# Page:Carroll - Game of Logic.djvu/31

§ 1.]
15
PROPOSITIONS.

and I must content myself with doing two or three, as specimens. You will do well to work out a lot more for yourself.

Taking the upper half by itself, so that our Subject is "new Cakes", how are we to represent "no new Cakes are wholesome"?

This is, writing letters for words, "no ${\displaystyle x}$ are ${\displaystyle m}$." Now this tells us that none of the Cakes, belonging to the upper half of the cupboard, are to be found inside the central Square: that is, the two compartments, No. 11 and No. 12, are empty. And this, of course, is represented by

 0 0

And now how are we to represent the contradictory Proposition "some ${\displaystyle x}$ are ${\displaystyle m}$"? This is a difficulty I have already considered. I think the best way is to place a red counter on the division-line between No. 11 and No. 12, and to understand this to mean that one of the two compartments is 'occupied,' but that we do not at present know which. This I shall represent thus:—

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