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The Ship of Theseus, also known as Theseus' paradox, or various variants, notably grandfather's axe and (in the UK) Trigger's Broom (based upon the BBC sitcom Only Fools and Horses) is a paradox that raises the question of whether an object which has had all its component parts replaced remains fundamentally the same object.
The paradox is most notably recorded by Plutarch in Life of Theseus from the late 1st century. Plutarch asked whether a ship which was restored by replacing all its wooden parts remained the same ship. The paradox had been discussed by more ancient philosophers such as Heraclitus, Socrates, and Plato prior to Plutarch's writings; and more recently by Thomas Hobbes and John Locke. This problem is "a model for the philosophers"; some say "it remained the same, some saying it did not remain the same".[1]
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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, 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, Theseus[2]
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.[3] Which ship, if either, is the original Ship of Theseus?
Another early variation involves a scenario in which Socrates and Plato exchange the parts of their carriages piece by piece until, finally, Socrates's carriage is made up of all the parts of Plato's original carriage and vice versa. The question is presented if or when they exchanged their carriages.
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, would it still be the same sock after a second patch was applied 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.
...as in the case of the owner of George Washington's axe which has three times had its handle replaced and twice had its head replaced!—Ray Broadus Browne, Objects of Special Devotion: Fetishism in Popular Culture, p. 134[4]
This has also been recited as "Abe Lincoln's axe";[5] Lincoln was well known for his ability with an axe, and axes associated with his life are held in various museums.[6]
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.[7] 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.
In the 1872 story "Dr. Ox's Experiment" by Jules Verne there is a reference to Jeannot's knife apropos of the van Tricasse's family. In this family, since 1340, each time one of the spouses died the other remarried with someone younger, who took the family name. Thus the family can be said to have been a single marriage lasting through centuries, rather than a series of generations. A similar concept is described in some detail in Robert Heinlein's novel The Moon Is a Harsh Mistress as a line marriage.
There are many examples of objects which might fall prey to Theseus's paradox: buildings and automobiles for example can undergo complete replacement while still maintaining some aspect of their identity. An example is found in the popular UK television show Only Fools and Horses in the episode Heroes and Villains, where road-sweeper Trigger is given a medal by the council for using the same broom for 20 years. He then adds that the broom has had 17 new heads and 14 new handles. When asked how can it be the same broom, Trigger produces a picture of himself and his broom and asks, "What more proof do you need?"
Businesses, colleges, and universities often change addresses and residences, thus completely "replacing" their old material structure for a new one, yet keeping the same purpose and often the same people that keep the organization functioning as it was. If two businesses merge, their identities merge.
For example, the original Yankee Stadium was built in 1923, but underwent an extensive renovation in the mid 1970s. The stadium was so heavily remodeled that some view the post-renovation stadium as a different building than the original structure.
Businesses, organizations, and political entities maintain their purpose and function but continually change their membership, so that at any given time the group of people composing them is different than at previous times.
Similarly, the human body constantly creates new cells as old cells die. The average age of non-bone cells in an adult body may be less than 10 years.[8] The body is analogous to Heraclitus' river in that it consumes and expels a steady flow of nutrients, gas and water, all of it processed by cell bodies and enzymes that are themselves destroyed and remade.
If one relates identity to actions and phenomena, identity becomes even harder to grasp. Depending upon one's chosen perspective of what identifies or continues a hurricane, if a Hurricane Evan collapses at a particular location and then one forms again at or near the same location, a person may be totally consistent to either choose to call the latter mentioned hurricane the same as the former (as in "Evan" was reinvigorated), or choose to call the latter a new hurricane with another name.
The National Public Radio show Car Talk has occasionally addressed this paradox in the context of automotive reliability. The consensus has emerged that if an unreliable or quirky vehicle has all of its parts replaced, the vehicle will remain unreliable or quirky, with the phenomenon sometimes being referred to as "Carma".
