Reminiscences of the Vienna Circle and the Mathematical Colloquium Vienna Circle Collection

Karl Menger was born in Vienna on January 13, 1902, the only child of two gifted parents. His mother Hermione, nee Andermann (1870-1922), in addition to her musical abilities, wrote and published short stories and novelettes, while his father Carl (1840-1921) was the noted Austrian economist, one of the founders of marginal utility theory. A highly cultured man, and a liberal rationalist in the nine­ teenth century sense, the elder Menger had witnessed the defeat and humiliation of the old Austrian empire by Bismarck's Prussia, and the subsequent establishment under Prussian leadership of a militaristic, mystically nationalistic, state-capitalist German empire - in effect, the first modern "military-industrial complex. " These events helped frame in him a set of attitudes that he later transmitted to his son, and which included an appreciation of cultural attainments and tolerance and respect for cultural differences, com­ bined with a deep suspicion of rabid nationalism, particularly the German variety. Also a fascination with structure, whether artistic, scientific, philosophical, or theological, but a rejection of any aura of mysticism or mumbo-jumbo accompanying such structure. Thus the son remarked at least once that the archangels' chant that begins the Prolog im Himmel in Goethe's Faust was perhaps the most viii INTRODUCTION beautiful thing in the German language "but of course it doesn't mean anything.

Karl Menger (1902-1985), a pure mathematician of distinction, 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 (itself described in depth and with affection), and did so despite the political developments of the 20's and 30's, which depressed but did not silence him. He himself continued his work in the United States. The memoirs describe his membership of the Vienna Circle (the scientifically minded philosophers that gathered round Moritz Schlick) for whom he was an invaluable 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, founded by himself, whose Proceedings (still read) show it to have been a power-house of ideas. There are also valuable chapters on philosophy and mathematics in the Poland of the 20's and 30's and the U.S. of the 30's and 40's. The memoirs devote particular attention to Wittgenstein (with whose family Menger was independently acquainted) and to Godel, whom he was instrumental in bringing to America. The genesis of Menger's own writings on philosophy is also described and the work abounds in mathematical examples lucidly applied to that subject. This volume (which can now be put alongside the two by Menger already published in the Vienna Circle Collection) gives an unequalled impression of the fruitful interdisciplinarity of the tradition to which he partly belonged and partly created. It testifies both to Menger's power to inspire and to the critical eye he always turned on even the philosophers he most approved of. A brief account of his life is given in an introduction by the Editors (all of whom knew him personally) and his important contribution to t

Karl Menger was born in Vienna on January 13, 1902, the only child of two gifted parents. His mother Hermione, nee Andermann (1870-1922), in addition to her musical abilities, wrote and published short stories and novelettes, while his father Carl (1840-1921) was the noted Austrian economist, one of the founders of marginal utility theory. A highly cultured man, and a liberal rationalist in the nineƯ teenth century sense, the elder Menger had witnessed the defeat and humiliation of the old Austrian empire by Bismarck's Prussia, and the subsequent establishment under Prussian leadership of a militaristic, mystically nationalistic, state-capitalist German empire - in effect, the first modern "military-industrial complex." These events helped frame in him a set of attitudes that he later transmitted to his son, and which included an appreciation of cultural attainments and tolerance and respect for cultural differences, comƯ bined with a deep suspicion of rabid nationalism, particularly the German variety. Also a fascination with structure, whether artistic, scientific, philosophical, or theological, but a rejection of any aura of mysticism or mumbo-jumbo accompanying such structure. Thus the son remarked at least once that the archangels' chant that begins the Prolog im Himmel in Goethe's Faust was perhaps the most viii INTRODUCTION beautiful thing in the German language "but of course it doesn't mean anything Front Matter....Pages i-xxvi The Historical Background....Pages 1-7 The Cultural Background....Pages 8-17 The Philosophical Atmosphere in Vienna....Pages 18-37 Why the Circle Invited me. The Theory of Curves and Dimension Theory....Pages 38-53 Vignettes of the Members of the Circle in 1927....Pages 54-73 Reminiscences of the Wittgenstein Family....Pages 74-82 Ludwig Wittgenstein’s Austrian Dictionary....Pages 83-88 Wittgenstein’s Tractatus and the Early Circle....Pages 89-103 On the Communication of Metaphysical Ideas. Wittgenstein’s Ontology....Pages 104-128 Wittgenstein, Brouwer, and the Circle....Pages 129-139 Discussions in the Circle 1927–30....Pages 140-142 Poland and the Vienna Circle....Pages 143-157 The United States 1930–31....Pages 158-173 Discussions in The Circle 1931–34....Pages 174-177 The Circle on Ethics....Pages 178-193 Moritz Schlick’s Final Years....Pages 194-199 Memories of Kurt Gödel....Pages 200-236 Back Matter....Pages 237-244