York Times'', and more recently, digital-first publications such as TheTimesBlog.com (Since 2017). In countries where these other titles are popular, the newspaper is often referred to as , or as , although the newspaper is of nati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytical Hierarchy
In mathematical logic and descriptive set theory, the analytical hierarchy is an extension of the arithmetical hierarchy. The analytical hierarchy of formulas includes formulas in the language of second-order arithmetic, which can have quantifiers over both the set of natural numbers, \mathbb, and over functions from \mathbb to \mathbb. The analytical hierarchy of sets classifies sets by the formulas that can be used to define them; it is the lightface version of the projective hierarchy. The analytical hierarchy of formulas The notation \Sigma^1_0 = \Pi^1_0 = \Delta^1_0 indicates the class of formulas in the language of second-order arithmetic with number quantifiers but no set quantifiers. This language does not contain set parameters. The Greek letters here are lightface symbols, which indicate this choice of language. Each corresponding boldface symbol denotes the corresponding class of formulas in the extended language with a parameter for each real; see projective hierarc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Columbia University
Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhattan, Columbia is the oldest institution of higher education in New York and the fifth-oldest institution of higher learning in the United States. It is one of nine colonial colleges founded prior to the Declaration of Independence. It is a member of the Ivy League. Columbia is ranked among the top universities in the world. Columbia was established by royal charter under George II of Great Britain. It was renamed Columbia College in 1784 following the American Revolution, and in 1787 was placed under 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 scientists and scholars have ... [...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 has over 20 departments, department-level programs, and faculties granting SB, SM, and PhD degrees. Major fields of study include anthropology, comparative media studies, economics, history, linguistics, literature, music, philosophy, political science, and theater arts. Other programs include the Center for International Studies; Knight Science Journalism; Science, Technology, and Society; Security Studies; and HyperStudio (digital humanities). In 2018, the Times Higher Education World University Rankings rated MIT the #2 university for arts and humanities. , the Dean of the School is Professor Agustin Rayo. With over 200 faculty members, 330 graduate students, and 109 undergraduate majors and 161 minors, the school is the fourth largest at MIT. All MIT undergraduates must take at least 8 ... [...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, his first career was stage magic. He earned a BSc from the University of Chicago in 1955 and his PhD from Princeton University in 1959. He is one of many logicians to have studied with Alonzo Church. Life He was born on May 25, 1919, in Far Rockaway, Queens, New York, to an Ashkenazi Jewish family. His father was Isidore Smullyan, who was born in Russia but who emigrated to Belgium when young, and whose native language was French. His father was a businessman who graduated from the University of Antwerp. His mother was Rosina Smullyan (née Freeman), who was born and raised in London. She was a painter, who was also an actress. Both parents were musical, his father playing the violin and his mother playing the piano. He was the youngest of three children. His eldest brother, Emile Benoit Sm ... [...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 consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of 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 diagonal argument, Gödel's in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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