The Game of Logic

by Lewis Carroll

Let us express the negative part first. This tells us that none of the Cakes, belonging to the upper half of the cupboard, are to be found OUTSIDE the central Square: that is, the two compartments, No. 9 and No. 10, are EMPTY. This, of course, is represented by

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| 0 | 0 |
| _____|_____ |
| | | | |
| | | | |
| | | | |
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But we have yet to represent "Some x are m." This tells us that there are SOME Cakes in the oblong consisting of No. 11 and No. 12: so we place our red counter, as in the previous example, on the division-line between No. 11 and No. 12, and the result is

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| 0 | 0 |
| _____|_____ |
| | | | |
| | -1- | |
| | | | |
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Now let us try one or two interpretations.

What are we to make of this, with regard to x and y?

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| | 0 |
| _____|_____ |
| | | | |
| | 1 | 0 | |
| | | | |
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This tells us, with regard to the xy'-Square, that it is wholly 'empty', since BOTH compartments are so marked. With regard to the xy-Square, it tells us that it is 'occupied'. True, it is only ONE compartment of it that is so marked; but that is quite enough, whether the other be 'occupied' or 'empty', to settle the fact that there is SOMETHING in the Square.

If, then, we transfer our marks to the smaller Diagram, so as to get rid of the m-subdivisions, we have a right to mark it

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| | |
| 1 | 0 |
| | |
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