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142
MEDIATE INFERENCE
examples of these circumstances, we explain what occurred
by reasonings in Barbara.
When speaking, in the present section, of the valid
moods of figure i., we ignored the
"
weakened moods,"
AAI and EAO, mentioned in 5. This is because,
though technically valid, they are practically superfluous.
They have been given the names Barbari and Celaront^
respectively. They are sometimes called
"
subaltern
moods," for the conclusion of Barbari can be inferred
by
"
"
subalternation
(ch. III. 7, p. 76)
from that of
Barbara, and the conclusion of Celaront in a similar
way from that of Celarent.
Of the remaining moods of fig. i., we may notice that
Celarent can prove only a universal negative that
nothing in a given class has certain stated qualities :
Nothing that increases taxation can be long popular ;
All wars increase taxation ;
.*. No wars can be long popular.
This mood is of less importance than Barbara^ for we
can only clear the ground, not directly advance know
ledge, by proving what things
are not :
Nothing involuntary can be cured by punishment :
Stupidity is involuntary ;
.*. Stupidity cannot be cured by punishment.
But no syllogism in Celarent could tell us how stupidity
may be cured.
7. The second figure proves only negatives. Its
valid moods are :
Cesare, Camestres, Festino, Baroco.
It is useful in establishing distinctions between things. 1
1 On Camestres in connection with the hypothetical syllogism, see
chap. VII. 4.