The Ship of Theseus, also known as Theseus's Paradox, is a paradox and common thought experiment about whether an object (in the most common stating of the paradox, a ship) is the same object after having all of its original components replaced with other ones over time, usually one by one.

In Greek mythology, Theseus, the mythical king of the city of Athens, rescued the children of Athens from King Minos after slaying the minotaur and then escaped onto a ship going to Delos. Each year, the Athenians would commemorate this by taking the craft on a pilgrimage to Delos to honour Apollo. Over time, some of its boards rotted and were replaced. A question was raised by ancient philosophers: If no pieces of the original made up the current ship, was it still the Ship of Theseus? If it was no longer the same, when had it ceased existing as the original ship? Seventeenth century philosopher Thomas Hobbes raised the further question of how to consider a second ship that had been built entirely from pieces removed from the original.

In contemporary philosophy, the thought experiment has applications to the philosophical study of identity over time. Within the contemporary philosophy of mind, it has inspired a variety of proposed solutions and concepts regarding the persistence of personal identity.

In its original formulation, the "Ship of Theseus" paradox concerns a debate over whether a ship that has had all of its components replaced one by one would remain the same ship. The account of the problem has been preserved by Plutarch in his Life of Theseus:

The ship wherein Theseus and the youth of Athens returned from Crete had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and strong timber in their places, 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 23.1

The seventeenth century philosopher Thomas Hobbes extended the thought experiment by supposing that a ship custodian gathered up all of the decayed parts as they were disposed and used those them to build a second ship, then asked which of the two—the custodian's or the Athenians'—was the "original" ship.

For if that Ship of Theseus (concerning the Difference whereof, made by continual restoration, in taking out the old Planks, and putting in new, the sophisters of Athens were wont to dispute) were, after all the Planks were changed, the same Numerical Ship it was at the beginning; and if some Man had kept the Old Planks as they were taken out, and by putting them afterward together in the same order, had again made a Ship of them, this would, without doubt, had also been the same Numerical Ship with that which was at the beginnings and so there would have been two Ships Numerically the same, which is absurd... But we must consider by what name anything is called when we inquire concerning the Identity of it... so that a Ship, which signifies Matter so figured, will be the same, as long as the Matter remains the same; but if no part of the Matter is the same, then it is Numerically another Ship; and if part of the Matter remains, and part is changed, then the Ship will be partly the same, and partly not the same.