An enthymeme is a syllogism that is missing a premise, and is thus a type of non sequitur, since the conclusion does not follow from the stated premise. The completed syllogism may or may not be valid or sound; this can only be judged once the missing premise has been provided.
- "John is a human, so he has two eyes." (The missing part is "humans have two eyes".)
- "Of course you're a Republican. You're from Texas." (The missing part is "all Texans are Republicans".)
- "I graduated from a good school, and am therefore an atheist." (The unstated premise is that good schools produce only atheist graduates.)
One common reason for omitting a premise is that it is obvious. For instance, one might say, "I didn't bring my piano on vacation, because I could only bring one suitcase". It is not normally necessary to point out that a piano cannot fit inside a suitcase.
The missing premise may also be deliberately omitted because it is obviously false, or is otherwise unpalatable. For instance: "The immigrant population in Springfield has risen sharply in recent years; we should put more police on the street." The unstated premise is that immigrants are more likely than the general population to commit crimes.
Enthymemes can also be effectively used for humorous purposes, such as in making indirect insults.