Page:Carroll - Game of Logic.djvu/23

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 $x$ and $y$" i. e. "some new are nice."

I think you will see, without further explanation, that

1

means "some $x$ are $y^{\prime }$" 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 $xy$-compartment is empty, which we may express by "no $x$ are $y$", 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 $x$ are $y^{\prime }$" or, "no new Cakes are not-nice."