George Boolos
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- This article is not about George Boole, another mathematical logician.
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.
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[edit] 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.
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".
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.
[edit] Work
Kurt Gödel 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 Gödel 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.
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.
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.
[edit] 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.
[edit] 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.
[edit] Reference
- Peter Simons (1982) "On understanding Lesniewski," History and Philosophy of Logic.
