Note 332 — Chapter II

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.