I'm curious how Jack would ever find out Claire was his sister at this point, though. If Claire's not one of the six, and his father is dead, and her mother is dead, then ... her mother's sister is about the only character left who knows, and ...
Wait! At any sort of memorial service or with any sort of media frenzy, her mother's sister could easily see the name Jack Shepard and make the connection with Christian Shepard ... and spill the beans to Jack.
But would she? She really didn't want to acknowledge Claire's parentage at all previously.