All free nations are enterprising;
     The Dutch are a free nation: 
   .’.  The Dutch are enterprising.

Reduced to Enthymemes, this argument may be put thus: 

In the First Order: 

      The Dutch are a free nation: 
    .’.  The Dutch are enterprising.

In the Second Order—­

      All free nations are enterprising;
    .’.  The Dutch are enterprising.

In the Third Order—­

    All free nations are enterprising;
    And the Dutch are a free nation.

It is certainly very common to meet with arguments whose statement may be represented by one 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 formally correct according to Barbara (or whatever the appropriate Mood); (2) whether the premises, or the ultimate premises, are true in fact.