Unexplored Dimensions: Karl Mengeron Economics and Philosophy (1923–1938): Volume 12

Karl Menger (1902–1985) was the mathematician son of the famous economist Carl Menger. He was professor of geometry at the University of Vienna from 1927 to 1938. During that period, which was crucial from a historical and philosophical point of view, he joined the Vienna Circle and founded his Mathematical Colloquium. Menger's memoirs of those Viennese years are recollected in his Reminiscences of the Vienna Circle, appeared in 1994 as the twentieth volume of the Vienna Circle Collection.

From passages quoted in Giandomenica Becchio's excellent introduction, it will be clear that I found Karl Menger an ideal subject when I was a series editor (of the Vienna Circle Collection) and he a contributor. He produced splendid copy, did his own translations, found his own references and was altogether easy to deal with – when he had his own way, of course, but that was usually the best course in any case. Alas he died before he and we could assemble a full set of reminiscences. The volume we brought out is still in demand and was greeted with enthusiasm by those interested in the intellectual history of its period. All the more it is a joy to learn that further papers of this nature have now been made available for publication.

For better understanding the connections between the Viennese circles in which Menger was involved, it is necessary to make some remarks on the Viennese context where they developed. Since the end of the 19th century up to the interwar period, Vienna was a very lively city from a cultural point of view, the birthplace of modernism (Janik & Toulmin, 1973). In the age of the late Habsburg monarchy as well as in the post-First War ‘Red Vienna’, the intellectual, scientific and artistic life of the Austrian capital was so fervent that those years are recalled by historians as the Viennese Enlightenment, the gay apocalypse and the golden autumn: ‘two generations were enough to cover the whole period. The economist Carl Menger (1841–1920) shaped the beginning, and his son, the mathematician Karl Menger (1902–1985), witnessed the end’ (Golland & Sigmund, 2000, p. 34). After the First World War, from an economic point of view, a high inflation overwhelmed the country; while from a political point of view, ‘the new Austria was fragmented and labyrinthine’ (Leonard, 1998, p. 6): the Christian socialists were the conservative part of the society, but one third of citizens supported the new social-democratic party, which had the majority in Vienna.

Menger disagreed with this view for various reasons. Also, the subjective expectation is infinite. There are many cases where man's behaviour fails to conform to mathematical expectations: games in which a player can win only one very large amount with a very small probability or games offering a single moderate amount with a very high probability. Furthermore, we can always find a sequence of payoffs x1, x2, x3,…, which yield infinite expected value, and then propose, say, that u(xn)=2ⁿ, so that expected utility is also infinite. Menger therefore proposed that utility must also be bounded above for paradoxes of this type to be resolved.

Before Menger's drafts are presented, an explanation of their main similarities and differences is required.¹

[The following pages are made up of those unprinted parts of chapter three of Menger's Reminiscences which deals with the philosophical background of the Vienna Circle. Some overlaps and reproductions are inevitable for the coherence of the discourse.]Like many continental cities, Vienna had a large number of coffee houses where people sat reading newspapers or meeting acquaintances and carrying on conversations. The productive coffee house discussions in Vienna were directed more towards belles lettres than in other cities and less towards logic and mathematics. For my part I untypically disliked the atmosphere of those places. But this is not the main reason why I cannot report a great deal that has come out of them. For if there had been much I should have heard about it.

Before talking about the Vienna Circle, I wish to sketch the earlier history of philosophy in Austria insofar as it is connected with ideas of the circle – by contrast or by similarity – but without any claim as to completeness of the list of authors considered or the work described.¹

The Vienna Circle and the work of Brentano, Meinong and Husserl were only indirectly related and mainly by opposition. The present chapter is devoted to Mach, Boltzmann and Mauthner, three precursors of the Circle, though quite unequally treated by the group. Mach was extolled, while the other two were practically ignored.

[In Menger's Reminiscences this part is Chapter Five (‘Vignettes of the members of the Circle in 1927’), where Moritz Schlick is described as ‘an extremely refined, somewhat introverted man’; Hans Hahn, ‘a strong, extroverted, highly articulate person who always spoke with a loud voice’; Olga Hahn Neurath, ‘always smoking a big cigar’; Otto Neurath, ‘a man of immense energy and curiosity, very fast in grasping new ideas, through an often distorting lens of socialist philosophy’; Rudolf Carnap, ‘systematic, sometimes to the point of pedantry…a truly liberal and completely tolerant man’; Victor Kraft ‘[who] like Schlick, Feigl and myself, by no means shared all the political ideas and ideals of Neurath’; Friedrich Waissman, ‘a very clear expositor [who] unfortunately dragged out his studies [of mathematics and philosophy] at the University’; Herbert Feigl, ‘[who] did probably more than anyone else to make some of the Viennese ideas known in America’; Theodor Radakovic, ‘a student of Hahn's…too shy to take part in the discussion of the Circle, although he attended the meetings regularly’; Edgar Zilsel, ‘a militant leftist [who] wanted to be considered only as close to, and not as a member of, the Circle’; and Felix Kaufmann, ‘a philosopher of law, an ardent phenomenologist, the only participant with a true sense of humour’ (Menger, 1994, pp. 55–68). These following parts are those unpublished].

[Part II in Menger's drafts is divided into four chapters. The first is mainly taken up with Menger's description of L. E. J. Brouwer, the Dutch mathematician with whom Menger worked as assistant during his stay in Amsterdam in the mid-1920s; none of this part is included in Menger's Reminiscences, although the book makes several references to Brouwer. Moreover, Menger's Selected Papers (Menger, 1979) contain a long and very detailed chapter, ‘My memories of L. E. J. Brouwer’, written in 1978, and therefore at the time of Menger's drafts. The second chapter deals with Menger's contacts within the Vienna Circle after his return from Holland (1927) until his sabbatical years spent in the USA (1930–31). In Menger's Reminiscences, Chapter Four (mainly devoted to his theory of curve and dimension) and the two-page Chapter Eleven cover that period, as do some passages in Menger's Introduction to Hahn's Philosophical Papers (Menger, 1980). The third chapter of the drafts is concerned with Menger's visits to the USA. Chapter Thirteen in Reminiscences deals with this topic, but it omits these following parts. Finally, the fourth chapter of the drafts describes Menger's years in Vienna between 1931 and 1938, when his Colloquium grew increasingly important. His disagreement with philosophical developments in the Circle became very evident, and the political situation in Austria was then lapsing into the fascist darkness; Menger's Reminiscences, which end with Schlick's death in 1936, wholly omit these parts].

In 1923, an issue entered the discussion between Schreier² and myself, though hardly anyone else in Vienna was interested in it at that time. Historically, the topic was connected with the question of intuition or Wesensschau, but substantially, in my opinion, the two were quite distinct. Elaborating on ideas of the 19th century algebraist L. Kronecker and eloquently supported by Weyl,³ the Dutch mathematician L. E. J. Brouwer developed what he called intuitionistic mathematics, the mathematical controversy centred on existential propositions. But those who closely associated intuitionism in mathematics with the intuition in Husserl's pure phenomenology or Bergson's metaphysics were misled by the similarity of the two words. Whatever, if anything, Brouwer's reconstruction of mathematics and the phenomenology in Husserl's Ideas had in common, they certainly had opposite effects: Husserl claimed for his Wesensschau (and Bergson for his intuition) insights that empiricists such as Schilck denied or regarded as empty words. Brouwer, to the contrary, rejected statements that everyone else claimed to be solid parts of mathematics, and he denied or regarded as empty words theorems proved by men such as Hilbert.

§ 1. My presentation to the Circle. When I presented my theory to the Circle, I found a mixed reception. Schlick, however, slightly shook his head, the mock-smile appeared on his face, and he tried to exchange glances. Only Waismann responded. Kaufmann was too loyal a friend to openly go against me even though he strongly felt that I was wrong. And Carnap was in deep thought.

[Chapter Thirteen of Menger's Reminiscences deals with Menger's visit to the United States in the academic year1930/31, but it is restricted to Menger's stay at Harvard, where he spent the fall semester and lectured on dimension theory and metric geometry. At Cambridge, Menger met, among others, ‘the outstanding mathematician’ G.D. Birkhoff; the philosopher H. M. Sheffer, who ‘had discovered in 1913 that all particles of the calculus of propositions can be expressed in terms of a single one’, ‘extensive[ly] used’ in Wittgenstein's Tractatus ‘without mentioning its author’; P. Weiss, N. Wiener and J. Schumpeter, the latter being a visiting scholar as well. But the person who most impressed Menger was P. Bridgman, who ‘appeared to him as a modern reincarnation of Mach’(Menger, 1994, pp. 158–173). The ‘Harvard sections’ of Menger's Reminiscences are comprised between paragraphs 14 and 15 of the present publication and are not reprinted].

§ 1. The first piece of news about Vienna that reached me in September 1931, after arriving in Genoa, was quite charming; I mention it and since many later recollections about Vienna that I shall have to record are quite the opposite of charming, Austrians have always been fond of swallows. There was a superstition, especially among peasants, that a house was safe from fire if they had built a nest under its roof. Every year, the Viennese smiled when the first swallows returned from the South – an event always recorded in the newspaper because it heralded the advent of summer, and when the swallows were leaving, everyone was a bit sad, because another summer was gone. In September 1931, however, something unprecedented happened. A sudden, premature frost caught the poor birds on their flight to the South. By the hundreds they fell exhausted to the ground, unable to continue their journey. But, as the newspapers reported, the Austrians chartered airplanes to take their little friends to Italy.

§ 1. In conclusion, I comment on two features of my mental make-up of which I have been aware since my earliest youth. They concern my memory. Compared to most people of my acquaintance, I have a memory that normally is at most average in breadth and intensity – probably less than average. But during an experience that I feel may be potentially useful to me I resolve to remember what I am seeing or hearing or understanding and then this experience remains engraved in my mind with complete accuracy for decades, perhaps to the end of my life. I don't know how far I could extend this faculty, which I have never tried to abuse in the sense of trying to remember too much. Even so, occasionally trivia pop up with perfect clarity which, however, for some long forgotten reason, may at one time well have seemed to me worth remembering. But all in all I am well satisfied with my past selections. Most of what I resolved to remember I later actually found useful. This usefulness is enhanced by the second feature of my memory. Interesting reminiscences tend to return spontaneously at the very moment when they are relevant, that is, when they are connected with a current experience or the subject of my momentary thinking. ‘Connected’ here is meant in the broadest sense: in space and/or time, by similarity contrast, by analogy or by any of various other relationships. My memory thus is, on the one hand, strongly regulated as to its content and, on the other hand, largely spontaneous as to its reproductions. I don’t know how common these features are, but I suspect that the second is rarer than the first.