. What
makes you think we have?"

_Author._ "Why, I thought you said that some of the Members----"
pg168
_Jones_ (_contemptuously_). "You don't seem to be aware that we're
working on strictly _Logical_ principles. A _Particular_ Proposition
does _not_ assert the existence of its Subject. I merely meant to say
that we've made a Rule not to admit _any_ Members till we have at least
_three_ Candidates whose incomes are over ten thousand a year!"

_Author._ "Oh, _that's_ what you meant, is it? Let's hear some more of
your Rules."

_Jones._ "Another is, that no one, who has been convicted seven times of
forgery, is admissible."

_Author._ "And here, again, I suppose you don't mean to assert there
_are_ any such convicts in existence?"

_Jones._ "Why, that's exactly what I _do_ mean to assert! Don't you know
that a Universal Negative _asserts_ the existence of its Subject? _Of
course_ we didn't make that Rule till we had satisfied ourselves that
there are several such convicts now living."

The Reader can now decide for himself how far this _second_ conceivable
view would fit in with the facts of life. He will, I think, agree with
me that Jones' view, of the 'Existential Import' of Propositions, would
lead to some inconvenience.

Thirdly, let us suppose that neither _I_ nor _E_ "asserts".

Now the supposition that the two Propositions, "Some x are y" and "No x
are not-y", do _not_ "assert", necessarily involves the supposition that
"All x are y" does _not_ "assert", since it would be absurd to suppose
that they assert, when combined, more than they do when taken
separately.

Hence the _third_ (and last) of the conceivable views is that neither
_I_, nor _E_, nor _A_, "asserts".

The advocates of this third view would interpret the Proposition "Some x
are y" to mean "If there _were_ any x in existence, some of them _would_
be y"; and so with _E_ and _A_.

It admits of proof that this view, as regards _A_, conflicts with the
accepted facts of Logic.

Let us take the Syllogism _Darapti_, which is universally accepted as
valid. Its form is

"All m are x;
All m are y.
.'. Some y are x".
pg169
This they would interpret as follows:--

"If there were any m in existence, all of them would be x;
If there were any m in existence, all of them would be y.