5.51 If E has only one value, then N(E) = Pp (not p); if it has two values,
then N(E) = Pp . Pq. (neither p nor g).
5.511 How can logic--all-embracing logic, which mirrors the world--use such
peculiar crotchets and contrivances? Only because they are all connected
with one another in an infinitely fine network, the great mirror.
5.512 'Pp' is true if 'p' is false. Therefore, in the proposition 'Pp',
when it is true, 'p' is a false proposition. How then can the stroke 'P'
make it agree with reality? But in 'Pp' it is not 'P' that negates, it is
rather what is common to all the signs of this notation that negate p. That
is to say the common rule that governs the construction of 'Pp', 'PPPp',
'Pp C Pp', 'Pp . Pp', etc. etc. (ad inf.). And this common factor mirrors
negation.
5.513 We might say that what is common to all symbols that affirm both p
and q is the proposition 'p . q'; and that what is common to all symbols
that affirm either p or q is the proposition 'p C q'. And similarly we can
say that two propositions are opposed to one another if they have nothing
in common with one another, and that every proposition has only one
negative, since there is only one proposition that lies completely outside
it. Thus in Russell's notation too it is manifest that 'q : p C Pp' says
the same thing as 'q', that 'p C Pq' says nothing.
5.
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