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 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.