So all problems disappear which are connected with such pseudo-propositions.

This is the place to solve all the problems with arise through Russell's "Axiom of Infinity".

What the axiom of infinity is meant to say would be expressed in language by the fact
that there is an infinite number of names with different meanings.

5.5351
There are certain cases in which one is tempted to use expressions of the form "a=a"
or "pp".
As, for instance, when one would speak of the archetype Proposition, Thing, etc.
So Russell in the Princples of Mathematics has rendered the nonsense "p is a proposition" in symbols by
"pp"
and has put it as hypothesis before certain propositions to show that their places for arguments could only be occupied by propositions.

(It is nonsense to place the hypothesis pp
before a proposition in order to ensure that its arguments have the right form,
because the hypotheses for a non-proposition as argument becomes not false but meaningless,
and because the proposition itself becomes senseless for arguments of the wrong kind,
and therefore it survives the wrong arguments no better and no worse than the senseless hypothesis attached for this purpose.)