5.441 This vanishing of the apparent logical constants also occurs in the
case of 'P(dx) . Pfx', which says the same as '(x) . fx', and in the case
of '(dx) . fx . x = a', which says the same as 'fa'.
5.442 If we are given a proposition, then with it we are also given the
results of all truth-operations that have it as their base.
5.45 If there are primitive logical signs, then any logic that fails to
show clearly how they are placed relatively to one another and to justify
their existence will be incorrect. The construction of logic out of its
primitive signs must be made clear.
5.451 If logic has primitive ideas, they must be independent of one
another. If a primitive idea has been introduced, it must have been
introduced in all the combinations in which it ever occurs. It cannot,
therefore, be introduced first for one combination and later reintroduced
for another. For example, once negation has been introduced, we must
understand it both in propositions of the form 'Pp' and in propositions
like 'P(p C q)', '(dx) . Pfx', etc. We must not introduce it first for the
one class of cases and then for the other, since it would then be left in
doubt whether its meaning were the same in both cases, and no reason would
have been given for combining the signs in the same way in both cases. (In
short, Frege's remarks about introducing signs by means of definitions (in
The Fundamental Laws of Arithmetic ) also apply, mutatis mutandis, to the
introduction of primitive signs.
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