(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 “∴”).