Last winter, my partner and I renovated our kitchen, a narrow room in an old Utrecht house that had been altered by at least four previous owners. By the end, we had replaced the floor, the cupboards, the worktop, the sink and most of the wiring. Only the window frame and a crooked shelf remained. Friends who visited said it looked like a different room. I kept insisting it was the same kitchen, improved. Neither of us, I realised, could say exactly what we meant.

The puzzle is an old one. Plutarch records that the Athenians preserved the ship in which Theseus had returned from Crete, replacing its planks one by one as they decayed, so that it became a standing example for philosophers arguing about growth and change. Was it still the same ship? Centuries later, Thomas Hobbes sharpened the problem. Suppose someone gathered the discarded planks and reassembled them. Now there are two ships. Which one sailed with Theseus?

There is no clean answer, and that is the point. We seem to hold two intuitions at once. One says identity lies in material: the real ship is made of the real wood. The other says identity lies in continuity: the ship that was continuously maintained, used and recognised as the ship is the ship, whatever it happens to be made of. Most of the time, these intuitions agree. Renovation, restoration and repair are the moments when they come apart.

Which scars to keep

Odile Marchetti-Rowe, who has restored antique furniture in Bruges for three decades, faces this question every week. A cabinet arrives with a cracked panel, a replacement leg from the 1920s and a century of wax and grime. Should she remove the later leg because it is not original, or keep it because it is now part of the cabinet's story? Should the grime go, or is it the patina that makes the piece what it is? Every decision, she says, is a small philosophical position.

Every restoration is an argument about identity. You decide which scars are the object and which are just damage.

The same puzzle applies, more intimately, to ourselves. Much of the material in our bodies is replaced over the years, and our opinions, tastes and friendships change even more. John Locke proposed that personal identity rests not on the substance we are made of but on continuity of consciousness, on memory linking the person I am now to the person I was. Like the Athenians' ship, his view implies that we can survive almost total renewal, provided the thread is not broken.

What the ship and the kitchen suggest is that identity is partly a matter of care. The Athenians' ship stayed the ship because they kept tending it, recognising it and telling its story. My kitchen remains my kitchen because we kept cooking in it through the chaos, eating toast on the stairs while the floor was up. Things become themselves through the attention we give them over time. Replace the planks, by all means. Just do not stop sailing.

It is a consoling thought for anyone in the middle of changing their life. People worry, when they move cities, leave marriages or retrain in middle age, that they are becoming someone else. The ship of Theseus suggests a gentler reading. We are always being rebuilt, plank by plank. The question is not whether we are made of the same material, but whether we are still, recognisably, making the same voyage.