But though a particular proposition
“p
or not-p” has no meaning, a
general proposition “for all p's, p or not-p” has a meaning
because this does not contain the nonsensical function “p or
not-p” but the function
“p
or not-q” just as “for all
x's xRx” contains the function
“xRy”.
* This is quite
arbitrary but, if we once have fixed on which order the poles have to
stand we must of course stick to our convention.
If for instance “a p b” says
p then
b p
a says
nothing.
(It does not say
~p
.)
But a
- a p b - b is the same symbol as
a p b (here the ab function
vanishes automatically) for here the new poles are related to the same
side of p as
the old ones.
The question is always: how are the new poles correlated to
p
compared with the way the old poles are correlated to
~p.
5