Kurt Grelling
Encyclopedia
Kurt Grelling was a logician, philosopher and member of the Berlin Circle
.
, with whom he tried to solve Russell's paradox
, which had shaken the foundations of mathematics
when it was announced in 1903. Their 1908 paper included new paradox
es, including a semantic paradox that was named the Grelling–Nelson paradox.
He received his doctorate in mathematics
from the same university in 1910 with a dissertation on the development of arithmetics in axiomatic set theory, advised by David Hilbert
. In a recorded interview with Herbert Enderton, Alfred Tarski
mentions a meeting he had with Grelling in 1938, and says that Grelling was the author of the earliest textbook in set theory
, probably but wrongly referring to this dissertation, since William Henry Young
and Grace Chisholm Young
's Set Theory was published in 1906.
As a skilled linguist, Grelling translated philosophical works from French, Italian and English to German, including four of Bertrand Russell
's works. He became a strong proponent of Russell's writings thereafter.
From 1911 to 1922 Grelling published exclusively journalistic articles in publications connected with the Social Democratic Party of Germany
, but from 1924 onwards his publications were exclusively in the field of positivist philosophy
.
Unable to find a university position in Göttingen
or Berlin
, Grelling had to teach mathematics, philosophy
and physics
in secondary schools. Nevertheless, he worked with Hans Reichenbach
in planning the meetings of the Berlin Circle, which was closely associated with the Vienna Circle
. In 1933, Reichenbach emigrated to Turkey
and the Nazis
forced Grelling to retire. But he struggled to keep the Berlin Circle active by organizing small seminars and colloquia.
Grelling collaborated with Kurt Gödel
and in 1936 he published an article in which he defended Gödel's incompleteness theorem against an erroneous interpretation, according to which Gödel's theorem is a paradox as Russell's paradox (see References).
Although many of his relatives and friends had fled Germany
, he did not think seriously about leaving until 1937, in which year he went to Brussels
to work with Paul Oppenheim
, this time writing several papers on the analysis of scientific explanation and on Gestalt psychology
.
On May 10, 1940, the first day of the German invasion in Belgium
, Grelling was arrested. He was deported to southern France
, where he was interned for over two years under the Vichy regime. Oppenheim and Hempel
tried to help Grelling by securing an appointment for him at the New School for Social Research in New York City
. News of the position and a visa to the USA reached the camp where Grelling had been joined by his wife Greta, who had refused to divorce him for safety reasons. But U.S. immigration officials were perplexed by Grelling's alleged propensity towards Communism, so there was a delay that was fatal to Grelling. He and his wife are supposed to have been shipped to Auschwitz, arriving there on September 18, 1942 and perishing in the gas chamber
s that day or soon thereafter, although it has been also reported that Grelling was killed in 1941 at the border between France and Spain
.
Berlin Circle (philosophy)
The Berlin Circle was a group that maintained logical empiricist views about philosophy.It was created in the late 1920s by Hans Reichenbach, Kurt Grelling and Walter Dubislav and composed of philosophers and scientists such as Carl Gustav Hempel, David Hilbert and Richard von Mises...
.
Life and work
Shortly after his arrival in 1905 at University of Göttingen, Grelling began a collaboration with philosopher Leonard NelsonLeonard Nelson
Leonard Nelson was a German mathematician and philosopher. He was part of the Neo-Friesian School and a friend of the mathematician David Hilbert, and devised the Grelling–Nelson paradox with Kurt Grelling...
, with whom he tried to solve Russell's paradox
Russell's paradox
In the foundations of mathematics, Russell's paradox , discovered by Bertrand Russell in 1901, showed that the naive set theory created by Georg Cantor leads to a contradiction...
, which had shaken the foundations of mathematics
Foundations of mathematics
Foundations of mathematics is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, type theory and recursion theory...
when it was announced in 1903. Their 1908 paper included new paradox
Paradox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...
es, including a semantic paradox that was named the Grelling–Nelson paradox.
He received his doctorate in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
from the same university in 1910 with a dissertation on the development of arithmetics in axiomatic set theory, advised by David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
. In a recorded interview with Herbert Enderton, Alfred Tarski
Alfred Tarski
Alfred Tarski was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of...
mentions a meeting he had with Grelling in 1938, and says that Grelling was the author of the earliest textbook in set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
, probably but wrongly referring to this dissertation, since William Henry Young
William Henry Young
William Henry Young was an English mathematician. Young was educated at City of London School and Peterhouse, Cambridge. He worked on measure theory, Fourier series, differential calculus amongst other fields, and made brilliant and long-lasting contributions to the study of functions of several...
and Grace Chisholm Young
Grace Chisholm Young
Grace Chisholm Young was an English mathematician. She was educated at Girton College, Cambridge, England and continued her studies at Göttingen University in Germany, where in 1895 she became the first woman to receive a doctorate in any field in that country...
