514 Once a notation has been established, there will be in it a rule
governing the construction of all propositions that negate p, a rule
governing the construction of all propositions that affirm p, and a rule
governing the construction of all propositions that affirm p or q; and so
on. These rules are equivalent to the symbols; and in them their sense is
mirrored.
5.515 It must be manifest in our symbols that it can only be propositions
that are combined with one another by 'C', '.', etc. And this is indeed the
case, since the symbol in 'p' and 'q' itself presupposes 'C', 'P', etc. If
the sign 'p' in 'p C q' does not stand for a complex sign, then it cannot
have sense by itself: but in that case the signs 'p C p', 'p . p', etc.,
which have the same sense as p, must also lack sense. But if 'p C p' has no
sense, then 'p C q' cannot have a sense either.
5.5151 Must the sign of a negative proposition be constructed with that of
the positive proposition? Why should it not be possible to express a
negative proposition by means of a negative fact? (E.g. suppose that "a'
does not stand in a certain relation to 'b'; then this might be used to say
that aRb was not the case.) But really even in this case the negative
proposition is constructed by an indirect use of the positive. The positive
proposition necessarily presupposes the existence of the negative
proposition and vice versa.
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