Gödel, Kurt

(1906–1978)

Mathematical logician. Born to German-speaking parents in Czechoslovakia, Gödel studied mathematics at the university of Vienna, where he also came into contact with the Vienna circle (see logical positivism ). His ground-breaking results of 1931 became his Habilitationsschrift (postdoctoral thesis) in 1932 (see Gödel's theorems ). In 1938 Gödel emigrated from Austria to America, and subsequently worked at the Institute for Advanced Studies at Princeton. Gödel's achievements are almost synonymous with those of mathematical logic in the middle years of the 20th century. They included the proof of the completeness of the first-order predicate calculus, and the ground-breaking results commonly referred to as Gödel's theorems . He also proved that no system can show its own consistency, effectively putting an end to Hilbert's programme, although Gentzen's proof that if transfinite induction is allowed the consistency of arithmetic can be demonstrated, afforded a kind of consolation to Hilbert himself. From 1943 onwards Gödel devoted himself largely to philosophy, including not only the philosophy of mathematics, but that of general relativity and cosmology. His philosophical views were diametrically opposed to those of the Vienna circle, and tended towards a Platonism that included abstract religious elements. In the following years Gödel was not free of eccentricities. Einstein tells the story of how Gödel called the game-theorist Morgenstern on the evening of his citizenship interview in the United States, to explain how he had discovered a logical problem in the Constitution: a non-standard model that would enable a dictatorship to be created consistently with it. After a period of ill-health, he effectively starved himself to death for fear that he was being poisoned. Gödel's extensive writings on the foundations of logic and mathematics are published in Kurt Gödel: Collected Works, vol. i, Publications 1929–1936 (1986), and vol. ii, Publications 1938–1974 (1990).