# Page:Carroll - Game of Logic.djvu/23

§1.]
7
PROPOSITIONS.

Of course any other Things would have done just as well as Cakes. We might make Propositions about "a Universe of Lizards", or even "a Universe of Hornets". (Wouldn't that be a charming Universe to live in?)

So far, then, we have learned that

 1

means "some ${\displaystyle x}$ and ${\displaystyle y}$" i. e. "some new are nice."

I think you will see, without further explanation, that

 1

means "some ${\displaystyle x}$ are ${\displaystyle y^{\prime }}$" i. e. "some new are not-nice."

Now let us put a grey counter into No. 5, and ask ourselves the meaning of

 0

This tells us that the ${\displaystyle xy}$-compartment is empty, which we may express by "no ${\displaystyle x}$ are ${\displaystyle y}$", or, "no new Cakes are nice". This is the second of the three Propositions at the head of this Section.

In the same way,

 0

would mean "no ${\displaystyle x}$ are ${\displaystyle y^{\prime }}$" or, "no new Cakes are not-nice."