Wittgenstein´s Critique of Gödel´s Incompleteness Results

It is often said that Gödel´s famous theorem of 1931 is
equal to the Cretian Liar, who says that everything that he
says is a lie. But Gödel´s result is only similar to this
sophism and not equivalent to it. When mathematicians
deal with Gödel´s theorem, then it is often the case that
they become poetical or even emotional: some of them
show a high esteem of it and others despise it. Wittgenstein
sees the famous Liar as a useless language game
which doesn´t excite anybody. Gödel´s first incompleteness
theorem shows us that in mathematics there are
puzzles which have no solution at all and therefore in
mathematics one should be very careful when one
chooses a puzzle on which one wants to work. Gödel´s
second imcompleteness theorem deals with hidden
contradictions – Wittgenstein shows a paradigmatic
solution: he simply shrugs his shoulders on this problem
and many mathematicians do so today as well. Wittgenstein
says than Gödel´s results should not be treated as
mathematical theorems, but as elements of the humanistic
sciences. Wittgenstein sees them as something which
should be worked on in a creative manner.