would be four terms in the syllogism.

The rule that in every syllogism there must be three, and only three,
propositions, sometimes given as a separate Canon, is only a corollary
from Canon I.

_Canon II._ The Middle Term must be distributed once at least in the
Premisses.

The Middle Term must either be wholly in, or wholly out of, one or
other of the Extremes before it can be the means of establishing a
connexion between them. If you know only that it is partly in both,
you cannot know from that how they lie relatively to one another: and
similarly if you know only that it is partly outside both.

The Canon of Distributed Middle is a sort of counter-relative
supplement to the _Dictum de Omni_. Whatever is predicable of a whole
distributively is predicable of all its several parts. If in neither
premiss there is a predication about the whole, there is no case for
the application of the axiom.

_Canon III._ No term should be distributed in the conclusion that was
not distributed in the premisses.

If an assertion is not made about the whole of a term in the
premisses, it cannot be made about the whole of that term in the
conclusion without going beyond what has been given.

The breach of this rule in the case of the Major term is technically
known as the Illicit Process of the Major: in the case of the Minor
term, Illicit Process of the Minor.

Great use is made of this canon in cutting off invalid moods. It
must be remembered that the Predicate term is "distributed" or taken
universally in O (Some S is not in P) as well as in E (No S is in P);
and that P is never distributed in affirmative propositions.

_Canon IV._ No conclusion can be drawn from two negative premisses.

Two negative premisses are really tantamount to a declaration that
there is no connexion whatever between the Major and Minor (as
quantified in the premisses) and the term common to both premisses; in
short, that this is not a Middle term--that the condition of a valid
Syllogism does not exist.

There is an apparent exception to this when the real Middle in an
argument is a contrapositive term, not-M. Thus:--

Nobody who is not thirsty is suffering from fever.
This person is not thirsty.
[.'.] He is not suffering from fever.

But in such cases it is really the absence of a quality or rather
the presence of an opposite quality on which we reason; and the Minor
Premiss is really Affirmative of the form S is in not-M.