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=                          Ship of Theseus                           =
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                             Introduction
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In the metaphysics of identity, the ship of Theseus is a thought
experiment that raises the question of whether an object that has had
all of its components replaced remains fundamentally the same object.
The concept is one of the oldest in Western philosophy, having been
discussed by the likes of Heraclitus and Plato by ca. 500-400 BC.


                          Thought experiment
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If it is supposed that the famous ship sailed by the hero Theseus in a
great battle has been kept in a harbour as a museum piece, and as the
years went by some of the wooden parts began to rot and were replaced
by new ones then, after a century or so, all of the parts had been
replaced.  The question then is if the "restored" ship is still the
same object as the original.

If it is then supposed that each of the removed pieces were stored in
a warehouse, and after the century, technology developed to cure their
rotting and enabled them to be put back together to make a ship, then
the question is if this "reconstructed" ship is still the original
ship. And if so, then the question also regards the restored ship in
the harbour still being the original ship as well.


 No identity over time
=======================
This theory states that two ships, while identical in all other ways,
are not identical if they exist at two different times. Each
ship-at-time is a unique "event".  So even without replacement of
parts, the ships in the harbour are different at each time.  This
theory is extreme in its denial of the everyday concept of identity,
which is relied on by most people in everyday use.

The concept of identity might then be replaced with some other
metaphysical device to fill its role. For example, we might consider
"Ship Of Theseusness" to be a property or class which is applied to
all the events in the harbour as well as to the reconstructed
ship-events.

This solution was first introduced by the Greek philosopher Heraclitus
who 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".


 Continual identity over time via final cause
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According to the philosophical system of Aristotle and his followers,
four causes or reasons describe a thing; these causes can be analyzed
to get to a solution to the paradox. The formal cause or 'form'
(perhaps best parsed as the cause of an object's form or of its having
that form) is the design of a thing, while the material cause is the
matter of which the thing is made.  Another of Aristotle's causes is
the 'end' or final cause, which is the intended purpose of a thing.
The ship of Theseus would have the same ends, those being, mythically,
transporting Theseus, and politically, convincing the Athenians that
Theseus was once a living person, though its material cause would
change with time. The efficient cause is how and by whom a thing is
made, for example, how artisans fabricate and assemble something; in
the case of the ship of Theseus, the workers who built the ship in the
first place could have used the same tools and techniques to replace
the planks in the ship.

According to Aristotle, the "what-it-is" of a thing is its formal
cause, so the ship of Theseus is the 'same' ship, because the formal
cause, or design, does not change, even though the matter used to
construct it may vary with time. In the same manner, for Heraclitus's
paradox, a river has the same formal cause, although the material
cause (the particular water in it) changes with time, and likewise for
the person who steps in the river.

This argument's validity and soundness as applied to the paradox
depend on the accuracy not only of Aristotle's expressed premise that
an object's formal cause is not only the primary or even sole
determiner of its defining characteristic(s) or essence ("what-it-is")
but also of the unstated, stronger premise that an object's formal
cause is the sole determiner of its 'identity' or "'which'-it-is"
('i.e.', whether the previous and the later ships or rivers are the
"same" ship or river).  This latter premise is subject to attack by
indirect proof using arguments such as "Suppose two ships are built
using the same design and exist at the same time until one sinks the
other in battle.  Clearly the two ships are not the same ship even
before, let alone after, one sinks the other, and yet the two have the
same formal cause; therefore, formal cause cannot by itself suffice to
determine an object's identity" or " [...] therefore, two objects' or
object-instances' having the same formal cause does not by itself
suffice to make them the same object or prove that they are the same
object."


 One ship in two locations
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In this theory, both the reconstructed and restored ships claim
identity with the original, as they can both trace their histories
back to it.   As such they are both identical with the original. As
identity is a transitive relation, the two ships are therefore also
identical with each other, and are a single ship existing in two
locations at the same time.


 Non-atomic logic
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A basic principle of logical atomism is that facts in the world exist
independently of one another.  Only if we deny this principle then we
can claim the following:   the restored ship claims continuity of
parts with the original over time and so, in the absence of other
arguments, claims identity with the original. However when the
reconstructed ship is completed and announced to the world, it
presents a better claim on continuity, which changes the status of the
restored ship making it lose its identity with the original.  As a
theory of observer-independent reality, this is hard to conceive; it
involves both action at a distance and a violation of logical atomism.
However it is more acceptable to Kantian style metaphysicists who
view their subject as a theory of psychology rather than reality, as
it described what biological humans are likely to believe in practice.
(For example, if these were real ships on display to the public for a
fee, it seems likely that the public would pay to see the
reconstructed rather than restored 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 other words the ambiguity of the term.
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.


