Ship of Theseus

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 component parts replaced remains fundamentally the same object.

Variations of the paradox

Greek legend

According to 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

Plutarch thus questions whether the ship would remain the same if it were entirely replaced, piece by piece. As a corollary, one can question what happens if the replaced parts were used to build a second ship. Which, if either, is the original Ship of Theseus?

Heraclitus's river

The Greek philosopher Heraclitus is notable for his unusual view of identity. Arius Didymus quoted him as saying:

Upon those who step into the same rivers, different and again different waters flow.

Plutarch also informs us of 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".

Locke's socks

John Locke (a 17th-century English writer) 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. If yes, then, would it still be the same sock after a second patch was applied? Indeed, would it still be the same sock many years later, even after all of the material of the original sock has been replaced with patches?

George Washington's axe

"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

Robert Graves employs the "grandfather's axe" version in his historical novel, The Golden Fleece, first published in 1945:

As the proverb says: "This is my grandfather's axe: my father fitted it with a new stock, and I have fitted it with a new head."

— Robert Graves, The Golden Fleece, p. 445

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, only it's called just "the family knife". The principle, however, remains the same.

This example is also used in Terry Pratchett's novel, The Fifth Elephant, where the Dwarf King Rhys Rhysson uses his axe as the example: "This, milord, is my family's axe. We have owned it for almost nine hundred years, see. Of course, sometimes it needed a new blade. And sometimes it has required a new handle, new designs on the metalwork, a little refreshing of the ornamentation . . . but is this not the nine hundred-year-old axe of my family? And because it has changed gently over time, it is still a pretty good axe, y'know. Pretty good."

Another example can be found in the popular UK television show Only Fools and Horses, where road-sweeper Trigger states that he's had the same broom for 20 years. But then he adds that the broom has had 17 new heads and 14 new handles.

"How can it be the same bloody broom then?" asks Sid the café owner. Trigger produces a picture of himself and his broom and asks: "what more proof do you need?"

Other examples

One can think of 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. 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. Similarly, the human body constantly creates new cells as old cells die. The average age of cells in an adult body may be less than 10 years. Moreover, the very atoms and molecules that support and pass through the cells are constantly changing. 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 "Frances" or "George" or "Herbert".

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 comprising them is different than at previous times. Likewise, the current personnel of some contemporary bands may contain few or none of the founding members, yet continue to use the same name. Menudo is an example of this phenomenon.

The concept of mind uploading brings Theseus's paradox to the question of human identity: it would seem to be 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. Nonetheless, the result of this process is an object entirely physically distinct from the starting point. This topic is discussed in Douglas Hofstadter's and Daniel Dennett's The Mind's I: Fantasies and reflections on self and soul (1981).

Proposed resolutions

Aristotle's causes

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 end, that is, transporting Theseus, 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.

Definitions of "the same"

One common argument found in the philosophical literature is that in the case of Heraclitus's river one is tripped up by two different definitions of "the same". In one sense things can be qualitatively the same, by having the same properties. In another sense they might be numerically the same by being "one". As an example, consider two bowling balls that look identical. They would be qualitatively, but not numerically, the same. If one of the balls was then painted a different color, it would be numerically, but not qualitatively, the same as its previous self.

By this argument, Heraclitus's river is qualitatively, but not numerically, different by the time one attempts to make the second step into it. For Theseus's ship, the same is true.

The main problem with this proposed solution to problems of identity is that if one construes the definition of "properties" broadly enough, qualitative identity collapses into numerical identity. For example, if one of the qualities of a bowling ball is its spatial or temporal location, then no two bowling balls that exist in different places or points in time could ever be qualitatively identical. Likewise, in the case of a river, since it has different properties at every point in time — such as variance in the peaks and troughs of the waves in particular spatial locations, changes in the amount of water in the river caused by evaporation — it can never be qualitatively identical at different points in time.

Four dimensionalism

Main article: Perdurantism

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 4-dimensional objects. An object is a spatially extended three-dimensional thing that also extends across the 4th dimension of time. This 4-dimensional object is made up of 3-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 4-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 3-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 (4-dimensional) river twice.

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.

Metaphysics of quality

Robert M. Pirsig's metaphysics of quality, presented in Lila: An Inquiry into Morals, defines a hierarchy of patterns and uses it to offer another solution to the paradox: the ship is simultaneously a set of lower-order patterns (the parts) which change, and a single higher-order pattern (the ship as a whole) which remains constant.

Cultural differences

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

Another Japanese example is the 20-year cycle of rebuilding the Shrine at Ise; the buildings of the inner shrine have been rebuilt every 20 years at least 60 times.

Jewish law

In Halacha, a container that was tamei 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 (ie not tamei) and therefore, no longer considered to be the same container.

In popular culture

• The Discworld series pays homage to Heraclitus' 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 it is possible to cross twice. There are also numerous references to the supposed inability of witches and wizards to cross the same river twice; the wizards refute this by demonstrating that an agile wizard can cross and recross a small river many times an hour.
• There is a reference to the paradox in the television comedy Only Fools and Horses. When one character (Trigger) wins an award for owning the same broom for 20 years, he reveals that it has had 17 new heads and 14 new handles, but insists it is still the same broom. The popularity of this comedy has resulted in the phrase "Trigger's broom" becoming widely used in the UK to refer to the paradox.
• 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.
• In the 1872 story "Dr. Ox's Experiment" by Jules Verne there is a reference to Jeannot's knife (the French equivalent of "Grandfather's old axe") 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.
• In The Wonderful Wizard of Oz 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. His discarded limbs become a part of the composite man, Chopfyt.
• In 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.
• The National Public Radio show Car Talk has occasionally addressed this paradox in the context of automotive reliability. The general 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 phenomena sometimes being referred to as "Carma".
• Depending on the underlying fictional technology, the concept of teleportation, especially of humans, suffers from the same paradox.

See also

• Identity and change
• Mereological essentialism
• Sorites paradox
• Śūnyatā