S:
1. S in M, but not in P;
2. S in the overlap of M and P;
3. S in M, some S in P.
]

Again, unless the Minor Premiss is affirmative, no matter what the
Major Premiss may be, you can draw no conclusion. For if the Minor
Premiss is negative, all that you know is that All S or Some S lies
somewhere outside M; and however M may be situated relatively to P,
that knowledge cannot help towards knowing how S lies relatively to P.
All S may be P, or none of it, or part of it. Given all M is in P; the
All S (or Some S) which we know to be outside of M may lie anywhere in
P or out of it.

[Illustration:

Concentric circles of P and M, M in center,
with 5 instances of circle of S:
1. S wholly outside P and M;
2. S partly overlapping both P and M, and partly outside both;
3. S overlapping P, but outside M;
4. S wholly within P, but wholly outside M;
5. S touching circle of P, but outside both circles.
]

Similarly, in the Second Figure, trial and simple inspection of all
possible conditions shows that there can be no conclusion unless the
Major Premiss is universal, and one of the premisses negative.

Another and more common way of eliminating the invalid forms,
elaborated in the Middle Ages, is to formulate principles applicable
irrespective of Figure, and to rule out of each Figure the moods that
do not conform to them. These regulative principles are known as The
Canons of the Syllogism.

_Canon I._ In every syllogism there should be three, and not more than
three, terms, and the terms must be used throughout in the same sense.

It sometimes happens, owing to the ambiguity of words, that there seem
to be three terms when there are really four. An instance of this is
seen in the sophism:--

He who is most hungry eats most.
He who eats least is most hungry.
[.'.] He who eats least eats most.

This Canon, however, though it points to a real danger of error in the
application of the syllogism to actual propositions, is superfluous
in the consideration of purely formal implication, it being a primary
assumption that terms are univocal, and remain constant through any
process of inference.

Under this Canon, Mark Duncan says (_Inst. Log._, iv. 3, 2), is
comprehended another commonly expressed in this form: There should be
nothing in the conclusion that was not in the premisses: inasmuch as
if there were anything in the conclusion that was in neither of the
premisses, there