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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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: Wolfgang Heuer
Date Deposited: 06 Dec 2020 14:53
Last Modified: 06 Dec 2020 14:53
URI: http://sammelpunkt.philo.at/id/eprint/3109

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