In the world of sport, Welsh football player Andy Melville wore the same pair of boots for five seasons. They had "new uppers, new soles, new studs, new everything. But ... they were the same boots."[9]
The current personnel of some contemporary bands may contain few or none of the founding members, yet continue to use the same name.[10] The singing group "The Temptations" fired and replaced members with such frequency that ex-Temps soon out-numbered the members of the "original" group. These men decided to form a second group, also called "The Temptations." Both groups toured at the same time, and both claimed to be the "real" Temptations. The British band Sugababes has also undergone numerous lineup changes, so that none of the original members are in the current line-up. Furthermore, the original line-up members wanted to do a reunion tour, but had legal troubles in using the original Sugababes name. The courts decided that the original line up would get to use the name, and the new line-up would have to stop using it. Sugababes are thus known as the "Trigger's Broom" of the music industry. Currently the American Southern Rock band Lynyrd Skynyrd tours using their original name despite only having one original band member, guitar player Gary Rossington. The band Menudo is another example of this phenomenon.
Robert Graves also employs the "grandfather's axe" version in his historical novel, The Golden Fleece, first published in 1945.[11]
In The Wonderful Wizard of Oz (1900) by L. Frank Baum, a lumberjack's cursed axe chopped all his limbs one by one, and each time a limb was cut off, a smith made him a mechanical one, finally making him a torso and a head, thus turning him into the Tin Woodman, an entirely mechanical being, albeit possessing the consciousness of the lumberjack he once was.[12] Conversely, in the book The Tin Woodman of Oz, the Tin Woodsman learns that his old human body parts (minus the head) were sewn together to create a new man who then married his old sweetheart.
David Wong's book "John Dies at the End", the book opens with David musing about the continual identity of an axe which has its handle replaced after it is damaged in the course of the slaying of a man, and then the head replaced after being used to slay a half-badger, half-anaconda monstrosity. The axe wielder, returning from the hardware store where the axe's new head was fitted, is confronted by the zombie of the man slain earlier who cries out in terror that he wields the axe that killed him. David muses over the validity of the zombie's statement. Although he doesn't revisit or attempt to answer the question, it becomes clear by the end of the book that the axe is merely a metaphor for a much stranger supernatural incident he was involved in.
Terry Pratchett's Discworld series pays homage to Heraclitus's statement by claiming that the (notoriously polluted and slow-moving to the point of being solid) River Ankh in the city of Ankh-Morpork is the only river that is possible to cross twice. There are also numerous references to the supposed inability of witches and wizards to cross the same river twice (e.g., in Lords and Ladies); the wizards refute this by demonstrating that an agile wizard can cross and recross a small river many times an hour. Also, Senior witch Granny Weatherwax possesses a flying broom whose handle and bristles have been replaced many times, yet remains unreliable to the point that she has to run up and down very quickly to essentially "bump-start" it. Pratchett also directly references the paradox in The Fifth Elephant, for instance in the axes of the dwarves, and in his early novels The Bromeliad.
All incarnations of the Ghost in the Shell franchise deeply involve Theseus' Paradox in terms of full-body prosthetics. A reoccurring theme is the question of what defines humanity, if the entire body has been replaced by machines.
Modern fiction shows concern with potential problems of personal identity. In the 1986 book Foundation and Earth by Isaac Asimov, the ancient robot R. Daneel Olivaw says that over the thousands of years of his existence, every part of him has been replaced several times, including his brain, which he has carefully redesigned six times, replacing it each time with a newly constructed brain having the positronic pathways containing his current memories and skills, along with free space for him to learn more and continue operating for longer. The Hitchhiker's Guide to the Galaxy series by Douglas Adams makes continuing sport of classic paradoxes. In the trilogy's fourth book So Long, and Thanks For All the Fish, Marvin the Paranoid Android says of himself: "Every part of me has been replaced at least fifty times...". In the sixth book of the series, character Trillian has had so many body parts and functions replaced by technology that she doubts she is still the same person, referring to her present self as New Trillian and the past as Old Trillian.
Japanese manga series Ghost in the Shell cyclically returns to this paradox of a "human" whose body is replaced by artificial parts. Theseus's paradox bears also on the question of virtual human identity discussed in Douglas Hofstadter's and Daniel Dennett's The Mind's I: Fantasies and reflections on self and soul (1981). Speculations concerning mind uploading suggest it is possible to transfer a human mind from an organic brain to a computer, incrementally and in such a way that consciousness is never interrupted, e.g. by replacing neurons one by one with electronics designed to simulate the neurons' firing patterns. Yet the result of this process is an object entirely physically distinct from the starting point. Depending on the underlying technological speculation, the concept of human teleportation introduces similar paradoxes. The plot of the James Blish novel "Spock Must Die!" hinges on this philosophical dilemma. The issue is addressed in the episode Life Support of Deep Space Nine Star Trek series. In the episode, the complete replacement of the human brain is considered the destruction of the individual.[13] Meanwhile in our world contemporary users of prosthesis have a tendency to suffer complications from phantom limb syndrome.
