ute the middle term. This rule
eliminates A.A.A., A.A.I., A.I.I., I.A.I.

(b) _The major premise must be universal._

For else, the conclusion being negative, there will be illicit process
of the major term. This eliminates I.A.I., O.A.O.; leaving six Moods,
including two subalterns.

Fig. III. (a) _The minor premise must be affirmative._

For else, in negative moods there will be illicit process of the major
term. This rule eliminates A.E.E., A.E.O., A.O.O.

(b) _The conclusion must be particular._

For, if not, the minor premise being affirmative, there will be illicit
process of the minor term. This eliminates A.A.A., A.E.E., E.A.E.;
leaving six Moods.

Fig. IV. (a) _When the major premise is affirmative, the minor must be
universal._

For else the middle term is undistributed. This eliminates A.I.I.,
A.O.O.

(b) _When the minor premise is affirmative the conclusion must be
particular._

Otherwise there will be illicit process of the minor term. This
eliminates A.A.A., E.A.E.

(c) _When either premise is negative, the major must be universal._

For else, the conclusion being negative, there will be illicit process
of the major term. This eliminates O.A.O.; leaving six Moods, including
one subaltern.

Sec. 6. Reduction is either--(1) Ostensive or (2) Indirect. Ostensive
Reduction consists in showing that an argument given in one Mood can
also be stated in another; the process is especially used to show that
the Moods of the second, third, and fourth Figures are equivalent to one
or another Mood of the first Figure. It thus proves the validity of the
former Moods by showing that they also essentially conform to the
_Dictum_, and that all Categorical Syllogisms are only superficial
varieties of one type of proof.

To facilitate Reduction, the recognised Moods have all had names given
them; which names, again, have been strung together into mnemonic verses
of great force and pregnancy:

Barbara, Celarent, Darii, Ferioque prioris:
Cesare, Camestres, Festino, Baroco, secundae:
Tertia, Darapti, Disamis, Datisi, Felapton,
Bocardo, Ferison, habet: Quarta insuper addit
Bramantip, Camenes, Dimaris, Fesapo, Fresison.

In the above verses the names of the Moods of Fig. I. begin with the
first four consonants B, C, D, F, in alphabetical order; and the names
of all other Moods likewise begin with these letters, thus signifying
(except in Baroco and Bocardo) the mood of Fig. I., to which ea