Preproceedings 2006 - Austrian Ludwig Wittgenstein Society

importance, since it appears no less than 8 times as a
heading line. In 1900, Hilbert had placed the problem of
the consistency of arithmetic second on his list of
problems, and judging by this common topic of discussion
between these two intellectuals, it can be said that
Wittgenstein was well informed about the fundamental
debate. It was in 1931 that Gödel proved the impossibility
of proving the consistency of arithmetic, and the records
published in 1979 end with the entry dated 1 st July 1932. In
1928, Fraenkel wrote that the problem of consistency was
an “urgent problem” (“eine brennende Frage”, page 362)
for mathematicians and Wittgenstein seems to have felt
the same way. Had he apprehended Gödel’s 2 nd
incompleteness result? While I am not seeking to assert
this, I should like to pose, as a research problem, the
question of when and how Wittgenstein was informed of
Gödel´s results. This must have been in approximately
1938 because, as Hacker writes (footnote 15, page 575),
Wittgenstein was familiar with the article by A. G. D.
Gasking.
After all, Gödel´s results concern “Principia
Mathematica and Related Systems”. In order to be
affected by incompleteness, such systems must only be
complex enough to allow multiplication and this is the case
with Euclidean geometry (consider the ray theorem).
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Wittgenstein, Waismann and Non-Euclidean Geometries - Martin Ohmacht
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