[skoodge]

Even the Remarks on the Foundations of Mathematics are only a selection of some of Wittgenstein's notebooks made by the editors of his posthumous publications. It is not a work by Wittgenstein in the same sense as the Tractatus or the Philosophical Investigations.

The Part II of the Remarks on the Foundations of Mathematics, which is the part on Cantor, is especially questionable. It is compiled from two documents of Wittgenstein's Nachlass, Ms-117 and Ms-121, but only about a third of the remarks in Ms-121 were included in the published book. There are also other notebooks were Wittgenstein discussed Cantor (most notably Ms-162a and Ms-126b) and which were not published at all. The editors made the decision to exclude some of these remarks because Wittgenstein's notebooks often contain merely drafts of remarks that were never fully developed, so it would be wrong to say that the published book is a deliberate misrepresentation of Wittgenstein's thoughts, but the situation is definitely quite nuanced and complex.

I personally think that the Remarks on the Foundations of Mathematics are very interesting, but that it's a disservice to Wittgenstein and any reader of his works to read his remarks on the philosophy of mathematics as a disconnected collection of aphorisms. The context really matters and his more mathematical remarks only make sense against the backdrop of the Philosophical Investigations and perhaps even his later writings such as On Certainty.