This article is not about George Boole, another mathematical logician.

George Stephen Boolos (September 4, 1940 - May 27, 1996) was a philosopher and a mathematical logician. He was a professor of linguistics and philosophy at the Massachusetts Institute of Technology.

Life

Boolos was born in New York City in 1940. He attended Princeton University, graduating in 1961 with a Bachelor's degree in mathematics. He attended Oxford University where he earned a B.Phil (1963). He held the first PhD in philosophy ever given at Massachusetts Institute of Technology in 1966. He taught at Columbia University for three years before returning to MIT in 1969.

He was an expert on puzzles of all kinds. In 1993 he reached the London Regional Final of the Times crossword competition, where his score was one of the highest recorded by an American.

He was a charismatic speaker, well-known for his clarity and wit. He on one occasion delivered a lecture, since collected in his Logic, Logic, and Logic, which included an account of Gödel's second incompleteness theorem, entirely in words of one syllable. According to another story, 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?" Unhesitating, Boolos replied, "It's part of it".

Work

He was one of the founders of provability logic, in which modal logic — the logic of necessity and possibility — is applied to the theory of mathematical proof. One of his books, The Logic of Provability, treated that topic. He also wrote a brilliant expository book, Computability and Logic, jointly with Richard Jeffrey.

He was an authority on the 19th-century German mathematician and philosopher Gottlob Frege. His work contributed to a re-evaluation of Frege's achievements, especially his attempt to show that the basic laws of arithmetic are themselves principles of logic (see neo-logicism).

Perhaps his most widely regarded work is Logic, Logic, and Logic, a collection of papers on logic, mostly chosen by him shortly before his death. The book includes papers on set theory, second-order logic and nonfirstorderizability, and plural quantifiers, on Frege, Dedekind, Cantor, and Russell; and on various topics in logic and proof theory, including three papers on the Gödel theorems.

Plural quantification

Boolos' idea was that monadic second-order logic can be interpreted as having no ontological commitments to entities other than those the first-order variables range over by thinking of second-order variables as plural terms.

This idea was later taken up by David Lewis, who used it to justify a new axiomatization of set theory in Parts of Classes.

Boolos is usually credited with the idea. However Peter Simons, ("On understanding Lesniewski,") in History and Philosophy of Logic, (1982), has argued that it originated with Stanislaw Lesniewski.