Figure I. Figure II. Figure III. Figure IV.
B—A A—B B—A A—B
C—B C—B B—C B—C
C—A C—A C—A C—A
All these figures are legitimate, though the fourth is comparatively valueless.
§ 566. It will be well to explain by an instance the meaning of the assertion previously made, that a difference of figure is internal to a difference of mood. We will take the mood EIO, and by varying the position of the terms, construct a syllogism in it in each of the four figures.
I.
E No wicked man is happy.
I Some prosperous men are wicked.
O .'. Some prosperous men are not happy.
II.
E No happy man is wicked.
I Some prosperous men are wicked.
O .'. Some prosperous men are not happy.
III.
E No wicked man is happy.
I Some wicked men are prosperous.
O .'. Some prosperous men are not happy.
IV.
E No happy man is wicked.
I Some wicked men are prosperous.
O .'. Some prosperous men are not happy.
§ 567. In the mood we have selected, owing to the peculiar nature of the premisses, both of which admit of simple conversion, it happens that the resulting syllogisms are all valid. But in the great majority of moods no syllogism would be valid at all, and in many moods a syllogism would be valid in one figure and invalid in another. As yet however we are only concerned with the conceivable combinations, apart from the question of their legitimacy.
§ 568. Now since there are four different figures and sixty-four different moods, we obtain in all 256 possible ways of arranging three terms in three propositions, that is, 256 possible forms of syllogism.