According to the ancient Greek historian Plutarch, the Athenians preserved the wooden ship on which the mythical hero Theseus returned from Crete after slaying the Minotaur. Over many years, as the original planks and timbers rotted, they were gradually replaced one by one with new but identical ones. Eventually, none of the original materials remained. This gave rise to the question among Greek philosophers - Is it still the same ship? Or is it a different one? If so, at what point did it become a different one? When the first plank was changed? When the last original plank was removed? At some intermediate state?
Later, the British philosopher Thomas Hobbes took it one step further. What if the old planks were put in a pile as they were removed, and at a later point, a new ship was built from these planks. Which ship is then the real ship of Theseus?
What are you? The physical materials that make out our bodies gets replaced over time, so if there is a persisting you, doesn't that you have to be something beyond just your physical body?