§ 744. Such syllogisms as those just treated of, if syllogisms they
are to be called, have a major and a middle term visible to the eye,
but appear to be destitute of a minor. The missing minor term is
however supposed to be latent in the transition from the conjunctive
to the simple form of proposition. When we say 'A is B,' we are taken
to mean, 'As a matter of fact, A is B' or 'The actual state of the
case is that A is B.' The insertion therefore of some such expression
as 'The case in hand,' or 'This case,' is, on this view, all that is
wanted to complete the form of the syllogism. When reduced in this
manner to the simple type of argument, it will be found that the
constructive conjunctive conforms to the first figure and the
destructive conjunctive to the second.
_Constructive Mood_. _Barbara_.
If A is B, C is D. \ / All cases of A being B are cases of
\ = / C being D.
A is B. / \ This is a case of A being B.
.'. C is D. / \ .'. This is a case of C being D.
_Destructive Mood._ Camestres.
If A is B, C is D. \ / All cases of A being B are cases of
\ = / C being D.
C is not D. / \ This is not a case of C being D.
.'. A is not B. / \ .'. This is not a case of A being B.
§ 745. It is apparent from the position of the middle term that the
constructive conjunctive must fall into the first figure and the
destructive conjunctive into the second. There is no reason, however,
why they should be confined to the two moods, Barbara and
Carnestres. If the inference is universal, whether as general or
singular, the mood is Barbara or Carnestres; if it is particular, the
mood is Darii or Baroko.
Barbara. Camestres.
If A is B, C is always D. \ If A is B, C is always D. \
A is always B. \ C is never D. \
.'. C is always D. \ .'. A is never B. \
| |
If A is B, C is always D. / If A is B, C is always D. /
A is in this case B. / C is not in this case D. /
.'. C is in this case D. / .'. A is not in this case B. /
Darii. Baroko.
If A is B, C is always D. If A is B, C is never D.
A is sometimes B. C is sometimes not D.
.'. C is sometimes D. .'. A is sometimes not B.
§ 746. The remaining moods of the first and second figure are obtained
by taking a negative proposition as the consequent in the major
premiss.
Celarent. Ferio.
If A is B, C is never D. If A is B, C is never D.
A is always B. A is sometimes B.
.'. C is never D. .'. C is sometimes not D.
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