-------------------
| 0       |       1 |
|    _____|_____    |
|   |     |     |   |
|   |     |     |   |
|   |     |     |   |
-------------------

This tells us, as to the xy-Square, that one of its compartments is ‘empty’.  But this information is quite useless, as there is no mark in the other compartment.  If the other compartment happened to be ‘empty’ too, the Square would be ‘empty’:  and, if it happened to be ‘occupied’, the Square would be ‘occupied’.  So, as we do not know which is the case, we can say nothing about this Square.

The other Square, the xy’-Square, we know (as in the previous example) to be ‘occupied’.

If, then, we transfer our marks to the smaller Diagram, we get merely this:—­

-----------
|     |     |
|     |  1  |
|     |     |
-----------

which means, you know, “some x are y’.”

These principles may be applied to all the other
oblongs.  For instance, to represent
“all y’ are m’” we should mark the -------
right-hand upright oblong (the one | |
that has the attribute y’) thus:-- |--- |
                                      | 0 | |
                                      |---|-1-|
                                      | 0 | |
                                      |--- |
                                      | |
                                       -------

and, if we were told to interpret the lower half of the cupboard, marked as follows, with regard to x and y,

-------------------
|   |     |     |   |
|   |     |  0  |   |
|   |     |     |   |
|    -----|-----    |
| 1       |       0 |
-------------------

we should transfer it to the smaller Diagram thus,

-----------
|     |     |
|  1  |  0  |
|     |     |
-----------

and read it “all x’ are y.”

Two more remarks about Propositions need to be made.

One is that, in every Proposition beginning with “some” or “all”, the actual existence of the ‘Subject’ is asserted.  If, for instance, I say “all misers are selfish,” I mean that misers actually exist. If I wished to avoid making this assertion, and merely to state the law that miserliness necessarily involves selfishness, I should say “no misers are unselfish” which does not assert that any misers exist at all, but merely that, if any did exist, they would be selfish.

The other is that, when a Proposition begins with “some” or “no”, and contains more that two Attributes, these Attributes may be re-arranged, and shifted from one Term to the other, “ad libitum.”  For example, “some abc are def” may be re-arranged as “some bf are acde,” each being equivalent to “some Things are abcdef”.  Again “No wise old men are rash and reckless gamblers” may be re-arranged as “No rash old gamblers are wise and reckless,” each being equivalent to “No men are wise old rash reckless gamblers.”