Ship of Theseus
Encyclopedia
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".
legend
as reported by Plutarch
,
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. 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.
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 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.
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.
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.
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?"
es, college
s, 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.
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. 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.
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
".
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."
may contain few or none of the founding members, yet continue to use the same name. 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. The band Menudo
is another example of this phenomenon.
also employs the "grandfather's axe" version in his historical novel, The Golden Fleece, first published in 1945.
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. 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.
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. Meanwhile in our world contemporary users of prosthesis have a tendency to suffer complications from phantom limb
syndrome.
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."
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.
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.
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.
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.
Alternatively, one can also say that the Ship of Theseus is not the Ship of Theseus, as ultimately nothing can be said to exist as "self" or "entity". Everything is anatta
.
Buddhism also explores the idea of khandha or compounds, in a way similar to this paradox.
, Douglas Adams
observed:
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.
Theseus
For other uses, see Theseus Theseus was the mythical founder-king of Athens, son of Aethra, and fathered by Aegeus and Poseidon, both of whom Aethra had slept with in one night. Theseus was a founder-hero, like Perseus, Cadmus, or Heracles, all of whom battled and overcame foes that were...
' paradox, or various variants, notably grandfather's axe and (in the UK) Trigger's Broom (based upon the BBC
BBC
The British Broadcasting Corporation is a British public service broadcaster. Its headquarters is at Broadcasting House in the City of Westminster, London. It is the largest broadcaster in the world, with about 23,000 staff...
sitcom Only Fools and Horses
Only Fools and Horses
Only Fools and Horses is a British sitcom, created and written by John Sullivan. Seven series were originally broadcast on BBC One in the United Kingdom between 1981 and 1991, with sporadic Christmas specials until 2003...
) is a paradox
Paradox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...
that raises the question of whether an object which has had all its component parts replaced remains fundamentally the same object
Identity (philosophy)
In philosophy, identity, from , is the relation each thing bears just to itself. According to Leibniz's law two things sharing every attribute are not only similar, but are the same thing. The concept of sameness has given rise to the general concept of identity, as in personal identity and...
.
The paradox is most notably recorded by Plutarch
Plutarch
Plutarch then named, on his becoming a Roman citizen, Lucius Mestrius Plutarchus , c. 46 – 120 AD, was a Greek historian, biographer, essayist, and Middle Platonist known primarily for his Parallel Lives and Moralia...
in Life of Theseus
Parallel Lives
Plutarch's Lives of the Noble Greeks and Romans, commonly called Parallel Lives or Plutarch's Lives, is a series of biographies of famous men, arranged in tandem to illuminate their common moral virtues or failings, written in the late 1st century...
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
Heraclitus
Heraclitus of Ephesus was a pre-Socratic Greek philosopher, a native of the Greek city Ephesus, Ionia, on the coast of Asia Minor. He was of distinguished parentage. Little is known about his early life and education, but he regarded himself as self-taught and a pioneer of wisdom...
, Socrates
Socrates
Socrates was a classical Greek Athenian philosopher. Credited as one of the founders of Western philosophy, he is an enigmatic figure known chiefly through the accounts of later classical writers, especially the writings of his students Plato and Xenophon, and the plays of his contemporary ...
, and Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...
prior to Plutarch's writings; and more recently by Thomas Hobbes
Thomas Hobbes
Thomas Hobbes of Malmesbury , in some older texts Thomas Hobbs of Malmsbury, was an English philosopher, best known today for his work on political philosophy...
and John Locke
John Locke
John Locke FRS , widely known as the Father of Liberalism, was an English philosopher and physician regarded as one of the most influential of Enlightenment thinkers. Considered one of the first of the British empiricists, following the tradition of Francis Bacon, he is equally important to social...
. This problem is "a model for the philosophers"; some say "it remained the same, some saying it did not remain the same".
