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." (4) If they are a Pair of Entities, it is a case of "Fallacy of two Entity-Premisses." [Work Examples § =4=, 1-11 (p. 100); § =5=, 1-12 (p. 101); § =6=, 7-12 (p. 106); § =7=, 7-12 (p. 108).] pg085 BOOK VII. SORITESES. CHAPTER I. _INTRODUCTORY._ When a Set of three or more Biliteral Propositions are such that all their Terms are Species of the same Genus, and are also so related that two of them, taken together, yield a Conclusion, which, taken with another of them, yields another Conclusion, and so on, until all have been taken, it is evident that, if the original Set were true, the last Conclusion would _also_ be true. Such a Set, with the last Conclusion tacked on, is called a '=Sorites='; the original Set of Propositions is called its '=Premisses='; each of the intermediate Conclusions is called a '=Partial Conclusion=' of the Sorites; the last Conclusion is called its '=Complete Conclusion=,' or, more briefly, its '=Conclusion='; the Genus, of which all the Terms are Species, is called its '=Universe of Discourse=', or, more briefly, its '=Univ.='; the Terms, used as Eliminands in the Syllogisms, are called its '=Eliminands='; and the two Terms, which are retained, and therefore appear in the Conclusion, are called its '=Retinends='. [Note that each _Partial_ Conclusion contains one or two _Eliminands_; but that the _Complete_ Conclusion contains _Retinends_ only.] The Conclusion is said to be '=consequent=' from the Premisses; for which reason it is usual to prefix to it the word "Therefore" (or the symbol ".'."). [Note that the question, whether the Conclusion is or is not _consequent_ from the Premisses, is not affected by the _actual_ truth or falsity of any one of the Propositions which make up the Sorites, by depends entirely on their _relationship to one another_. pg086 As a specimen-Sorites, let us take the following Set of 5 Propositions:-- (1) "No a are b'; (2) All b are c; (3) All c are d; (4) No e' are a'; (5) All h are e'". Here the first and second, taken together, yield "No a are c'". This, taken along with the third, yields "No a are d'". This, taken along with the fourth, yields "No d' are e'". And this, taken along with the fifth, yields "All h are d".