n
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. In other words, we do not at first
know any relation between 'Cicero' and 'vanity'; but we know that these
two terms are severally related to a third term, 'author,' hence called
a Middle Term; and thus we perceive, by mediate evidence, that they are
related to one another. This sort of proof bears an obvious resemblance
(though the relations involved are not the same) to the mathematical
proof of equality between two quantities, that cannot be directly
compared, by showing the equality of each of them to some third
quantity: A = B = C .'. A = C. Here B is a middle term.

We have to inquire, then, what conditions must be satisfied in order
that a Syllogism may be formally conclusive or valid. A specious
Syllogism that is not really valid is called a Parasyllogism.

Sec. 2. General Canons of the Syllogism.

(1) A Syllogism contains three, and no more, distinct propositions.

(2) A Syllogism contains three, and no more, distinct univocal terms.

These two Canons imply one another. Three propositions with less than
three terms can only be connected in some of the modes of Immediate
Inference. Three propositions with more than three terms do not show
that connection of two terms by means of a third, which is requisite for
proving a Mediate Inference. If we write--

All authors are vain;
Cicero is a statesman--

there are four terms a