The Ship of Theseus

The positions people take divide on a prior question: does an object persist by being wholly present at each moment, or by having a different part at each moment?

Endurantism: the object is wholly there each time you look

This is the common-sense view. The ship in the harbour today is not a slice of a larger four-dimensional object; it is the whole ship, present now, and it was also wholly present in 300 BCE. Persistence is a matter of one and the same thing existing at two times.

Endurantists then have to say something about the two ships, and there are several things to say.

Matter wins. Roderick Chisholm defended a strict view on which an object cannot survive the loss of any part at all, so nothing survives the first plank. The Athenian ship of any later year is a different object, loosely and conveniently called by the same name. This is consistent but concedes that almost all our ordinary identity talk is loose.

Continuity wins. The dominant intuition: the harbour ship is Theseus's ship, and the reassembled ship is a very interesting replica made of authentic material. The awkwardness is explaining why the warehouse ship is not the original when it is made of every original piece, and why the answer would change if the planks had merely been stored rather than reassembled.

Constitution rather than identity. Lynne Rudder Baker and others distinguish the ship from the wood that constitutes it, as a statue is distinguished from the clay. Two objects can occupy the same place if they have different persistence conditions: the clay survives being squashed, the statue does not. Applied here, the harbour ship is the ship, and the warehouse assembly is the original wood doing a convincing impression. Critics object that this puts two objects in one place and asks us to believe the difference is not detectable.

Relative identity. Peter Geach argued that "same" is always implicitly "same F" — same ship, same collection of planks — and that the two can diverge without contradiction. This dissolves the puzzle at the cost of abandoning the standard logic of identity, and few have followed him.

Perdurantism: the object is a worm in spacetime

Theodore Sider (Four-Dimensionalism, 2001) and, earlier, David Lewis take the other route. Objects are extended in time as well as space, and have temporal parts — the ship-on-Tuesday, the ship-in-300-BCE — as they have spatial parts. An object persists by having a part at each time it exists, not by being wholly present at each.

This gives the puzzle a clean answer, and the answer is that the question was badly posed.

There are two ships in the story, and there always were. One four-dimensional object runs from Theseus's launch to the harbour ship of today. Another runs from Theseus's launch to the warehouse ship. The two share their early temporal parts completely — before the first repair, they overlap exactly, the way two roads can share a stretch of tarmac before diverging. Asking "which one is the ship of Theseus?" is asking which of two overlapping objects a name picks out, and the honest answer is that ordinary usage never had to decide.

Sider adds an argument that pushes hard in this direction: identity cannot be vague, but composition and persistence plainly are, and the only way to have determinate identity with indeterminate boundaries is to let objects be four-dimensional and admit far more of them than common sense does.

The cost is a headcount problem. If two ships were in the harbour in 300 BCE, why did nobody see two? Perdurantists reply that we count by temporal parts, not by worms — at that moment there was one ship-stage, and one is the number you would report.

Persons: where the puzzle stops being academic

Psychological continuity. John Locke, in the chapter on identity added to the Essay in 1694, separated the person from the man and from the substance. A person is constituted by continuity of consciousness — memory, in his formulation. If you can remember doing it, you are the one who did it. His prince-and-cobbler case, in which a prince's consciousness moves into a cobbler's body, makes the point that we follow the mind.

Thomas Reid's brave officer objection (1785) is the standard reply: an old general remembers being a young officer, and the young officer remembered being a flogged schoolboy, but the general remembers nothing of the boy. Direct memory is not transitive, so it cannot ground identity. Modern versions patch this with overlapping chains of psychological connection.

Biological continuity. Eric Olson and other animalists reverse the priority: you are a human organism, you began before you had any psychology and may continue after it goes, and identity tracks the life of the animal. A brain transplant, on this view, does not move you — it moves an organ, and you stay with the body. Animalism handles the persistent vegetative state and the foetus cleanly, and handles the prince and the cobbler badly.

Neither. Derek Parfit (Reasons and Persons, 1984) argues that the whole dispute is a mistake. Consider fission: the two hemispheres of your brain are separated and transplanted into two bodies, each with your memories and character. You cannot be identical to both, since they are not identical to each other. You cannot be identical to just one, since there is nothing to choose between them. And it is hard to say you died, since you would have survived if only one hemisphere had been transplanted.

Parfit's conclusion is that identity is not what matters. What matters is psychological continuity and connectedness, which can hold one-to-many, and which comes in degrees. Once you know all the physical and psychological facts about the two ships, or the two people, there is no further fact you are missing. The question "but which one is really me?" is empty.

