Enthymeme

An enthymeme (Greek: ἐνθύμημα, enthumēma), in its modern sense, is an informally stated syllogism (a three-part deductive argument) with an unstated assumption that must be true for the premises to lead to the conclusion. In an enthymeme, part of the argument is missing because it is assumed. In a broader usage, the term "enthymeme" is sometimes used to describe an incomplete argument of forms other than the syllogism, or a less-than-100% argument. For Aristotle, who defined it in his Rhetoric, an enthymeme was a "rhetorical syllogism" which was based on probable opinions, thus distinguishing it from a scientific syllogism. It is aimed at persuasion while scientific syllogism is aimed at demonstration.

Formal requirements

While syllogisms lay out all of their premises and conclusion explicitly, enthymemes keep at least one of the premises or conclusion unsaid. The assertion left unsaid is intended to be so obvious as to not need stating.

Thus, enthymemes allow the speaker both to avoid alienating listeners with long chains of inferences and appeal to the audience's common sense without depleting the argument any of its logical force. For instance, a lawyer might say: "Only she had the means, the motive and the opportunity to kill him. She must be the killer." Logically, what's missing? A connection between the statements, which we tend to fill in automatically. Something like "Only the killer had the means, motive and opportunity to kill him." But a lawyer who spelled this detail out to the jury might be considered pedantic.

Though they require some filling in, enthymemes are intended to have the form of valid deductive syllogisms, so a complete enthymeme has the same premise-premise-conclusion structure as any syllogism, and is intended to guarantee the truth of its conclusion based on the truth of its premises.

Hence the argument...

P1: Only she had the means, the motive and the opportunity to kill him.

P2: The killer had the means, motive and opportunity to kill him. (unstated)

C: She must be the killer.

...is clearly valid and deductive when the unstated premise is made explicit. But leaving the second premise to the imagination of the jurors is more appealing from a rhetorical standpoint.

Order

There are three conventional orders of enthymemes. A first-order enthymeme suppresses the major premise. A second-order enthymeme suppresses the minor premise. A third-order enthymeme suppresses the conclusion. Other orders of enthymemes, in which 2 elements of the syllogism are suppressed, could be postulated.

Examples

Informal Syllogism

• "Socrates is mortal because he's human."

The complete syllogism would be the classic:

All humans are mortal. (major premise - assumed)

Socrates is human. (minor premise - stated)

Therefore, Socrates is mortal. (conclusion - stated)

Maxim, or a less-than-100% argument

• Klamer et al argue in their 2007 paper that Aristotle addressed this use of enthymeme:

"Aristotle noted that most arguments take the form of an "enthymeme" ("EN-thu-miem"), an incomplete or not-quite-air-tight syllogism. 'Free trade is good' or 'Taxes reduce output' are enthymemes, not-syllogistic arguments. The average French economist may find such arguments 45 percent true, whereas the average American economist may find them 80 percent true. Arguing an enthymeme is successful when the economist defends the 45 or 80 percent true as “true enough.” Economics, like other sciences, works in approximations."

See also

• Logical fallacy
• Rogerian argument
• Senator, you are no Jack Kennedy
• modus ponens

External links

• Extensive bibliography of enthymeme in scholarly literature
• The enthymeme in modern speech
• Audio illustrations of enthymeme