If the truth of one proposition follows from the
truth of others, this expresses itself in relations in which
the forms of these propositions stand to one another, and we
do not need to put them in these relations first by connecting
them with one another in a proposition; for these relations are
internal, and exist as soon as, and by the very fact that, the
propositions exist.
When we conclude from p v q and
~p to q the relation between the forms of the
propositions "p v q" and
"~p" is here concealed by the method
of symbolizing. But if we write, e.g. instead of
"p v q"
"p | q .|. p | q" and instead of
"~p"
"p | p" (p | q = neither p nor
q), then the inner connexion becomes obvious.
(The fact that we can infer fa from (x) . fx
shows that generality is present also in the symbol
"(x) . fx".