_Mood AO._ All A is B. Some C is not B. .'. Some C is not A, (Baroko), or Illicit Process. _Mood EA._ No A is B. All C is B. .'. No C is A, or No A is C, (Cesare & Carnestres). _Mood EI_ No A is B. Some C is B. .'. Some C is not A, (Festino), or Illicit Process. _Mood IA._ Some A is B. All C is B. .'. Undistributed Middle. _Mood IE._ Some A is B. No C is B. .'. Illicit Process, or Some A is not C, (Festino). _Mood OA._ Some A is not B. All C is B. .'. Illicit Process, or Some A is not C, (Baroko). § 664. Here again we have six valid moods, which yield four direct conclusions corresponding to Cesare, CARNESTRES, FESTINO and BAROKO. The same four are repeated in the indirect moods. § 665. FIGURE III. _Mood AA._ All B is A. All B is C. .'. Some C is A, or Some A is C, (Darapti). _Mood AE._ All B is A. No B is C. .'. Illicit Process, or Some A is not C, (Felapton). _Mood AI._ All B is A, Some B is C. .'. Some C is A, or Some A is C, (Datisi & Disamis). _Mood AO._ All B is A. Some B is not C. .'. Illicit Process, Or Some A is not C, (Bokardo). _Mood EA._ No B is A. All B is C. .'. Some C is not A, (Felapton), or Illicit Process. _Mood EI._ No B is A. Some B is C. .'. Some C is not A, (Ferison), or Illicit Process. _Mood IA._ Some B is A. All B is C. .'. Some C is A, Or Some A is C, (Disamis & Datisi). _Mood IE._ Some B is A. No B is C. .'. Illicit Process, or Some A is not C, (Ferison). _Mood QA._ Some B is not A. All B is C. .'. Some C is not A, (Bokardo), or Illicit Process. § 666. In this figure every mood is valid, either directly or indirectly. We have six direct moods, answering to Darapti, Disamis, Datisi, Felapton, Bokardo and Ferison, which are simply repeated by the indirect moods, except in the case of Darapti, which yields a conclusion not provided for in the mnemonic lines. Darapti, though going under one name, has as much right to be considered two moods as Disamis and Datisi. CHAPTER XVIII. _Of Reduction._ § 667. We revert now to the standpoint of the old logicians, who regarded the Dictum de Omni et Nullo as the principle of all syllogistic reasoning. From this point of view the essence of mediate inference consists in showing that a special case, or class of cases, comes under a general rule. But a great deal of our ordinary reasoning does not conform to this type. It was therefore judged necessary to show that it might by a little manipulation be brought into conformity with it. This process is called Reduction. § 668. Reduction is of two kinds-- (1) Direct or Ostensive. (2) Indirect or Ad Impossibile. § 669. The problem of direct, or ostensive, reduction is this--