Also the first and second Propositions contain the Pair of codivisional Classes "cats" and "cats"; the first and third contain the Pair "creatures understanding French" and "creatures understanding French"; and the second and third contain the Pair "chickens" and "chickens". pg058 Also the three Propositions are (as we shall see at p. 64) so related that, if the first two were true, the third would be true. (The first two are, as it happens, _not_ strictly true in _our_ planet. But there is nothing to hinder them from being true in some _other_ planet, say _Mars_ or _Jupiter_--in which case the third would _also_ be true in that planet, and its inhabitants would probably engage chickens as nursery-governesses. They would thus secure a singular _contingent_ privilege, unknown in England, namely, that they would be able, at any time when provisions ran short, to utilise the nursery-governess for the nursery-dinner!) Hence the Trio is a _Syllogism_; the Genus "creatures" is its 'Univ.'; the two Propositions, "All cats understand French" and "Some chickens are cats", are its _Premisses_, the Proposition "Some chickens understand French" is its _Conclusion_; the Terms "cats" and "cats" are its _Eliminands_; and the Terms, "creatures understanding French" and "chickens", are its _Retinends_. Hence we may write it thus:-- "All cats understand French; Some chickens are cats; .'. Some chickens understand French".] pg059 CHAPTER II. _PROBLEMS IN SYLLOGISMS._ § 1. _Introductory._ When the Terms of a Proposition are represented by _words_, it is said to be '=concrete='; when by _letters_, '=abstract=.' To translate a Proposition from concrete into abstract form, we fix on a Univ., and regard each Term as a _Species_ of it, and we choose a letter to represent its _Differentia_. [For example, suppose we wish to translate "Some soldiers are brave" into abstract form. We may take "men" as Univ., and regard "soldiers" and "brave men" as _Species_ of the _Genus_ "men"; and we may choose x to represent the peculiar Attribute (say "military") of "soldiers," and y to represent "brave." Then the Proposition may be written "Some military men are brave men"; _i.e._ "Some x-men are y-men"; _i.e._ (omitting "men," as explained at p. 26) "Some x are y." In practice, we should merely say "Let Univ. be "men", x = soldiers, y = brave", and at once translate "Some soldiers are brave" into "Some x are y."] The Problems we shall have to solve are of two kinds, viz.