's Set Theory was published in 1906.
As a skilled linguist, Grelling translated philosophical works from French, Italian and English to German, including four of Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
's works. He became a strong proponent of Russell's writings thereafter.
From 1911 to 1922 Grelling published exclusively journalistic articles in publications connected with the Social Democratic Party of Germany
Social Democratic Party of Germany
The Social Democratic Party of Germany is a social-democratic political party in Germany...
, but from 1924 onwards his publications were exclusively in the field of positivist philosophy
Positivism
Positivism is a a view of scientific methods and a philosophical approach, theory, or system based on the view that, in the social as well as natural sciences, sensory experiences and their logical and mathematical treatment are together the exclusive source of all worthwhile information....
.
Unable to find a university position in Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
or Berlin
Berlin
Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...
, Grelling had to teach mathematics, philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
and physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
in secondary schools. Nevertheless, he worked with Hans Reichenbach
Hans Reichenbach
Hans Reichenbach was a leading philosopher of science, educator and proponent of logical empiricism...
in planning the meetings of the Berlin Circle, which was closely associated with the Vienna Circle
Vienna Circle
The Vienna Circle was an association of philosophers gathered around the University of Vienna in 1922, chaired by Moritz Schlick, also known as the Ernst Mach Society in honour of Ernst Mach...
. In 1933, Reichenbach emigrated to Turkey
Turkey
Turkey , known officially as the Republic of Turkey , is a Eurasian country located in Western Asia and in East Thrace in Southeastern Europe...
and the Nazis
Nazism
Nazism, the common short form name of National Socialism was the ideology and practice of the Nazi Party and of Nazi Germany...
forced Grelling to retire. But he struggled to keep the Berlin Circle active by organizing small seminars and colloquia.
Grelling collaborated with Kurt Gödel
Kurt Gödel
Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...
and in 1936 he published an article in which he defended Gödel's incompleteness theorem against an erroneous interpretation, according to which Gödel's theorem is a paradox as Russell's paradox (see References).
Although many of his relatives and friends had fled Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
, he did not think seriously about leaving until 1937, in which year he went to Brussels
Brussels
Brussels , officially the Brussels Region or Brussels-Capital Region , is the capital of Belgium and the de facto capital of the European Union...
to work with Paul Oppenheim
Paul Oppenheim
Paul Oppenheim was a German chemist, philosopher, independent scholar and industrialist....
, this time writing several papers on the analysis of scientific explanation and on Gestalt psychology
Gestalt psychology
Gestalt psychology or gestaltism is a theory of mind and brain of the Berlin School; the operational principle of gestalt psychology is that the brain is holistic, parallel, and analog, with self-organizing tendencies...
.
On May 10, 1940, the first day of the German invasion in Belgium
Belgium
Belgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...
, Grelling was arrested. He was deported to southern France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
, where he was interned for over two years under the Vichy regime. Oppenheim and Hempel
Carl Gustav Hempel
Carl Gustav "Peter" Hempel was a philosopher of science and a major figure in 20th-century logical empiricism...
tried to help Grelling by securing an appointment for him at the New School for Social Research in New York City
New York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
. News of the position and a visa to the USA reached the camp where Grelling had been joined by his wife Greta, who had refused to divorce him for safety reasons. But U.S. immigration officials were perplexed by Grelling's alleged propensity towards Communism, so there was a delay that was fatal to Grelling. He and his wife are supposed to have been shipped to Auschwitz, arriving there on September 18, 1942 and perishing in the gas chamber
Gas chamber
A gas chamber is an apparatus for killing humans or animals with gas, consisting of a sealed chamber into which a poisonous or asphyxiant gas is introduced. The most commonly used poisonous agent is hydrogen cyanide; carbon dioxide and carbon monoxide have also been used...
s that day or soon thereafter, although it has been also reported that Grelling was killed in 1941 at the border between France and Spain
Spain
Spain , officially the Kingdom of Spain languages]] under the European Charter for Regional or Minority Languages. In each of these, Spain's official name is as follows:;;;;;;), is a country and member state of the European Union located in southwestern Europe on the Iberian Peninsula...
.