This will puzzle you a little, I expect. Evidently you must put a red counter SOMEWHERE in the x-half of the cupboard, since you know there are SOME new Cakes. But you must not put it into the LEFT-HAND compartment, since you do not know them to be NICE: nor may you put it into the RIGHT-HAND one, since you do not know them to be NOT-NICE. What, then, are you to do? I think the best way out of the difficulty is to place the red counter ON THE DIVISION-LINE between the xy-compartment and the xy'-compartment. This I shall represent (as I always put '1' where you are to put a red counter) by the diagram ----------- | | | | -1- | | | | ----------- Our ingenious American cousins have invented a phrase to express the position of a man who wants to join one or the other of two parties--such as their two parties 'Democrats' and 'Republicans'--but can't make up his mind WHICH. Such a man is said to be "sitting on the fence." Now that is exactly the position of the red counter you have just placed on the division-line. He likes the look of No. 5, and he likes the look of No. 6, and he doesn't know WHICH to jump down into. So there he sits astride, silly fellow, dangling his legs, one on each side of the fence! Now I am going to give you a much harder one to make out. What does this mean? ----------- | | | | 1 | 0 | | | | ----------- This is clearly a DOUBLE Proposition. It tells us not only that "some x are y," but also the "no x are NOT y." Hence the result is "ALL x are y," i.e. "all new Cakes are nice", which is the last of the three Propositions at the head of this Section. We see, then, that the Universal Proposition "All new Cakes are nice" consists of TWO Propositions taken together, namely, "Some new Cakes are nice," and "No new Cakes are not-nice." In the same way ----------- | | | | 0 | 1 | | | | ----------- would mean "all x are y' ", that is, "All new Cakes are not-nice." Now what would you make of such a Proposition as "The Cake you have given me is nice"? Is it Particular or Universal? "Particular, of course," you readily reply. "One single Cake is hardly worth calling 'some,' even."