The above two Canons are, indeed, involved in the definition of a categorical syllogism, which may be thus stated:  A Categorical Syllogism is a form of proof or reasoning (way of giving reasons) in which one categorical proposition is established by comparing two others that contain together only three terms, or that have one and only one term in common.

The proposition established, derived, or inferred, is called the Conclusion:  the evidentiary propositions by which it is proved are called the Premises.

The term common to the premises, by means of which the other terms are compared, is called the Middle Term; the subject of the conclusion is called the Minor Term; the predicate of the conclusion, the Major Term.

The premise in which the minor term occurs is called the Minor Premise; that in which the major term occurs is called the Major Premise.  And a Syllogism is usually written thus: 

Major Premise—­All authors (Middle) are vain (Major);

Minor Premise—­Cicero (Minor) is an author (Middle): 

Conclusion—.’.  Cicero (Minor) is vain (Major).

Here we have three propositions with three terms, each term occurring twice.  The minor and major terms are so called, because, when the conclusion is an universal affirmative (which only occurs in Barbara; see chap. x.  Sec. 6), its subject and predicate are respectively the less and the greater in extent or denotation; and the premises are called after the peculiar terms they contain:  the expressions ‘major premise’ and ‘minor premise’ have nothing to do with the order in which the premises are presented; though it is usual to place the major premise first.

(3) No term must be distributed in the conclusion unless it is distributed in the premises.

It is usual to give this as one of the General Canons of the Syllogism; but we have seen (chap. vi.  Sec. 6) that it is of wider application.  Indeed, ‘not to go beyond the evidence’ belongs to the definition of formal proof.  A breech of this rule in a syllogism is the fallacy of Illicit Process of the Minor, or of the Major, according to which term has been unwarrantably distributed.  The following parasyllogism illicitly distributes both terms of the conclusion: 

      All poets are pathetic;
      Some orators are not poets: 
    .’.  No orators are pathetic.

(4) The Middle Term must be distributed at least once in the premises (in order to prove a conclusion in the given terms).

For the use of mediate evidence is to show the relation of terms that cannot be directly compared; this is only possible if the middle term furnishes the ground of comparison; and this (in Logic) requires that the whole denotation of the middle should be either included or excluded by one of the other terms; since if we only know that the other terms are related to some of the middle, their respective relations may not be with the same part of it.