(1) "Given a Pair of Propositions of Relation, which contain between them a pair of codivisional Classes, and which are proposed as Premisses: to ascertain what Conclusion, if any, is consequent from them." (2) "Given a Trio of Propositions of Relation, of which every two contain a pair of codivisional Classes, and which are proposed as a Syllogism: to ascertain whether the proposed Conclusion is consequent from the proposed Premisses, and, if so, whether it is _complete_." These Problems we will discuss separately. pg060 § 2. _Given a Pair of Propositions of Relation, which contain between them a pair of codivisional Classes, and which are proposed as Premisses: to ascertain what Conclusion, if any, is consequent from them._ The Rules, for doing this, are as follows:-- (1) Determine the 'Universe of Discourse'. (2) Construct a Dictionary, making m and m (or m and m') represent the pair of codivisional Classes, and x (or x') and y (or y') the other two. (3) Translate the proposed Premisses into abstract form. (4) Represent them, together, on a Triliteral Diagram. (5) Ascertain what Proposition, if any, in terms of x and y, is _also_ represented on it. (6) Translate this into concrete form. It is evident that, if the proposed Premisses were true, this other Proposition would _also_ be true. Hence it is a _Conclusion_ consequent from the proposed Premisses. [Let us work some examples. (1) "No son of mine is dishonest; People always treat an honest man with respect". Taking "men" as Univ., we may write these as follows:-- "No sons of mine are dishonest men; All honest men are men treated with respect". We can now construct our Dictionary, viz. m = honest; x = sons of mine; y = treated with respect. (Note that the expression "x = sons of mine" is an abbreviated form of "x = the Differentia of 'sons of mine', when regarded as a Species of 'men'".) The next thing is to translate the proposed Premisses into abstract form, as follows:-- "No x are m'; All m are y". pg061 Next, by the process described at p. 50, we represent these on a Triliteral Diagram, thus:-- ·---------------· |(O) | (O)| | ·---|---· | | | |(O)| | |---|(I)|---|---| | | |(O)| | | ·---|---· | | | | ·---------------· Next, by the process described at p. 53, we transfer to a Biliteral Diagram all the information we can. ·-------· | |(O)| |---|---| | | | ·-------· The result we read as "No x are y'" or as "No y' are x," whichever we prefer. So we refer to our Dictionary, to see which will look best; and we choose "No x are y'",