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

AND THE ARISTOTELIAN SYLLOGISM. 131
We shall now work a few examples which may be solved
by direct application of the above rules.
(1) Prove that when the minor term is predicate in its
premise, the conclusion cannot be A. [L.]
It is required to show that the conclusion is either neg
ative, or, if affirmative, is not A. Now it is given that the
minor term is predicate in its premise. It must be either
distributed or undistributed. If the minor term is dis
tributed in its premise, this premise is negative, and there
fore the conclusion is negative (rule 6). If the minor term
is undistributed in its premise, it is undistributed in the
conclusion (rule 4) z>., the conclusion is particular.
(2) If the major term of a syllogism be predicate in
the major premise, what do we know about the minor
premise ? [L.]
The major term must be either distributed or undis
tributed in the major premise. If distributed, the major
premise is negative, and therefore the minor is affirmative
(rule 5). If undistributed, it is undistributed also in the
conclusion (rule 4) and ; as it is the predicate of the con
clusion, the conclusion must be affirmative ; therefore both
1
are affirmative z>.,
premises
the minor is affirmative.
(3) () What can we tell about a valid syllogism if we
know that only the middle term is distributed?
If neither the major nor the minor term is distributed,
the conclusion can contain no distributed term, and must
therefore be an I proposition.
(6) How much can we tell about a valid syllogism if
we know that only the middle and minor terms are
distributed ?
The major term is not distributed, therefore the conclu
sion cannot be negative.
4. Syllogisms are divided into three classes, called
figures (a-^fiara), according to the position of the
middle term.
In the first figure the middle term is the subject of
1
For, if one premise were negative, the conclusion must be
negative (rule 6), which it is not.