Vienna Circle

From the Internet Encyclopedia of Philosophy, this article is an excellent introduction to the philosophy and philosophers of the Vienna Circle. 

Excerpt:

Group of philosophers who gathered round Moritz Schlick, after his coming in Vienna in 1922. They organized a philosophical association, named Verein Ernst Mach (Ernst Mach Association). However, meetings on philosophy of science and epistemology began as early as 1907, promoted by Frank, Hahn and Neurath, who later arranged to bring Schlick at the University of Vienna. Among Vienna Circle's members were M. Schlick, R. Carnap, H. Feigl, P. Frank, K. Gödel, H. Hahn, V. Kraft, O. Neurath, F. Waismann. Also K. R. Popper and H. Kelsen had many contacts with the Vienna Circle, although they did not belong to it. At the meetings was also discussed Wittgenstein's Tractatus, and there were several meetings between Wittgenstein, Schlick, Waismann and Carnap. In 1929 Hahn, Neurath and Carnap published the manifesto of the circle: Wissenschaftliche Weltauffassung. Der Wiener Kreis (A scientific world-view. The Vienna Circle).

Vienna Circle was very active in advertising the new philosophical ideas of logical positivism. Several congresses on epistemology and philosophy of science were organized, with the help of the Berlin Circle. There were some preparatory congresses: Prague (1929), Könisberg (1930), Prague (1934) and then the first congress on scientific philosophy held in Paris (1935), followed by congresses in Copenhagen (1936), Paris (1937), Cambridge, England (1938), Cambridge, Mass. (1939). The Könisberg congress (1930) was very important, for Gödel announced he has proved the completeness of first order logic and the incompleteness of arithmetic. Another very interesting congress was the one held in Copenhagen (1936), which was dedicated to quantum physics and causality...


Institute Vienna Circle

Society for the Advancement of the Scientific World View.

The international Institute Vienna Circle, a nonprofit society founded in Vienna in October 1991, has set the following goals, documentation and further contributions to the development of the 'Vienna Circle' in the areas of science and adult education; and secondly to cultivate and apply logical empiricism, critical rationalism and linguistic analysis in the sense of a scientific philosophy and coordinated with general socio-cultural developments.

An important goal of this effort is the democratization of knowledge and of science understood as a process of enlightenment in contrast to irrationalism, dogmatism and fundamentalism in any social setting, but in cooperation with developments of research.  


Philipp Frank

From the MacTutor History of Mathematics archive

Excerpt:

Philipp Frank (1884 - 1966) obtained a doctorate from Vienna working under Boltzmann. He worked on a wide range of topics, calculus of variations, Fourier series, function spaces, geometrical optics, Schrödinger wave mechanics and relativity.

Frank was a life long friend of both von Mises and Einstein. He loved philosophy of science and his ideas influenced Einstein. On Einstein's recommendation he succeeded him to the chair of theoretical physics in Prague. In 1947 Frank wrote an excellent biography Einstein: His Life and Times .

Click here for Books by and about Philipp Frank and the Vienna Circle.


Kurt Gödel

From the MacTutor History of Mathematics archive

Excerpt:

Kurt Gödel (1906 - 1978) proved fundamental results about axiomatic systems, proving the Undecidability Theorems .

Kurt Gödel attended school in Brünn, completing his school studies in 1923. His brother Rudolf Gödel said:-
  

Even in High School my brother was somewhat more one-sided than me and to the astonishment of his teachers and fellow pupils had mastered university mathematics by his final Gymnasium years. ... Mathematics and languages ranked well above literature and history. At the time it was rumoured that in the whole of his time at High School not only was his work in Latin always given the top marks but that he had made not a single grammatical error.
Kurt entered the University of Vienna in 1923. He was taught by Furtwängler, Hahn, Wirtinger, Menger, Helly and others. As an undergraduate he took part in a seminar run by Schlick which studied Russell's book Introduction to mathematical philosophy. Olga Tausky-Todd, a fellow student of Gödel's, wrote:-
  
It became slowly obvious that he would stick with logic, that he was to be Hahn's student and not Schlick's, that he was incredibly talented. His help was much in demand.
He completed his doctoral dissertation under Hahn's supervision in 1929 and became a member of the faculty of the University of Vienna in 1930, where he belonged to the school of logical positivism until 1938....
   

Other Sites:

  • Kurt Gödel Society -- The Kurt Gödel Society is an international organization for the promotion of research in the areas of Logic, Philosophy, History of Mathematics, above all in connection with the biography of Kurt Gödel, and in other areas to which Gödel made contributions, especially mathematics, physics, theology, philosophy - Kurt Gödel was part of the so-called 'Schlick circle', the core of the Vienna Circle, as he was a member of the faculty of the University of Vienna-, and Leibniz studies.

Click here for books by and about Kurt Gödel and the Vienna Circle.


Hans Hahn

From the MacTutor History of Mathematics archive

Excerpt:

Hans Hahn (1879 - 1934)  was a student at the Technische Hochschule in Vienna. There he formed a close friendship with three other students of mathematics, Paul Ehrenfest, Heinrich Tietze and Herglotz. They were known as the 'inseparable four'.

He also studied in Strasbourg, Munich and Göttingen. He was appointed to the teaching staff in Vienna in 1905 and he became professor of mathematics there in 1921. In session 1905-06 Hahn substituted for Otto Stolz at Innsbruck.

Hahn was a pioneer in set theory and functional analysis and is best remembered for the Hahn-Banach theorem. He also made important contributions to the calculus of variations, developing ideas of Weierstrass.

Click here for books by and about Hans Hahn and the Vienna Circle.


Karl Menger

From the MacTutor History of Mathematics archive

Excerpt:

 Karl Menger (1902 - 1985) attended the Doblinger Gymnasium in Vienna (1913-1920) where one of his fellow students was Pauli. Karl entered the University of Vienna in 1920 to study physics. However Hahn became a lecturer in Vienna in 1921 and Menger attended a course he gave on What's new concerning the concept of a curve.

Menger became interested in the topic and was encouraged by Hahn to work on the topic. Menger's work led him to a definition of dimension independently of Urysohn, however Urysohn had died in a drowning accident before he could publish his work and Menger was not aware of it.

After a severe lung disease which forced Menger to spend more than a year in a sanatorium, he returned with important papers he had written on dimension while in the sanatorium and completed his doctorate in 1924.

Other sites:

  • Menger's Sponge -- Menger's Sponge Menger's sponge (sometimes wrongly called Sierpinski's Sponge) is a fractal solid that can be described as follows. Take a cube, divide it into 27 = 3 x 3 x 3 smaller cubes of the same size and remove the cube...

Click here for books by and about Karl Menger and the Vienna Circle.