Similarly, the only two, available for ym, are No. 11 and No. 13.  Of these, No. 11 is already marked as ‘empty’; so our red counter must go into No. 13.

The final result is

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

And now how much of this information can usefully be transferred to the smaller Diagram?

Let us take its four compartments, one by one.

As to No. 5?  This, we see, is wholly ‘empty’. (So mark it with a grey counter.)

As to No. 6?  This, we see, is ‘occupied’. (So mark it with a red counter.)

As to No. 7?  Ditto, ditto.

As to No. 8?  No information.

The smaller Diagram is now pretty liberally marked:—­

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

And now what Conclusion can we read off from this?  Well, it is impossible to pack such abundant information into one Proposition:  we shall have to indulge in two, this time.

First, by taking x as Subject, we get “all x are y’”, that is,

“All Dragons are not-Scotchmen”: 

secondly, by taking y as Subject, we get “all y are x’”, that is,

“All Scotchmen are not-Dragons”.

Let us now write out, all together, our two Premisses and our brace of Conclusions.

“All Dragons are uncanny;
All Scotchmen are canny.
&there4 All Dragons are not-Scotchmen;

                  All Scotchmen are not-Dragons.”

Let me mention, in conclusion, that you may perhaps meet with logical treatises in which it is not assumed that any Thing exists at all, by “some x are y” is understood to mean “the Attributes x, y are compatible, so that a Thing can have both at once”, and “no x are y” to mean “the Attributes x, y are incompatible, so that nothing can have both at once”.

In such treatises, Propositions have quite different meanings from what they have in our ‘Game of Logic’, and it will be well to understand exactly what the difference is.

First take “some x are y”.  Here we understand “are” to mean “are, as an actual fact”—­which of course implies that some x-Things exist. But they (the writers of these other treatises) only understand “are” to mean “Can be”, which does not at all imply that any exist. So they mean less than we do:  our meaning includes theirs (for of course “some x are y” includes “some x can be y"), but theirs does not include ours.  For example, “some Welsh hippopotami are heavy” would be true, according to these writers (since the Attributes “Welsh” and “heavy” are quite compatible in a hippopotamus), but it would be false in our Game (since there are no Welsh hippopotami to be heavy).