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).

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