The ship of Theseus was an actual ship that was repaired so often that all its parts had been replaced, which causes some to raise the question whether it was the same ship. Hobbes raised the further question of what we would think if someone had saved all the parts that were removed by repair and had re-assembled them into a new ship.
The problem seems to fade when we consider our actual responses to such things: everyone considers the ship that sails to be the ship, and the fact that we call it “the ship of Theseus problem” is a sign that we are taking it this way. No one cares if Air Force One is the same 747, or even whether Lassie is the same collie. Conversely, if, acting Hobbeswise, you saved all the cast off parts and made a ship out of them no one would consider it the “real” ship of Theseus.
Unlike substances, the good of artifacts is external. They can have functions of themselves but their purpose is for some person or persons. Artifacts have existence as individuals only so far as they are seen as essentially tied to individual agents (like a Caravaggio or Stradivarius).
So if Theseus were a master builder of ships whose products everyone revered, then it would take very few replacements before the ship ceased to be a Thesian ship, just as it takes very few replacements to make a violin cease being a Stradivarius. If the ship is the one the Athenian community designates to make its voyage, then it lasts as long as the Athenians designate something as the ship, regardless of how many there are, just as we do with Air Force One does. Its purpose or good is not in the peculiar materials with their individual form, and so is transferable.
But what if it were called the Ship were the ship of Theseus because he loved it? This might be the closest artifacts can get to existing for themselves. This might be the sense of the Pinocchio/ Pygmalion myth.
Still, for all this artifacts appear to have, at best, a purely participated individuality. Relation to a particular individual by generation or love might make the artifact irreplaceable, but it still does not have individuality for itself. AI seems to be an attempt to transcend this division, though we could just read the Chinese Room as a critique that any machine could have a self.