be A, and if one of them is E, the other must be I. Hence the
conclusion must be particular, otherwise there will be illicit process
of the Minor, or of the Major, or of the Middle.

The argument may be more briefly put as follows:

In an affirmative mood, with one premiss particular, only one term can
be distributed in the premisses, and this cannot be the Minor without
leaving the Middle undistributed. In a negative mood, with one premiss
particular, only two terms can be distributed, and the Minor cannot
be one of them without leaving either the Middle or the Major
undistributed.

Armed with these canons, we can quickly determine, given any
combination of three propositions in one of the Figures, whether it is
or is not a valid Syllogism.

Observe that though these canons hold for all the Figures, the Figure
must be known, in all combinations containing A or O, before we can
settle a question of validity by Canons II. and III., because
the distribution of terms in A and O depends on their order in
predication.

Take AEE. In Fig. I.--

All M is in P
No S is in M
No S is in P--

the conclusion is invalid as involving an illicit process of the
Major. P is distributed in the conclusion and not in the premisses.

In Fig. II. AEE--

All P is in M
No S is in M
No S is in P--

the conclusion is valid (Camestres).

In Fig. III. AEE--

All M is in P
No M is in S
No S is in P--

the conclusion is invalid, there being illicit process of the Major.

In Fig. IV. AEE is valid (Camenes).

Take EIO. A little reflection shows that this combination is valid in
all the Figures if in any, the distribution of the terms in both cases
not being affected by their order in predication. Both E and I are
simply convertible. That the combination is valid is quickly seen
if we remember that in negative moods both Major and Middle must be
distributed, and that this is done by E.

EIE is invalid, because you cannot have a universal conclusion with
one premiss particular.

AII is valid in Fig. I. or Fig. III., and invalid in Figs. II. and
IV., because M is the subject of A in I. and III. and predicate in II.
and IV.

OAO is valid only in Fig. III., because only in that Figure would this
combination of premisses distribute both M and P.

Simple exercises of this kind may be multiplied till all possible
combinations are exhausted, and it is seen that only the recognised
moods stand the test.

If