{ A A I E E ― } Fourth figure { A E A A I ― } 19 { I E I O O ― } A Of these nineteen moods it is not much of a tax to remember that A is A E valid only in the first figure; whereas A is valid in the first and E A E second figures; I in the first and third; while I is valid in all. This I O 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. =4. SPECIAL CANONS OF THE FOUR FIGURES.= As a deductive exercise in clear, logical thought, the indirect proof involved in establishing certain principles underlying the four figures, is of immense value. On no account should this section be omitted. The mere fact that it appears to be a difficult section is proof positive that the student is in need of just such exercises. _Canons of the first figure._ (1) The minor premise must be affirmative. (2) The major premise must be universal. _Problem: The minor premise must be affirmative._ _Data_: Given the form of the first figure, which is, M ― G S ― M ――――― S ― G _Proof_: (1) If the minor premise is not affirmative then it must be negative; because affirmative and negative propositions, being contradictory in nature, admit of no middle ground. (2) If the minor premise is negative, the conclusion must be negative; for the reason that a negative premise necessitates a negative conclusion. (3) If the conclusion is negative then its predicate, G, must be distributed; since all negatives distribute their predicates. (4) If the predicate of the conclusion, which is the major term, is distributed, then it must be distributed in the premise where it occurs, which is the major premise; for any term which is distributed in the conclusion must be distributed in the premise where it occurs. (5) If the major term, which is the predicate of the major premise, is distributed, then the major premise must be negative; because only negatives distribute their predicates. (6) The result of this argument, then, gives _two_ negative premises, and we know from rule 3 that a conclusion from two negatives is untenable.