In the fourth figure it may be proved (1) that if the major is affirmative, the minor must be universal in order to distribute the middle term; (2) that if the minor is affirmative, the conclusion must be particular in order to avoid committing the fallacy of illicit minor; (3) that if either premise is negative, the major must be universal to avoid the fallacy of illicit major. (5) A knowledge of the special canons is helpful in that it may be used to check fallacious reasoning. (6) Certain mnemonic lines were used by the Schoolmen as an aid in recalling the nineteen valid moods, and also as a suggestive device to aid in the process known as Reduction. The process of reduction is merely a matter of changing to the first figure the moods of the other figures. This process is no longer thought to be necessary. (7) The first figure, called the perfect figure, is the one used most by scientists, as it is the only figure which proves a universal affirmative truth. The second figure is the negative, or figure of disproof, and is used mainly for the purpose of eliminating all the conditions of the inquiry save _one_. The third figure serves a purpose in affording an easy way to contradict a universal assertion; this is the figure of particulars. The fourth figure, because it so closely resembles the first, is of little value. =10. ILLUSTRATIVE EXERCISES.= Question 1a. By making use of the rules for negatives and particulars, O A A test the validity of the following moods: I I A A A I Answer: The first mood has the negative O as its major premise, and the affirmative A as its conclusion; the mood is thus invalid; because a negative premise necessitates a negative conclusion according to rule 6. The second mood contains the particular proposition I as its minor premise, and thus should have a particular conclusion according to rule 8. But the conclusion A is universal and, therefore, the mood is invalid. The premises of the third mood are universal and the conclusion particular. The mood, however, is valid, because rule 8 does not work both ways, as does rule 6. When a universal can just as well be drawn, then the particular becomes a weakened conclusion. (1b) Using the rules for negatives and particulars, test the validity A E E of the following: A O A E O O (2a) Paying no regard to “figure,” derive as many conclusions as possible from the following sets of premises: E A I E Answer: _E_. The major premise of this mood, being negative, _I_