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.’