Page:Carroll - Game of Logic.djvu/39

We have now to express the other Premiss, namely, "some new Cakes are unwholesome (Cakes)", i.e. "some ${\displaystyle x}$-Cakes are ${\displaystyle m^{\prime }}$-(Cakes)". This tells us that some of the Cakes in the ${\displaystyle x}$-half of the cupboard are in its ${\displaystyle m^{\prime }}$-compartments. Hence one of the two compartments, No. 9 and No. 10, is 'occupied': and, as we are not told in which of these two compartments to place the red counter, the usual rule would be to lay it on the division-line between them: but, in this case, the other Premiss has settled the matter for us, by declaring No. 9 to be empty. Hence the red counter has no choice, and must go into No. 10, thus:—
And now what counters will this information enable us to place in the smaller Diagram, so as to get some Proposition involving ${\displaystyle x}$ and ${\displaystyle y}$ only, leaving out ${\displaystyle m}$? Let us take its four compartments, one by one.