This seems to _me_ entirely clear and convincing. Still, "to make sicker", I may as well throw the above (_soi-disant_) Syllogism into a concrete form, which will be within the grasp of even a _non_-logical Reader. Let us suppose that a Boys' School has been set up, with the following system of Rules:-- "All boys in the First (the highest) Class are to do French, Greek, and Latin. All in the Second Class are to do Greek only. All in the Third Class are to do Latin only." Suppose also that there _are_ boys in the Third Class, and in the Second; but that no boy has yet risen into the First. It is evident that there are no boys in the School doing French: still we know, by the Rules, what would happen if there _were_ any. pg170 We are authorised, then, by the _Data_, to assert the following two Propositions:-- "If there were any boys doing French, all of them would be doing Greek; If there were any boys doing French, all of them would be doing Latin." And the Conclusion, according to "The Logicians" would be "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 with a non-existent First Class----will serve admirably to illustrate this new flaw in the theory of "The Logicians." pg171 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."