Kurt Gödel (1906–1978)
Undoubtedly one of the greatest logicians of the twentieth-century, Kurt Gödel has been hailed as the most important philosopher of logic since Aristotle for his celebrated incompleteness theorems. These theorems, born out of an engagement with the Zermelo-Frankel axiomatization of set theory and controversies surrounding the axiom of choice, proved that 1) if the system is consistent, it cannot be complete; and 2) the consistency of the axioms cannot be proved within the system. Gödel’s theorems were the capstone of a half-century of effort, beginning with Frege, to establish logically the foundations of mathematics.
Born in Brno, Moravia (Austria-Hungary) Gödel excelled as a student of mathematics. He followed courses by David Hilbert and consulted Russell and Whitehead’s Principia Mathematica, engagement with which led to the publication of his incompleteness theorems in Vienna in 1931, shortly after the completion of his own doctoral work in 1930. Due to his personal closeness to Jewish members of the Vienna Circle, Gödel sought escape from Europe following the annexation of Austria-Hungary by Nazi Germany in 1938. After a trans-Siberian and transpacific voyage, Gödel crossed the North American continent by train, arriving in Princeton, New Jersey in the spring of 1940. Resuming contacts he had made there in the early 1930s, Gödel would remain affiliated with the Institute of Advanced Study at Princeton for the rest of his life. He was a particularly close associate of Albert Einstein’s, who was unreserved in his esteem for Gödel and once said that he came to the IAS not to pursue his own research, but for his walks with Gödel. A lifelong sufferer of mental disturbances, Gödel experienced severe bouts of depression. In his later years, he developed an obsessive fear that his food was poisoned and would only eat meals prepared by his wife. When she was hospitalized for an extended period in 1977, Gödel refused to eat, eventually starving himself to death.
In the Cahiers pour l’Analyse
|Kurt Gödel, ‘La logique mathématique de Russell’, CpA 10.5||[HTML]||[PDF]||[SYN]|
|Alain Badiou, ‘Marque et manque: à propos du zéro’, CpA 10.8||[HTML]||[PDF]||[SYN]|
- ‘Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I’. Monatshefte für Mathematik und Physik, 1931, 38: 173-98. [A pdf of a translation by Martin Hirzel is available at: http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf]
- ‘The completeness of the axioms of the functional calculus of logic’ (1930a) and ‘Some metamathematical results on completeness and consistency’, ‘On formally undecidable propositions of Principia mathematica and related systems I’, and ‘On completeness and consistency’ (1930b, 1931, 1931a). In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879-1931, ed. Jean van Heijenoort. Cambridge, MA: Harvard University Press, 1967, 582-617.
- The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory. Princeton: Princeton University Press, 1940.