propositions where the predicate is conceived as so essential to the subject that a separation in one case involves a separation in all. Now, as we have seen, the ordinary formula for Opposition is founded upon nothing but the first of these meanings, where no necessary connection is involved between subject and predicate. Thus, if I affirm distributively that "All men believe in the existence of a first cause," it is sufficient to show the falsity of the proposition if some one proves that "some men (say certain savages) do not believe in the existence of a first cause." If the former be true, however, the latter is false, as we know. But if any affirmation be collective in its meaning, the case is different. Thus I affirm, "The English constitute a nation," meaning, of course, "all Englishmen " taken collectively. Now, according to the ordinary rule, the truth of this would involve the falsity of the proposition O, "some Englishmen do not constitute a nation." But, in comparison with the former, this is true instead of being false, and I would be false instead of true. The Square of Opposition would then stand as in Fig. I.
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This is in some respects simpler than the ordinary theory because of the order of contradictories involved. Not that it can be substituted for it, but that there is a usage, and a very extended one, that requires the application of the principle involved in collective conceptions. At the same time, we could just as well attempt to make this the universal formula as to do so with the accepted theory. The real truth is that neither one of them has a universal application, and that for actual practice we need the use of both of them.
