lled 'Subalterns' because their conclusions are subaltern
(chap. vii. Sec. 2) to those of other Moods, there remain 19 Moods that are
valid and generally recognised.

Sec. 4. How these 19 Moods are determined must be our next inquiry. There
are several ways more or less ingenious and interesting; but all depend
on the application, directly or indirectly, of the Six Canons, which
were shown in the last chapter to be the conditions of Mediate
Inference.

(1) One way is to begin by finding what Moods of Figure I. conform to
the _Dictum_. Now, the _Dictum_ requires that, in the major premise, P
be predicated of a term distributed, from which it follows that no Mood
can be valid whose major premise is particular, as in I.A.I. or O.A.O.
Again, the _Dictum_ requires that the minor premise be affirmative
("with which term another is identified"); so that no Mood can be valid
whose minor premise is negative, as in A.E.E. or A.O.O. By such
considerations we find that in Figure I., out of 64 Moods possible, only
six are valid, namely, those above-mentioned in Sec. 3, including the two
subalterns. The second step of this method is to test the Moods of the
Second, Third, and Fourth Figures, by trying whether they can be reduced
to one or other of the four Moods of the First (as briefly illustrated
in Sec. 1, and to be further explained in Sec. 6).

(2) Another way is to take the above six General or Common Canons, and
to deduce from them Special Canons for testing each Figure: an
interesting method, which, on account of its length, will be treated of
separately in the next section.

(3) Direct application of the Common Canons is, perhaps, the simplest
plan. First write out the 64 Moods that are possible without regard to
Figure, and then cross out those which violate any of the Canons or
Corollaries, thus:

[Transcriber's Note: Moods surrounded with square brackets were crossed
out in the original text.]

AAA, [AAE] (6th Can. b). AAI. [AAO] (6th Can. b).
[AEA] (6th Can. a) AEE, [AEI] (6th Can. a) AEO,
[AIA] (Cor. ii.) [AIE] (6th Can. b) AII, [AIO] (6th Can. b)
[AOA] (6th Can. a) [AOE] (Cor. ii.) [AOI] (6th Can. a) AOO.

Whoever has the patience to go through the remaining 48 Moods will
discover that of the whole 64 only 11 are valid, namely:

A.A.A., A.A.I., A.E.E., A.E.O., A.I.I., A.O.O.,
E.A.E., E.A.O., E.I.O., I.A.I., O.A.O.

These 11 Moods have next to be examined in each Figure, and if valid in
every Figure there wi