Ancient philosophy
The paradox was first raised in GreekGreece
Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....
legend
Legend
A legend is a narrative of human actions that are perceived both by teller and listeners to take place within human history and to possess certain qualities that give the tale verisimilitude...
as reported by Plutarch
Plutarch
Plutarch then named, on his becoming a Roman citizen, Lucius Mestrius Plutarchus , c. 46 – 120 AD, was a Greek historian, biographer, essayist, and Middle Platonist known primarily for his Parallel Lives and Moralia...
,
Plutarch thus questions whether the ship would remain the same if it were entirely replaced, piece by piece. Centuries later, the philosopher Thomas Hobbes
Thomas Hobbes
Thomas Hobbes of Malmesbury , in some older texts Thomas Hobbs of Malmsbury, was an English philosopher, best known today for his work on political philosophy...
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. Which ship, if either, is the original Ship of Theseus?
Another early variation involves a scenario in which Socrates
Socrates
Socrates was a classical Greek Athenian philosopher. Credited as one of the founders of Western philosophy, he is an enigmatic figure known chiefly through the accounts of later classical writers, especially the writings of his students Plato and Xenophon, and the plays of his contemporary ...
and Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...
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.
Enlightenment era
John LockeJohn Locke
John Locke FRS , widely known as the Father of Liberalism, was an English philosopher and physician regarded as one of the most influential of Enlightenment thinkers. Considered one of the first of the British empiricists, following the tradition of Francis Bacon, he is equally important to social...
proposed a scenario regarding a favorite sock
Sock
A sock is an item of clothing worn on the feet. The foot is among the heaviest producers of sweat in the body, as it is able to produce over of perspiration per day. Socks help to absorb this sweat and draw it to areas where air can evaporate the perspiration. In cold environments, socks decrease...
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 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.
This has also been recited as "Abe Lincoln's
Abraham Lincoln
Abraham Lincoln was the 16th President of the United States, serving from March 1861 until his assassination in April 1865. He successfully led his country through a great constitutional, military and moral crisis – the American Civil War – preserving the Union, while ending slavery, and...
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.
In the 1872 story "Dr. Ox's Experiment
Dr. Ox's Experiment
"Dr. Ox's Experiment" is a short story by the French writer and pioneer of science-fiction, Jules Verne, published in 1872. It describes an experiment by one Dr. Ox and his assistant Gedeon Ygene. A prosperous scientist Dr. Ox offers to build a novel gas lighting system to an unusually stuffy...
" by Jules Verne
Jules Verne
Jules Gabriel Verne was a French author who pioneered the science fiction genre. He is best known for his novels Twenty Thousand Leagues Under the Sea , A Journey to the Center of the Earth , and Around the World in Eighty Days...
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
Robert A. Heinlein
Robert Anson Heinlein was an American science fiction writer. Often called the "dean of science fiction writers", he was one of the most influential and controversial authors of the genre. He set a standard for science and engineering plausibility and helped to raise the genre's standards of...
novel The Moon Is a Harsh Mistress
The Moon Is a Harsh Mistress
The Moon Is a Harsh Mistress is a 1966 science fiction novel by American writer Robert A. Heinlein, about a lunar colony's revolt against rule from Earth....
as a line marriage.
Modern examples
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 HorsesOnly Fools and Horses
Only Fools and Horses is a British sitcom, created and written by John Sullivan. Seven series were originally broadcast on BBC One in the United Kingdom between 1981 and 1991, with sporadic Christmas specials until 2003...
in the episode Heroes and Villains
Heroes and Villains (Only Fools and Horses)
"Heroes and Villains" is an episode of the BBC sit-com, Only Fools and Horses, first screened on 25 December, 1996 as the first part of the 1996 Christmas trilogy...
, where road-sweeper Trigger
Trigger (Only Fools and Horses)
Trigger is a character in the popular BBC sitcom Only Fools and Horses. He is played by actor Roger Lloyd Pack....
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?"
Buildings and institutions
BusinessBusiness
A business is an organization engaged in the trade of goods, services, or both to consumers. Businesses are predominant in capitalist economies, where most of them are privately owned and administered to earn profit to increase the wealth of their owners. Businesses may also be not-for-profit...
es, college
College
A college is an educational institution or a constituent part of an educational institution. Usage varies in English-speaking nations...
s, and universities
University
A university is an institution of higher education and research, which grants academic degrees in a variety of subjects. A university is an organisation that provides both undergraduate education and postgraduate education...
