§ 745. It is apparent from the position of the middle term that the constructive conjunctive must fall into the first figure and the destructive conjunctive into the second. There is no reason, however, why they should be confined to the two moods, Barbara and Carnestres. If the inference is universal, whether as general or singular, the mood is Barbara or Carnestres; if it is particular, the mood is Darii or Baroko.
Barbara. Camestres.
If A is B, C is always D. \ If A is B, C is always D. \
A is always B. \ C is never D. \
.'. C is always D. \ .'. A is never B. \
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If A is B, C is always D. / If A is B, C is always D. /
A is in this case B. / C is not in this case D. /
.'. C is in this case D. / .'. A is not in this case B. /
Darii. Baroko.
If A is B, C is always D. If A is B, C is never D.
A is sometimes B. C is sometimes not D.
.'. C is sometimes D. .'. A is sometimes not B.
§ 746. The remaining moods of the first and second figure are obtained by taking a negative proposition as the consequent in the major premiss.
Celarent. Ferio.
If A is B, C is never D. If A is B, C is never D.
A is always B. A is sometimes B.
.'. C is never D. .'. C is sometimes not D.
Cesare. Festino.
If A is B, C is never D. If A is B, C is never D.
C is always D. C is sometimes D.
.'. A is never B. .'. A is sometimes not B.
§ 747. As the partly conjunctive syllogism is thus reducible to the simple form, it follows that violations of its laws must correspond with violations of the laws of simple syllogism. By our throwing the illicit moods into the simple form it will become apparent what fallacies are involved in them.
Denial of Anteceded.
If A is B, C is D. \ / All cases of A being B are cases of C
\ = / being D.
A is not B. / \ This is not a case of A being B.
.'. C is not D. / \ .'. This is not a case of C being D.