# Karl Menger on Hans Hahn

Hans Hahn wrote eight philosophical papers on Empiricism, logic, and mathematics between 1919 and 1934. An English translation by Hans Kaal of these essays was published in 1980 by the D Reidel Publishing Company. Mario Bunge writes:-
The eight philosophical papers collected in this volume were written by a distinguished analyst who, together with Otto Neurath, Philipp Frank and Moritz Schlick, founded the Vienna Circle. They were originally published in German between 1919 and 1934, and appear here translated into English for the first time. The essays are nontechnical models of clarity.... The paper on the foundations of mathematics was strongly influenced by Wittgenstein's "Tractatus", in particular the view that languages and theories mirror experience. However, Hahn had no use for Wittgenstein's later philosophy. Menger's introduction exhibits the historical context and tells about Hahn's interest in parapsychology. Altogether an indispensable work for students in the history and philosophy of mathematics.
Below we give an extract from Karl Menger's Introduction which is on Hans Hahn and the Vienna Circle:-

### Introduction

The role Hans Hahn played in the Vienna Circle has not always been sufficiently appreciated. It was important in several ways.

In the first 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 northeast 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 mathematical achievements. He remained in Bonn until the spring of 1921 when he returned to Vienna and a chair of mathematics 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 Stöhr; and Hahn saw a chance to realize his and his friends' old plan. It was mainly through Hahn's influence that the chair was offered to Moritz Schlick, then in Kiel. Soon after his arrival in Vienna, Schlick began to arrange discussions for a small invited group, with Hahn and Neurath as the first principal participants. Frank was in Prague where he had gone before the war as the successor of Einstein; however, he visited Vienna at least twice a year. Then there was Victor Kraft and, at Hahn's suggestion, the geometer, Kurt Reidemeister, who in 1923 came to Vienna for about two years. Soon after he left, Rudolf Carnap arrived and joined the group to which Schlick had also brought promising students of philosophy working in his seminars, among them Herbert Feigl and Friedrich Waismann. Thus, ultimately through Hahn's efforts, his, Neurath's and Frank's old plan had become a reality. "Man kann," Frank wrote in his obituary of Hahn in Erkenntnis, Vol. 4, "Hahn als den eigentlichen Begründer des Wiener Kreises ansehen." ("Hahn may be regarded as the real founder of the Vienna Circle.")

Secondly, it was Hahn who directed the interest of the Circle toward logic. Schlick, a student of Planck's and admirer of Einstein, had until then been mainly interested in the philosophy of nature and in epistemology up to (but not beyond) studies of the axiomatic method. Otto Neurath and Olga Hahn (the blind sister of Hans, later Otto's wife) had written - individually and jointly - papers on Boolean algebra in the years 1909 and 1910; but thereafter and especially during the war Neurath's interests turned again to economics, sociology and history, while Frank was engrossed in the philosophy of physics and the study of causality. Carnap, having been a student of Frege's, was well-versed in logic, but was mainly concerned with the philosophy of science at the time he moved to Vienna. Hahn, however, right after his return, began an intense study of symbolic logic with an eye to related philosophical problems. In 1922 he offered a course on Boolean algebra. During the year 1924/ 25 he conducted a memorable seminar on the Principia Mathematica of Whitehead-Russell in which, after some introductory lectures, he let advanced students, young Ph.D.s and lecturers report on the contents of the book, chapter by chapter. This seminar had a very large audience and was of great influence not only on the development of many Viennese students of mathematics and philosophy but also on the trend of the discussions in the Circle.

Thirdly, until his untimely death in 1934, Hahn greatly contributed to the Circle as a prominent participant in the discussions. Since he was carrying out very interesting mathematical research in addition to his extensive activity at the University he unfortunately found little time to publish many of the ideas he proposed in the meetings. But his penetrating criticism, the clarity of his ideas and his skill in presenting them greatly impressed everyone, and often influenced Neurath and Carnap as well as Schlick and Waismann. "One can say," Frank wrote in the obituary already quoted, "that in a certain sense Hahn was always a centre of the group. He always represented its central ideas without entering into differences of opinion on side issues. No one knew as well as he how to present those leading ideas in such a simple as well as thorough way, in such a logical as well as suggestive form."

While Hahn's mathematical knowledge was unusually extensive, his familiarity with traditional philosophy was more limited. His favourite author was Hume, whose works, as he once told me, he found not only intellectually delightful but also morally uplifting. Furthermore he greatly admired Leibniz to whose identitas indiscernibilium he gave much thought, and Bolzano, whose Paradoxes of Infinity he edited. Kant, on the other hand, he strongly disliked because of the changes - from chapter to chapter and often from sentence to sentence - of the meaning of the terms used in his writings. Of the more modem philosophers Hahn favoured Ernst Mach; and during the early 1920's he developed a great admiration for the works of Bertrand Russell. He reviewed some of them in the Monatshefte für Mathematik und Physik. In one of these reviews Hahn suggested that one day Russell might well be regarded as the most important philosopher of his time a statement remarkable at a period when few philosophers in Central Europe knew or even cared to know Russell's writings.

In the early 1930's, after Carnap had gone to Prague, a controversy about a related topic arose in the Circle when Waismann proclaimed that one could not speak about language. Hahn took strong exception to this view. Why should one not - if perhaps in a higher-level language - speak about language? To which Waismann replied essentially that this would not fit into the texture of Wittgenstein's latest ideas. The debate recurred several times up to Hahn's death: Hahn asking, "Why?" and Waismann answering, in the last analysis, "Because". Schlick sided with Waismann, Neurath with Hahn. Kurt Gödel and I, though reticent in most debates in the Circle, strongly supported Hahn in this one.

Another topic that Hahn raised in the Circle was a view on history that he had developed - his contribution to the Neurath-Carnap program of Unity of Science. Despite great reservations that I had with regard to the general program I felt that Hahn's interesting and, as far as I knew, original idea was quite independent of those generalities. Its starting point was Poincaré's remark that physicists are not interested in historical propositions such as Caesar crossed the Rubicon because they yield no predictions: Caesar will not cross the Rubicon again. Hahn took issue with a part of Poincaré's remark. He pointed out that assertions about Caesar are based on countless old manuscripts, paintings, documents, excavations, coins and the like; and that the core of the proposition, which is capable of further verification or of falsification, actually is a prediction, namely, the prediction that all old manuscripts, paintings, documents etc. to be found in the future will be consistent with the present assertions.

On several occasions, the mathematicians in the Circle helped the philosophers by providing them with technical information - often concerning their own results. I remember, for instance, a discussion about inductive processes in physics. In order to obtain formulae describing actual as well as potential observations, Carnap and Schlick suggested interpolation - the passing of a polynomial through the finite number of observed data. Hahn convinced them of the impracticability of this idea by reporting results of a paper of his. If one starts with a given continuous curve, $C$, the following phenomenon may occur: One begins with a finite set, $S_{1}$, of points on $C$ and interpolates, thereby obtaining a curve, $C_{1}$; then one adds a few points to $S$, obtaining a set $S_{2}$ and by interpolation a curve $C_{2}$ ; and so on. However, the curves $C_{1} , C_{2} , ...$ need not approach $C$. For between the points of the set $S_{n}$ , where $C_{n}$ and $C$ agree, the curve $C_{n}$ may swing far away from $C$; and with increasing $n$, more and more oscillations with appreciable amplitudes may accumulate and prevent the curves $C_{n} , C_{n+1} , ...$ from approaching any continuous curve. A fortiori, the same may occur in the more realistic situation where no curve $C$ is given at the outset, but only a (potentially infinite) set of points representing observed data.

Carnap and Neurath as well as Schlick and Waismann often gratefully acknowledged Hahn's role. So, during Schlick's absence on a visit to the United States in 1929, Frank asked Hahn to deliver the inaugural address at the First Congress of the Epistemology of Science (in Prague), while Neurath and Carnap asked him to be the principal signer of the pamphlet Wissenschaftliche Weltauffassung.

Hahn's address formulated with masterful succinctness and precision a kind of creed for logical positivism and the scientific Weltanschauung. It contrasted them with mysticism, metaphysics and various other tendencies then prevailing in philosophy (especially in German philosophy), and also delimited them vis-à-vis pure empiricism and rationalism.

The pamphlet, whose genesis I had occasion to observe, was mainly written by Neurath; Carnap cooperated to some extent; Hahn received the final draft. It was well written and informative in various ways. Yet Schlick, to whom the booklet was dedicated, was not altogether pleased with it when he received it upon his return to Vienna. It lacked the depth and the precision of Hahn's address to the Prague congress. Also, it introduced political views and tendencies, which Neurath never completely separated from epistemological insights, whereas Schlick always insisted on the strict separation of the latter from value judgments of any kind. Moreover, some of those views were, if only in passing, presented as common to all members of the highly individualistic group, while some members, including Schlick himself, did not fully share them.

