2. THE MOODS OF THE SYLLOGISM.
By the mood of a syllogism is meant some particular arrangement of the propositions which compose the syllogisms. “Mood” stands for an arrangement of the propositions, while “figure” represents an arrangement of the terms in any syllogism.
Combining any three of the four logical propositions gives a mood, as, e. g., (1) E
A
E (2) A
I
I (3) E
I
O.
are moods. The first one has an E proposition for the major premise, an A for the minor and an E for the conclusion. This syllogism represents the first mood given above:
E No men are trees,
A All Americans are men,
E ∴ No Americans are trees.
It would not be difficult to determine by actual experiment, just how many moods could be formed, and of these, how many would admit of valid conclusions. It may be seen that there are sixty-four permutations of the four logical propositions, taken three at a time. These are in part:
| (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) |
| A | A | A | A | A | A | A | A |
| A | A | A | A | E | E | E | E |
| A | E | I | O | A | E | I | O |
| (9) | (10) | (11) | (12) | (13) | (14) | (15) | (16) |
| A | A | A | A | A | A | A | A |
| I | I | I | I | O | O | O | O |
| A | E | I | O | A | E | I | O |
And so the permutations could be continued. Substituting E for the major premise of the above group would give another group of sixteen, while a like substitution of I and O would result in two more groups, sixteen in each.This gives sixty-four in all.[10]