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
Government
Government refers to the legislators, administrators, and arbitrators in the administrative bureaucracy who control a state at a given time, and to the system of government by which they are organized...
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.
Human body
Similarly, the human bodyHuman body
The human body is the entire structure of a human organism, and consists of a head, neck, torso, two arms and two legs.By the time the human reaches adulthood, the body consists of close to 100 trillion cells, the basic unit of life...
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. 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.
Hurricanes
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.Automobiles
The National Public Radio show Car TalkCar Talk
Car Talk is a radio talk show broadcast weekly on National Public Radio stations throughout the United States and elsewhere. Its subjects are automobiles and repair, and it often takes humorous turns...
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
Karma
Karma in Indian religions is the concept of "action" or "deed", understood as that which causes the entire cycle of cause and effect originating in ancient India and treated in Hindu, Jain, Buddhist and Sikh philosophies....
".
Sport
In the world of sport, WelshWales
Wales is a country that is part of the United Kingdom and the island of Great Britain, bordered by England to its east and the Atlantic Ocean and Irish Sea to its west. It has a population of three million, and a total area of 20,779 km²...
football player Andy Melville
Andy Melville
Andrew Roger Melville is a former Wales international footballer. In the early years of his career, he played in midfield. He was later converted into a central defender....
wore the same pair of boots
Football boot
Football boots, called cleats or soccer shoes in North America, are an item of footwear worn when playing association football. Those designed for grass pitches have studs on the bottom to aid grip...
for five seasons. They had "new uppers, new soles, new studs, new everything. But ... they were the same boots."
Music ensembles
The current personnel of some contemporary bandsMusical ensemble
A musical ensemble is a group of people who perform instrumental or vocal music. In classical music, trios or quartets either blend the sounds of musical instrument families or group together instruments from the same instrument family, such as string ensembles or wind ensembles...
may contain few or none of the founding members, yet continue to use the same name. The singing group "The Temptations
The Temptations
The Temptations is an American vocal group having achieved fame as one of the most successful acts to record for Motown Records. The group's repertoire has included, at various times during its five-decade career, R&B, doo-wop, funk, disco, soul, and adult contemporary music.Formed in Detroit,...
" 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
Sugababes
The Sugababes are an English pop girl group based in London, consisting of members Heidi Range, Amelle Berrabah and Jade Ewen. The Sugababes were formed in 1998 with founding members Siobhán Donaghy, Mutya Buena and Keisha Buchanan. Their debut album, One Touch, was released in 2000 under London...
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. The band Menudo
Menudo (band)
Menudo was a Puerto Rican boy band that was formed in the 1970s by producer Edgardo Díaz, releasing their first album in 1977. The band achieved much success, especially during the 1980s, becoming the most popular Latin American teen musical group of the era....
is another example of this phenomenon.
In literature
Robert GravesRobert Graves
Robert von Ranke Graves 24 July 1895 – 7 December 1985 was an English poet, translator and novelist. During his long life he produced more than 140 works...
also employs the "grandfather's axe" version in his historical novel, The Golden Fleece, first published in 1945.
In The Wonderful Wizard of Oz
The Wonderful Wizard of Oz
The Wonderful Wizard of Oz is a children's novel written by L. Frank Baum and illustrated by W. W. Denslow. Originally published by the George M. Hill Company in Chicago on May 17, 1900, it has since been reprinted numerous times, most often under the name The Wizard of Oz, which is the name of...
(1900) by L. Frank Baum
L. Frank Baum
Lyman Frank Baum was an American author of children's books, best known for writing The Wonderful Wizard of Oz...
, 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
Tin Woodman
The Tin Woodman, sometimes referred to as the Tin Man or the Tin Woodsman , is a character in the fictional Land of Oz created by American author L. Frank Baum...
