Let us consider certain views that may logically be held, and thus settle which of them may conveniently be held; after which I shall hold myself free to declare which of them I intend to hold.
The kinds of Propositions, to be considered, are those that begin with “some”, with “no”, and with “all”. These are usually called Propositions “in I”, “in E”, and “in A”.
First, then, a Proposition in I may be understood as asserting, or else as not asserting, the existence of its Subject. (By “existence” I mean of course whatever kind of existence suits its nature. The two Propositions, “dreams exist” and “drums exist”, denote two totally different kinds of “existence”. A dream is an aggregate of ideas, and exists only in the mind of a dreamer: whereas a drum is an aggregate of wood and parchment, and exists in the hands of a drummer.)
First, let us suppose that I “asserts” (i.e. “asserts the existence of its Subject”).
Here, of course, we must regard a Proposition in A as making the same assertion, since it necessarily contains a Proposition in I.
We now have I and A “asserting”. Does this leave us free to make what supposition we choose as to E? My answer is “No. We are tied down to the supposition that E does not assert.” This can be proved as follows:—
If possible, let E “assert”. Then (taking x, y, and z to represent Attributes) we see that, if the Proposition “No xy are z” be true, some things exist with the Attributes x and y: i.e. “Some x are y.”
[pg167]Also we know that, if the Proposition “Some xy are z” be true, the same result follows.
But these two Propositions are Contradictories, so that one or other of them must be true. Hence this result is always true: i.e. the Proposition “Some x are y” is always true!
Quod est absurdum. (See [Note (A), p. 195]).