Anderson family paradox

The entire Anderson family is born under a paradoxical time loop that renders the existance of everyone involved impossible.

Paradox
Luke Anderson, from the time of the Global Civil War, learns that he is the descendant of the two warriors, James (grandfather) & Jack (father), of the Alliance for the Survival of Humanity back in the 2160s-80s. Anderson, who had finished the civil war between the Global & Separatist States, realizes that the future seems bleak for him with the post-war overthrow of the Global State & he uncovers an artifact called the Time Map, which he uses on a warp gate to travel back to 2145 to live the rest of his life in the time before the Second Dark War. There, he meets a girl named Maureen. The two get marryed & Maureen later gives birth to a boy they name James after Luke's ancestor. Shortly after James' birth, the Second Dark War begins. This leads Luke to realize that James is his ancestor, the James Anderson who was his grandfather is his son. However, before Luke can ultimately disclose this to Maureen, James is separated from them in his infancy & Maureen & Luke are traumatized by a shadowghost attack that leaves their memorys distorted, in which Maureen's parents are killed, they end up believing that James is Maureen's cousin. James then goes onto bear a son he named Jack. Jack then defeats Core & Cyber Erol & bears another son named Luke. Luke wins the Global Civil War for the Global State, which collapses shortly after, restarting the entire time loop.