Abstract

At once a distinguished mathematician and an important figure in the Vienna Circle, Hans Hahn conducted a seminar in 1924-25 on the Principia Mathematica to "a very large audience" of mathematicians and philosophers. Translated from the German and edited by Brian McGuinness, with a biographical introduction by Karl Menger, the present volume consists largely of papers in the philosophy of mathematics covering the years 1929-34. "Our adoption of Russell’s position," writes Hahn, "may cause some surprise in Germany where all ears are tuned, to the controversy between... Hilbert and Brouwer." It turns out, however, that Wittgenstein has made the decisive move: mathematics consists of tautologies, Russell having "shown" how to get by without sets.