Wittgenstein on Gödelian 'Incompleteness', Proofs and Mathematical Practice: Reading _Remarks on the Foundations of Mathematics_, Part I, Appendix III, Carefully

We argue that Wittgenstein’s philosophical perspective on Gödel’s most famous theorem is even more radical than has commonly been assumed. Wittgenstein shows in detail that there is no way that the Gödelian construct of a string of signs could be assigned a useful function within (ordinary) mathematics. — The focus is on Appendix III to Part I of Remarks on the Foundations of Mathematics. The present reading highlights the exceptional importance of this particular set of remarks and, more specifically, emphasises its refined composition and rigorous internal structure.