Sec. 1.  In ordinary discussion, whether oral or written, it is but rarely that the forms of Logic are closely adhered to.  We often leave wide gaps in the structure of our arguments, trusting the intelligence of those addressed to bridge them over; or we invert the regular order of propositions, beginning with the conclusion, and mentioning the premises, perhaps, a good while after, confident that the sagacity of our audience will make all smooth.  Sometimes a full style, like Macaulay’s, may, by means of amplification and illustration, spread the elements of a single syllogism over several pages—­a pennyworth of logic steeped in so much eloquence.  These practices give a great advantage to sophists; who would find it very inconvenient to state explicitly in Mood and Figure the pretentious antilogies which they foist upon the public; and, indeed, such licences of composition often prevent honest men from detecting errors into which they themselves have unwittingly fallen, and which, with the best intentions, they strive to communicate to others:  but we put up with these drawbacks to avoid the inelegance and the tedium of a long discourse in accurate syllogisms.

Many departures from the strictly logical statement of reasonings consist in the use of vague or figurative language, or in the substitution for one another of expressions supposed to be equivalent, though, in fact, dangerously discrepant.  Against such occasions of error the logician can provide no safeguard, except the advice to be careful and discriminating in what you say or hear.  But as to any derangement of the elements of an argument, or the omission of them, Logic effectually aids the task of restoration; for it has shown what the elements are that enter into the explicit statement of most ratiocinations, namely, the four forms of propositions and what that connected order of propositions is which most easily and surely exposes the validity or invalidity of reasoning, namely, the premises and conclusion of the Syllogism.  Logic has even gone so far as to name certain abbreviated forms of proof, which may be regarded as general types of those that actually occur in debate, in leading articles, pamphlets and other persuasive or polemic writings—­namely, the Enthymeme, Epicheirema and Sorites.

Sec. 2.  The Enthymeme, according to Aristotle, is the Syllogism of probable reasoning about practical affairs and matters of opinion, in contrast with the Syllogism of theoretical demonstration upon necessary grounds.  But, as now commonly treated, it is an argument with one of its elements omitted; a Categorical Syllogism, having one or other of its premises, or else its conclusion, suppressed.  If the major premise be suppressed, it is called an Enthymeme of the First Order; if the minor premise be wanting, it is said to be of the Second Order; if the conclusion be left to be understood, there is an Enthymeme of the Third Order.

Let the following be a complete Syllogism: