§ 620. Proof of Rule 6.—Neither of the premisses can lie a, PARTICULAR NEGATIVE.
If the major premiss were a particular negative, the conclusion would be negative. Therefore the major term would be distributed in the conclusion. But the major premiss being particular, the major term could not be distributed there. Therefore we should have an illicit process of the major term.
If the minor premiss were a particular negative, then, since the major must be affirmative (by Rule 5), we should have undistributed middle.
CHAPTER XIV
Of the Determination of the Moods that are valid in the Four Figures.
§ 621. By applying the special rules just given we shall be able to determine how many of the eleven legitimate moods are valid in the four figures.
$622. These eleven legitimate moods were found to be
AAA. AAI. AEE. AEO. AII. AOO. EAE. EAO. EIO. IAI. OAO.
FIGURE 1.
§ 623. The rule that the major premiss must be universal excludes the last two moods, IAI, OAO. The rule that the minor premiss must be affirmative excludes three more, namely, AEE, AEO, AOO.