|---|---| |---|---|---|---| |---|---|---|---|
| | | | | | |(O)| | | | |(O)| | |
| .---|---. | | .---|---. | | .---|---. |
| | | | | | | | |
.---------------. .---------------. .---------------.

(3)

"No x' are m';
All m are y".

Here we begin by breaking up the Second into the two
Propositions to which it is equivalent. Thus we have _three_
Propositions to represent, viz.--

(1) "No x' are m';
(2) Some m are y;
(3) No m are y'".

These we will take in the order 1, 3, 2.

First we take No. (1), viz. "No x' are m'". This gives us
Diagram a.
pg052
Adding to this, No. (3), viz. "No m are y'", we get Diagram b.

This time the "I", representing No. (2), viz. "Some m are y,"
has to sit on the fence, as there is no "O" to order it off!
This gives us Diagram c.

a b c
.---------------. .---------------. .---------------.
| | | | | | | | |
| .---|---. | | .---|---. | | .---|---. |
| | | | | | | |(O)| | | | |(O)| |
|---|---|---|---| |---|---|---|---| |---|(I)|---|---|
| | | | | | | |(O)| | | | |(O)| |
| .---|---. | | .---|---. | | .---|---. |
|(O) | (O)| |(O) | (O)| |(O) | (O)|
.---------------. .---------------. .---------------.

(4)

"All m are x;
All y are m".

Here we break up _both_ Propositions, and thus get _four_ to
represent, viz.--

(1) "Some m are x;
(2) No m are x';
(3) Some y are m;
(4) No y are m'".

These we will take in the order 2, 4, 1, 3.

First we take No. (2), viz. "No m are x'". This gives us Diagram
a.

To this we add No. (4), viz. "No y are m'", and thus get Diagram
b.

If we were to add to this No. (1), viz. "Some m are x", we
should have to put the "I" on a fence: so let us try No. (3)
instead, viz. "Some y are m". This gives us Diagram c.

And now there is no need to trouble about No. (1), as it would