pdf-Download - Society for Gestalt Theory and its Applications (GTA)

antinomy and others had appeared simply as a result of employing definitions and deductive
methods which had been customary in mathematics. (p. 98) [3]
At the 1904 International Congress of Mathematicians in Heidelberg, HILBERT spoke of the
importance of laying a sound foundation for both logic and arithmetic that would avoid the
antinomies. In Göttingen mathematicians and philosophers (both belonged to the Philosophy
Faculty) turned to these issues, engaging in collaborative research. Volker PECKHAUS has written
extensively about these collaborative efforts and about HILBERTs program to axiomatize
mathematics.[4] In particular, he has written about the collaboration between Kurt GRELLING and
the philosopher Leonard NELSON (1882-1927).[5]
Soon after GRELLINGs arrival, he had become allied with NELSON who in 1903 had changed from
the University of Berlin to the University of Göttingen, which granted him the doctorate in
philosophy in 1904. GRELLING and NELSON worked together (as did other mathematicians and
philosophers) to attempt to solve or resolve RUSSELLs paradox. In the course of these attempts,
GRELLING discovered some new paradoxes, including the one named after him. It was published in
the joint paper by GRELLING and NELSON.
An early version of GRELLINGs paradox, then known as "not autological," was sent by NELSON to
the mathematician Gerhard HESSENBERG (1873-1925), who responded enthusiastically:
The paradox of "not autological" is so wonderfully formal ... by propounding new paradoxes
GRELLING earns great honors. One can see from it that they [the antinomies] are not so singular
and that they have by no means only one origin that was called "The Contradiction" by RUSSELL.
(p. 9)[5]
NELSON was already the head of a school of philosophy, the Neue Fries'sche Schule, in the spirit of
the post-Kantian philosopher, Jacob Friedrich FRIES (1773-1843). The concern was with the
revitalization and application of FRIES' critical philosophy to mathematics and to ethical and
political issues. GRELLING was NELSONs closest collaborator, but he was no mindless disciple,
according to a fellow scholar, Max BORN (1882-1970). BORN was HILBERTs assistant when
GRELLING arrived and later a professor of physics at Göttingen and much later (in 1954) a Nobel
Laureate in Physics. After BORNs habilitation [which gave him the title of Privatdozent and venia
legendi: permission to lecture at Göttingen] he lived in the same rooming house as GRELLING and
regularly lunched with him. BORN attended some of the Friesian school's meetings and referred to
them in his autobiography:
The people of the Friesian school assembled in NELSONs room for discussions. Some of them were
sincere, clever and straightforward like himself; for instance the mathematicians HESSENBERG
(professor in Bonn) and GRELLING (from Berlin). But there were [others] who did not do much
thinking for themselves but took NELSONs wisdom as dogma. (p. 93) [6]
As a student, NELSON had helped establish, together with HESSENBERG, the new series of the
Abhandlungen der Fries'schen Schule, to provide a forum for members of his school. It was in this
journal that GRELLINGs paradox was described in the 1908 article co-authored with NELSON, who
admitted in a letter to HESSENBERG that the article could have had only GRELLINGs name as
author since he did most of the work. But NELSON thought the co-authorship might be helpful in
his own efforts at habilitation. The thesis that NELSON presented for habilitation had been
rejected for his doctoral degree and was also rejected for habilitation. NELSONs efforts were
4