In his later years, Hahn spent a minor but appreciable part of his free time on parapsychological studies. Many friends of his and admirers of his intellect found this interest of his very odd and wondered how the topic of parapsychology could even be broached in a group as strictly scientific in its orientation as the Vienna Circle. A partial explanation lies in the way Hahn's interest originated. In the first years after World War I a new influx of mediums had appeared in Vienna. They were viewed by the intelligentsia with the utmost scepticism. Finally, one day in the early 1920s, the newspapers claimed that two professors of physics at the University of Vienna, Stephan Meyer and Karl Przibram, had exposed the entire spiritualistic swindle. What had happened, the newspapers elaborated, was that Professor Meyer had invited many people to his house for a séance. The guests sitting in a circle and holding hands in a dark room, had clearly observed the phenomenon of levitation - more specifically, a figure in white rising several feet into the air. But at that moment the host unexpectedly turned on the lights and everyone could see that the apparition was none other than the tall professor Przibram who, in the dark, had managed to cover himself with a bed sheet and to climb on a chair. In the midst of general laughter the two physicists claimed that they had produced a levitation and exposed the mediums.

It goes without saying that the parapsychological groups were outraged; and for once, in a reversal of the ordinary situation, the mediums called all scientists swindlers. But there was also great indignation in the intellectual community; and a group including besides Schlick and Hahn the eminent neurophysiologist and physician Julius von Wagner-Jauregg, the physicist Hans Thirring and a number of others (most of them scientists) formed a committee for the serious investigation of mediums. Very soon, however, members began to drop out: first Wagner-Jauregg; soon after him Schlick. By 1927 apart from non-scientists only Hahn and Thirring were left in the group. They were, as they told me, not convinced that any of the phenomena produced by the mediums were genuine; but they were even less sure that all of them were not. They believed, rather, that some parapsychological claims might well be justified; and that certainly the matter warranted further serious investigation.

Hahn devoted a few interesting public lectures to the subject. I remember especially two points from these lectures. One was taken from the physiologist Charles Richet, an early French Nobel laureate, who suggested that one should imagine a world in which all men with the exception of a few scattered individuals had completely lost the sense of smell. Walking between two high stone walls one of those few might say, "There are roses behind these walls." And to everyone's amazement, his assertion would be verified. Upon beginning to open some drawer he might say, "There is lavender in this drawer," and if none should be found he would insist, "Then there was lavender in this drawer." And sure enough, it would be established that two years earlier there was indeed some lavender in that drawer. Are mediums with extraordinary perceptions and exceptional abilities in our world what the few people with a sense of smell are in Richet's?

The second point goes back to Hahn himself Some mediums claim that great thinkers and poets speak through them while they are in trance, but actually those mediums utter only lines that are far below the level of their supposed authors. This well-known fact is usually construed as proving that the uneducated mediums simply say what they think their sources would say. Hahn, however, pointed out that many mediumistic revelations are so trivial and incoherent that even a medium with little education would not consider them as utterances of their supposed sources, and that in fact they are definitely below the medium's own level. To Hahn this indicated that such chatter was not the product of the medium's conscious mind, but was generated subconsciously. Its very triviality combined with the tormented stammering in which the babble is frequently uttered, suggested to Hahn that in many cases one is dealing with a genuine phenomenon of some kind.

In his public lectures Hahn was of supreme clarity; but he also prepared his daily courses meticulously. He applied a technique that I have never seen anyone else carry to such extremes: he proceeded by almost imperceptible steps and at the end of each hour left his audience amazed at the mass of material covered. How stimulating his lectures were I have tried to describe - in Chapter 21 of my book Selected Papers in Logic and Foundations, Didactics, Economics (Vol. 10 of the Vienna Circle Collection) by the example of the effect on myself of the first lecture he gave after his return to Vienna in 1921.

Politically, Hahn was a socialist of deep conviction and took part in several phases of the social-democratic movement. He never spared any pains to serve the public. In particular, he furthered adult education and did whatever he could for competent underprivileged students. Where he saw injustice or oppression, he tried to help the injured. Once on the street, when a coachman maltreated his horse and Hahn's protest was ignored, he dragged the ruffian to the police. Hahn was respected even by his opponents.

Karl Menger

Last Updated August 2006