If two opposite judgements presuppose a contingent impossible, or arbitrary condition, both—in spite of their opposition (which is, however, not properly or really a contradiction)—fall away; because the condition, which ensured the validity of both, has itself disappeared.
If we say: "Everybody has either a good or a bad smell," we have omitted a third possible judgement—it has no smell at all; and thus both conflicting statements may be false. If we say: "It is either good-smelling or not good-smelling (vel suaveolens vel non-suaveolens)," both judgements are contradictorily opposed; and the contradictory opposite of the former judgement—some bodies are not good-smelling—embraces also those bodies which have no smell at all. In the preceding pair of opposed judgements (per disparata), the contingent condition of the conception of body (smell) attached to both conflicting statements, instead of having been omitted in the latter, which is consequently not the contradictory opposite of the former.
If, accordingly, we say: "The world is either infinite in extension, or it is not infinite (non est infinitus)"; and if the former proposition is false, its contradictory opposite—the world is not infinite—must be true. And thus I should deny the existence of an infinite, without, however affirming the existence of a finite world. But if we construct our proposition thus: "The world is either infinite or finite (non-infinite)," both statements may be false. For, in this case, we consider the world as per se determined in regard to quantity, and while, in the one judgement, we deny its infinite and consequently, perhaps, its independent existence; in the other, we append to the world, regarded as a thing in itself, a certain determination—that of finitude; and the latter may be false as well as the former, if the world is not given as a thing in itself, and thus neither as finite nor as infinite in quantity. This kind of opposition I may be allowed to term dialectical; that of contradictories may be called analytical opposition. Thus then, of two dialectically opposed judgements both may be false, from the fact, that the one is not a mere contradictory of the other, but actually enounces more than is requisite for a full and complete contradiction.
When we regard the two propositions—"The world is infinite in quantity," and, "The world is finite in quantity," as contr
