The letter m between a and e indicates that the major and minor premises of the given syllogism must be interchanged. The letters following both e’s suggest that the minor premise and the conclusion of the syllogism must be converted simply.
This is the resulting syllogism:
E No M
just person shows G
partiality,
A All S
true teachers are M
just persons,
E ∴ No S
true teacher shows G
partiality.
Here, then, is the E
A
E of the first figure or the mood in Celarent.
According to the ancient theory, reduction is necessary as a matter of final and absolute proof that the conclusionfollows from the given premises. But, as this claim has been satisfactorily refuted by modern logicians, we need not give more space to the process. The meaning of k, as related to “indirect reduction,” is explained in most of the earlier works on logic. See Hyslop, page 193.
7. RELATIVE VALUE OF THE FOUR FIGURES.
The first figure.
The first figure is known as the perfect figure; because it is the only one which proves all of the four logical propositions. Recalling the moods of the first figure makes this evident: