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 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.
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