Collected Works

Collected Works #5

by Kurt Gödel, Solomon Feferman (Editor), Warren Goldfarb (Editor)

Kurt Godel was one of the most outstanding logicians of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Godel's writings. The first three volumes, already published consists of the papers and essays of Godel. The final two volumes of the set deal with Godel's correspondence with his contemporary mathematicians, this fifth volume consists of material from correspondents from H-Z.

Genres: Philosophy, Logic

690 pages, Hardcover

First published June 5, 2003

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.

Reviews

[Nikita Danilov]

In the world I would like to live in, they would make movies based on books like this.