The Grandfather Paradox

The grandfather paradox is a paradox of what may happen if one were able to travel backwards in time. The paradox is as follows:
Suppose Peter travels backwards in time and kills his biological grandfather (before his grandfather has the chance to meet his "present day" grandmother). In doing so, one of Peter's parents would not be conceived - the upshot of which being Peter himself would not have been conceived. However, if Peter was non-existent it would have been impossible to travel for him to travel backwards in time. And if he did not travel backwards in time, it would have been impossible for him to kill his grandfather and so... Peter and his grandfather would both still be alive. Now that Peter is alive... he can travel backwards in time and kill his grandfather (again!)...

The paradox is also known as autoinfanticide in philosophy circles.