§ 625. The rule that the conclusion must be particular confines us to eight moods, two of which, namely AEE and AOO, are excluded by the rule that the minor premiss must be affirmative.
Thus we are left with six moods which are valid in the third figure, namely,
§ 626. The first of the eleven moods, AAA, is excluded by the rule that the conclusion cannot be a universal affirmative.
Two more moods, namely AOO and OAO, are excluded by the rule that neither of the premisses can be a particular negative.
AII violates the rule that when the major premiss is affirmative, the minor must be universal.
EAE violates the rule that, when the minor premiss is affirmative, the conclusion must be particular. Thus we are left with six moods which are valid in the fourth figure, namely,
§ 627. Thus the 256 possible forms of syllogism have been reduced to two dozen legitimate combinations of mood and figure, six moods being valid in each of the four figures.
FIGURE I. AAA. EAE. AII. EIO. (AAI. EAO.)
FIGURE II. EAE. AEE. EIO. AGO. (EAO. AEO.)
FIGURE III. AAI. IAI. AII. EAO. OAO. EIO.
FIGURE IV. AAI. AEE. IAI. EAO. EIO. (AEO.)
§ 628. The five moods enclosed in brackets, though valid, are useless. For the conclusion drawn is less than is warranted by the premisses. These are called Subaltern Moods, because their conclusions might be inferred by subalternation from the universal conclusions which can justly be drawn from the same premisses. Thus AAI is subaltern to AAA, EAO to EAE, and so on with the rest.
§ 629. The remaining 19 combinations of mood and figure, which are loosely called 'moods,' though in strictness they should be called 'figured moods,' are generally spoken of under the names supplied by the following mnemonics--
Barbara, Celarent, Darii, Ferioque prioris; Cesare, Camestres, Festino, Baroko secundæ; Tertia Darapti, Disamis, Datisi, Felapton, Bokardo, Ferison habet; Quarta insuper addit Bramantip, Camenes, Dimaris, Fesapo, Fresison: Quinque Subalterni, totidem Generalibus orti, Nomen habent nullum, nee, si bene colligis, usum.
§ 630. The vowels in these lines indicate the letters of the mood. All the special rules of the four figures can be gathered from an inspection of them. The following points should be specially noted.
