“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.”
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