Let us try AII in the four figures:

AM — G G — M M — G G — M
IS — M S — M M — S M — S
IS — 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 should be underscored. It is now evident that A
I
I is not valid in figures 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 be universal. A
E
O illustrates this as the conclusion could be E.This 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)
First figure A
A
A		E
A
E		A
I
I		E
I
O		—
—
—		—
—
—		 4
Second figure E
A
E		A
E
E		A
O
O		E
I
O		—
—
—		—
—
—		 8
Third figure A
A
I		I
A
I		A
I
I		E
A
O		O
A
O		E
I
O		 14
Fourth figure A
A
I		A
E
E		I
A
I		E
A
O		E
I
O		—
—
—		 19

Of these nineteen moods it is not much of a tax to remember that A
A
A is valid only in the first figure; whereas E
A
E is valid in the first and second figures; A
I
I in the first and third; while E
I
O is valid in all. This knowledge, however, should be used only as one would employ the answers in arithmetic. Testing the validity of a mood in the four figures is an exceedingly valuable thought-exercise, which a knowledge of the final result might easily vitiate. It is, no doubt, best to test the value of any mood without such knowledge, and then compare the result by referring to the foregoing list of valid moods. It is not always wise to work with the answer in mind, yet it is most satisfying to know of a certainty that one’s reasoning has led to a truth which others have verified.