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

We have now to express the other Premiss, namely, “some new Cakes are unwholesome (Cakes)”, i.e. “some x-Cakes are m’-(Cakes)”.  This tells us that some of the Cakes in the x-half of the cupboard are in its m’-compartments.  Hence one of the two compartments, No. 9 and No. 10, is ‘occupied’:  and, as we are not told in which of these two compartments to place the red counter, the usual rule would be to lay it on the division-line between them:  but, in this case, the other Premiss has settled the matter for us, by declaring No. 9 to be empty.  Hence the red counter has no choice, and must go into No. 10, thus:—­

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

And now what counters will this information enable us to place in the smaller Diagram, so as to get some Proposition involving x and y only, leaving out m?  Let us take its four compartments, one by one.

First, No. 5.  All we know about this is that its outer portion is empty:  but we know nothing about its inner portion.  Thus the Square may be empty, or it may have something in it.  Who can tell?  So we dare not place any counter in this Square.

Secondly, what of No. 6?  Here we are a little better off.  We know that there is something in it, for there is a red counter in its outer portion.  It is true we do not know whether its inner portion is empty or occupied:  but what does that matter?  One solitary Cake, in one corner of the Square, is quite sufficient excuse for saying “This Square is occupied”, and for marking it with a red counter.

As to No. 7, we are in the same condition as with No. 5—­we find it partly ‘empty’, but we do not know whether the other part is empty or occupied:  so we dare not mark this Square.

And as to No. 8, we have simply no information at all.

The result is

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

Our ‘Conclusion’, then, must be got out of the rather meager piece of information that there is a red counter in the xy’-Square.  Hence our Conclusion is “some x are y’ “, i.e. “some new Cakes are not-nice (Cakes)”:  or, if you prefer to take y’ as your Subject, “some not-nice Cakes are new (Cakes)”; but the other looks neatest.

We will now write out the whole Syllogism, putting the symbol &there4[*] for “therefore”, and omitting “Cakes”, for the sake of brevity, at the end of each Proposition.

[*][Note from Brett:  The use of “&there4” is a rather arbitrary selection.  There is no font available in general practice which renders the “therefore” symbol correction (three dots in a triangular formation).  This can be done, however, in html, so if this document is read in a browser, then the symbol will be properly recognized.  This is a poor man’s excuse.]