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Encyclopedia > George Boolos

George Stephen Boolos (September 4, 1940, New York City - May 27, 1996) was a philosopher and a mathematical logician. He taught linguistics and philosophy at the Massachusetts Institute of Technology. September 4 is the 247th day of the year (248th in leap years). ... 1940 (MCMXL) was a leap year starting on Monday (the link is to a full 1940 calendar). ... Flag Seal Nickname: Big Apple Location Location in the state of New York Government Counties (Boroughs) Bronx (The Bronx) New York (Manhattan) Queens (Queens) Kings (Brooklyn) Richmond (Staten Island) Mayor Michael Bloomberg (R) Geographical characteristics Area     City 1,214. ... May 27 is the 147th day (148th in leap years) of the year in the Gregorian calendar, with 218 days remaining. ... 1996 (MCMXCVI) was a leap year starting on Monday of the Gregorian calendar, and was designated the International Year for the Eradication of Poverty. ... A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... Linguistics is the scientific study of human language, and someone who engages in this study is called a linguist. ... The Massachusetts Institute of Technology, or MIT, is a private research university located in the city of Cambridge, Massachusetts, USA. Its mission and culture are guided by an emphasis on teaching and research grounded in practical applications of science and technology. ...

Contents


Life

Boolos graduated from Princeton University in 1961 with a BA in mathematics. Oxford University awarded him the B.Phil in 1963. In 1966, he obtained the first Ph.D. in philosophy ever awarded by the Massachusetts Institute of Technology , under the direction of Hilary Putnam. After teaching 3 years at Columbia University, he returned to MIT in 1969, where he spent the rest of his career. Princeton University is a coeducational private university located in Princeton, New Jersey. ... The University of Oxford, located in the city of Oxford in England, is the oldest university in the English-speaking world. ... The Massachusetts Institute of Technology, or MIT, is a private research university located in the city of Cambridge, Massachusetts, USA. Its mission and culture are guided by an emphasis on teaching and research grounded in practical applications of science and technology. ... Hilary Whitehall Putnam (born July 31, 1926) is a key figure in the philosophy of mind during the 20th century. ... Columbia University is a private university in the Morningside Heights neighborhood of the Borough of Manhattan in New York City. ... 1969 (MCMLXIX) was a common year starting on Wednesday (the link is to a full 1969 calendar). ...


A charismatic speaker well-known for his clarity and wit, he once delivered a lecture, since collected in his Logic, Logic, and Logic, which gave an account of Gödel's second incompleteness theorem, employing only one-syllable words. A possibly apocryphal story has it that at the end of his viva, Hilary Putnam asked him, "And tell us, Mr. Boolos, what does the analytical hierarchy have to do with the real world?" An unhesitating Boolos replied, "It's part of it". Kurt Gödel (IPA: ) (April 28, 1906 Brno, then Austria-Hungary, now Czech Republic – January 14, 1978 Princeton, New Jersey) was a logician, mathematician, and philosopher of mathematics. ... In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proven by Kurt Gödel in 1931. ... Hilary Whitehall Putnam (born July 31, 1926) is a key figure in the philosophy of mind during the 20th century. ... In mathematical logic and descriptive set theory, the analytical hierarchy is a second-order analogue of the arithmetical hierarchy. ...


An expert on puzzles of all kinds, in 1993 Boolos reached the London Regional Final of the Times crossword competition. His score was one of the highest ever recorded by an American. The Times is a national newspaper published daily in the United Kingdom since 1785, and under its current name since 1788. ... The crossword is the most common variety of word puzzle in the world. ...


Work

Kurt Godel wrote the first paper on provability logic, modal logic — the logic of necessity and possibility — applied to the theory of mathematical proof. But Boolos took it much further than Godel ever did, making it the subject of an entire monograph The Logic of Provability. A few years after the first edition appeared, Boolos discovered major work on the subject written in Russian, which he translated with the help of a dictionary. Upon discovering the value of the Russian work, he rewrote the book; the result is the second edition. He also wrote the university text Computability and Logic with Richard Jeffrey. Kurt Gödel Kurt Gödel [ kurt gøːdl ], (April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher of mathematics, whose biography lists quite a few nations, although he is usually associated with Austria. ... Provability logic, or the logic of provability, is a modal logic where the necessity operator is interpreted as provability in a reasonably rich formal theory such as Peano arithmetic. ... A modal logic is any logic for handling modalities: concepts like possibility, impossibility, and necessity. ... In mathematics, a proof is a demonstration that, assuming certain axioms, some statement is necessarily true. ... Richard C. Jeffrey (5 August 1926 – 9 November 2002) was an American philosopher, logician, and probability theorist. ...


