Mood IA.
Some B is A.
All C is B.
.'. Undistributed Middle.
Mood IE.
Some B is C. Some B is not A.
No A is B. All C is B.
.'. Illicit Process, or Some C is not A, (Fresison).
Mood OA.
Some B is not A.
All C is B.
.'. Undistributed Middle.
§ 661. Thus we are left with six valid moods, which yield four direct conclusions and five indirect ones, corresponding to the four moods of the original first figure and the five moods of the original fourth, which appear now as indirect moods of the first figure.
§ 662. But why, it maybe asked, should not the moods of the first figure equally well be regarded as indirect moods of the fourth? For this reason-that all the moods of the fourth figure can be elicited out of premisses in which the terms stand in the order of the first, whereas the converse is not the case. If, while retaining the quantity and quality of the above premisses, i. e. the mood, we were in each case to transpose the terms, we should find that we were left with five valid moods instead of six, since AI in the reverse order of the terms involves undistributed middle; and, though we should have Celarent indirect to Camenes, and Darii to Dimaris, we should never arrive at the conclusion of Barbara or have anything exactly equivalent to Ferio. In place of Barbara, Bramantip would yield as an indirect mood only the subaltern AAI in the first figure. Both Fesapo and Fresison would result in an illicit process, if we attempted to extract the conclusion of Ferio from them as an indirect mood. The nearest approach we could make to Ferio would be the mood EAO in the first figure, which may be elicited indirectly from the premisses of CAMENES, being subaltern to CELARENT. For these reasons the moods of the fourth figure are rightly to be regarded as indirect moods of the first, and not vice versâ.
$663. FIGURE II.
Mood AA.
All A is B.
All C is B.
.'. Undistributed Middle.
Mood AE.
All A is B.
No C is B.
.'. No C is A, or No A is C, (Camestres & Cesare).
Mood AI.
All A is B.
Some C is B.
.'. Undistributed Middle.
Mood AO.
All A is B.
Some C is not B.
.'. Some C is not A, (Baroko), or Illicit Process.