[pg084]§ 4.
Method of proceeding with a given Pair of Propositions.
Let us suppose that we have before us a Pair of Propositions of Relation, which contain between them a Pair of codivisional Classes, and that we wish to ascertain what Conclusion, if any, is consequent from them. We translate them, if necessary, into subscript-form, and then proceed as follows:—
(1) We examine their Subscripts, in order to see whether they are
(a) a Pair of Nullities;
or (b) a Nullity and an Entity;
or (c) a Pair of Entities.
(2) If they are a Pair of Nullities, we examine their Eliminands, in order to see whether they are Unlike or Like.
If their Eliminands are Unlike, it is a case of Fig. I. We then examine their Retinends, to see whether one or both of them are asserted to exist. If one Retinend is so asserted, it is a case of Fig. I (α); if both, it is a case of Fig. I (β).
If their Eliminands are Like, we examine them, in order to see whether either of them is asserted to exist. If so, it is a case of Fig. III.; if not, it is a case of “Fallacy of Like Eliminands not asserted to exist.”
(3) If they are a Nullity and an Entity, we examine their Eliminands, in order to see whether they are Like or Unlike.
If their Eliminands are Like, it is a case of Fig. II.; if Unlike, it is a case of “Fallacy of Unlike Eliminands with an Entity-Premiss.”