CHAPTER IX.
FORMAL CONDITIONS OF MEDIATE INFERENCE Sec.1.A Mediate Inference is a proposition that depends for proof upon two or more other propositions, so connected together by one or more terms (which the evidentiary propositions, or each pair of them, have in common) as to justify a certain conclusion, namely, the proposition in question.

The type or (more properly) the unit of all such modes of proof, when of a strictly logical kind, is the Syllogism, to which we shall see that all other modes are reducible.

It may be exhibited symbolically thus: M is P; S is M: .'.

S is P.
Syllogisms may be classified, as to quantity, into Universal or Particular, according to the quantity of the conclusion; as to quality, into Affirmative or Negative, according to the quality of the conclusion; and, as to relation, into Categorical, Hypothetical and Disjunctive, according as all their propositions are categorical, or one (at least) of their evidentiary propositions is a hypothetical or a disjunctive.
To begin with Categorical Syllogisms, of which the following is an example: All authors are vain; Cicero is an author: .'.

Cicero is vain.
Here we may suppose that there are no direct means of knowing that Cicero is vain; but we happen to know that all authors are vain and that he is an author; and these two propositions, put together, unmistakably imply that he is vain.