The Second Conference on the Epistemology of the Exact Sciences (german: 2. Tagung für Erkenntnislehre der exakten Wissenschaften in Königsberg) was held on 5–7 September 1930 in

Königsberg Königsberg (, ) was the historic Prussian city that is now Kaliningrad, Russia. Königsberg was founded in 1255 on the site of the ancient Old Prussian settlement ''Twangste'' by the Teutonic Knights during the Northern Crusades, and was named ...

, then located in

East Prussia East Prussia ; german: Ostpreißen, label=Low Prussian; pl, Prusy Wschodnie; lt, Rytų Prūsija was a province of the Kingdom of Prussia from 1773 to 1829 and again from 1878 (with the Kingdom itself being part of the German Empire from 187 ...

. It was at this conference that

Kurt Gödel Kurt Friedrich Gödel ( , ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an imme ...

first presented his

incompleteness theorems Complete may refer to: Logic * Completeness (logic) * Completeness of a theory, the property of a theory that every formula in the theory's language or its negation is provable Mathematics * The completeness of the real numbers, which implies t ...

, though just "in an off-hand remark during a general discussion on the last day".Mancosu, Paolo "Between Vienna and Berlin: The immediate reception of Gödel's incompleteness theorems", History and Philosophy of Logic, 20, 1999, 33-45. The real first presentation took place in Vienna. The conference was organised by

Kurt Reidemeister Kurt Werner Friedrich Reidemeister (13 October 1893 – 8 July 1971) was a mathematician born in Braunschweig (Brunswick), Germany. Life He was a brother of Marie Neurath. Beginning in 1912, he studied in Freiburg, Munich, Marburg, and Götting ...

of the

University of Königsberg The University of Königsberg (german: Albertus-Universität Königsberg) was the university of Königsberg in East Prussia. It was founded in 1544 as the world's second Protestant academy (after the University of Marburg) by Duke Albert of Prussi ...

. The presentations were grouped around two themes: firstly, the foundation of mathematics and secondly philosophical questions arising from Quantum mechanics. The conference was closely related to the journal ''

Erkenntnis ''Erkenntnis'' is a journal of philosophy that publishes papers in analytic philosophy. Its name is derived from the German word "Erkenntnis", meaning "knowledge, recognition". The journal was also linked to organisation of conferences, such as the ...

'' who published the associated papers and accounts of the discussion in ''Erkenntnis'' (1931), 2 pp 87-190.

The foundation of mathematics

The presentations as regards the

foundation of mathematics Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathe ...

were as follows: Session 1: *

Rudolf Carnap Rudolf Carnap (; ; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism. He ...

(

Vienna en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...

), presented the thought of the logicist school as developed by

Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ...

Arend Heyting __NOTOC__ Arend Heyting (; 9 May 1898 – 9 July 1980) was a Dutch mathematician and logician. Biography Heyting was a student of Luitzen Egbertus Jan Brouwer at the University of Amsterdam, and did much to put intuitionistic logic on a foot ...

(

Enschede Enschede (; known as in the local Twents dialect) is a municipality and city in the eastern Netherlands in the province of Overijssel and in the Twente region. The eastern parts of the urban area reaches the border of the German city of Gronau ...

), presented the thought of the

intuitionist In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fu ...

school as developed by

L. E. J. Brouwer Luitzen Egbertus Jan Brouwer (; ; 27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and compl ...

John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...

(

Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...

), presented the thought of the formalist school as developed by

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...

Friedrich Waismann Friedrich Waismann (; 21 March 18964 November 1959) was an Austrian mathematician, physicist, and philosopher. He is best known for being a member of the Vienna Circle and one of the key theorists in logical positivism. Biography Born to a Jewis ...

(Vienna), presented the thought of the

linguistic Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Linguis ...

school as developed by

Ludwig Wittgenstein Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is considere ...

(Vienna), "On the Completeness of the Logical Calculus" *

Arnold Scholz Arnold Scholz (24 December 1904 in Berlin – 1 February 1942 in Flensburg) was a German mathematician who proved Scholz's reciprocity law and introduced the Scholz conjecture. Scholz participated in the Second Conference on the Epistemology ...

(

Freiburg Freiburg im Breisgau (; abbreviated as Freiburg i. Br. or Freiburg i. B.; Low Alemannic: ''Friburg im Brisgau''), commonly referred to as Freiburg, is an independent city in Baden-Württemberg, Germany. With a population of about 230,000 (as o ...

), "On the Use of the Term Holism in Axiomatics" Session 2: *

Otto Neugebauer Otto Eduard Neugebauer (May 26, 1899 – February 19, 1990) was an Austrian-American mathematician and historian of science who became known for his research on the history of astronomy and the other exact sciences as they were practiced in anti ...

(

Göttingen Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...

), "On Pre-Greek Mathematics" Session 3: Discussion on the foundation of mathematics involving Hans Hahn, Carnap, Heyting, von Neumann, Gödel, Scholz and Reidemeister

Philosophical questions arising from quantum mechanics

There were two key presentations. Session 4: *

Hans Reichenbach Hans Reichenbach (September 26, 1891 – April 9, 1953) was a leading philosopher of science, educator, and proponent of logical empiricism. He was influential in the areas of science, education, and of logical empiricism. He founded the ''Gesel ...

(Berlin), presented on the supersession of two-value logic by probability logic *

Werner Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series ...

(

Leipzig Leipzig ( , ; Upper Saxon: ) is the most populous city in the German state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's eighth most populous, as wel ...

), presented on the meaninglessness of strict assertions about natural phenomena at the micro level. Session 5: Discussion on Causality and Quantum Mechanics involving

Gerhard Herzberg Gerhard Heinrich Friedrich Otto Julius Herzberg, (; December 25, 1904 – March 3, 1999) was a German-Canadian pioneering physicist and physical chemist, who won the Nobel Prize for Chemistry in 1971, "for his contributions to the knowledge o ...

, Heisenberg,

Phillip Frank Philipp Frank (March 20, 1884 – July 21, 1966) was a physicist, mathematician and philosopher of the early-to-mid 20th century. He was a logical positivist, and a member of the Vienna Circle. He was influenced by Mach and was one of the Machis ...

Maria Goeppert Mayer Maria Goeppert Mayer (; June 28, 1906 – February 20, 1972) was a German-born American theoretical physicist, and Nobel laureate in Physics for proposing the nuclear shell model of the atomic nucleus. She was the second woman to win a Nobel Pr ...

, ,

Georg Hamel Georg Karl Wilhelm Hamel (12 September 1877 – 4 October 1954) was a German mathematician with interests in mechanics, the foundations of mathematics and function theory. Biography Hamel was born in Düren, Rhenish Prussia. He studied at Aa ...

, von Neumann,

Kurt Grelling Kurt Grelling (2 March 1886 – September 1942) was a German logician and philosopher, member of the Berlin Circle. Life and work Kurt Grelling was born on 2 March 1886 in Berlin. His father, the Doctor of Jurisprudence Richard Grelling, ...

, Reichenbach.

References

{{reflist Vienna Circle

The foundation of mathematics

Philosophical questions arising from quantum mechanics

See also

References