Wittgenstein's inversion of Gödel's theorem (Q1583756)

The author interprets Wittgenstein's remarks on Gödel's first incompleteness theorem. According to the author, Wittgenstein commits a mistake in his ``Remarks on the foundations of mathematics'' when he assumes that Gödel's diagonal sentence must be interpreted in natural language for carrying out Gödel's proof. However, Wittgenstein's mistake does not affect Wittgenstein's main points. Given Wittgenstein's own conception of truth, he is justified in claiming that there cannot be a true but unprovable proposition. Furthermore Wittgenstein at least doubts that the diagonal sentence is meaningful. In further remarks that have caused offence, Wittgenstein emphasizes, in the mind of the author, that the diagonal sentence is only demonstrably unprovable if the system of Principia Mathematica is presupposed to be consistent. Finally the author discusses alternative interpretations of Gödel's remarks by Floyd and Goodstein.