1 Answer

A fallacy in which a conclusion does not follow logically from what preceded it. And these are taken from the more serious aspect of its uses..

http://en.wikipedia.org/wiki/Non_sequitur_%28logic%29#Non_sequitur_in_everyday_speech

More examples..

In everyday speech, a non sequitur is a statement in which the final part is totally unrelated to the first part, for example:

Life is life and fun is fun, but it's all so quiet when the goldfish die.

—West with the Night, Beryl Markham^[2]

It can also refer to a response that is totally unrelated to the original statement or question:

Mary: I wonder how Mrs. Knowles next door is doing.
Jim: Did you hear that the convenience store two blocks over got robbed last night? Thieves got away with a small fortune.^[3]

A common non sequitur response:

Mary: I don't like the video you've posted.
Jim: Don't watch it then!