'fx is possible ' as Russell does. The certainty, possibility, or
impossibility of a situation is not expressed by a proposition, but by an
expression's being a tautology, a proposition with a sense, or a
contradiction. The precedent to which we are constantly inclined to appeal
must reside in the symbol itself.


5.526 We can describe the world completely by means of fully generalized
propositions, i.e. without first correlating any name with a particular
object.


5.5261 A fully generalized proposition, like every other proposition, is
composite. (This is shown by the fact that in '(dx, O) . Ox' we have to
mention 'O' and 's' separately. They both, independently, stand in
signifying relations to the world, just as is the case in ungeneralized
propositions.) It is a mark of a composite symbol that it has something in
common with other symbols.


5.5262 The truth or falsity of every proposition does make some alteration
in the general construction of the world. And the range that the totality
of elementary propositions leaves open for its construction is exactly the
same as that which is delimited by entirely general propositions. (If an
elementary proposition is true, that means, at any rate, one more true
elementary proposition.)


5.53 Identity of object I express by identity of sign, and not by using a
sign for identity. Difference of objects I express by difference of signs.