Philosophy Index

Kurt Gödel

Kurt Gödel (1906–1978) was an Austrian-American mathematician and philosopher, and one of the most important logicians in history.

Incompleteness Theorems

Gödel is perhaps best known for his two incompleteness theorems which demonstrate the limits of existing systems of logic and mathematics.

The first theorem states that any sound axiomatic system of number theory is incomplete — that is, there are true things that can be expressed in the system but are unprovable (or undecidable).

The second theorem states that any theory sophisticated enough to formally express its own soundness (i.e., consistency) within its system can do so if and only if it is unsound (i.e., inconsistent).

Selected Works

  • The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory (1940)

Vitals

Name: Kurt Gödel
Born: April 28, 1906
Died: January 14, 1978
Awards: Albert Einstein Award (1951)