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. The first figure proves any kind of conclusion, and is the only one which can prove A. The second figure proves only negatives. The third figure proves only particulars. The fourth figure proves any conclusion except A. § 631. The first figure is called the Perfect, and the rest the Imperfect figures. The claim of the first to be regarded as the perfect figure may be rested on these grounds-- 1. It alone conforms directly to the Dictum de Omni et Nullo. 2. It suffices to prove every kind of conclusion, and is the only figure in which a universal affirmative proposition can be established. 3. It is only in a mood of this figure that the major, middle and minor terms are to be found standing in their relative order of extension. § 632. The reason why a universal affirmative, which is of course infinitely the most important form of proposition, can only be proved in the first figure may be seen as follows. _Proof that A can only be established in figure I._ An A conclusion necessitates both premisses being A propositions (by Rule 7). But the minor term is distributed in the conclusion, as being the subject of an A proposition, and must therefore be distributed in the minor premiss, in order to which it must be the subject. Therefore the middle term must be the predicate and is consequently undistributed. In order therefore that the middle term may be distributed, it must be subject in the major premiss, since that also is an A proposition. But when the middle term is subject in the major and predicate in the minor premiss, we have what is called the first figure. CHAPTER XV. _Of the Special Canons of the Four Figures._