This tells us that there is at least one Thing in the Inner portion of the North Half; that is, that this Compartment is occupied. And this we can evidently represent by placing a Red Counter on the partition which divides it.
[In the “books” example, this Proposition would mean “Some old bound books exist” (or “There are some old bound books”).]
Similarly we may represent the seven similar Propositions, “Some xm′ exist”, “Some x′m exist”, “Some x′m′ exist”, “Some ym exist”, “Some ym′ exist”, “Some y′m exist”, and “Some y′m′ exist”.
[pg044]Let us take, next, the Proposition “No xm exist”.
This tells us that there is nothing in the Inner portion of the North Half; that is, that this Compartment is empty. And this we can represent by placing two Grey Counters in it, one in each Cell.
Similarly we may represent the seven similar Propositions, in terms of x and m, or of y and m, viz. “No xm′ exist”, “No x′m exist”, &c.
These sixteen Propositions of Existence are the only ones that we shall have to represent on this Diagram.