epresent a _Grey_ Counter (this may be interpreted to mean "There is
_nothing_ here").
The Pair of Propositions, that we shall have to represent, will always
be, one in terms of x and m, and the other in terms of y and m.
When we have to represent a Proposition beginning with "All", we break
it up into the _two_ Propositions to which it is equivalent.
When we have to represent, on the same Diagram, Propositions, of which
some begin with "Some" and others with "No", we represent the _negative_
ones _first_. This will sometimes save us from having to put a "I" "on a
fence" and afterwards having to shift it into a Cell.
[Let us work a few examples.
(1)
"No x are m';
No y' are m".
Let us first represent "No x are m'". This gives us Diagram a.
Then, representing "No y' are m" on the same Diagram, we get
Diagram b.
pg051
a b
.---------------. .---------------.
|(O) | (O)| |(O) | (O)|
| .---|---. | | .---|---. |
| | | | | | | |(O)| |
|---|---|---|---| |---|---|---|---|
| | | | | | | |(O)| |
| .---|---. | | .---|---. |
| | | | | |
.---------------. .---------------.
(2)
"Some m are x;
No m are y".
If, neglecting the Rule, we were begin with "Some m are x", we
should get Diagram a.
And if we were then to take "No m are y", which tells us that
the Inner N.W. Cell is _empty_, we should be obliged to take the
"I" off the fence (as it no longer has the choice of _two_
Cells), and to put it into the Inner N.E. Cell, as in Diagram c.
This trouble may be saved by beginning with "No m are y", as in
Diagram b.
And _now_, when we take "Some m are x", there is no fence to sit
on! The "I" has to go, at once, into the N.E. Cell, as in
Diagram c.
a b c
.---------------. .---------------. .---------------.
| | | | | | | | |
| .---|---. | | .---|---. | | .---|---. |
| | (I) | | | |(O)| | | | |(O)|(I)| |
|---|---
|