be solved at this point. What the axiom of
infinity is intended to say would express itself in language through the
existence of infinitely many names with different meanings.

5.5351 There are certain cases in which one is tempted to use
expressions of the form 'a = a' or 'p z p' and the like. In fact, this
happens when one wants to talk about prototypes, e.g. about proposition,
thing, etc. Thus in Russell's Principles of Mathematics 'p is a
proposition'--which is nonsense--was given the symbolic rendering 'p z
p' and placed as an hypothesis in front of certain propositions in order
to exclude from their argument-places everything but propositions. (It
is nonsense to place the hypothesis 'p z p' in front of a proposition,
in order to ensure that its arguments shall have the right form, if only
because with a non-proposition as argument the hypothesis becomes not
false but nonsensical, and because arguments of the wrong kind make the
proposition itself nonsensical, so that it preserves itself from wrong
arguments just as well, or as badly, as the hypothesis without sense
that was appended for that purpose.)

5.5352 In the same way people have wanted to express, 'There are
no things ', by writing 'P(dx). x = x'. But even if this were a
proposition, would it not be equally true if in fact 'there were things'
but they were not identical with themselves?

5.54 In the general propositional form propositions occur in other
propositions only as bases of truth-operations.

5.541 At first sight it looks as if it were also possible for one
proposition to occur in another in a different way. Particularly with
certain forms of proposition in psychology, such as 'A believes that p
is the case' and A has the thought p', etc. For if these are considered
superficially, it looks as if the proposition p stood in some kind of
relation to an object A. (And in modern theory of knowledge (Russell,
Moore, etc.) these propositions have actually been construed in this
way.)

5.542 It is clear, however, that 'A believes that p', 'A has the thought
p', and 'A says p' are of the form '"p" says p': and this does
not involve a correlation of a fact with an object, but rather the
correlation of facts by means of the correlation of their objects.

5.5421 This shows too that there is no such thing as the soul--the
subject, etc.--as it is conceived in the superficial psychology of the
present day. Indeed a composite soul would no longe