“Some new Cakes are unwholesome;
No nice Cakes are unwholesome
&there4 Some new Cakes are not-nice.”

And you have now worked out, successfully, your first ‘syllogism’.  Permit me to congratulate you, and to express the hope that it is but the beginning of a long and glorious series of similar victories!

We will work out one other Syllogism—­a rather harder one than the last—­and then, I think, you may be safely left to play the Game by yourself, or (better) with any friend whom you can find, that is able and willing to take a share in the sport.

Let us see what we can make of the two Premisses—­

              “All Dragons are uncanny;
               All Scotchmen are canny.”

Remember, I don’t guarantee the Premisses to be facts.  In the first place, I never even saw a Dragon:  and, in the second place, it isn’t of the slightest consequence to us, as logicians, whether our Premisses are true or false:  all we have to do is to make out whether they lead logically to the conclusion, so that, if they were true, it would be true also.

You see, we must give up the “Cakes” now, or our cupboard will be of no use to us.  We must take, as our ‘Universe’, some class of things which will include Dragons and Scotchmen:  shall we say ‘Animals’?  And, as “canny” is evidently the Attribute belonging to the ‘Middle Terms’, we will let m stand for “canny”, x for “Dragons”, and y for “Scotchmen”.  So that our two Premisses are, in full,

“All Dragon-Animals are uncanny (Animals);
All Scotchman-Animals are canny (Animals).”

And these may be expressed, using letters for words, thus:—­

“All x are m’;
All y are m.”

The first Premiss consists, as you already know, of two parts:—­

“Some x are m’,”
and “No x are m.”

And the second also consists of two parts:—­

“Some y are m,”
and “No y are m’.”

Let us take the negative portions first.

We have, then, to mark, on the larger Diagram, first, “no x are m”, and secondly, “no y are m’”.  I think you will see, without further explanation, that the two results, separately, are

-----------           -----------
|     |     |         |0    |     |
|   --|--   |         |   --|--   |
|  |0 | 0|  |         |  |  |  |  |
|--|--|--|--|         |--|--|--|--|
|  |  |  |  |         |  |  |  |  |
|   --|--   |         |   --|--   |
|     |     |         |0    |     |
-----------           -----------

and that these two, when combined, give us

-----------
|0    |     |
|   --|--   |
|  |0 | 0|  |
|--|--|--|--|
|  |  |  |  |
|   --|--   |
|0    |     |
-----------

We have now to mark the two positive portions, “some x are m’” and “some y are m”.

The only two compartments, available for Things which are xm’, are No. 9 and No. 10.  Of these, No. 9 is already marked as ‘empty’; so our red counter must go into No. 10.