Empiricism, Logic and Mathematics

The role Hans Hahn played in the Vienna Circle has not always been sufficiently appreciated. It was important in several ways. In the ftrst place, Hahn belonged to the trio of the original planners of the Circle. As students at the University of Vienna and throughout the fIrst decade of this century, he and his friends, Philipp Frank and Otto Neurath, met more or less regularly to discuss philosophical questions. When Hahn accepted his fIrSt professorial position, at the University of Czernowitz in the north­ east of the Austrian empire, and the paths of the three friends parted, they decided to continue such informal discussions at some future time - perhaps in a somewhat larger group and with the cooperation of a philosopher from the university. Various events delayed the execution of the project. Drafted into the Austrian army during the first world war" Hahn was wounded on the Italian front. Toward the end of the war he accepted an offer from the University of Bonn extended in recognition of his remarkable 1 mathematical achievements. He remained in Bonn until the spring of 1921 when he returm:d to Vienna and a chair of mathe­ matics at his alma mater. There, in 1922, the Mach-Boltzmann professorship for the philosophy of the inductive sciences became vacant by the death of Adolf Stohr; and Hahn saw a chance to realize his and his friends' old plan.

Hans Hahn (1879-1934) war einer der bedeutendsten Mathematiker des 20. Jahrhunderts. Er hat zahlreiche Gebiete der Analysis entscheidend geprägt und zählt zu den Vätern der Funktionalanalysis. Aber auch die Maßtheorie und die harmonische Analyse wurden von ihm nachhaltig angeregt, und die allgemeine Topologie verdankt ihm wesentliche Impulse. Darüber hinaus hat Hahn, als einer der Gründer des Wiener Kreises, auch die Philosophie dieses Jahrhunderts stark beeinflusst. Sowohl Kurt Gödel als auch Karl Popper, von dem die Einleitung zu diesem Werk stammt, waren seine Schüler. Der erste Band der gesammelten mathematischen und philosophischen Werke von Hans Hahn enthält dessen grundlegende Beiträge zur Funktionalanalysis, Topologie (raumfüllende Kurven) und Algebra (geordnete Gruppen), mit Kommentaren der Professoren Heuser, Sagan und Fuchs.

I Superfluous Entities, or Occam's Razor (1930).- II The Significance of the Scientific World View, Especially for Mathematics and Physics (1930).- III Discussion about the Foundations of Mathematics (1930).- IV Empiricism, Mathematics, and Logic (1929).- V Reflections on Max Planck's Positivismus und reale Aussenwelt (?1931).- VI Review of Alfred Pringsheim, Vorlesungen über Zahlen- und Funktionenlehre, Vol. I, parts I and II, Leipzig and Berlin 1916 (1919).- VII The Crisis in Intuition (1933).- VIII Does the Infinite exist? (1934).- Bibliography of the Works of H. Hahn.