This tells us that there is nothing in the North-West Cell; that is, that the North-West Cell is empty. And this we can represent by placing a Grey Counter in it.
[In the “books” example, this Proposition would be “No old English books exist”.]
Similarly we may represent the three similar Propositions “No xy′ exist”, “No x′y exist”, and “No x′y′ exist”.
[The Reader should make out all these for himself. In the “books” example, these three Propositions would be “No old foreign books exist”, &c.]
We have seen that the Proposition “No x exist” may be represented by placing two Grey Counters in the North Half, one in each Cell.
We have also seen that these two Grey Counters, taken separately, represent the two Propositions “No xy exist” and “No xy′ exist”.
Hence we see that the Proposition “No x exist” is a Double Proposition, and is equivalent to the two Propositions “No xy exist” and “No xy′ exist”.
[In the “books” example, this Proposition would be “No old books exist”.
Hence this is a Double Proposition, and is equivalent to the two Propositions “No old English books exist” and “No old foreign books exist”.]