Whether that is liberating or evasive is exactly where the debate stands. It is also, straightforwardly, Hobbes's two-ships problem transplanted into a skull.

c. 500 BCE. Heraclitus is reported as saying that different waters flow upon those who step into the same rivers. The fragments (DK B12, B49a) are terse and their interpretation is disputed — the "you cannot step into the same river twice" form is Plato's paraphrase in the Cratylus, not Heraclitus's words — but the question of how something persists while its matter flows through it is recognisably the same.

c. 380 BCE. Plato's Symposium (207d–208b) has Diotima observe that a person is called the same from childhood to old age although hair, flesh, bones and even memories are constantly departing and being replaced. The observation is offered as a fact about mortal nature rather than as a puzzle.

c. 100 CE. Plutarch, in chapter 23 of the Life of Theseus, records that the Athenians preserved the thirty-oared ship down to the time of Demetrius of Phalerum — which dates the practice to at least the late fourth century BCE — and that as timbers decayed they were replaced with new ones. He adds the crucial line: the ship had become a standing example among philosophers for the disputed question of things that grow, one party holding it remained the same, the other that it did not. Plutarch reports the dispute; he did not invent it, does not name the parties, and does not take a side.

1655. Thomas Hobbes, in De Corpore Part II chapter 11, adds the move that turns a disagreement into a paradox: keep the old planks, and build a second ship from them. He observes that on one criterion the repaired ship is the original and on the other the reassembled one is, so that there would be two bodies numerically the same — which he rejects as absurd. Hobbes's own resolution is deflationary: identity claims are relative to the name under which a thing is considered, so the same matter can be one body and a different ship.

1694. John Locke adds "Of Identity and Diversity" to the second edition of the Essay Concerning Human Understanding. His key move is that identity conditions depend on the kind of thing in question, and that persons — unlike masses of matter and unlike living organisms — persist by continuity of consciousness.

1785. Thomas Reid publishes the brave officer objection, showing that memory is not transitive and so cannot by itself constitute identity.

1971–1984. Derek Parfit's paper "Personal Identity" and then Reasons and Persons introduce fission cases and the thesis that identity is not what matters in survival.

1976. David Lewis's "Survival and Identity" gives the perdurantist treatment of fission: two persons sharing earlier stages, counted as one by the practice of counting stages.

2001. Theodore Sider's Four-Dimensionalism assembles the case for temporal parts, including the argument from vagueness, and makes the two-overlapping-worms answer the standard alternative to the endurantist picture.

The name "the Ship of Theseus" for the whole family of problems is modern. Plutarch has the ship; Hobbes has the paradox; the label came later.

It shows that "the same thing" was never one question. Matter, form, function, continuous path and name are five different criteria that coincide in almost every real case. Discovering that they can be pulled apart is the beginning of serious metaphysics, and every subsequent theory of persistence is an attempt to say which criterion is doing the real work.

Law has to answer it, and does, arbitrarily. Vehicle identity is settled by statute and registration rather than by parts: jurisdictions specify how much of a car can be replaced before the rebuilt vehicle needs a new identity, and kit-car and salvage-title rules exist precisely because the metaphysics does not determine the answer. Corporate law does the same for companies — a firm that has changed every employee, every product, its name and its headquarters is still the same legal person, liable for what it did decades ago, because continuity of the charter is stipulated to be what counts.

Heritage conservation is a live argument about it. After the 2019 fire, the rebuilding of Notre-Dame de Paris turned on whether authenticity lives in the original material or in the form and the craft. The Nara Document on Authenticity (1994) was written to accommodate traditions like Ise, where periodic rebuilding is the preservation, against a European convention that had treated original fabric as the thing to save. Two continents took opposite sides of Plutarch's dispute and had to write a treaty about it.

It sets the terms for questions about people that are becoming practical. Advance directives ask whether a person with advanced dementia is bound by the wishes of the person who wrote the document. Criminal justice asks whether it is just to punish someone for what they did at nineteen. Both are the Ship of Theseus with consequences, and both are usually settled by legal continuity of the body — which is to say, by animalism, adopted without argument.

Teleportation and uploading. A device that scans you, destroys the original and reassembles an identical body elsewhere is Hobbes's second ship, built at speed. Whether you should step into it is the Ship of Theseus with your life attached, and the split in public intuition matches the split in the literature almost exactly.

