2. Giving a function fx whose values for all values of x are
the propositions to be described; 3. Giving a formal law that governs
the construction of the propositions, in which case the bracketed
expression has as its members all the terms of a series of forms.

5.502 So instead of '(-----T)(E,....)', I write 'N(E)'. N(E) is the
negation of all the values of the propositional variable E.

5.503 It is obvious that we can easily express how propositions may be
constructed with this operation, and how they may not be constructed
with it; so it must be possible to find an exact expression for this.

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.

5.514 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',