The Ship of Theseus paradox, also known as Theseus' paradox or the Heraclitian paradox, is a philosophical thought experiment that raises questions about the nature of identity and continuity over time. The paradox is named after the legendary Athenian hero Theseus, who sailed on a ship with a crew of Athenians to defeat the Minotaur.

The paradox asks whether a ship, which has had all of its parts replaced over time, is still the same ship. Suppose that the planks of Theseus' ship were replaced, one by one, until every single part of the ship had been replaced. Would the ship still be Theseus' ship, or would it be a new ship entirely?

One possible answer is that the ship is still Theseus' ship, despite the fact that it has been completely rebuilt. This answer is based on the idea that identity is determined by continuity over time. In other words, the ship is still the same ship because it has a continuous history that can be traced back to Theseus' original ship.

Another possible answer is that the ship is no longer Theseus' ship, since it has been completely rebuilt. This answer is based on the idea that identity is determined by the material composition of an object. In other words, the ship is no longer the same ship because it is made up of entirely different material than Theseus' original ship.

The Ship of Theseus paradox has been applied to many different areas of philosophy, including personal identity, the nature of change, and the relationship between mind and body. It is a fascinating and thought-provoking paradox that challenges us to think deeply about the nature of identity and continuity over time.