And now what kind of Cakes would you expect to find in compartment No. 5?

It is part of the upper half, you see; so that, if it has any Cakes in it, they must be new:  and it is part of the left-hand half; so that they must be nice.  Hence if there are any Cakes in this compartment, they must have the double ‘attribute’ “new and nice”:  or, if we use letters, the must be “x y.”

Observe that the letters x, y are written on two of the edges of this compartment.  This you will find a very convenient rule for knowing what Attributes belong to the Things in any compartment.  Take No. 7, for instance.  If there are any Cakes there, they must be “x’ y”, that is, they must be “not-new and nice.”

Now let us make another agreement—­that a red counter in a compartment shall mean that it is ‘occupied’, that is, that there are some Cakes in it. (The word ‘some,’ in Logic, means ’one or more’ so that a single Cake in a compartment would be quite enough reason for saying “there are some Cakes here").  Also let us agree that a grey counter in a compartment shall mean that it is ‘empty’, that is that there are no Cakes in it.  In the following Diagrams, I shall put ‘1’ (meaning ‘one or more’) where you are to put a red counter, and ‘0’ (meaning ‘none’) where you are to put a grey one.

As the Subject of our Proposition is to be “new Cakes”, we are only concerned, at present, with the upper half of the cupboard, where all the Cakes have the attribute x, that is, “new.”

Now, fixing our attention on this upper half, suppose we found it marked like this,

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

that is, with a red counter in No. 5.  What would this tell us, with regard to the class of “new Cakes”?

Would it not tell us that there are some of them in the x y-compartment?  That is, that some of them (besides having the Attribute x, which belongs to both compartments) have the Attribute y (that is, “nice").  This we might express by saying “some x-Cakes are y-(Cakes)”, or, putting words instead of letters,

“Some new Cakes are nice (Cakes)”,

or, in a shorter form,

“Some new Cakes are nice”.

At last we have found out how to represent the first Proposition of this Section.  If you have not clearly understood all I have said, go no further, but read it over and over again, till you do understand it.  After that is once mastered, you will find all the rest quite easy.

It will save a little trouble, in doing the other Propositions, if we agree to leave out the word “Cakes” altogether.  I find it convenient to call the whole class of Things, for which the cupboard is intended, the ‘universe.’  Thus we might have begun this business by saying “Let us take a Universe of Cakes.” (Sounds nice, doesn’t it?)