Enthymeme
Encyclopedia
An enthymeme 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. This definition of an enthymeme held fast until the 20th century, when Saul Kripke
developed Modal logic
. In the context of Modal logic, with
Semantic tableaux as developed by Evert Willem Beth
, the definition of an enthymeme alters: Rather than suppressing one of the major premises, minor premises, or the conclusion, any incorrect logical inference or proof that is persuasive, satisfies a concept of an enthymeme.
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 "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 one with the means, motive and opportunity to kill him is the killer. (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.
Syllogism
A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...
(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
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
, who defined it in his Rhetoric
Rhetoric (Aristotle)
Aristotle's Rhetoric is an ancient Greek treatise on the art of persuasion, dating from the 4th century BC. In Greek, it is titled ΤΕΧΝΗ ΡΗΤΟΡΙΚΗ, in Latin Ars Rhetorica. In English, its title varies: typically it is titled Rhetoric, the Art of Rhetoric, or a Treatise on...
, an enthymeme was a "rhetorical syllogism
Syllogism
A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...
" which was based on probable opinions, thus distinguishing it from a scientific syllogism. It is aimed at persuasion
Persuasion
Persuasion is a form of social influence. It is the process of guiding or bringing oneself or another toward the adoption of an idea, attitude, or action by rational and symbolic means.- Methods :...
while scientific syllogism is aimed at demonstration. This definition of an enthymeme held fast until the 20th century, when Saul Kripke
Saul Kripke
Saul Aaron Kripke is an American philosopher and logician. He is a professor emeritus at Princeton and teaches as a Distinguished Professor of Philosophy at the CUNY Graduate Center...
developed Modal logic
Modal logic
Modal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...
. In the context of Modal logic, with
Semantic tableaux as developed by Evert Willem Beth
Evert Willem Beth
Evert Willem Beth was a Dutch philosopher and logician, whose work principally concerned the foundations of mathematics.- Biography :...
, the definition of an enthymeme alters: Rather than suppressing one of the major premises, minor premises, or the conclusion, any incorrect logical inference or proof that is persuasive, satisfies a concept of an enthymeme.
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 "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 one with the means, motive and opportunity to kill him is the killer. (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.Informal syllogism
- "SocratesSocratesSocrates was a classical Greek Athenian philosopher. Credited as one of the founders of Western philosophy, he is an enigmatic figure known chiefly through the accounts of later classical writers, especially the writings of his students Plato and Xenophon, and the plays of his contemporary ...
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 enthymemes as maxims:
"AristotleAristotleAristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
noted that most argumentArgumentIn philosophy and logic, an argument is an attempt to persuade someone of something, or give evidence or reasons for accepting a particular conclusion.Argument may also refer to:-Mathematics and computer science:...
s take the form of an 'enthymeme' ('EN-thu-miem'), an incomplete or not-quite-air-tight syllogismSyllogismA syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...
.' 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.' EconomicsEconomicsEconomics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
, like other sciences, works in approximations."
See also
- Chewbacca defenseChewbacca defenseThe Chewbacca defense is a legal strategy used in episode 27 of South Park, "Chef Aid", which premiered on October 7, 1998, as the fourteenth episode of the second season. The aim of the argument is deliberately to confuse the jury by making use of the fallacy known as ignoratio elenchi, or a red...
- Logical fallacy
- Rogerian argumentRogerian argumentRogerian argument is a conflict solving technique based on finding common ground instead of polarizing debate.-Origin:American psychologist Carl R. Rogers described his "principles of communications," a form of discussion based on finding common ground...
- Senator, you are no Jack KennedySenator, you are no Jack Kennedy"Senator, you're no Jack Kennedy" was a quotation used during the 1988 United States vice-presidential debate by Democratic vice-presidential candidate Senator Lloyd Bentsen to Republican vice-presidential candidate Senator Dan Quayle. Jack Kennedy was a reference to John F. Kennedy, the 35th...
- modus ponensModus ponensIn classical logic, modus ponendo ponens or implication elimination is a valid, simple argument form. It is related to another valid form of argument, modus tollens. Both Modus Ponens and Modus Tollens can be mistakenly used when proving arguments...