, an entirely mechanical being, albeit possessing the consciousness of the lumberjack he once was. Conversely, in the book The Tin Woodman of Oz
The Tin Woodman of Oz
The Tin Woodman of Oz: A Faithful Story of the Astonishing Adventure Undertaken by the Tin Woodman, Assisted by Woot the Wanderer, the Scarecrow of Oz, and Polychrome, the Rainbow's Daughter is the twelfth Land of Oz book written by L. Frank Baum and was originally published on May 13, 1918...
, 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
David Wong
David Wong may refer to:* David Wong Louie, American writer of novels and short stories * Dave Wong , Chinese singer* David Wong , philosophy professor at Duke University...
's book "John Dies at the End
John Dies at the End
John Dies at the End is a comedic horror novel written by Jason Pargin that was first published online as a webserial beginning in 2001, then as an edited manuscript in 2004 and printed paperback in 2007 via Permuted Press. An estimated 70,000 people read the free online versions before they were...
", 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
Terry Pratchett
Sir Terence David John "Terry" Pratchett, OBE is an English novelist, known for his frequently comical work in the fantasy genre. He is best known for his popular and long-running Discworld series of comic fantasy novels...
's Discworld
Discworld
Discworld is a comic fantasy book series by English author Sir Terry Pratchett, set on the Discworld, a flat world balanced on the backs of four elephants which, in turn, stand on the back of a giant turtle, Great A'Tuin. The books frequently parody, or at least take inspiration from, J. R. R....
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
Lords and Ladies (novel)
Lords and Ladies is the fourteenth Discworld book by Terry Pratchett. It was originally published in 1992.-Synopsis:At the end of Witches Abroad, Magrat Garlick, Nanny Ogg and Granny Weatherwax left Genua bound for home, in Lancre...
); 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
The Fifth Elephant
The Fifth Elephant is the 24th Discworld novel by Terry Pratchett. It introduces the clacks, a long-distance semaphore system. The novel was nominated for the Locus Award in 2000.-Plot summary:...
, for instance in the axes of the dwarves, and in his early novels The Bromeliad
The Bromeliad
The Nome Trilogy, also known in the US as The Bromeliad Trilogy, is a trilogy of children's books by Terry Pratchett, consisting of#Truckers #Diggers #Wings...
.
All incarnations of the Ghost in the Shell
Ghost in the Shell
is a Japanese multimedia franchise composed of manga, animated films, anime series, video games and novels. It focuses on the activities of the counter-terrorist organization Public Security Section 9 in a futuristic, cyberpunk Japan ....
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.
Prosthesis
Modern fiction shows concern with potential problems of personal identity. In the 1986 book Foundation and EarthFoundation and Earth
Foundation and Earth is a Locus Award nominated science fiction novel by Isaac Asimov, the fifth novel of the Foundation series and chronologically the last in the series...
by Isaac Asimov
Isaac Asimov
Isaac Asimov was an American author and professor of biochemistry at Boston University, best known for his works of science fiction and for his popular science books. Asimov was one of the most prolific writers of all time, having written or edited more than 500 books and an estimated 90,000...
, the ancient robot R. Daneel Olivaw
R. Daneel Olivaw
R. Daneel Olivaw is a fictional robot created by Isaac Asimov. The "R" initial in his name stands for "robot," a naming convention in Asimov's future society...
says that over the thousands of years of his existence, every part of him has been replaced several times, including his brain
Brain
The brain is the center of the nervous system in all vertebrate and most invertebrate animals—only a few primitive invertebrates such as sponges, jellyfish, sea squirts and starfishes do not have one. It is located in the head, usually close to primary sensory apparatus such as vision, hearing,...
