3. TESTING THE VALIDITY OF THE MOODS.

In order to put the moods to good use, it is necessary to ascertain which ones yield a valid conclusion in any figure. If each were valid in all of the four figures, there would be 256. But it is obvious that such is not the case.

Referring to the sixteen permutations given above, we find that the “negative-conclusion” rule makes invalid 2, 4, 5, 7, 10, 12, 13 and 15; whereas the rule for particulars throws out 9 and 14. This leaves the following as the probable valid moods in one or more of the figures: 1, 3, 6, 8, 11, 16. But to be certain of this the investigation must be continued. The mood A
A
A has stood the test of the rules for negative and particular conclusions; now let us test this mood from the standpoint of the distribution of terms, using it in all four figures:

First Second Third Fourth
AM — G G — M M — G G — M
AS — M S — M M — S M — S
AS — 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
A is invalid in the second, because of “undistributed middle,” and 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:

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.