Kurt Gödel: Collected Works: Selected Correspondence, A-Z Volumes IV and V

by Kurt Gödel (Editor), Charles Parsons

Kurt Godel was one of the most outstanding logicians of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computation theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory, permitting time travel into the past. These books are the fourth and fifth part of a five-volume set, which is the first to make available all of Godel's writings in the one place. The first three volumes have received acclaim, and consist of the papers and essays of Godel. The final two volumes of the set deal with Godel's correspondence with his contemporary mathematicians. The fourth volume consists of material from correspondents from A-G, with explanatory and introductory material. The final volume consists of the remaining correspondence from H-Z. The Collected Works of Kurt Godel is designed to be useful and accessible to a wide audience without sacrificing scientific or historical accuracy. They are the only complete editions available in English, and are essential to students and professionals in logic, mathematics, philosophy, history of science and computer science as well as those curious about one of the great minds of the twentieth century.

1374 pages, Hardcover

First published January 13, 2005

About the author

Kurt Gödel was an Austrian-American logician, mathematician and philosopher. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N. Whitehead and David Hilbert, were pioneering the use of logic and set theory to understand the foundations of mathematics.

Gödel is best known for his two incompleteness theorems, published in 1931 when he was 25 years of age, one year after finishing his doctorate at the University of Vienna. The more famous incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.

He also showed that the continuum hypothesis cannot be disproved from the accepted axioms of set theory, if those axioms are consistent. He made important contributions to proof theory by clarifying the connections between classical logic, intuitionistic logic, and modal logic.