n 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._

Sec. 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.

(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
Sec. 2.

_Given