The Ship of Theseus is a replacement paradox. (Also known as Theseus' Paradox)

According to an ancient Greek legend, Theseus had a warship that was preserved as a historical relic by the Athenians. Some of its boards rotted and had to be replaced. After many, many years, many such replacements occurred. Eventually, none of the original boards were present. Philosophers could then debate whether it was the same ship that Theseus had used, and if not, when it had ceased to be so.

There is also an additional question: if the replaced parts were stored in a warehouse and later used to reconstruct the ship, which--if either--would be the original ship of Theseus?

George Washington's axe

A similar story is told about George Washington's axe, with which the young George Washington is supposed, in an apocryphal story, to have cut down his father's cherry tree. The axe is supposedly on display in an (unverifiable) American museum, although, having had both its handle and its head replaced several times, no part of the original axe remains.

A modern embellishment

If Theseus paid a nontransferable fee, allowed to be used for only one ship, for the privilege of docking in a particular harbor, would he violate the non-transferability of his license if repeated replacement of boards eventually had the result described above?

See also identity and change.