5.533 The identity-sign, therefore, is not an essential constituent of
conceptual notation.


5.534 And now we see that in a correct conceptual notation pseudo-
propositions like 'a = a', 'a = b . b = c . z a = c', '(x) . x = x', '(dx)
. x = a', etc. cannot even be written down.


5.535 This also disposes of all the problems that were connected with such
pseudo-propositions. All the problems that Russell's 'axiom of infinity'
brings with it can 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