, 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
The Hitchhiker's Guide to the Galaxy
The Hitchhiker's Guide to the Galaxy is a science fiction comedy series created by Douglas Adams. Originally a radio comedy broadcast on BBC Radio 4 in 1978, it was later adapted to other formats, and over several years it gradually became an international multi-media phenomenon...
series by Douglas Adams
Douglas Adams
Douglas Noel Adams was an English writer and dramatist. He is best known as the author of The Hitchhiker's Guide to the Galaxy, which started life in 1978 as a BBC radio comedy before developing into a "trilogy" of five books that sold over 15 million copies in his lifetime, a television...
makes continuing sport of classic paradoxes. In the trilogy's fourth book So Long, and Thanks For All the Fish
So Long, and Thanks for All the Fish
So Long, and Thanks for All the Fish is the fourth book of the Hitchhiker's Guide to the Galaxy "trilogy" written by Douglas Adams. Its title is the message left by the dolphins when they departed Planet Earth just before it was demolished to make way for a hyperspace bypass, as described in The...
, Marvin the Paranoid Android
Marvin the Paranoid Android
Marvin, the Paranoid Android, is a fictional character in The Hitchhiker's Guide to the Galaxy series by Douglas Adams. Marvin is the ship's robot aboard the starship Heart of Gold...
says of himself: "Every part of me has been replaced at least fifty times...". In the sixth book of the series, character Trillian
Trillian (character)
Tricia McMillan, also known as Trillian Astra, is a fictional character from Douglas Adams' series The Hitchhiker's Guide to the Galaxy. She is most commonly referred to simply as "Trillian", a modification of her birth name, which she adopted because it sounded more "space-like". According to the...
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
Ghost in the Shell
is a Japanese multimedia franchise composed of manga, animated films, anime series, video games and novels. It focuses on the activities of the counter-terrorist organization Public Security Section 9 in a futuristic, cyberpunk Japan ....
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
Douglas Hofstadter
Douglas Richard Hofstadter is an American academic whose research focuses on consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics...
's and Daniel Dennett
Daniel Dennett
Daniel Clement Dennett is an American philosopher, writer and cognitive scientist whose research centers on the philosophy of mind, philosophy of science and philosophy of biology, particularly as those fields relate to evolutionary biology and cognitive science. He is currently the Co-director of...
's The Mind's I: Fantasies and reflections on self and soul
The Mind's I
The Mind's I: Fantasies and reflections on self and soul is a 1981 book composed and arranged by Douglas R. Hofstadter and Daniel C. Dennett...
(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
Teleportation
Teleportation is the fictional or imagined process by which matter is instantaneously transferred from one place to another.Teleportation may also refer to:*Quantum teleportation, a method of transmitting quantum data...
introduces similar paradoxes. The plot of the James Blish
James Blish
James Benjamin Blish was an American author of fantasy and science fiction. Blish also wrote literary criticism of science fiction using the pen-name William Atheling, Jr.-Biography:...
novel "Spock Must Die!
Spock Must Die!
Spock Must Die! is a Star Trek novel by James Blish released in 1970. It was published by Bantam Books. It is notable as the second of hundreds of original novels to be based upon the Star Trek franchise....
" hinges on this philosophical dilemma. The issue is addressed in the episode Life Support of Deep Space Nine
Deep Space Nine
Deep Space Nine may refer to:* Star Trek: Deep Space Nine, a 1993-1999 television series* Deep Space Nine , the television show's setting...
Star Trek
Star Trek
Star Trek is an American science fiction entertainment franchise created by Gene Roddenberry. The core of Star Trek is its six television series: The Original Series, The Animated Series, The Next Generation, Deep Space Nine, Voyager, and Enterprise...
series. In the episode, the complete replacement of the human brain is considered the destruction of the individual. Meanwhile in our world contemporary users of prosthesis have a tendency to suffer complications from phantom limb
Phantom limb
A phantom limb is the sensation that an amputated or missing limb is still attached to the body and is moving appropriately with other body parts. 2 out of 3 combat veterans report this feeling. Approximately 60 to 80% of individuals with an amputation experience phantom sensations in their...
syndrome.
