The Athenians kept the ship. Thirty oars. They kept it for something close to a thousand years, and keeping it meant a standing policy: when a plank rotted, the plank came out and a new one went in.

They took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same.

Plutarch, Life of Theseus 23 (Dryden)

Plutarch does not take a side. He is writing a life, the dispute was already old when he reached it, and he moves on in the next sentence to something else entirely.

The detail that survives least often is the one that made it possible. Somebody was employed to decide, plank by plank and year by year, that this one had gone and that one would hold another season. The paradox is a by-product of a shipwright’s ordinary working week.

He records the question and declines it. It has been in continuous use ever since, which is longer than the ship lasted.