Part 26 (1/2)

Rule 2. The conclusion must be negative.

Rule 3. The major premiss must be universal.

FIGURE III.

Rule 1. The minor premiss must be affirmative.

Rule 2. The conclusion must be particular.

FIGURE IV.

Rule 1. When the major premiss is affirmative, the minor must be universal.

Rule 2. When the minor premiss is particular, the major must be negative.

Rule 3, When the minor premiss is affirmative, the conclusion must be particular.

Rule 4. When the conclusion is negative, the major premiss must be universal.

Rule 5. The conclusion cannot be a universal affirmative.

Rule 6. Neither of the premisses can be a particular negative.

-- 607. The special rules of the first figure are merely a rea.s.sertion in another form of the Dictum de Omni et Nullo. For if the major premiss were particular, we should not have anything affirmed or denied of a whole cla.s.s; and if the minor premiss were negative, we should not have anything declared to be contained in that cla.s.s.

Nevertheless these rules, like the rest, admit of being proved from the position of the terms in the figure, combined with the rules for the distribution of terms (-- 293).

_Proof of the Special Rules of the Four Figures._

FIGURE 1.

-- 608. Proof of Rule 1.--_The minor premiss must be affirmative_.

B--A C--B C--A

If possible, let the minor premiss be negative. Then the major must be affirmative (by Rule 5), [Footnote: This refers to the General Rules of Syllogism.] and the conclusion must be negative (by Rule 6). But the major being affirmative, its predicate is undistributed; and the conclusion being negative, its predicate is distributed. Now the major term is in this figure predicate both in the major premiss and in the conclusion. Hence there results illicit process of the major term. Therefore the minor premiss must be affirmative.

-- 609. Proof of Rule 2.--_The major premiss must be universal._

Since the minor premiss is affirmative, the middle term, which is its predicate, is undistributed there. Therefore it must be distributed in the major premiss, where it is subject. Therefore the major premiss must be universal.

FIGURE II.

-- 610. Proof of Rule 1,--_One or other premiss must be negative_.

A--B C--B C--A