The noun non sequitur refers to a statement or conclusion that does not follow logically from what preceded it. It is two words. It comes from Latin, where it means, literally, it does not follow. Non sequitur is unhyphenated except when it’s a phrasal adjective preceding a noun. Because it has been in English a long time, it is unitalicized.
A non sequitur isn’t just a random statement that comes out of nowhere. It is a statement that conspicuously does not follow what precedes it. For example, if I walk up to you and say, “The elephant gestation period is 22 months,” it would be random, but not a non sequitur (because nothing preceded it). If you ask how I am and I answer by saying something about elephants, that would be a non sequitur.
What seems a non sequitur makes sense in the context of the jumbled, disorienting music. [Wall Street Journal]
Like the late Hedberg, the New York-based comedian specializes in quick, everyday observations punctuated by hilarious non sequiturs. [Minneapolis Star-Tribune]
This song comes complete with its own collection of non sequiturs you’d usually expect from chemically enhanced dance music. [BBC News]
If the impetus for reform is the futility of prosecution … then decriminalization is a non-sequitur response. [National Post]