James Moriarty is truly dead. Only his brother is not. In the actual books they were brothers. Professer James Moriarty (Jim) and Colonel James Moriarty (James). Jim was put on trial for the crown jewel robbery and James posed as Richard Brooke. James Moriarty met Sherlock on top of Bart's and shot himself. He is dead while his brother is still alive. I doubt even Sherlock notices that there were two of them but the only person on the show that could figure it out would be Mycroft.