Vienna Circle Institute Library Mathematical Logic in

This book is a record of a seminar on mathematical logic Kurt Gödel and Hans Hahn held in Vienna in 1931-32. The book also adds an important aspect to the intellectual history of Vienna, as both Gödel and Hahn were members of the Vienna Circle group of philosophers and scientists. Kurt Gödel (1906-1978) created a sensation by his incompleteness theorems of 1931, now seen as one of the high points of 20th century mathematics and science more generally. His professor at the University of Vienna Hans Hahn decided to organize a seminar on mathematical logic for the academic year 1931/32, with Gödel in charge for most of the practical side. The seminar proceedings, given in English translation in this book, are a unique witness of the state of research in logic and foundations of mathematics right after Gödel's theorems. They also add an important aspect to the intellectual history of these times in Vienna, both Hahn and Gödel having been members of the Vienna Circle. One fourth of the seminars were dedicated to Gödel's results: First the doctoral thesis about the completeness of predicate logic, then incompleteness, and last his results on intuitionistic logic. The seminars explain all these results in detail, in contrast to Gödel's publications of the time that often were quite laconic and extremely short. This book also contains Gödel's trial lecture on intuitionistic logic held in Vienna in 1933. The manuscript, recently found among the Gödel papers kept in Princeton, is preserved in Gödel's forgotten German shorthand and published here in an English translation.