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.