Page:Carroll - Game of Logic.djvu/39

§ 2.] We have now to express the other Premiss, namely, "some new Cakes are unwholesome (Cakes)", i.e. "some $$x$$-Cakes are $$m^\prime$$-(Cakes)". This tells us that some of the Cakes in the $$x$$-half of the cupboard are in its $$m^\prime$$-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 $$x$$ and $$y$$ only, leaving out $$m$$? Let us take its four compartments, one by one.

First, No. 5. All we know about this is that its outer portion is empty: but we know nothing about its inner portion. Thus the Square may be empty, or it may have something in it. Who can tell? So we dare not place any counter in this Square.