An introductory text-book of logic - Mellone, Sydney - Rare Books at ...

AND THE ARISTOTELIAN SYLLOGISM. 137
name each of them by the symbols of its three proposi
tions. They
are :
AAA, EAE, All, EIO,
together with the two weakened moods :
AAI, EAO.
By similar applications of the rules the student will
be able to arrive at the following results. In the second
figure, where the middle is predicate in both premises,
the valid moods, including two weakened moods, are
these : EAE (together
with the corresponding weakened
mood EAO), AEE (and AEO), EIO, AOO. In the
third figure, where the middle is subject in both pre
mises, the valid moods are these : AAI, IAI, All, EAO,
OAO, EIO. In the fourth figure, where the middle
is predicate in the major premise and subject
in the
minor, the valid moods, including one weakened mood,
are these : AAI, AEE (and AEO), IAI, EAO, EIO.
It is an error to say that Aristotle overlooked the fourth
figure ; but he paid no attention to it beyond recognising its
possibility. He seems to have considered it an awkward
and useless variety of the first figure. His pupils, Theophrastus
and Eudemus, worked out its five principal moods
"
"
and added them as indirect moods to i.
fig. Some writers
have supposed that Claudius Galenus was the first to make
these moods into a separate "fourth figure";
fourth has been called the
"
Galenian figure."
hence the
The formation of the five moods as a subordinate variety
of fig. i. may be based on suggestions made by Aristotle,
An. Prior., i. 7 and ii. i. We take the eight possible com
binations of premises which we have examined in fig. i.,
namely :
MaP MaP MaP MaP
SaM SeM SiM SoM
MeP MeP MiP MoP
SaM SiM SaM SaM