Reminiscences of the Vienna Circle and the Mathematical Colloquium

Karl Menger (1902-1985), a pure mathematician, also took an active interest in both philosophy and economics. In this memoir, which he was composing at the time of his death, he relates how all these subjects developed and flourished against the Viennese background (described in depth), and did so despite the political developments of the 20s and 30s, which depressed but did not silence him. He continued his work in the United States. The memoir describes his membership of the Vienna Circle (the scientifically minded philosophers that gathered around Moritz Schlick) for whom he was an intermediary, bringing them into contact with Brouwer's intuitionism, with the work of the Polish logicians, especially that of Tarski, but more generally with rigorous mathematical thinking. Indeed, the other Viennese group described here is the Mathematical Colloquium, which he founded, whose Proceedings show it to have been a powerhouse of ideas. There are also chapters on philosophy and mathematics in the Poland of the 20s and 30s and the United States of the 30s and 40s.The memoir devotes particular attention to Wittgenstein (with whose family Menger was acquainted) and to Goedel, whom he was instrumental in bringing to America. The genesis of Menger's own writings on philosophy is also described and the work features many mathematical examples applied to that subject. This volume gives an impression of the interdisciplinarity of the tradition to which he partly belonged and partly created. A brief account of his life is given in an introduction by the editors (all of whom knew him personally), and his contribution to the social sciences - only touched on in the text - is elucidated by Professor Lionello Punzo.