An enthymeme (, enthýmēma) is an argument with a hidden premise. Enthymemes are usually developed from premises that accord with the audience's view of the world and what is taken to be common sense. However, where the general premise of a syllogism is supposed to be true, making the subsequent deduction necessary, the general premise of an enthymeme is merely probable, which leads only to a tentative conclusion. Originally theorized by Aristotle, there are four types of enthymeme, at least two of which are described in Aristotle's work.
Aristotle referred to the enthymeme as "the body of proof", "the strongest of rhetorical proofs...a kind of syllogism" ( Rhetoric I, 1.3,11). He considered it to be one of two kinds of proof, the other of which was the paradeigma. Maxims, Aristotle thought, were a derivative of enthymemes. ( Rhetoric II.XX.1). Aristotle discusses two types of enthymemes: demonstrative deiktika and refutative elentika. ( Rhetoric II.XXII.14). Demonstrative enthymemes are of the fact that something is or is not the case; they draw a conclusion from what is agreed. Refutative enthymemes draw conclusions that are not agreed to by the opponent. ( Rhetoric II.XXII.15). According to Aristotle, refutative enthymemes are better liked by audiences because the inconsistencies or opposing arguments are clearer when placed side by side. ( Rhetoric II.XXIII.30). Enthymemes are derived from probabilities, or what happens for the most part, and signs, which sometimes point to a necessary conclusion and other times are refutable.
Here is an example of an enthymeme derived from a syllogism through truncation (shortening) of the syllogism:
While syllogisms lay out all of their premises and conclusion explicitly, these kinds of enthymemes keep at least one of the premises or the conclusion unstated.
In the examples, 'having a cough', 'having a child', and 'yawning' are signs of illness, giving birth, and sleepiness, respectively. In those cases, the enthymeme is only probably true because there are other sources of coughs besides pathogens, children besides parturition, and reasons for yawning besides sleepiness, such as allergies, adoption, and fatigue from exercising, respectively.
Some examples of this kind of enthymeme are as follows:
In the first case, the missing term of the syllogism is "French novels are irreverent" and might be an assumption held by an audience that would make sense of the enthymematic argument. In the second case, the missing term of the syllogism is "Starbucks customers all enjoy coffee" and this might be another assumption held by audiences to make sense of that particular argument. Such unstated premises can also rise to the level of axioms (statements so commonly accepted as to be thought universally true) and Formal fallacy.
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