 Gradual loss of identity
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As the parts of the ship are replaced, the identity of the ship
gradually changes, as the name "Theseus' Ship" is a truthful
description only when the historical memory of Theseus' use of the
ship - his physical contact with, and control of, its matter - is
accurate. For example, the museum curator, prior to any restoration,
may say with perfect truthfulness that the bed in the captain's cabin
is the same bed in which Theseus himself once slept; but once the bed
has been replaced, this is no longer true, and the claim would then be
an imposture, because a different description would be more accurate,
i.e.; "a replica of Theseus' bed." The new bed would be as foreign to
Theseus as a completely new ship. This is true of every other piece of
the original boat. As the parts are replaced, the new boat becomes
exactly that: a new boat. Hobbes' proposed restored boat built from
the original parts will be the original ship, as its parts are the
actual pieces of matter that participated in Theseus' journeys.


 Four-dimensionalism
=====================
Ted Sider and others have proposed that considering objects to extend
across time as four-dimensional causal series of three-dimensional
"time-slices" could solve the ship of Theseus problem because, in
taking such an approach, all four-dimensional objects remain
numerically identical to themselves while allowing individual
time-slices to differ from each other.  The aforementioned river,
therefore, comprises different three-dimensional time-slices of itself
while remaining numerically identical to itself across time; one can
never step into the same river-time-slice twice, but one can step into
the same (four-dimensional) river twice.


 There is no ship
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Ships do not exist.  A "ship" is a label for a particular organization
of matter and energy in space and time. The old "ship" is just a
concept in the human mind.  Similarly, the new "ship" (that has had
all its parts replaced) is another concept in the human mind.  If the
two concepts were exactly the same, the human mind would not be
capable of comparing them - there would be nothing to compare.
Therefore, the old ship and the new ship 'must not be the same' for
the simple reason that humans are able to compare these two concepts
against each other.


 Cognitive science
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According to Noam Chomsky, as described in 'Of Minds and Language
(2009)', the paradox arises because of extreme externalism: the
assumption that what is true in our minds is true in the world. This
is not an unassailable assumption, from the perspective of the natural
sciences, because human intuition is often mistaken. Cognitive science
would treat this paradox as the subject of a biological investigation,
as a mental phenomenon internal to the human brain. Studying this
human confusion can reveal much about the brain's operation, but
little about the nature of the human-independent external world.


                               History
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The paradox had been discussed by other ancient philosophers such as
Heraclitus and Plato prior to Plutarch's writings, and more recently
by Thomas Hobbes and John Locke. Several variants are known, including
the grandfather's axe, which has had both head and handle replaced,
and the similar idea "Trigger's Broom".

This particular version of the paradox was first introduced in Greek
legend as reported by the historian, biographer, and essayist
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. Hobbes asked which ship, if
either, would be the original Ship of Theseus.


                             Applications
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The paradox appears in several more applied fields of philosophy.

In philosophy of mind, the ship is replaced by a person whose identity
over time is called into question.

In both philosophy of law and practical law, the paradox appears when
the ownership of an object or of the rights to its name are disagreed
in court. For example, groups of people such as companies, sports
teams, and musical bands may all change their parts and see their old
members re-form into rivals, leading to legal actions between the old
and new entities. Also, texts and computer programs may be edited
gradually but so heavily that none of the original remains, posing the
legal question of whether the owners of the original have any claim on
the result.

In ontological engineering such as the design of practical databases
and AI systems, the paradox appears regularly when data objects change
over time.

A literal example of a Ship of Theseus is DSV Alvin, a submarine that
has retained its identity despite all of its components being replaced
at least once.


                                Media
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* In 'The Wonderful Wizard of Oz,' the Tin Woodsman's origin story was
that he was an ordinary flesh-and-blood man named Nick Chopper who
gradually lost all his limbs, his torso, and finally his head, having
each replaced by tin. The question of whether or not he remains the
same person is brought up in a humorous fashion through the rest of
the 'Oz' series, culminating in the Tin Woodsman meeting a version of
himself created from his flesh parts, with the two debating which of
them is the "real" Nick Chopper.
* The name of the paradox, "the ship of Theseus" is alluded to in the
name of the 2013 Indian drama film 'Ship of Theseus'.
* The ship of Theseus is referenced to as the name of the fictional
novel in Doug Dorst's novel, 'S.'
* In the 'Warhammer 40,000' franchise, it is mentioned many human war
machines such as tanks have had all their parts replaced due to
constant battle damage over thousands of years of war. Nonetheless,
the generations of pilots and crews all consider the vehicle to be the
same object, even after every original part has been replaced.
*In the video game 'Nier: Automata' androids 2B and 9S help an android
shopkeeper with a damaged leg to find parts. When asked why the