A writer of fiction may include physically impossible events and objects, from faster-than-light travel to fire-breathing vertebrates, and describe them in as much detail as desired. A writer of fiction may include the mathematically impossible, introducing a character who has squared the circle or discovered the greatest prime; but cannot go into detail about these achievements, on pain of incoherence. This, at least, is the received wisdom. Graham Priest, as an exponent of paraconsistent logic, dissents, and to make good his dissent has written a fictional story which tells how he and Nick Griffin, Richard Sylvan’s literary executor, discovered among Richard’s things an impossible object; and describes what they decided to do with it (which is, naturally enough, something impossible). He then draws lessons, mostly contrary to the received wisdom, from the story.