The Ship of Theseus is a famous philosophical problem first posed in its current form during the time of ancient Greece. It is supposed that the famous ship sailed by the hero Theseus in a great battle was kept in a harbor as a museum piece, and as the years went by some of the wooden parts began to rot and were replaced by new ones; then, after a century or so, every part had been replaced.
The question then is if the “restored” ship is still the same object as the original. If it is, then suppose the removed pieces were stored in a warehouse, and after the century, technology was developed that cured their rot and enabled them to be reassembled into a ship? Is this “reconstructed” ship the original ship? If it is, then what about the restored ship in the harbor still being the original ship as well? And if that rebuilt ship set sail for a new destination, while the other stayed in the museum, had the ship really been there? Had its crew been on board the same ship?
This has been in interesting problem without a real solution for centuries, but it never really had a practical application until the birth of the Exalted… digital humans that were brought into existence by the destruction of the original brain and capable of copying themselves and having multiple copies acting at once.
Philosophers have never stopped arguing about the idea, or about at what point a divergence a copy of one of the Exalted becomes a new person instead of a theoretical copy, but for their part the Exalted have solved the problem to their satisfaction. For the most part, they subscribe to Heraclitus’ original solution… the idea that identity is an inherently fluid and changing concept, and that nothing remains “itself” for any period of time anyway. The change to their identity made in the evolution between biological and machine life, to them, is no more severe than the change to a boy’s identity the first time he learns his street address… he is no longer the same person, but the consciousness of the first and second person merge – the idea that it is impossible to step twice into the same river, as even as the water flows and replenishes itself, the original is gone. Just like that, human consciousness is always moving on as well… flowing effortlessly from place to place capable of maintaining it. Maintaining some degree to continuity of consciousness is all that matters to them.
In practical terms, how they approach this is to minimize the flow and maximize continuity. An Exalted copy made seeks to return to a central location and join with her other copies as soon as possible, merging their memories. As long the memories and experiences continue to be merged, continuity of consciousness is maintained and the Exalted as satisfied that they, their original, biological mind, and their copies are all the same being, not different beings.
(Even by the standards of this story, this is a simplistic explanation of the problem, and there isn’t really a “right” answer to the paradox. If you are encountering this idea for the first time and are curious, I urge you to read more about it)