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. § 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. § 3. A Monosyllogism is a syllogism considered as standing alone or without relation to other arguments. But, of course, a disputant may be asking to prove the premises of any syllogism; in which case other syllogisms may be advanced for that purpose. When the conclusion of one syllogism is used to prove another, we have a chain-argument which, stated at full length, is a Polysyllogism. In any Polysyllogism, again, a syllogism whose conclusion is used as the premise of another, is called in relation to that other a Prosyllogism; whilst a syllogism one of whose premises is the conclusion of another syllogism, is in relation to that other an Episyllogism. Two modes of abbreviating a Polysyllogism, are usually discussed, the Epicheirema and the Sorites. § 4. An Epicheirema is a syllogism for one or both of whose premises a reason is added; as-- All men are mortal, for they are animals; Socrates is a man, for rational bipeds are men: ∴ Socrates is mortal.