David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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It is often said that GödelÂ´s famous theorem of 1931 is equal to the Cretian Liar, who says that everything that he says is a lie. But GödelÂ´s result is only similar to this sophism and not equivalent to it. When mathematicians deal with GödelÂ´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 doesnÂ´t excite anybody. GödelÂ´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. GödelÂ´s second imcompleteness theorem deals with hidden contradictions â€“ Wittgenstein shows a paradigmatic solution: he simply shrugs his shoulders on this problem and many mathematicians do so today as well. Wittgenstein says than GödelÂ´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.
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