Chapter 29

ENTHYMEMES.

There is a certain variety in the use of the word Enthymeme among logicians. In the narrowest sense, it is a valid formal syllogism, with one premiss suppressed. In the widest sense it is simply an argument, valid or invalid, formal in expression or informal, with only one premiss put forward or hinted at, the other being held in the mind ([Greek: en thymo]). This last is the Aristotelian sense.

It is only among formal logicians of the straitest sect that the narrowest sense prevails. Hamilton divides Enthymemes into three classes according as it is the Major Premiss, the Minor Premiss, or the Conclusion that is suppressed. Thus, a full syllogism being:--

All liars are cowards: Caius is a liar: [.'.] Caius is a coward:--

this may be enthymematically expressed in three ways.

I. Enthymeme of the First Order (_Major understood_).

Caius is a coward; for Caius is a liar.

II. Enthymeme of the Second Order (_Minor understood_).

Caius is a coward; for all liars are cowards.

III. Enthymeme of the Third Order (_Conclusion understood_).

All liars are cowards, and Caius is a liar.

The Third Order is a contribution of Hamilton's own. It is superfluous, inasmuch as the conclusion is never suppressed except as a rhetorical figure of speech. Hamilton confines the word Enthymeme to valid arguments, in pursuance of his view that Pure Logic has no concern with invalid arguments.

Aristotle used Enthymeme in the wider sense of an elliptically expressed argument. There has been some doubt as to the meaning of his definition, but that disappears on consideration of his examples. He defines an Enthymeme (Prior Analyt., ii. 27) as "a syllogism from probabilities or signs" ([Greek: syllogismos ex eikoton e semeion]). The word syllogism in this connexion is a little puzzling. But it is plain from the examples he gives that he meant here by syllogism not even a correct reasoning, much less a reasoning in the explicit form of three terms and three propositions. He used syllogism, in fact, in the same loose sense in which we use the words reasoning and argument, applying without distinction of good and bad.

The sign, he says, is taken in three ways, in as many ways as there are Syllogistic Figures.

(1) A sign interpreted in the First Figure is conclusive. Thus: "This person has been drowned, for he has froth in the trachea". Taken in the First Figure with "All who have froth in the trachea have been drowned" as a major premiss, this argument is valid. The sign is conclusive.

(2) "This patient is fever-stricken, for he is thirsty." Assumed that "All fever-stricken patients are thirsty," this is an argument in the Second Figure, but it is not a valid argument. Thirst is a sign or symptom of fever, but not a conclusive sign, because it is indicative of other ailments also. Yet the argument has a certain probability.

(3) "Wise men are earnest ([Greek: spoudaioi]), for Pittacus is earnest." Here the suppressed premiss is that "Pittacus is wise". Fully expressed, the argument is in the Third Figure:--

Pittacus is earnest. Pittacus is wise. [.'.] Wise men are earnest.

Here again the argument is inconclusive and yet it has a certain probability. The coincidence of wisdom with earnestness in one notable example lends a certain air of probability to the general statement.

Such are Aristotle's examples or strict parallels to them. The examples illustrate also what he says in his _Rhetoric_ as to the advantages of enthymemes. For purposes of persuasion enthymemes are better than explicit syllogisms, because any inconclusiveness there may be in the argument is more likely to pass undetected. As we shall see, one main use of the Syllogism is to force tacit assumptions into light and so make their true connexion or want of connexion apparent. In Logic enthymemes are recognised only to be shown up: the elliptical expression is a cover for fallacy, which it is the business of the logician to strip off.

In Aristotle's examples one of the premisses is expressed. But often the arguments of common speech are even less explicit than this. A general principle is vaguely hinted at: a subject is referred to a class the attributes of which are assumed to be definitely known. Thus:--

He was too ambitious to be scrupulous in his choice of means.

He was too impulsive not to have made many blunders.

Each of these sentences contains a conclusion and an enthymematic argument in support of it. The hearer is understood to have in his mind a definite idea of the degree of ambition at which a man ceases to be scrupulous, or the degree of impulsiveness that is incompatible with accuracy.

One form of enthymeme is so common in modern rhetoric as to deserve a distinctive name. It may be called the ENTHYMEME OF THE ABSTRACTLY DENOMINATED PRINCIPLE. A conclusion is declared to be at variance with the principles of Political Economy, or contrary to the doctrine of Evolution, or inconsistent with Heredity, or a violation of the sacred principle of Freedom of Contract. It is assumed that the hearer is familiar with the principles referred to. As a safeguard against fallacy, it may be well to make the principle explicit in a proposition uniform with the conclusion.