# Page:Carroll - Game of Logic.djvu/32

16
[Ch. I
NEW LAMPS FOR OLD.

Now let us express "all ${\displaystyle x}$ are ${\displaystyle m}$."

This consists, we know, of two Propositions,

"Some ${\displaystyle x}$ are ${\displaystyle m}$,"

and "No ${\displaystyle x}$ are ${\displaystyle m^{\prime }}$."

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 ${\displaystyle x}$ are ${\displaystyle m}$." 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

 0 0 —

Now let us try one or two interpretations.

What are we to make of this, with regard to ${\displaystyle x}$ and ${\displaystyle y}$?

 0 1 0