This is quite an interesting case presented by my Minds and Machines professor.

A man named Theseus owns a relatively old boat and feels he should fix it up. Theseus hires a carpenter to remove one plank from the boat and replace that plank with a new plank immediately afterwards. The carpenter does this for every plank on the boat, removing and replacing each one at a time.

Once the carpenter has replaced every plank of the boat is the boat still Theseus' original boat or is it an entirely new boat? And if the carpenter were to construct another boat out of the planks that had originally been in Theseus' boat, would this second boat be Theseus' original boat or a new one?
Sure, i understand the logic behind the question, but i also see a flaw that is generated from the choice of object:

A ship is made of more than just planks. There are probably a few very large pieces of wood that run through the ship that connect everything together. Trying to remove on of these pieces of wood would cause the rest of the ship to collapse. So the base frame of the ship could not be replaced piece-wise.

What if every node from E2 was removed and replaced? Would it still be E2? What if they were re-pieced together into another E2? Now there is a mind bender.
This is not "a man" named Theseus and he does not own the boat nor hire the carpenter. Theseus was the legendary king of Athens and slayer of the Minotaur. His ship was preserved in Athens long after him, but as time passed it had to be repaired and replaced bit by bit. It was a traditional sophistical question whether it was the same ship, and if not, when it ceased to be, or would cease to be. Aristotle discussed this.

The image was borrowed for a rather different purpose by W.V.O. Quine, who talked about mending one's ship while at sea: because our coherent system of beliefs all fit together with no one subset underpinning the rest (he claimed), revising our beliefs in a fundamental way, as in a paradigm shift, requires the equivalent of replacing much of the boat while it's still in use.

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