ositions into terms.
The syllogism was conceived by Aristotle as a reasoning together
of terms. His prime discovery was that whenever two propositions
necessarily contain or imply a conclusion, they have a common term,
that is, only three terms between them: that the other two terms which
differ in each are the terms of the conclusion; and that the relation
asserted in the conclusion between its two terms is a necessary
consequence of their relations with the third term as declared in the
premisses.

Such was Aristotle's conception of the Syllogism and such it has
remained in Logic. It is still, strictly speaking, a syllogism of
terms: of propositions only secondarily and after they have been
analysed. The conclusion is conceived analytically as a relation
between two terms. In how many ways may this relation be established
through a third term? The various moods and figures of the Syllogism
give the answer to that question.

The use of the very abstract word "relation" makes the problem appear
much more difficult than it really is. The great charm of Aristotle's
Syllogism is its simplicity. The assertion of the conclusion is
reduced to its simplest possible kind, a relation of inclusion or
exclusion, contained or not contained. To show that the one term is
or is not contained in the other we have only to find a third which
contains the one and is contained or not contained in the other.

The practical difficulties, of course, consist in the reduction of
the conclusions and arguments of common speech to definite terms thus
simply related. Once they are so reduced, their independence or the
opposite is obvious. Therein lies the virtue of the Syllogism.

Before proceeding to show in how many ways two terms may be Syllogised
through a third, we must have technical names for the elements.

The third term is called the MIDDLE (M) ([Greek: to meson]): the other
two the Extremes ([Greek: akra]).

The EXTREMES are the Subject (S) and the Predicate (P) of the
conclusion.

In an affirmative proposition (the normal form) S is contained in P:
hence P is called the MAJOR[1] term ([Greek: to meixon]), and S the
MINOR ([Greek: to elatton]), being respectively larger and smaller in
extension. All difficulty about the names disappears if we remember
that in bestowing them we start from the conclusion. That was the
problem ([Greek: problema]) or thesis in dialectic, the question in
dispute.

The two Premisses, or propositions