Identity over change

If every part of a thing is replaced one by one, is it still the same thing?

Plutarch reports that the Athenians kept the ship Theseus sailed home in, replacing each plank as it rotted, until the philosophers could not agree whether it was still his ship. Hobbes sharpened it centuries later: suppose someone had collected every discarded plank and rebuilt the original arrangement. Now there are two ships. Which one is Theseus's?

The instinct is to feel that one answer must be correct and we have simply not been clever enough to find it. I want to press on that instinct rather than satisfy it — because the puzzle is not hiding an answer. It is showing us that the word "same" has been doing several different jobs while wearing one uniform.

Begin by asking what could make two things the same thing at different times. Not similar — philosophers separate qualitative identity, being alike, from numerical identity, being one and the same. Two new coins off the press are qualitatively identical and numerically two. The ship question is about the second. So what candidates are there for the relation that carries an object across time?

One is material continuity: same thing, same stuff. Clean, and immediately in trouble. On that rule you are not the person born under your name, since almost none of that matter remains; nor is any river the same river. A rule that condemns almost every ordinary persistence claim we make is not capturing what we meant.

A second is continuity of form: same arrangement, however the matter turns over. This handles you and the river well, and it is what makes the repaired ship feel like the ship. But it licenses the second ship too, since the reassembled planks have the original arrangement as well. Form alone cannot break the tie.

A third is continuity of function and use: the thing that keeps sailing, that the Athenians keep sending to Delos, that is crewed and moored in the same berth. This decides most real cases, and notice that it is not a fact about planks at all.

A fourth is spatiotemporal continuity: an unbroken path through space and time. This favours the repaired ship strongly — there is a continuous ship-shaped trail from the harbour to today, whereas the rebuilt one has a gap of years spent as a woodpile.

Now look at what has happened. Each criterion is coherent, and they agree on almost every ordinary case, which is exactly why we never noticed they were four things. Theseus's ship is an engineered scenario in which they come apart — so of course they give different verdicts. Asking which verdict is the right one is asking which of four questions your one word was secretly asking.

Two further moves are worth naming, as the serious attempts to say more than "it depends".

The four-dimensionalist move says objects are extended in time as well as space, made of temporal parts — so what exists is not a ship wholly present at each moment but a long spacetime worm. Then there is no contradiction: the repaired ship and the rebuilt ship are two worms sharing their early stages, the way two roads can share a stretch. "Which is the original?" becomes a question about how we chose to trace the worm, not about a hidden fact.

The psychological-continuity move addresses the case we actually care about, ourselves. Locke argued that a person is the same person as an earlier one in virtue of continuity of consciousness, not sameness of body or soul — which is why the body criterion feels wrong for people even when it feels natural for ships. Parfit pushed further, arguing that in the hard cases identity is not what we should care about anyway: what matters is the continuity, and identity is a coarse label laid over it. That is contested, and I flag it as a live position rather than a settled result.

The tempting misreading is that this makes identity arbitrary, a matter of taste. It does not. Each criterion is perfectly determinate; what is unfixed is which one a given question is asking about, and usually the context fixes that without our noticing. A shipwright asking whether it is the same ship means the timber. A registrar means the continuous legal object, and will tell you plainly that the vessel with the unbroken registration is the ship, whatever happened to the planks. A historian may mean the one Theseus stood on. Three correct answers to three different questions.

Hence the discipline sometimes put as: identity claims need a sortal — same what? Same matter, same vessel, same legal entity. Answer that first and much of the vertigo goes.

Which leaves the honest residue. In the cases we care about most, especially personal identity, we want the criteria to agree and are distressed when they cannot, because our practices — responsibility, promise-keeping, grief, self-concern — were built on the assumption that there is one fact there. That distress is not confusion to be dissolved. It is the real finding.

• Parfit's teletransportation and fission cases, where psychological continuity itself splits in two.
• The constitution view: that a statue is made of its clay without being identical to it, and what that buys.

Every term the collection defines is gathered in the glossary.