Heraclitus
The Greek philosopher HeraclitusHeraclitus
Heraclitus of Ephesus was a pre-Socratic Greek philosopher, a native of the Greek city Ephesus, Ionia, on the coast of Asia Minor. He was of distinguished parentage. Little is known about his early life and education, but he regarded himself as self-taught and a pioneer of wisdom...
attempted to solve the paradox by introducing the idea of a river where water replenishes it. Arius Didymus
Arius Didymus
Arius Didymus of Alexandria, was a Stoic philosopher and teacher of Augustus. Fragments of his handbooks summarizing Stoic and Peripatetic doctrines are preserved by Stobaeus and Eusebius.-Life:...
quoted him as saying "upon those who step into the same rivers, different and again different waters flow." Plutarch
Plutarch
Plutarch then named, on his becoming a Roman citizen, Lucius Mestrius Plutarchus , c. 46 – 120 AD, was a Greek historian, biographer, essayist, and Middle Platonist known primarily for his Parallel Lives and Moralia...
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."
Aristotle's causes
According to the philosophicalPhilosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
system of Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
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.
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, "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.
Four-dimensionalism
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.
A seeming difficulty with this is that in special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
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.
Buddhism
For the relativist interpreter of Buddhism, 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.Alternatively, one can also say that the Ship of Theseus is not the Ship of Theseus, as ultimately nothing can be said to exist as "self" or "entity". Everything is anatta
Anatta
In Buddhism, anattā or anātman refers to the notion of "not-self." In the early texts, the Buddha commonly uses the word in the context of teaching that all things perceived by the senses are not really "I" or "mine," and for this reason one should not cling to them.In the same vein, the Pali...
.
Buddhism also explores the idea of khandha or compounds, in a way similar to this paradox.
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 SeeLast Chance to See
Last Chance to See is a 1989 BBC radio documentary series and its accompanying book, written and presented by Douglas Adams and Mark Carwardine. In the series, Adams and Carwardine travel to various locations in the hope of encountering species on the brink of extinction...
, Douglas Adams
Douglas Adams
Douglas Noel Adams was an English writer and dramatist. He is best known as the author of The Hitchhiker's Guide to the Galaxy, which started life in 1978 as a BBC radio comedy before developing into a "trilogy" of five books that sold over 15 million copies in his lifetime, a television...
observed:
Jewish law
In Halacha, a container that was tamei (impure) can lose this status if it develops a hole that would let a pomegranatePomegranate
The pomegranate , Punica granatum, is a fruit-bearing deciduous shrub or small tree growing between five and eight meters tall.Native to the area of modern day Iran, the pomegranate has been cultivated in the Caucasus since ancient times. From there it spread to Asian areas such as the Caucasus as...
through, even if it is later repaired. The Gemara
Gemara
The Gemara is the component of the Talmud comprising rabbinical analysis of and commentary on the Mishnah. After the Mishnah was published by Rabbi Judah the Prince The Gemara (also transliterated Gemora or, less commonly, Gemorra; from Aramaic גמרא gamar; literally, "[to] study" or "learning by...
(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.
See also
- HaecceityHaecceityHaecceity is a term from medieval philosophy first coined by Duns Scotus which denotes the discrete qualities, properties or characteristics of a thing which make it a particular thing...
- Identity and changeIdentity and changeThe relationship between identity and change in the philosophical field of metaphysics seems, at first glance, deceptively simple, and belies the complexity of the issues involved. This article explores "the problem of change and identity".- Change :...
- Mereological essentialismMereological essentialismMereological essentialism is a philosophical thesis about the relationship between wholes and its parts, and the conditions for their persistence...
- Sorites paradoxSorites paradoxThe sorites paradox is a paradox that arises from vague predicates. The paradox of the heap is an example of this paradox which arises when one considers a heap of sand, from which grains are individually removed...
- Śūnyatā
- Vehicle restorationVehicle restorationVehicle restoration is the process of restoring a vehicle that is either partially scrapped or otherwise life expired back to its original working condition. Automotive restoration can be applied to many different eras of automobile. Heritage railways and railway museums aim to restore and operate...
- USS Constellation (1854)USS Constellation (1854)USS Constellation constructed in 1854 is a sloop-of-war and the second United States Navy ship to carry this famous name. According to the US Naval Registry the original frigate was disassembled on 25 June 1853 in Gosport Navy Yard in Norfolk, Virginia, and the sloop-of-war was constructed in the...
- Neurath's boat