Plutarch reports that the Athenians preserved the ship Theseus sailed home from Crete, replacing each plank as it rotted. Philosophers of the time asked whether the ship in the harbor was still his.

Thomas Hobbes added the move that makes it genuinely hard. Suppose someone collected the discarded planks and rebuilt the original ship from them. Now there are two ships, and each has a serious claim.

Two claims, both good

The repaired ship. It never stopped existing. It sat in the harbor, it was continuously maintained, and it was called Theseus' ship on every single day of the process. There is no moment anyone could point to where it became a different ship, and a change that never happens at any moment did not happen.

The reassembled ship. It is made of the original planks, every one of them. Take the parts a thing is made of seriously and this is simply the ship taken apart and put back together, which is what a ship is.

They cannot both be it, since they are two. And nothing about the case makes one claim obviously stronger.

What each candidate criterion says

This is the useful part, because the puzzle sorts the available theories of identity and shows what each costs.

Matter. Same stuff, same thing. The reassembled ship wins. The cost is severe: on this criterion you are not the person you were seven years ago, and a river is a different river each second.

Form or structure. Same arrangement, same thing. The repaired ship wins, and so would a perfect copy built yesterday from new timber — which most people reject, so the criterion is too generous.

Spatiotemporal continuity. Same continuous path through space and time. The repaired ship wins again, and this is the criterion most people use without stating it. It handles ordinary cases well and says nothing useful when a thing is disassembled and reassembled, which is exactly the case at hand.

Origin and causal history. Descent from the original. Arguably both qualify, which is why the case is hard.

Function and use. Whichever the Athenians sailed and called theirs. This is the deflationary answer: identity over time for an artifact is a matter of practice, not of metaphysics.

The answer that is probably right

The strongest position is that the question has no determinate answer, and that this is a fact about ships rather than about our ignorance.

Ship is a concept we built for ordinary cases, where matter, structure, continuity and use all travel together. It was never given a rule for what to do when they come apart, because they do not come apart in ordinary life. Presented with a case that splits them, the concept does not have an answer to give.

That is not evasion. It is a specific claim: the usefulness of a concept does not require it to have a determinate extension in every possible case, and demanding one is what produces the appearance of a paradox.

Why it matters past the harbor

The same structure holds for you, and there it is not academic.

Your material is replaced continuously, your psychology changes, and your continuity is unbroken. Which of those is doing the work is exactly the question of personal identity, and Parfit's fission case is a ship of Theseus with a person in it — two equally good claimants, no fact to settle between them.

It is also the test case for substance. If there is an underlying bearer that persists through the replacement of every property, then one of the two ships has it and the question has an answer we cannot access. If there is no such bearer and a thing is its properties arranged as they are, then there is nothing for the answer to be about, and bundle theory predicts exactly the indeterminacy we find.

The puzzle is thus a good instrument. It does not tell you what identity is, and it tells you precisely what each theory of identity is committed to.