# Page:Carroll - Game of Logic.djvu/25

§1.]
9
PROPOSITIONS.

What, then, are you to do? I think the best way out of the difficulty is to place the red counter on the division-line between the ${\displaystyle xy}$-compartment and the ${\displaystyle xy^{\prime }}$-compartment. This I shall represent (as I always put '1' where you are to put a red counter) by the diagram

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Our ingenious American cousins have invented a phrase to express the position of a man who wants to join one or other of two parties——such as their two parties 'Democrats' and 'Republicans'——but ca'n't make up his mind which. Such a man is said to be "sitting on the fence." Now that is exactly the position of the red counter you have just placed on the division-line. He likes the look of No. 5, and he likes the look of No. 6, and he doesn't know which to jump down into. So there he sits astride, silly fellow, dangling his legs, one on each side of the fence!

Now I am going to give you a much harder one to make out. What does this mean?

 1 0

This is clearly a double Proposition. It tells us, not only that "some ${\displaystyle x}$ are ${\displaystyle y}$," but also that "no ${\displaystyle x}$ are not ${\displaystyle y}$." Hence the result is "all ${\displaystyle x}$ are ${\displaystyle y}$," i. e. "all new Cakes are nice", which is the last of the three Propositions at the head of this Section.