⎯⎯
S – P
and it can be deduced from the general rules of the syllogism that in this figure:—
(1) The minor premiss must be affirmative. For if it were negative, the major premiss would have to be affirmative by rule 5, and the conclusion negative by rule 6. The major term would therefore be distributed in the conclusion, and undistributed in its premiss; and the syllogism would be invalid by rule 4.
(2) The major premiss must be universal. For the middle term, being undistributed in the affirmative minor premiss, must be distributed in the major premiss.
311 Rule (1) shews that AE and AO and rule (2) that IA and OA, yield no conclusions in this figure. We are accordingly left with only four combinations, namely, AA, AI, EA, EI From the rules that a particular premiss cannot yield a universal conclusion or a negative premiss an affirmative conclusion, while conversely a negative conclusion requires a negative premiss, it follows further that AA will justify either of the conclusions A or I, EA either E or O, AI only I, EI only O. There are then six moods in figure 1 which do not offend against any of the rules of the syllogism,[332] namely, AAA, AAI, AII, EAE, EAO, EIO.
[332] Rule (2) provides against undistributed middle, and rule (1) against illicit major. We cannot have illicit minor, unless we have a universal conclusion with a particular premiss, and this also has been provided against.
Mr Johnson points out that the following symmetrical rules may be laid down for the correct distribution of terms in the different figures; and that these rules (three in each figure) taken together with the rules of quality are sufficient to ensure that no syllogistic rule is broken.
(i) To avoid undistributed middle: in figure 1, If the minor is affirmative, the major must be universal; in figure 4, If the major is affirmative, the minor must be universal; in figure 2, One premiss must be negative; in figure 3, One premiss must be universal. (The last of these rules is of course superfluous if the corollaries contained in section [200] are supposed given.)
(ii) To avoid illicit major: in figures 1 and 3, If the conclusion is negative, the major must be negative and, therefore, the minor affirmative; in figures 2 and 4, If the conclusion is negative, the major must be universal.
(iii) To avoid illicit minor: in figures 1 and 2, If the minor is particular, the conclusion must be particular; in figures 3 and 4, If the minor is affirmative, the conclusion must be particular. (The first of these two rules is again superfluous as a special rule if the corollaries are supposed given.)
The above rules are substantially identical with those given in the text.