Wittgenstein´s Critique of Gödel´s Incompleteness Results

Ohmacht, Martin (2003) Wittgenstein´s Critique of Gödel´s Incompleteness Results. In: Pre-Proceedings of the 26th International Wittgenstein Symposium. Austrian Ludwig Wittgenstein Society, Kirchberg am Wechsel, pp. 269-271.

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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.

Item Type: Book Section
Uncontrolled Keywords: Incompleteness Theorem; common sense philosophy; Liar´s Paradox; Goedel, A.; Wittgenstein, L.
Subjects: Philosophie > Philosophische Journale, Kongresse, Vereinigungen > Wittgenstein Symposium Kirchberg, Pre-Proceedings > Kirchberg 2003
Philosophie > Philosophische Disziplinen > Logik, analytische Philosophie
Philosophie > Geschichte der Philosophie > g) 20.Jahrhundert
Depositing User: Stefan Köstenbauer
Date Deposited: 17 Apr 2008 06:40
Last Modified: 08 Sep 2011 18:52
URI: http://sammelpunkt.philo.at/id/eprint/1674

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