Boolos was an authority on the 19th-century German mathematician and philosopher Gottlob Frege. Boolos argued that the system of Frege's Grundgesetze, long thought vitiated by Russell's paradox, could be freed of inconsistency by replacing one of its axioms, the notorious Basic Law V. Edward Zalta and others have pursued this idea, which has given a new lease on life to (a chastened form of) logicism, the argument that the basic laws of arithmetic can be seen as theorems of logic. Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ... Friedrich Ludwig Gottlob Frege (8 November 1848, Wismar – 26 July 1925, Bad Kleinen) was a German mathematician who evolved into a logician and philosopher. ... Russells paradox (also known as Russells antinomy) is a paradox discovered by Bertrand Russell in 1901 which shows that the naive set theory of Frege is contradictory. ... Friedrich Ludwig Gottlob Frege (8 November 1848, Wismar – 26 July 1925, Bad Kleinen) was a German mathematician who evolved into a logician and philosopher. ... Edward N. Zalta is a Senior Research Scholar at the Center for the Study of Language and Information. ... Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic. ...


Shortly before his death, Boolos made a selection of his papers to be published in book form. The result is perhaps his most widely regarded work, his posthumous Logic, Logic, and Logic. The papers in this book treat of set theory, second-order logic and nonfirstorderizability, and plural quantification. There are also papers on Frege, Dedekind, Cantor, and Russell; and on various topics in logic and proof theory, including three papers on Gödel's Incompleteness Theorem. Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... In mathematical logic, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. ... In formal logic, nonfirstorderizability is the inability of an expression to be adequately captured in standard first-order logic. ... In mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular values. ... Friedrich Ludwig Gottlob Frege Friedrich Ludwig Gottlob Frege (November 8, 1848 - July 26, 1925) was a German mathematician, logician, and philosopher who is regarded as a founder of both modern mathematical logic and analytic philosophy. ... Richard Dedekind Julius Wilhelm Richard Dedekind (October 6, 1831 – February 12, 1916) was a German mathematician who did important work in abstract algebra and the foundations of the real numbers. ... Georg Cantor Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845, St. ... Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970), was a British philosopher, logician, and mathematician, working mostly in the 20th century. ... Proof theory, studied as a branch of mathematical logic, represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. ... In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proven by Kurt Gödel in 1931. ...


Plural quantification

Boolos argued that if one reads the second-order variables in monadic second-order logic as plural terms, this logic can be interpreted as making no ontological commitments to entities other than those over which the first-order variables range. This idea was later taken up by David Lewis, who used it in his Parts of Classes to derive a system in which Zermelo-Fraenkel set theory and the Peano axioms were all theorems. While Boolos is usually credited with plural quantification, Peter Simons (1982) has argued that Stanislaw Lesniewski was the first to employ it. In mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular values. ... In mathematical logic, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. ... In philosophy, ontology (from the Greek , genitive : of being (part. ... First-order predicate calculus or first-order logic (FOL) is a theory in symbolic logic that permits the formulation of quantified statements such as there is at least one X such that. ... The name David Lewis may refer to several people: David Lewis (philosopher) (1941-2001), an American-born philosopher famous for his theory of modal realism and his love for Australia. ... Zermelo-Fraenkel set theory, commonly abbreviated ZFC, is the most common form of axiomatic set theory, and as such is the most common foundation of mathematics. ... In mathematics, the Peano axioms (or Peano postulates) are a set of second-order axioms proposed by Giuseppe Peano which determine the theory of arithmetic. ... Peter Simons is a professor of philosophy at the University of Leeds and a director of the Franz Brentano Foundation. ... Stanisław Leśniewski (March 30, 1886–May 13, 1939) was a Polish mathematician, philosopher and logician. ...


Books by Boolos

  • 19nn (with Richard Jeffrey). Computability and Logic, 3rd ed. Cambridge Univ. Press.
  • 1995. The Logic of Provability. Cambridge Univ. Press.
  • 1999. Logic, Logic, and Logic, Richard Jeffrey and John Burgess, eds. Harvard Univ. Press.

Richard C. Jeffrey (5 August 1926 – 9 November 2002) was an American philosopher, logician, and probability theorist. ... Richard C. Jeffrey (5 August 1926 – 9 November 2002) was an American philosopher, logician, and probability theorist. ...

Reference

  • Peter Simons (1982) "On understanding Lesniewski," History and Philosophy of Logic.

  Results from FactBites:
 
George Boolos at AllExperts (660 words)
Boolos graduated from Princeton University in 1961 with a BA in mathematics.
Boolos was an authority on the 19th-century German mathematician and philosopher Gottlob Frege.
Boolos argued that if one reads the second-order variables in monadic second-order logic as plural terms, this logic can be interpreted as making no ontological commitments to entities other than those over which the first-order variables range.
Arché TWiki . Main . GeorgeBoolos (771 words)
George Boolos, "The justification of mathematical induction", PSA 1984 (1985), pp.
George Boolos, Giovanni Sambin, "Provability: The emergence of a mathematical modality", Studia Logica 50 (1991), pp.
George Boolos, "Provability in arithmetic and a schema of Grzegorczyk", Fundamenta Mathematicae 106 (1980), pp.
  More results at FactBites »

 
 

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