The ship of Theseus, also known as Theseus' paradox, is a thought experiment that raises the question of whether an object that has had all of its components replaced remains fundamentally the same object. The paradox is most notably recorded by Plutarch in Life of Theseus from the late first century. Plutarch asked whether a ship that had been restored by replacing every single wooden part remained the same ship.
The paradox had been discussed by other ancient philosophers such as Heraclitus and Plato prior to Plutarch's writings, and more recently by Thomas Hobbes and John Locke. Several variants are known, including the grandfather's axe, which has had both head and handle replaced.
Variations of the paradox
This particular version of the paradox was first introduced in Greek legend as reported by the historian, biographer, and essayist 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 places, 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.”
— Plutarch, Theseus
Plutarch thus questions whether the ship would remain the same if it were entirely replaced, piece by piece. Centuries later, the philosopher Thomas Hobbes introduced a further puzzle, wondering what would happen if the original planks were gathered up after they were replaced, and used to build a second ship. Hobbes asked which ship, if either, would be the original Ship of Theseus.
John Locke proposed a scenario regarding a favorite sock that develops a hole. He pondered whether the sock would still be the same after a patch was applied to the hole, and if it would be the same sock after a second patch was applied, and a third, etc., until all of the material of the original sock has been replaced with patches.
George Washington's axe (sometimes "my grandfather's axe") is the subject of an apocryphal story of unknown origin in which the famous artifact is "still George Washington's axe" despite having had both its head and handle replaced.
This has also been recited as "Abe Lincoln's axe"; Lincoln was well known for his ability with an axe, and axes associated with his life are held in various museums.
The French equivalent is the story of Jeannot's knife, where the eponymous knife has had its blade changed fifteen times and its handle fifteen times, but is still the same knife. In some Spanish-speaking countries, Jeannot's knife is present as a proverb, though referred to simply as "the family knife". The principle, however, remains the same.
A Hungarian version of the story features "Lajos Kossuth's pocket knife", having its blade and handle continuously replaced but still being referred to as the very knife of the famous statesman. As a proverbial expression it is used for objects or solutions being repeatedly renewed and gradually replaced to an extent that it has no original parts.
A comedic version of the story appears in the popular TV sitcom Only Fools and Horses, in which the character Trigger explains that his broom... "has had 17 new heads and 14 new handles in it's time".
One version is often discussed in introductory Jurisprudence and Evidence classes in law school, discussing whether a weapon used in a murder, for example, would still be considered the "murder weapon" if both its handle and head/blade were to be replaced at separate, subsequent times. (Perhaps yes if the issue is whether tracing the history of 'its' possession may lead one back to the murderer; perhaps no if the issue is whether fingerprints from the murder may still be on 'it'. This shows how a philosophical paradox can be resolved, perhaps in different ways in different contexts, when converted into a question about the physical world. Likewise mathematical paradoxes in physics, for example the significance of whether or not a number is rational in Hofstadter's butterfly.)
In popular culture
The paradox appears in various forms in fictional contexts, particularly in fantasy or science-fiction, for example where a character has body parts swapped for artificial replacements until the person has been entirely replaced. There are many other variations with reference to the same concept in popular culture for example axes and brooms.
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".
According to the philosophical system of Aristotle and his followers, four causes or reasons describe a thing; these causes can be analyzed to get to a solution to the paradox. The formal cause or 'form' (perhaps best parsed as the cause of an object's form or of its having that form) is the design of a thing, while the material cause is the matter of which the thing is made. Another of Aristotle's causes is the 'end' or final cause, which is the intended purpose of a thing. The ship of Theseus would have the same ends, those being, mythically, transporting Theseus, and politically, convincing the Athenians that Theseus was once a living person, though its material cause would change with time. The efficient cause is how and by whom a thing is made, for example, how artisans fabricate and assemble something; in the case of the ship of Theseus, the workers who built the ship in the first place could have used the same tools and techniques to replace the planks in the ship.
According to Aristotle, the "what-it-is" of a thing is its formal cause, so the ship of Theseus is the 'same' ship, because the formal cause, or design, does not change, even though the matter used to construct it may vary with time. In the same manner, for Heraclitus's paradox, a river has the same formal cause, although the material cause (the particular water in it) changes with time, and likewise for the person who steps in the river.
This argument's validity and soundness as applied to the paradox depend on the accuracy not only of Aristotle's expressed premise that an object's formal cause is not only the primary or even sole determiner of its defining characteristic(s) or essence ("what-it-is") but also of the unstated, stronger premise that an object's formal cause is the sole determiner of its identity or "which-it-is" (i.e., whether the previous and the later ships or rivers are the "same" ship or river). This latter premise is subject to attack by indirect proof using arguments such as "Suppose two ships are built using the same design and exist at the same time until one sinks the other in battle. Clearly the two ships are not the same ship even before, let alone after, one sinks the other, and yet the two have the same formal cause; therefore, formal cause cannot by itself suffice to determine an object's identity" or " [...] therefore, two objects' or object-instances' having the same formal cause does not by itself suffice to make them the same object or prove that they are the same object."
Definitions of "the same"
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.
Note that some languages differentiate between these two forms of identity. In German, for example, "gleich" ("equal") and "selbe" ("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, "gleich" is also used in place of "selbe", however.
Ted Sider and others have proposed that considering objects to extend across time as four-dimensional causal series of three-dimensional "time-slices" could solve the ship of Theseus problem because, in taking such an approach, each time-slice and all four dimensional objects remain numerically identical to themselves while allowing individual time-slices to differ from each other. The aforementioned river, therefore, comprises different three-dimensional time-slices of itself while remaining numerically identical to itself across time; one can never step into the same river-time-slice twice, but one can step into the same (four-dimensional) river twice.
In Japan, Shinto shrines are rebuilt every twenty years with entirely "new wood". The continuity over the centuries is spiritual and comes from the source of the wood in the case of the Ise Jingu's Naiku shrine, which is harvested from an adjoining forest that is considered sacred. The shrine has currently been rebuilt 62 times.