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Wittgenstein´s Critique of Gödel´s Incompleteness Results

By Martin Ohmacht

Abstract

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

Topics: Kirchberg 2003, Logik, analytische Philosophie, g) 20.Jahrhundert
Publisher: Austrian Ludwig Wittgenstein Society
Year: 2003
OAI identifier: oai:sammelpunkt.philo.at:1674
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