§ 3.
Representation of Propositions of Relation.
Let us take, first, the Proposition “Some x are y”.
This tells us that at least one Thing, in the North Half, is also in the West Half. Hence it must be in the space common to them, that is, in the North-West Cell. Hence the North-West Cell is occupied. And this we can represent by placing a Red Counter in it.
[Note that the Subject of the Proposition settles which Half we are to use; and that the Predicate settles in which portion of it we are to place the Red Counter.
In the “books” example, this Proposition would be “Some old books are English”.]
Similarly we may represent the three similar Propositions “Some x are y′”, “Some x′ are y”, and “Some x′ are y′”.
[The Reader should make out all these for himself. In the “books” example, these three Propositions would be “Some old books are foreign”, &c.]
[pg031]Let us take, next, the Proposition “Some y are x”.