_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. .'. If there were any y in existence, some of them would be x". That this Conclusion does _not_ follow has been so briefly and clearly explained by Mr. Keynes (in his "Formal Logic", dated 1894, pp. 356, 357), that I prefer to quote his words:-- "_Let no proposition imply the existence either of its subject or of its predicate._ "Take, as an example, a syllogism in _Darapti_:-- '_All M is P_, _All M is S_, _.'. Some S is P_.' "Taking S, M, P, as the minor, middle, and major terms respectively, the conclusion will imply that, if there is an S, there is some P. Will the premisses also imply this? If so, then the syllogism is valid; but not otherwise. "The conclusion implies that if S exists P exists; but, consistently with the premisses, S may be existent while M and P are both non-existent. An implication is, therefore, contained in the conclusion, which is not justified by the premisses."