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16

[Ch. I

*NEW LAMPS FOR OLD.*

Now let us express "all are ."

This consists, we know, of *two* Propositions,

"Some are ,"

and "No are ."

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

0 | 0 | ||

But we have yet to represent "Some are ." 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

0 | 0 | ||

— |

Now let us try one or two interpretations.

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

0 | |||

1 | 0 |