# Page:Carroll - Game of Logic.djvu/22

6
[Ch.I.
NEW LAMPS FOR OLD.

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 ${\displaystyle xy}$-compartment? That is, that some of them (besides having the Attribute ${\displaystyle x}$, which belongs to both compartments) have the Attribute ${\displaystyle y}$ (that is, "nice"). This we might express by saying "some ${\displaystyle x}$-Cakes are ${\displaystyle y}$-(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?)