The ship of Theseus, also known as Theseus’s paradox, is a paradox that raises the question of whether an object which has had all its components replaced remains fundamentally the same object or not.
Theseus is remembered in Greek mythology as the slayer of the Minotaur. For years, the Athenians had been sending sacrifices to be given to the Minotaur, a half-man, half-bull beast who inhabited the labyrinth of Knossos, Crete. One year, Theseus braved the labyrinth, and killed the Minotaur. The ship in which he returned was long preserved. As parts of the ship needed repair, it was rebuilt plank by plank.
The paradox was first raised in Greek legend as reported by Plutarch
“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 stronger timber in their place, in so much 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.”
The question raised by Plutarch – “Does the ship remains the same even if every piece is replaced by a new one?” is quite interesting and puzzling at the same time. Centuries later, the philosopher Thomas Hobbes added to the puzzle, wondering: “What would happen if the original planks were gathered up after they were replaced, and used to build a second ship?”
If this happened, then, then it would seem that Theseus had returned from Knossos in two ships. First, there would have been Theseus’ ship that has had each of its parts replaced one by one. Second, there would have been Theseus’ ship that had been dismantled, restored, and then reassembled. Each of them would have been Theseus’ ship.
Theseus, though, sailed in only one ship. Which one?
The Greek philosopher Heraclitus attempted to solve the paradox by introducing the idea of a river where water replenishes it. Arius Didymus quoted him as saying “upon those who step into the same rivers, different and again different waters flow”. Plutarch disputed Heraclitus’ claim about stepping twice into the same river, citing that it cannot be done because “it scatters and again comes together, and approaches and recedes”.
One common argument found in the philosophical literature is that in the case of Heraclitus’ river one is tripped up by two different definitions of “the same”. In one sense things can be “qualitatively identical”, by sharing some properties. In another sense they might be “numerically identical” by being “one”. As an example, consider two different marbles that look identical. They would be qualitatively, but not numerically, identical. A marble can be numerically identical only to itself.
One common argument found in the philosophical literature is that in the case of Heraclitus’ river one is tripped up by two different definitions of “the same”. In one sense things can be “qualitatively identical”, by sharing some properties. In another sense they might be “numerically identical” by being “one”. As an example, consider two different marbles that look identical. They would be qualitatively, but not numerically, identical. A marble can be numerically identical only to itself.
Infact some languages like German, for example, “gleich” (“equal”) and “selbst” (“self-same”) are the pertinent terms, respectively. At least in formal speech, the former refers to qualitative identity (e.g. die gleiche Murmel, “the same[qualitative] marble”) and the latter to numerical identity (e.g. die selbe Murmel, “the same[numerical] marble”). Colloquially, the terms are sometimes used interchangeably however.