Software migration. The strangler-fig pattern replaces a live system one component at a time. Teams routinely find that the interesting question is not technical but nominal — whether the result is version 4 of the old system or a new system that inherited a name — and the answer determines budgets, ownership and on-call rotas.

Digital preservation. An emulated program running on hardware that did not exist when it was written, from a file that has been migrated across a dozen storage formats, raises the question in an unusually crisp form: nothing physical persists, only the pattern. Archivists have largely settled on the harbour ship, and preserve behaviour rather than bits.

Machine learning models. A model that has been fine-tuned, quantised, pruned and distilled until none of the original weights survive is still shipped under the original name and the original licence. Model provenance and licensing law are currently working out what makes two sets of weights the same model, without much awareness that Hobbes got there first.

Bands, teams and institutions. A touring group with no original members, a football club that has changed ground, colours and ownership, a university that shares only a name with its medieval founder: the disputes are fierce, they are conducted entirely in terms of continuity of matter versus continuity of form, and they are never settled.

Write $A$ for the ship at launch, $B$ for the fully repaired ship in the harbour at $t_1$, and $C$ for the ship reassembled from the original planks at $t_1$.

The two intuitions are identity claims:

$$A = B \quad \text{(continuity of form and function)} \qquad A = C \quad \text{(continuity of matter)}$$

Identity is an equivalence relation, so symmetry and transitivity give $B = C$. But Leibniz's Law — if $x = y$ then $x$ and $y$ share every property — refutes that immediately, because $B$ is in the harbour and $C$ is in the warehouse:

$$\exists P ,\big( P(B) \wedge \neg P(C) \big) ;\Rightarrow; B \neq C$$

So ${A = B,; A = C}$ is inconsistent. At most one intuition survives, and the puzzle is the absence of any principle that selects between them.

The perdurantist reconstruction. Let an object be a maximal aggregate of temporal parts. Define two worms:

$$W_1 = {, s_t : t \in [t_0, t_1] ,}\ \text{ending in the harbour ship}, \qquad W_2 = {, s'_t : t \in [t_0, t_1] ,}\ \text{ending in the warehouse ship}$$

with $s_t = s'_t$ for all $t$ before the first plank is replaced. $W_1$ and $W_2$ are distinct objects that share an initial segment. There is no contradiction: "$A$" was never a name for a worm, only for a stage in the shared segment, and a stage belongs to both worms. Leibniz's Law is satisfied throughout, since $W_1$ and $W_2$ differ in their later parts and were therefore never identical.

The residual question is semantic, not metaphysical: which worm does the Athenian name track? Nothing in Athenian practice settled it, so nothing settles it now.

Stage theory (Katherine Hawley, and Sider's own preferred variant) goes further. Ordinary singular terms denote instantaneous stages, and "the ship existed yesterday" is analysed as: the present stage bears a temporal counterpart relation $R$ to a stage located yesterday. Because $R$ is a similarity-and-causation relation rather than identity, it need not be transitive, and it may be one-to-many. Fission is then unproblematic — a stage can have two future counterparts — and this is the formal version of Parfit's claim that what matters can branch while identity cannot.

Sider's argument from vagueness, compressed:

1. If composition is restricted, there are borderline cases of composition.
2. A borderline case of composition would be a case in which it is indeterminate how many objects exist.
3. Numerical sentences contain no vague expressions, so their truth value cannot be indeterminate.
4. Therefore composition is unrestricted — any plurality composes something.

Unrestricted composition plus temporal parts yields an ontology containing $W_1$, $W_2$, and every other aggregate of stages, which is why the four-dimensionalist can afford to say "both, and there were always two". The argument's second premise is where most of the resistance lands, and it is worth noticing that this is the sorites argument doing the work.

Persons. Let $R$ be the ancestral of direct psychological connectedness — overlapping chains of memory, intention and character. Locke's account effectively proposes $x = y \iff xRy$, which fails Reid's objection unless the ancestral is taken. Even taken, $R$ can hold one-to-many, so the biconditional cannot be right, since identity cannot. Standard repairs add a non-branching clause:

$$x = y \iff xRy \ \wedge\ \neg\exists z,(z \ne y \wedge xRz)$$

This restores a genuine equivalence relation but makes your survival depend on whether an unconnected duplicate exists somewhere else — the only x and y problem. Parfit's response is to deny that identity is the thing worth caring about and to let $R$ carry the practical weight on its own.