| All B is C |
| Some A is B, |
from which it obviously follows, that
| Some A is C. |
In the same manner, or in a manner on which after these examples it is not necessary to enlarge, every mood of the second, third, and fourth figures may be reduced to some one of the four moods of the first. In other words, every conclusion which can be proved in any of the last three figures, may be proved in the first figure from the same premises, with a slight alteration in the mere manner of expressing them. Every valid ratiocination, therefore, may be stated in the first figure, that is, in one of the following forms:—
| Every B is C | No B is C | ||||
| All A | } | is B, | All A | } | is B, |
| Some A | Some A | ||||
| therefore | therefore | ||||
| All A | } | is C. | No A is | } | C. |
| Some A | Some A is not | ||||
Or if more significant symbols are preferred:—
To prove an affirmative, the argument must admit of being stated in this form:—
| All animals are mortal; | ||
| All men | } | are animals; |
| Some men | ||
| Socrates | ||
| therefore | ||
| All men | } | are mortal. |
| Some men | ||
| Socrates | ||
To prove a negative, the argument must be capable of being expressed in this form:—
| No one who is capable of self-control is necessarily vicious; | ||
| All negroes | } | are capable of self-control; |
| Some negroes | ||
| Mr. A's negro | ||
| therefore | ||
| No negroes are | } | necessarily vicious. |
| Some negroes are not | ||
| Mr. A's negro is not | ||