FIGURE IV.
§ 615. Proof of Rule I.—When the major premiss is affirmative, the minor must be universal.
If the minor were particular, there would be undistributed middle. [Footnote: Shorter proofs are employed in this figure, as the student is by this time familiar with the method of procedure.]
§ 616. Proof of Rule 2.—When the minor premiss is particular, the major must be negative.
A—B B—C C—A
This rule is the converse of the preceding, and depends upon the same principle.
§ 617. Proof of Rule 3.—When the minor premiss is affirmative, the conclusion must be particular.
If the conclusion were universal, there would be illicit process of the minor.
§ 618. Proof of Rule 4.—When the conclusion is negative, the major premiss must be universal.
If the major premiss were particular, there would be illicit process of the major.
§ 619. Proof of Rule 5.—The conclusion CANNOT be A UNIVERSAL affirmative.
The conclusion being affirmative, the premisses must be so too (by Rule 7). Therefore the minor term is undistributed in the minor premiss, where it is predicate. Hence it cannot be distributed in the conclusion (by Rule 4). Therefore the affirmative conclusion must be particular.
§ 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.