It must be recognized in our symbols that what is connected by "v", ".", etc., must be propositions.

And this is the case, for the symbols "p" and "q" presuppose "v", "~", etc.
If the sign "p" in "p v q" does not stand for a complex sign, then by itself it cannot have sense;
but then also the signs "p v p", "p. p", etc. which have the same sense as "p" have no sense.
If, however, "p v p" has no sense, then also "p v q" can have no sense.

5.5151
Must the sign of the negative proposition be constructed by means of the sign of the positive?
Why should one not be able to express the negative proposition by means of a negative fact?
(Like: if "a" does not stand in a certain relation to "b", it could express that aRb is not the case.)

But here also the negative proposition is indirectly constructed with the positive.