Wittgenstein’s “notorious paragraph” about the Gödel Theorem

Timm Lampert

Abstract



Recently a number of papers have taken up the debate on Wittgenstein’s remarks on
Gödel. In the focus of the discussion is the question what Wittgenstein’s argument is
for his claim that “the interpretation ‘P is not provable’”
of the Gödel formula P has to be given up if one assumes
that either P or ¬P is provable
in Principia Mathematica (PM). In this paper it is shown that
the given interpretations are not satisfactory, and a detailed reconstruction of
Wittgenstein’s argument is offered. Furthermore, it will be put forward that
according to all interpretations Wittgenstein’s remarks on Gödel cannot be understood
as an expression of “remarkable insight”.

Keywords


philosophy; 20th century philosophy; Wittgenstein Ludwig; foundations of mathematics; completeness proof

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