xm_{0} + y_{1}m_{0} x_{1}m_{0} + y_{1}m_{0} ·---------------· ·---------------· | | | | (I) | | ·---|---· | | ·---|---· | | |(O)|(O)| | | |(O)|(O)| | |(I)|---|---|---| |(I)|---|---|---| | |(O)| | | | |(O)| | | | ·---|---· | | ·---|---· | | | | | | | ·---------------· ·---------------· pg083 (2) _Fallacy of Unlike Eliminands with an Entity-Premiss._ Here the given Pair may be represented by (xm_{0} + ym'_{1}) with or without x_{1} or m_{1}. These, set out on Triliteral Diagrams, are xm_{0} + ym'_{1} x_{1}m_{0} + ym'_{1} m_{1}x_{0} + ym'_{1} ·---------------· ·---------------· ·---------------· | | | | (I) | | | | | ·---|---· | | ·---|---· | | ·---|---· | | |(O)|(O)| | | |(O)|(O)| | | |(O)|(O)| | |(I)|---|---|---| |(I)|---|---|---| |(I)|---|---|---| | | | | | | | | | | | | (I) | | | ·---|---· | | ·---|---· | | ·---|---· | | | | | | | | | | ·---------------· ·---------------· ·---------------· (3) _Fallacy of two Entity-Premisses._ Here the given Pair may be represented by either (xm_{1} + ym_{1}) or (xm_{1} + ym'_{1}). These, set out on Triliteral Diagrams, are xm_{1} + ym_{1} xm_{1} + ym'_{1} ·---------------· ·---------------· | | | | | | | ·---|---· | | ·---|---· | | | (I) | | | | (I) | | |---|(I)|---|---| |(I)|---|---|---| | | | | | | | | | | | ·---|---· | | ·---|---· | | | | | | | ·---------------· ·---------------· 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 (a); if both, it is a case of Fig. I (b).