There is the well-known paradox of traveling into the past to kill your mother before you were born. Actually, it works for anyone known by anyone else. The contradiction is that if you were never born, how did you go back in time to kill your mother?
It seems that time only moves in one direction, not counting the subatomic particles that seem to defy that. If we imagine space-time as a closed four-dimensional space, NOT embedded into a five-dimensional space, then, space-time would end at some moment - not necessarily a zero-dimensional moment - and one could "wrap-around" through the end of time to the beginning of time and change things without contradiction.