_Of the Syllogism with three figures._
§ 656. It will be remembered that in beginning to treat of figure (§
565) we pointed out that there were either four or three ligures
possible according as the conclusion was assumed to be known or
not. For, if the conclusion be not known, we cannot distinguish
between the major and the minor term, nor, consequently, between one
premiss and another. On this view the first and the fourth figures are
the same, being that arrangement of the syllogism in which the middle
term occupies a different position in one premiss from what it does in
the other. We will now proceed to constitute the legitimate moods and
figures of the syllogism irrespective of the conclusion.
§ 657. When the conclusion is set out of sight, the number of possible
moods is the same as the number of combinations that can be made of
the four things, A, E, I, O, taken two together, without restriction
as to repetition. These are the following 16:--
AA EA IA OA
AE -EE- IE -OE-
AI EI -II- -OI-
AO -EO- -IO- -OO-
of which seven may be neglected as violating the general rules of the
syllogism, thus leaving us with nine valid moods--
AA. AE. AI. AO. EA. EI. IA. IE. OA.
§ 658. We will now put these nine moods successively into the three
figures. By so doing it will become apparent how far they are valid in
each.
§ 659. Let it be premised that
when the extreme in the premiss that stands first is predicate in
the conclusion, we are said to have a Direct Mood;
when the extreme in the premiss that stands second is predicate in
the conclusion, we are said to have an Indirect Mood.
§ 660. FIGURE 1.
_Mood AA._
All B is A.
All C is B.
.'. All C is A, or Some A is C, (Barbara & Bramantip).
_Mood AE._
All B is A.
No C is B.
.'. Illicit Process, or Some A is not C, (Fesapo).
_Mood AI._
All B is A.
Some C is B.
.'. Some C is A, or Some A is C. (Darii & Disamis).
_Mood AO._
All B is A.
Some C is not B.
.'. Illicit Process, (Ferio).
_Mood EA._
No B is A.
All C is B.
.'. No C is A, or No A is C, (Celarent & Camenes).
_Mood EI._
No B is A.
Some C is B.
.'. Some C is not A, or Illicit Process.
_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.
_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.