denumerability

Wittgenstein's criticism of non-denumerability is primarily implicit during the middle period.

Wittgenstein's Philosophy of Mathematics Rodych, Victor 2007

As we shall see in Section 3.4, the later Wittgenstein analyzes Cantor's diagonal and claims of non-denumerability in some detail.

Wittgenstein's Philosophy of Mathematics Rodych, Victor 2007

As with his intermediate views on genuine irrationals and the Multiplicative Axiom, Wittgenstein here looks at the diagonal proof of the non-denumerability of “the set of transcendental numbers” as one that shows only that transcendental numbers cannot be recursively enumerated.

Wittgenstein's Philosophy of Mathematics Rodych, Victor 2007

The oddest of which is the following from p. 443: "The emphasis on extensionality [in PM 2nd ed.] hardly fitts well with a logicism in which, for example, non-denumerability is central."

Words and Other Things 2009

This seems odd to me because I'm not sure what non-denumerability has to do with extensionality.

Words and Other Things 2009

In his core criticism of set theory, however, the later Wittgenstein denies this, saying that the diagonal proof does not prove non-denumerability, for “[i] t means nothing to say: “Therefore the X numbers are not denumerable” (RFM II, §10).

Wittgenstein's Philosophy of Mathematics Rodych, Victor 2007

Though Cantor's diagonal is not a proof of non-denumerability, when it is expressed in a constructive manner, as Wittgenstein himself expresses it at (RFM II,

Wittgenstein's Philosophy of Mathematics Rodych, Victor 2007