The word non-sequitur is derived from a Latin phrase meaning "it does not follow." There are two different connotations of a non-sequitur – one can be found in the philosophical world of logic, while the other is a literary device based on an illogical premise. Some legal arguments presented in court rely on a logical non-sequitur, while a number of comedies and jokes depend on an illogical non-sequitur for success.

In the sense of pure logic, a non-sequitur begins with the presentation of two or more statements called premises. Premise A could be "God is love." Premise B could be "Love is blind." Premise C states "Ray Charles is blind." The non-sequitur conclusion based on these premises would be "Therefore, Ray Charles is God."

What went wrong? Each of the premises could be considered true, at least philosophically, but the outcome is a non-sequitur. When the conclusion is not supported logically by the preceding premises, it is said to be a non-sequitur, even if it is true.

Both the prosecution and the defense in a court case may use this form of non-sequitur logic to guide a jury towards a specific conclusion. The prosecutor may argue that the crime took place in an architectural firm. The defendant is an architect at that firm. Therefore, the defendant must have committed the crime.

The conclusion that the defendant committed the crime would be a logical non-sequitur. In reality, the location of the crime scene may be irrelevant, and the defendant is not necessarily the only architect working for the firm. The defense attorney could argue that the prosecution's argument is invalid based on this non-sequitur conclusion.

In a literary sense, a non-sequitur can be any unexpected response to a set of predictable circumstances. A non-sequitur could also be a deliberately illogical response offered for comedic effect. The British comedy troupe Monty Python often uses non-sequiturs to bring their sketches to an abrupt end.

Characters in absurdist plays may hold entire conversations consisting of one non-sequitur line after another: "I made pancakes this morning." "Oh, do you think it might rain?" "Only if a dingo ate my baby." "Ran out of wallpaper paste again, eh?" The humor lies in the complete unpredictability that a non-sequitur provides.

Many jokes also rely on a non-sequitur ending, although the audience may have to abandon all hopes of linear thought to understand them. A non-sequitur works best when it does not follow the predicted course of the script at all. A non-sequitur does not have to be completely absurd in order to be funny, but it does have to go against the audience's expectations. Two gangsters involved in a tense stand-off could suddenly decide to run away and get married, for example. This would be an effective use of non-sequitur, since the audience would have expected a cliched ending, such as the police breaking down the door. Comedy sketch shows like Saturday Night Live and MadTV use non-sequitur endings quite often, especially when a more logical ending would not be possible.