or other of these three forms; indeed, the
Enthymeme is the natural substitute for a full syllogism in oratory:
whence the transition from Aristotle's to the modern meaning of the
term. The most unschooled of men readily apprehend its force; and a
student of Logic can easily supply the proposition that may be wanted in
any case to complete a syllogism, and thereby test the argument's formal
validity. In any Enthymeme of the Third Order, especially, to supply the
conclusion cannot present any difficulty at all; and hence it is a
favourite vehicle of innuendo, as in Hamilton's example:

Every liar is a coward;
And Caius is a liar.

The frankness of this statement and its reticence, together, make it a
biting sarcasm upon Caius.

The process of finding the missing premise in an Enthymeme of either the
First or the Second Order, so as to constitute a syllogism, is sometimes
called Reduction; and for this a simple rule may be given: Take that
term of the given premise which does not occur in the conclusion (and
which must therefore be the Middle), and combine it with that term of
the conclusion which does not occur in the given premise; the
proposition thus formed is the premise which was requisite to complete
the Syllogism. If the premise thus constituted contain the predicate of
the conclusion, the Enthymeme was of the First Order; if it contain the
subject of the conclusion, the Enthymeme was of the Second Order.

That a statement in the form of a Hypothetical Proposition may really be
an Enthymeme (as observed in chap. v. Sec. 4) can easily be shown by
recasting one of the above Enthymemes thus: _If all free nations are
enterprising, the Dutch are enterprising_. Such statements should be
treated according to their true nature.

To reduce the argument of any ordinary discourse to logical form, the
first care should be to make it clear to oneself what exactly the
conclusion is, and to state it adequately but as succinctly as possible.
Then look for the evidence. This may be of an inductive character,
consisting of instances, examples, analogies; and, if so, of course its
cogency must be evaluated by the principles of Induction, which we
shall presently investigate. But if the evidence be deductive, it will
probably consist of an Enthymeme, or of several Enthymemes one depending
on another. Each Enthymeme may be isolated and expanded into a
syllogism. And we may then inquire: (1) whether the syllogisms are
fo