Ship of Theseus

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In the metaphysics of Identity, the ship of Theseus (or Theseus's paradox) is a thought experiment that raises the question of whether a ship—standing for an object in general—that has had all of its components replaced remains fundamentally the same object.

The thought experiment

First, suppose that the famous ship sailed by the hero Theseus in a great battle has been kept in a harbour as a museum piece. As the years go by some of the wooden parts begin to rot and are replaced by new ones. After a century or so, all of the parts have been replaced. Is the "restored" ship still the same object as the original?

Second, suppose that each of the removed pieces were stored in a warehouse, and after the century, technology develops to cure their rotting and enable them to be put back together to make a ship. Is this "reconstructed" ship the original ship? And if so, is the restored ship in the harbour still the original ship too?

Proposed resolutions

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 "ShipOfTheseusness" 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".[1] 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".[2]

Continual identity over time via final cause

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[clarification needed] 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."[citation needed]

One ship in two locations

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.

Two ships with non-transitive identity

In this theory, the reconstructed and restored ships are considered to be separate objects, both are identical to the original, but they are not identical to each other. This requires us to drop the transitivity of identity, ie. deny that "A=B" and "A=C" entails "B=C".

Non-atomic logic

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 vagueness 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.[citation needed] A marble can be numerically identical only to itself.


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.[3]

Empirical study

A 2010 psychology study reported that 20 members of the public considered the restored ship to be the original while 24 considered the reconstructed to be the original.[4]


The paradox had been discussed by other ancient philosophers such as Heraclitus and Plato prior to Plutarch's writings,[5] 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.

This particular version of the paradox was first introduced in Greek legend as reported by the historian, biographer, and essayist 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 places, 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[6]

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.[7] Hobbes asked which ship, if either, would be the original Ship of Theseus.


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. Daniel Dennett asked: should one step into a teleporter which destroys one's original body and reconstructs it elsewhere? Or one which does not destroy the original but creates a second copy which is then destroyed some time later? The Russian nobleman problem asks whether a young socialist with an inheritance should kill himself in order to kill his enemy: the bourgeois elderly male whom he expects to become later in life.

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 reform into rivals, leading to legal actions between the old and new entities. (A particularly perfect and notorious example was the band Sugababes whose original members all left and later reformed as a different band, while the old band continued to replace members and exist under the original name.) 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? The USS Constellation (1854) is the only actual ship whose identity has been legally debated precisely as in the thought experiment.

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

There are many more examples of the paradox found in real-life and in fiction.

See also


  1. ^ Didymus, Fr 39.2, Dox. gr. 471.4
  2. ^ Plutarch. "On the 'E' at Delphi". Retrieved 2008-07-15. 
  3. ^ David Lewis, "Survival and Identity" in Amelie O. Rorty [ed.] The Identities of Persons (1976; U. of California P.) Reprinted in his Philosophical Papers I.
  4. ^ "The Ship of Theseus: Using Mathematical and Computational Models for Predicting Identity Judgments" (PDF). 2010. 
  5. ^ Plato (1925). Parmenides. 9. Translated by N. Fowler, Harold. London: Harvard University Press. p. 139. 
  6. ^ Plutarch. "Theseus (23.1)". The Internet Classics Archive. Retrieved 2008-07-15. 
  7. ^ De Corpore, ch 11.7

External links

  • Quotations related to Ship of Theseus at Wikiquote
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