the middle term may be subject of both premises, as in the third of the
above examples; and this is called the Third Figure. Or, finally, the
middle term may be predicate of the major premise, and subject of the
minor, as in the fourth example given above; and this is the Fourth
Figure.

It may facilitate the recollection of this most important point if we
schematise the figures thus:

I. II. III. IV.

M---P P---M M---P P---M
\ | | /
\ | | /
\ | | /
S---M S---M M---S M---S

The horizontal lines represent the premises, and at the angles formed
with them by the slanting or by the perpendicular lines the middle term
occurs. The schema of Figure IV. resembles Z, the last letter of the
alphabet: this helps one to remember it in contrast with Figure I.,
which is thereby also remembered. Figures II. and III. seem to stand
back to back.

Sec. 3. The Moods of each Figure are the modifications of it which arise
from different combinations of propositions according to quantity and
quality. In Figure I., for example, four Moods are recognised: A.A.A.,
E.A.E., A.I.I., E.I.O.

A. All M is P;
A. All S is M:
A. .'. All S is P.

E. No M is P;
A. All S is M:
E. .'. No S is P.

A. All M is P;
I. Some S is M:
I. .'. Some S is P.

E. No M is P;
I. Some S is M:
O. .'. Some S is not P.

Now, remembering that there are four Figures, and four kinds of
propositions (A. I. E. O.), each of which propositions may be major
premise, minor premise, or conclusion of a syllogism, it appears that in
each Figure there may be 64 Moods, and therefore 256 in all. On
examining these 256 Moods, however, we find that only 24 of them are
valid (i.e., of such a character that the conclusion strictly follows
from the premises), whilst 5 of these 24 are needless, because their
conclusions are 'weaker' or less extensive than the premises warrant;
that is to say, they are particular when they might be universal. Thus,
in Figure I., besides the above 4 Moods, A.A.I. and E.A.O. are valid in
the sense of being conclusive; but they are superfluous, because
included in A.A.A. and E.A.E. Omitting, then, these 5 needless Moods,
which are ca