_First_ _Second_ _Third_ _Fourth_ A M ― G G ― M M ― G G ― M ― ― ― ― A S ― M S ― M M ― S M ― S ― ― ― ― ――――――― ――――――― ――――――― ――――――― A S ― G S ― G S ― G S ― G ― ― ― ― As an A proposition distributes its subject only, we underscore the subject of each proposition in all the figures. (This underscoring is a simple way to indicate distribution.) We now find that the mood is valid in the first figure, because the middle term is distributed at least once; namely, in the major premise, and there is no term distributed in the conclusion which is not already distributed in the premise where it occurs. On the other hand, the mood A A is invalid in the second, because of “_undistributed middle_,” and A invalid in the third and fourth, because S is distributed in the conclusion but not distributed in the premise where it occurs (illicit minor). Let us try AII in the four figures: A M ― G G ― M M ― G G ― M ― ― ― ― I S ― M S ― M M ― S M ― S ――――― ――――― ――――― ――――― I S ― G S ― G S ― G S ― G We underscore the subject of the A proposition in each of the four figures. As I distributes neither subject nor predicate, no other term A should be underscored. It is now evident that I is not valid in figures I two and four, because in both figures the middle term is undistributed (undistributed middle). In a like manner all the other moods might be tested. Logicians, who have done this, have found 24 to be valid. Five of these have weakened conclusions; i. e., a particular conclusion when it could just as well A be universal. E illustrates this as the conclusion _could be E_. This O syllogism exemplifies the weakened conclusion: A All trees grow, E No sticks are trees, O ∴ Some sticks do not grow. This conclusion is true, since “some” means “some at least.” Yet the conclusion is weak, because there is nothing to interfere with the broader and stronger conclusion that, “No sticks grow.” There are, therefore, only 19 valid and serviceable moods. These are as follows: (1) (2) (3) (4) (5) (6) { A E A E ― ― } First figure { A A I I ― ― } 4 { A E I O ― ― } { E A A E ― ― } Second figure { A E O I ― ― } 8 { E E O O ― ― } { A I A E O E } Third figure { A A I A A I } 14 { I I I O O O }