Ship of Theseus

The Ship of Theseus is a paradox also known as Theseus' paradox. It raises the question of whether an object, which has had all its component parts replaced, remains fundamentally the same.

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 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 (Lost) 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?

Grandfather's old axe

"Grandfather's old axe" is a colloquial expression of unknown origin describing something of which little original remains: "it's had three new heads and four new handles but it's still the same old axe." The phrase has also been used in banter as in: "This is George Washington's original axe…", while holding up an apparently new axe. This example is used explicitly to explain significant points of the plot in The Fifth Elephant by Terry Pratchett. A similar example was also seen in Only Fools and Horses, where Trigger (a central character) won an award for using the same broom to sweep the streets for twenty years, even though he’d replaced the head 17 times and the handle 14 times. The meaning of the expression and its relationship to murder are questioned in the opening of the novel John Dies at the End by David Wong.

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 whilst 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 (or one is consumed by the other). 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.

If we relate 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 "Frank" or "Georgia".

One could also see the bands Napalm Death, Zao and The Little River Band as contemporary examples of Theseus's paradox. These bands' current line-ups contain none of the founding members, yet they continue to use the same name.

A somewhat, more layman's example is in most Herbie films. In these films, when any part of the protagonist (a "living" car named Herbie) is replaced, no one thinks anything of it, however; if one were to replace all of Herbie's parts at once, which part would contain his "soul", and if a certain car part DID contain his soul, would it be transferred if the part were attached to ANOTHER car?

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.

This probably won't do as a solution to the problem, though, since the material cause does change over time, and we have been shown no reason to privilege one of the causes over another in the determination of continuity of identity.

Definitions of "the same"

One common argument found in the philosophical literature is that in the case of Heraclitus's river we are 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 we construe our 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. Since nothing can be qualitatively different without also being numerically different, the river must be numerically different at different points in time.

Four dimensionalism

One solution to this paradox may come from the concept of four-dimensionalism. David Lewis 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 you can never step into the same river time-slice twice, but you 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, you are 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.

Madhyamika Buddhism

Within the Madhyamika school of Mahayana Buddhism, Candrakirti identifies the self as:

an essence of things that does not depend on others; it is an intrinsic nature. The non-existence of that is selflessness.

— Bodhisattvayogacaryācatuḥśatakaṭikā 256.1.7

Indeed the concept of Buddhist Emptiness is the strong assertion that all phenomena are empty of any essence – demonstrating that anti-essentialism lies at the very root of Buddhist praxis. Therefore, within this school it is the innate belief in essence that is considered to be the affliction which serves as the base of all suffering. However, the school also rejects the tenets of Idealism and Materialism; instead, the ideas of truth or existence, along with any assertions that depend upon them are limited to their function within the contexts and conventions that assert them, akin to Relativism or Pragmatism. For Madhyamakas, replacement paradoxes such as Ship of Theseus are answered by stating that the Ship of Thesesus remains so (within the conventions that assert it) until it ceases to function as the Ship of Theseus.

Cultural differences

This concept may differ among different cultures. As an anedocal evidence it seems that in the east this is not a paradox. Quoting Douglas Adams from the book Last Chance to See:

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.

In popular culture

The Ship of Theseus paradox is addressed in Terry Pratchett's Discworld novel The Fifth Elephant. Here it is about an axe which periodically gets a new handle or a new blade. The characters in this book reason that, while it might not be the same axe physically, it will always remain the same axe emotionally. The Discworld series also 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 is a reference to the paradox in the BBC comedy Only Fools and Horses. The character Trigger, who is a road sweeper, wins an award for having used the same broom for many years and thus saving money. When he is asked about it, he reveals naively that both the handle and head of the broom have been replaced several times. Trigger is a dim-witted character who makes foolish remarks, and the joke here is that he believes the broom to be the same one as he has always had.

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 So Long, and Thanks for All the Fish by Douglas Adams, Marvin the android claims he has undergone the same renovation, with the exception of the diodes down his left side (ironically, throughout the books he constantly complains of pain from just those diodes).

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 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.

The Heraclitus's river paradox is featured in Francis Ford Coppola's Apocalypse Now Redux in the newly added French plantation scene in a dialogue between Captain Willard and French colonist Roxanne:

Roxanne: "Do you know why you can never step into the same river twice?"

Willard: "Yeah, 'cause it's always moving."

It is also featured in Disney's Pocahontas, during the song "Just Around the Riverbend", in which Pocahontas sings "What I love most about rivers is you can't step in the same river twice; The water's always changing, always flowing"

A variation of the paradox exists in the manga and anime, Ghost in the Shell.

Depending on the underlying technology, teleportation suffers from the same paradox.

See also

• Identity and change
• Mereological essentialism
• Philosophical zombie
• Sorites paradox
• Shunyata
• Standing wave