§ 633. So far we have given only a negative test of legitimacy, having
shown what moods are not invalidated by running counter to any of the
special rules of the four figures. We will now lay down special canons
for the four figures, conformity to which will serve as a positive
test of the validity of a given mood in a given figure. The special
canon of the first figure--will of course be practically equivalent to
the Dictum de Omni et Nullo. All of them will be expressed in terms of
extension, for the sake of perspicuity.
_Special Canons of the Four Figures._
FIGURE 1.
§ 634. CANON. If one term wholly includes or excludes another, which
wholly or partly includes a third, the first term wholly or partly
includes or excludes the third.
Here four cases arise--
[Illustration]
(1) Total inclusion (Barbara).
All B is A.
All C is B.
.'. All C is A.
[Illustration]
(2) Partial inclusion (Darii).
All B is A.
Some C is B.
.'. Some C is A.
[Illustration]
(3) Total exclusion (Celarent).
No B is A.
All C is B.
.'. No C is A.
[Illustration]
(4) Partial exclusion (Ferio).
No B is A.
Some C is B.
.'. Some C is not A.
FIGURE II.
§ 635. CANON. If one term is excluded from another, which wholly or
partly includes a third, or is included in another from which a third
is wholly or partly excluded, the first is excluded from the whole or
part of the third.
Here we have four cases, all of exclusion--
(1) Total exclusion on the ground of inclusion in an excluded term
(Cesare).
[Illustration]
No A is B.
All C is B.
.'. No C is A.
(2) Partial exclusion on the ground of a similar partial inclusion
(Festino).
[Illustration]
No A is B.
Some C is B.
.'. Some C is not A.
(3) Total exclusion on the ground of exclusion from an including
term (Camestres).
[Illustration]
All A is B.
No C is B.
.'. No C is A.
(4) Partial exclusion on the ground of a similar partial exclusion
(Baroko).
[Illustration]
All A is B.
Some C is not B.
.'. Some C is not A.
FIGURE III.
§ 636. CANON. If two terms include another term in common, or if the
first includes the whole and the second a part of the same term, or
vice versâ, the first of these two terms partly includes the second;
and if the first is excluded from the whole of a term which is wholly
or in part included in the second, or is excluded from part of a term
which is wholly included in the second, the first is excluded from
part of the second.
Here it is evident from the statement that six cases arise--
(1) Total inclusion of the same term in two others
(Darapti).
[Illustration]
All B is A.
All B is C.
.'. some C is A.
(2) Total inclusion in the first and partial inclusion
in the second (Datisi).
[Illustration]
All B is A.
Some B is C.
.'. some C is A.
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