“If there were any boys doing Latin, some of them would be doing Greek.”
Here, then, we have two true Premisses and a false Conclusion (since we know that there are boys doing Latin, and that none of them are doing Greek). Hence the argument is invalid.
Similarly it may be shown that this “non-existential” interpretation destroys the validity of Disamis, Datisi, Felapton, and Fresison.
Some of “The Logicians” will, no doubt, be ready to reply “But we are not Aldrichians! Why should we be responsible for the validity of the Syllogisms of so antiquated an author as Aldrich?”
Very good. Then, for the special benefit of these “friends” of mine (with what ominous emphasis that name is sometimes used! “I must have a private interview with you, my young friend,” says the bland Dr. Birch, “in my library, at 9 a.m. tomorrow. And you will please to be punctual!”), for their special benefit, I say, I will produce another charge against this “non-existential” interpretation.
It actually invalidates the ordinary Process of “Conversion”, as applied to Proposition in ‘I’.
Every logician, Aldrichian or otherwise, accepts it as an established fact that “Some x are y” may be legitimately converted into “Some y are x.”
But is it equally clear that the Proposition “If there were any x, some of them would be y” may be legitimately converted into “If there were any y, some of them would be x”? I trow not.
The example I have already used——of a Boys’ School [pg171]with a non-existent First Class——will serve admirably to illustrate this new flaw in the theory of “The Logicians.”
Let us suppose that there is yet another Rule in this School, viz. “In each Class, at the end of the Term, the head boy and the second boy shall receive prizes.”