Chapter I: Introductory

When a Trio of Biliteral Propositions of Relation is such that

(1) all their six Terms are Species of the same Genus,

(2) every two of them contain between them a Pair of
codivisional Classes,

(3) the three Propositions are so related that, if the first
two were true, the third would be true,

the Trio is called a '=Syllogism='; the Genus, of which each of the six Terms is a Species, is called its ='Universe of Discourse=', or, more briefly, its '=Univ.='; the first two Propositions are called its '=Premisses=', and the third its '=Conclusion='; also the Pair of codivisional Terms in the Premisses are called its '=Eliminands=', and the other two its '=Retinends='.

The Conclusion of a Syllogism is said to be '=consequent=' from its
Premisses: hence it is usual to prefix to it the word "Therefore" (or
the Symbol ".'.").
pg057
[Note that the 'Eliminands' are so called because they are
_eliminated_, and do not appear in the Conclusion; and that the
'Retinends' are so called because they are _retained_, and _do_
appear in the Conclusion.

Note also 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 of the Trio, but depends entirely on
their _relationship to each other_.

As a specimen-Syllogism, let us take the Trio

"No x-Things are m-Things;
No y-Things are m'-Things.
No x-Things are y-Things."

which we may write, as explained at p. 26, thus:--

"No x are m;
No y are m'.
No x are y".

Here the first and second contain the Pair of codivisional
Classes m and m'; the first and third contain the Pair x and x;
and the second and third contain the Pair y and y.

Also the three Propositions are (as we shall see hereafter) so
related that, if the first two were true, the third would also
be true.

Hence the Trio is a _Syllogism_; the two Propositions, "No x are
m" and "No y are m'", are its _Premisses_; the Proposition "No x
are y" is its _Conclusion_; the Terms m and m' are its
_Eliminands_; and the Terms x and y are its _Retinends_.

Hence we may write it thus:--

"No x are m;
No y are m'.
.'. No x are y".

As a second specimen, let us take the Trio

"All cats understand French;
Some chickens are cats.
Some chickens understand French".

These, put into normal form, are

"All cats are creatures understanding French;
Some chickens are cats.
Some chickens are creatures understanding French".

Here all the six Terms are Species of the Genus "creatures."

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