Non Sequitur

Latin for "(it) does not follow". Applied to a statement that's supposed to be a logical consequent of a line of reasoning but in fact is not. Technically, a non sequitur is a superclass of many logical fallacies for which a putative consequent doesn't follow the precedent, such as UndistributedMiddle and ArgumentByAnalogy, but use should be restricted to consequents that don't fall into another class. For example, in the argument: "Socrates is a man and men are mortal, therefore Socrates is dead," the fragment "Socrates is dead" is a non sequitur. The greater the apparent randomness of a supposed consequent, the more likely to be accurate is the appellation.

Often used of OffTheWall remarks in ordinary discourse.