Visiting Gödel

Prof. Karlis Podnieks
University of Latvia

This work is licensed under a Creative Commons License and is copyrighted © 2010 by me, Karlis Podnieks.

Vienna: Searching for Cafe Reichsrat

Kurt Gödel proved his Incompleteness Theorem in Vienna, during the summer of 1930, and he first told about it to his colleagues on Tuesday, August 26 at the Cafe Reichsrat:

Picture #054 from the excellent gallery published by BVI.

[According to Carnap's diary], "...Carnap was probably the first one to learn about the [Goedel's] results on August 26, 1930 during a conversation at the Cafe Reichsrat in Vienna [Austria]. Feigl was apparently also there and Waismann joined the the group later that afternoon."

Full text: Paolo Mancosu. Between Vienna and Berlin: The Immediate Reception of Godel's Incompleteness Theorems. History and Philosophy of Logic, 1999, Vol.20, N1, pp.33-45 (available online from Taylor & Francis Group).

For an attempt of a detailed reconstruction of the meeting, see

John L. Casti. The One True Platonic Heaven: A Scientific Fiction on the Limits of Knowledge. The National Academies Press, 2003, 224 pp.

September 10, 2010: the same door?

I took this picture September 10, 2010 sitting at the table in the patio of a wonderful Wiener Cafe – Cafe Conditorei Sluka at Rathausplatz 8.

I knew about the problem from

Godel's Viennese Hangouts -- Cafes Arkaden, Josephinum and Reichsrat by Paul Raymont:

“... it looks like the Sluka expanded at some time into the Cafe Reichsrat's location.”

This fact is not mentioned on the web-site of Conditorei Sluka at www.sluka.at. Neither was it known to the very kind personnel of the Cafe I talked to.

But there is another door...

in the same building that is more likely the true door of the former Cafe Reichsrat. On the plate, one can read:

M.Gruber

Uhren & Juwelen Handelsges. m.b.H.

1070 Wien, Mariahilfer Strasse 88

Details of the company can be found here, and here.

Cafe Reichsrat, July 15-16, 1927

“Gemeinderat Schleifer schreibt:

... Etwa um 3/4 4 Uhr nachmittags begab ich mich mit dem Gemeinderat Reismann vom Parlament zu der von einer Sanitätskolonne des Schutzbundes im Café Reichsrat errichteten Sanitätsstation. Obgleich vor dem Kaffeehause eine rote Fahne mit dem weißen Kreuz gehißt war, wurde von der Polizei auch diese Sanitätsstation beschossen. Während unserer Anwesenheit erhielt ein Sanitätsmann, der beim Kaffeehauseingang stand, einen Bauchschuß.”

Full text:

Karl Kraus: Vor der Walpurgisnacht - Aufsätze 1925-1936 – Kapitel 9: Der Hort der Republik. Projekt Gutenberg-DE, SPIEGEL-ONLINE.

See also: Julirevolte in Wien.

A chronology of some facts about the

Turning point in the human intellectual history

K. Goedel [1931] Ueber formal unentscheidbare Saetze der Principia Mathematica und verwandter Systeme. "Monatshefte fuer Mathematik und Physik", 1931, Vol. 38, pp. 173-198.

Richard Kaye. Arithmetic and the Incompleteness Theorems. August 12, 2000, 37 pp.

Wir muessen wissen -- wir werden wissen! David Hilbert's Radio Broadcast, Koenigsberg, 8 September 1930 (audio record published by James T.Smith, and translations in 7 languages published by Laurent Siebenmann). "...according to Gödel's biographer John Dawson, Hilbert and Gödel never discussed it, they never spoke to each other. The story is so dramatic that it resembles fiction. They were both at a meeting in Koenigsberg in September 1930. On September 7th Goedel off-handedly announced his epic results during a round-table discussion. Only von Neumann immediately grasped their significance... The very next day, September 8th, Hilbert delivered his famous lecture on ``Logic and the understanding of nature.'' As is touchingly described by Hilbert's biographer Constance Reid (see Reid [1996] - K.P.), this was the grand finale of Hilbert's career and his last major public appearance. Hilbert's lecture ended with his famous words: ``Wir muessen wissen. Wir werden wissen.'' We must know! We shall know!" (from a G.J.Chaitin's lecture, Buenos Aires, 1998).

"Historians and Mathematicians agree, 1930 was Goedel’s most profound year – if one was to include the latter part of 1929 as well. It is in this year that Goedel states he first heard of Hilbert’s proposed outline of a proof of the continuum hypotheses. In the summer, Goedel began work on trying to prove the relative consistency of analysis. Goedel soon discovered that truth in number theory is undefinable – he later went on to prove a combinational form of the Incompleteness Theorem.

In 1930, Goedel traveled several days to attend the Second Conference on Epistemology of the Exact Sciences (September 5-7). Towards the end of the Conference on the last day, Goedel spoke for the first time and, "criticized the formalist assumption that consistency of ‘transfinite’ axioms assures the nonderivability of any consequence that is ‘contentually false.’ He concluded, ‘For of no formal system can one affirm with certainty that all contentual considerations are representable in it.’ And then v. Neumann interjected, ‘It is not a foregone conclusion whether all rules of inference that are intuitionistically permissible may be formally reproduced.’" It was after this statement, that Goedel made the announcement of his incompleteness result, "Under the assumption of the consistency of classical mathematics, one can give examples of propositions…that are contentually true, but are unprovable in the formal system of classical mathematics." It was these events which preceded the formal 1931 publishing of Goedel’s article Uber formal unentscheidbare Saetze der Principia Mathematica und verwandter Systeme." (A fragment from Goedel, and his Incompleteness Theorem by Mark Wakim).

For a complete biography see

John W. Dawson Jr. Logical Dilemmas. The Life and Work of Kurt Godel. A. K. Peters, 1997.

Photo gallery by BVI.