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."[14] 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."[15]
According to the philosophical system of Aristotle and his followers, there are four causes or reasons that describe a thing; these causes can be analyzed to get to a solution to the paradox. The formal cause or form is the design of a thing, while the material cause is the matter that the thing is made of. The "what-it-is" of a thing, according to Aristotle, 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.
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, even 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.
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, "selbst" ("self-same") and "gleich" ("equal") are the pertinent terms. At least in formal speech, the former refers to numerical identity (e.g. die selbe Murmel, "the same[numerical] marble") and the latter to qualitative identity (e.g. die gleiche Murmel, "the same[qualitative] marble"). Colloquially, the terms are sometimes used interchangeably however.
One solution to this paradox may come from the concept of four-dimensionalism. Ted Sider and others have proposed that these problems can be solved by considering all things as four-dimensional objects. An object is a spatially extended three-dimensional thing that also extends across the fourth dimension of time. This four-dimensional object is made up of three-dimensional time-slices. These are spatially extended things that exist only at individual points in time. An object is made up of a series of causally related time-slices. All time-slices are numerically identical to themselves. And the whole aggregate of time-slices, namely the four-dimensional object, is also numerically identical with itself. But the individual time-slices can have qualities that differ from each other.
The problem with the river is solved by saying that at each point in time, the river has different properties. Thus the various three-dimensional time-slices of the river have different properties from each other. But the entire aggregate of river time-slices, namely the whole river as it exists across time, is identical with itself. So one can never step into the same river time-slice twice, but one can step into the same (four-dimensional) river twice.[16]
A seeming difficulty with this is that in special relativity there is not a unique "correct" way to make these slices — it is not meaningful to speak of a "point in time" extended in space. However, this does not prove to be a problem: any way of slicing will do (including no 'slicing' at all), provided that the boundary of the object changes in a fashion which can be agreed upon by observers in all reference frames. Special relativity still ensures that "you can never step into the same river time-slice twice," because even with the ability to shift around which way spacetime is sliced, one is still moving in a timelike fashion, which will not multiply intersect a time-slice, which is spacelike.
For Madhyamika following Candrakirti replacement paradoxes such as Ship of Theseus are answered by stating that the Ship of Theseus remains so (within the conventions that assert it) until it ceases to function as the Ship of Theseus.
Understandings of this concept may differ between cultures, with anecdotal evidence indicating that it is not regarded as a paradox in Japan. In his book Last Chance to See, Douglas Adams observed:
I remembered once, in Japan, having been to see the Gold Pavilion Temple in Kyoto and being mildly surprised at quite how well it had weathered the passage of time since it was first built in the fourteenth century. I was told it hadn't weathered well at all, and had in fact been burnt to the ground twice in this century. "So it isn't the original building?" I had asked my Japanese guide.
"But yes, of course it is," he insisted, rather surprised at my question.
"But it's burnt down?"
"Yes."
"Twice."
"Many times."
"And rebuilt."
"Of course. It is an important and historic building."
"With completely new materials."
"But of course. It was burnt down."
"So how can it be the same building?"
"It is always the same building."
I had to admit to myself that this was in fact a perfectly rational point of view, it merely started from an unexpected premise. The idea of the building, the intention of it, its design, are all immutable and are the essence of the building. The intention of the original builders is what survives. The wood of which the design is constructed decays and is replaced when necessary. To be overly concerned with the original materials, which are merely sentimental souvenirs of the past, is to fail to see the living building itself.—Douglas Adams, Last Chance to See, p. 149[17]
In Halacha, a container that was tamei (impure) can lose this status if it develops a hole that would let a pomegranate through, even if it is later repaired. The Gemara (Shabbat 112b) addresses this paradox with regard to a container that had a small hole, was repaired, etc. until, had it not been repaired, it would have let a pomegranate through. This container is tahor (pure, opposite of tamei) because it is no longer considered to be the same container.