Wittgenstein´s Critique of Gödel´s Incompleteness Results

摘要

It is often said that Gödel´s famous theorem of 1931 isudequal to the Cretian Liar, who says that everything that heudsays is a lie. But Gödel´s result is only similar to thisudsophism and not equivalent to it. When mathematiciansuddeal with Gödel´s theorem, then it is often the case thatudthey become poetical or even emotional: some of themudshow a high esteem of it and others despise it. Wittgensteinudsees the famous Liar as a useless language gameudwhich doesn´t excite anybody. Gödel´s first incompletenessudtheorem shows us that in mathematics there areudpuzzles which have no solution at all and therefore inudmathematics one should be very careful when oneudchooses a puzzle on which one wants to work. Gödel´sudsecond imcompleteness theorem deals with hiddenudcontradictions – Wittgenstein shows a paradigmaticudsolution: he simply shrugs his shoulders on this problemudand many mathematicians do so today as well. Wittgensteinudsays than Gödel´s results should not be treated asudmathematical theorems, but as elements of the humanisticudsciences. Wittgenstein sees them as something whichudshould be worked on in a creative manner.