An introductory text-book of logic - Mellone, Sydney - Rare Books at ...

134
MEDIATE INFERENCE
are universal affirmative ; IA, that the major is particular
affirmative, the minor universal affirmative ; and so on.
In each case the first of the two letters denotes the
major, and the second the minor, premise.
We cannot take for granted that all of these are valid
that is, lead to correct conclusions in each or any
figure. The valid moods will have to be found in
another way. Aristotle discovered the valid moods by
testing one by one the possible cases in each figure.
But the principal methods by which he examined or
tested them were afterwards formally drawn up, and
known as the Rules or Canons of the Syllogism, as
explained in the previous section.
There are, then, sixteen possible moods to examine.
Seven of these lead to no valid conclusions, in any
figure, by the rules: EE, EO, OO, OE are excluded
by the rule against two negatives, and IO, II, OI by
that against two particulars. This leaves us with nine
possible moods AA, AE, AI, AO, EA, El, IA, IE, OA.
But it may be further proved from the general rules of
the syllogism alone that the mood IE can yield no
conclusion in any figure :
If possible, let there be a conclusion : then it must
be negative.
And every negative proposition distributes its predicate
(the major term) ;
But the major premise I distributes neither subject
nor predicate;
Therefore there would be an Illicit Major.
We are thus left with eight moods, and we shall
examine each of these in each of the four figures, testing
the results by the rules.