We see, then, that the supposition “I asserts” necessarily leads to “A asserts, but E does not”. And this is the first of the various views that may conceivably be held.
Next, let us suppose that I does not “assert.” And, along with this, let us take the supposition that E does “assert.”
Hence the Proposition “No x are y” means “Some x exist, and none of them are y”: i.e. “all of them are not-y,” which is a Proposition in A. We also know, of course, that the Proposition “All x are not-y” proves “No x are y.” Now two Propositions, each of which proves the other, are equivalent. Hence every Proposition in A is equivalent to one in E, and therefore “asserts”.
Hence our second conceivable view is “E and A assert, but I does not.”
This view does not seen to involve any necessary contradiction with itself or with the accepted facts of Logic. But, when we come to test it, as applied to the actual facts of life, we shall find I think, that it fits in with them so badly that its adoption would be, to say the least of it, singularly inconvenient for ordinary folk.
Let me record a little dialogue I have just held with my friend Jones, who is trying to form a new Club, to be regulated on strictly Logical principles.
Author. “Well, Jones! Have you got your new Club started yet?”
Jones (rubbing his hands). “You’ll be glad to hear that some of the Members (mind, I only say ‘some’) are millionaires! Rolling in gold, my boy!”
Author. “That sounds well. And how many Members have entered?”
Jones (staring). “None at all. We haven’t got it started yet. What makes you think we have?”