Handbook of the History of Logic: - Fordham University Faculty

The Assimilation of Aristotelian and Arabic Logic up to the Later Thirteenth Century 329
8. If the major premise in a second figure mood is particular, then no conclusion
follows.
9. If the premises are both affirmative in a second figure mood then no conclusion
follows.
10. In the second figure only negative conclusions follow.
There are only four valid moods in this figure.
X.
No A is B
Every C is B
No C is A
XI.
Every A is B
No C is B
No C is A
XII.
No A is B
Some C is B
Some C is not A
XIII.
Every A is B
Some C is not B
Some C is not A
(X) is reduced to (II) by simple conversion of the major premise. (XI) is also
reduced to (II) but this time by simple conversion of the minor premise and the
conclusion, by transposing the premises and renaming the terms. (XII) is reduced
to (IV) by simple conversion of the major premise. (XIII) cannot b reduced and
is hence proved through impossibility.
The proof through impossibility is very simple and proceeds from positing the
negation of the conclusion and deriving a contradiction. The negation of the
conclusion is: ‘Every C is A’, and together with the major premise ‘Every C is B’
follows, which is the negation of the minor premise.
The third figure is also governed by two rules, namely:
11. If the major premise is negative in a third figure syllogism, then no conclusion
follows.
12. Only particular conclusions follow in the third figure.
There are six valid moods in this figure.