Theseus' Ship

Theseus is famous in Greek mythology as the slayer of the Minotaur, a half-man, half-bull monster who lived in the Labyrinth in the island of Crete. According to Plutarch, the ship in which Theseus sailed back to Athens was preserved for many generations, its old planks being replaced by new ones as they decayed.

Now suppose that a few hundred years later, all the original parts of the ship had been replaced, one by one, so that none of the original ship remained. Is the preserved ship still Theseus' ship? Or is it a copy? And if the latter, then at what point did it cease to be Theseus' ship?

It seems that if just one plank were replaced, it would still be Theseus' ship. And if it was still his ship, and another plank were replaced, then it should still be Theseus' ship. By this reasoning (which is the same as in the sorites paradox), it would be Theseus' ship even after all planks are replaced.

This problem is not merely another version of the sorites, however. It involves the notion of identity, of what we mean by something being the "same" object. Suppose that we regard the final ship as Theseus' ship. What if all the old planks, nails, etc., had been stored in a warehouse and someone put them back together again. Would there then be two Theseus' ships?

Similar paradoxes of identity arise in certain science fiction scenarios and in connection with the philosophy of mind. Suppose you are teleported by having your body disintegrated in one place and reassembled in another from new materials. Are you still "you"? Your body is made of different atoms, but it is still you as far as your mind is concerned, right? But what if instead of having your original body disintegrated you merely have a copy made? Then is the copy still you?