Grandfather Paradox

"The grandfather paradox is a paradox of time travel, first described by the science fiction writer René Barjavel in his 1943 book Le Voyageur Imprudent (The Imprudent Traveller). The paradox is this: suppose a man traveled back in time and killed his biological grandfather before the latter met the traveller's grandmother. As a result, one of the traveller's parents (and by extension, the traveller himself) would never have been conceived. This would imply that he could not have travelled back in time after all, which in turn implies the grandfather would still be alive, and the traveller would have been conceived, allowing him to travel back in time and kill his grandfather. Thus each possibility seems to imply its own negation, a type of logical paradox."

-Wikipedia