The Ship of Theseus
Replace every plank and the puzzle dissolves — once you notice "same" is doing two different jobs.
Plutarch reports that the Athenians kept the ship Theseus sailed home from Crete as a memorial, and that as its timbers decayed they took out the old planks and put in new ones. The ship stayed in the harbour, seaworthy, visited. And it became, he says, a standing example for philosophers arguing about growth and change: one side saying the ship remained the same, the other saying it did not.
Two thousand years later the puzzle is still in circulation, usually presented as a charming unanswerable. It is not unanswerable. It is a question that contains an ambiguity, and the interesting work is locating it.
Hobbes makes it worse
Hobbes added the move that turns a puzzle into a genuine problem. Suppose someone collected every discarded plank as it came out, kept them in a warehouse, and at the end assembled them in the original arrangement. Now there are two ships.
One has sailed continuously in the harbour, repaired plank by plank, with an unbroken history and the same crew and the same name painted on it. The other is made of precisely the original matter, in precisely the original configuration, and has never been anything else.
Ask which is the ship of Theseus and you will find you have strong intuitions on both sides, which is the signature of a question that has more than one thing in it.
Two jobs for one word
The first thing to separate is a distinction later philosophers made explicit. Qualitative identity is exact similarity: two coins off the same press are "the same" in this sense. Numerical identity is being one and the same thing: this coin now and this coin tomorrow. Nobody is confused about the coins. The ship puzzle is entirely about the numerical sense, and it is hard because numerical identity over time has to survive change, and there is no obvious rule for how much change it survives.
The second thing to separate is what the criterion of continuity is tracking. Two candidates are in play, and both are respectable:
Continuity of matter says a thing is the same thing when it is made of the same stuff. This is the criterion the warehouse ship satisfies. Continuity of form and function says a thing is the same thing when its organisation and role persist through gradual replacement of parts. This is what the harbour ship satisfies, and it is the criterion we apply, without hesitation, to ourselves — the atoms in a human body turn over steadily, and nobody concludes they are a different person than they were a decade ago.
Once the two criteria are on the table, the puzzle stops being about the ship. It is about which criterion the word "same" was invoking, and the honest answer is that ordinary usage never settled it, because ordinary usage never had to deal with a warehouse.
"Is it the same ship?" is an incomplete question, like asking whether a file is large. Same for what purpose — ownership, sentiment, seaworthiness, insurance? Each practice has a criterion, each criterion gives a determinate answer, and the puzzle survives only where no practice has had to choose.
Where the choice has been forced
Law, unlike metaphysics, cannot leave it open, and what it does is instructive: it picks a criterion per domain and does not pretend the choice was discovered. A company that replaces every employee, its premises, its product and its name is still the same legal person, because the criterion is an unbroken chain of registration. A restored vintage car has criteria specified by the certifying body, usually a percentage of original components, chosen because a line had to be somewhere.
The same forcing happens with software. Rewrite a service module by module until no original line remains and you have the harbour ship: same name, same interface, same responsibilities, continuous history in the repository. Fork the original at its last commit and revive it and you have the warehouse ship. Which one is "the" service is not a question the code answers — it is answered by what you are tracking, and teams argue about it precisely because they are using different criteria without saying so.
The version that matters
Run the puzzle on a person and the stakes change. Locke proposed that personal identity follows psychological continuity rather than matter — you are the same person as the one who has your memories, whatever your body is made of. It is a criterion with famous consequences: it implies that a perfect copy of your psychology would be you, and that severe amnesia is a kind of ending.
Nobody has produced a criterion here that survives all the cases. The teleporter that disassembles you and rebuilds you atom-for-atom elsewhere is Hobbes' warehouse with a person in it, and the fact that intelligent people divide sharply on whether stepping into it is travel or death shows the ambiguity is not academic.
Derek Parfit's response was to accept the whole result: identity is not what matters. What matters, he argued, is psychological continuity and connectedness, and these come in degrees, so the question "will it still be me?" can lack a determinate answer without anything being left unknown. That is a genuinely unsettling position, and it is the most honest one on offer — it does not solve the puzzle, it denies that a solution was ever required.
The ship has no single answer because "the same" is two criteria wearing one word: continuity of matter and continuity of form. Every practice that has needed an answer has picked one and written it down. The puzzle persists only where nothing has forced the choice — which is why it feels deepest when applied to ourselves.