5.535 Thereby also all problems that were connected with such pseudo-propositions take care of themselves.
All the problems that arise from Russell’s “Axiom of Infinity” are ready to be solved here.
What the Axiom of Infinity is supposed to say would be expressed in language by there being infinitely many names with different meanings.
See also Russell’s Introduction to Mathematical Philosophy p. 142, where he says that if this axiom is not the case then “it must be theoretically possible for analysis to reach ultimate subjects, and it is these that give the meaning of “particulars” or “individuals.”” See Wittgenstein’s comment on what he means here on p. 50 of Letters to
Black (p. 296) notes that it sounds as though Wittgenstein wants to ban certain formulas as pseudo-propositions, but that he says in 6.2 that mathematics consists entirely of pseudo-propositions. So maybe he doesn’t want to ban them after all.