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

(<) The
AND THE ARISTOTELIAN SYLLOGISM. 147
subject in the conclusion is also subject
in its premise, and the predicate in the con
clusion is predicate in its premise.
The most fundamental of these considerations is of
course the first, which rests on an assumption of what
true reasoning is. On this ground also, we were able
to prove the special rules of the first figure. They
are really a repetition of the Canon of Reasoning itself.
These special rules may be proved
general rules of the syllogism.
Proof of the Special Rules of Fig. i.
Rule i. The minor premise must be affirmative.
The form for fig. i. is :
M P,
S Mj
. .S P7
also from the
If possible let the minor premise be negative. Then the
major must be affirmative, and P is undistributed there ;
and also the conclusion must be negative, and P is dis
tributed there. Hence if the minor premise is negative
we have an Illicit Major. Therefore the minor must be
affirmative.
Rule 2. The major premise must be universal.
Since the minor premise is affirmative, the middle term
is not distributed there. Hence it must be distributed in
the major premise ; and as it is subject there, this premise
must be universal.
EXERCISE IX.
Prove, from the General Rules of the syllogism, the fol
lowing Special Rules for the second and third figures
respectively.
Fig. ii.
1. One premise must be negative.
2. The conclusion must be negative.
3. The major premise must be universal.