Abstract

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.