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An enthymeme is an informal or abbreviated version of a syllogism. A syllogism is a structured argument in deductive logic that contains two premises that are assumed to be true and a conclusion drawn from those premises. Enthymemes usually omit one of the premises and are often structured as "because" statements. In addition to logic and philosophy, enthymemes are used in rhetoric.
A syllogism contains a major premise, a minor premise and a conclusion. They are simple logical constructs which presume that because the premises are true, the conclusion is proved to be true. For example, "All dogs are canines. Sally is a dog. Therefore, Sally is a canine" is a syllogism.
An enthymeme takes the premises and conclusion of the syllogism and abbreviates them: "Sally is a canine because she is a dog." This sentence condenses the minor premise and the conclusion into a single sentence and omits the major premise altogether. An enthymeme might be used when one premise seems obvious, as in the case of the canine example. Alternatively, an enthymeme might be used to strengthen an argument when one premise is not particularly strong or might hurt the main point of the argument.
By omitting the conclusion rather than the premise of the syllogism, an enthymeme allows the reader to infer the conclusion for themselves. Forcing the audience to take that final step strengthens the argument, theoretically, because the readers have to think of the concluding statement for themselves rather than having it told to them. For example, the enthymeme "people who graduate from culinary school know how to cook. Sophie graduated from culinary school" omits the conclusion that Sophie knows how to cook, leaving the readers to infer this for themselves.
Enthymemes and syllogisms do not always deal with straightforward concepts such as canines and cooking schools, however. Their purpose is more often to simplify abstract concepts to obtain a better understanding of the validity of those ideas. This concept is clearly seen in rhetoric, where enthymemes often explicitly or implicitly serve as theses for essays.
For example, a basic argument for legalized abortion can be stated as both a syllogism and an enthymeme. The syllogism states the basic logic behind the argument: "Women have a right control what happens to their own bodies. Prohibiting abortion removes that right. Therefore, it is wrong to outlaw abortion." The enthymeme becomes the thesis: "It is wrong to outlaw abortion because women have a right to control what happens to their bodies."
Alternatively, the counterargument can be stated in the same way: "Every child has a right to live. Abortion eliminates that right. Therefore, abortion should be outlawed." The enthymeme becomes "Abortion should be outlawed because every child has a right to live."