_Of the Special Rules of the Four Figures_.
§ 606. Our next task must be to determine how far the 11 moods which
we arrived at in the last chapter are valid in the four figures. But
before this can be done, we must lay down the
_Special Rules of the Four Figures_.
FIGURE 1.
Rule 1, The minor premiss must be affirmative.
Rule 2. The major premiss must be universal.
FIGURE II.
Rule 1. One or other premiss must be negative.
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 reassertion
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 class; and if the minor premiss were negative, we
should not have anything declared to be contained in that class.
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
The middle term being predicate in both premisses, one or other must
be negative; else there would be undistributed middle.
§ 611. Proof of Rule 2.--_The conclusion must be negative._
Since one of the premisses is negative, it follows that the conclusion
also must be so (by Rule 6).
§ 612. Proof of Rule 3.--_The major premiss must be universal._
The conclusion being negative, the major term will there be
distributed. But the major term is subject in the major
premiss. Therefore the major premiss must be universal (by Rule 4).
FIGURE III.
§ 613. Proof of Rule 1.--_The minor premiss must be affirmative._
B--A
B--C
C--A
The proof of this rule is the same as in the first figure, the two
figures being alike so far as the major term is concerned.
§ 614. Proof of Rule 2.--_The conclusion must be particular_.
The minor premiss being affirmative, the minor term, which is its
predicate, will be undistributed there. Hence it must be undistributed
in the conclusion (by Rule 4). Therefore the conclusion must be
particular.
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.