A thing's identity doesn't reside in the object itself, but rather the person or persons doing the identifying. Also, identity can be split into elements. The name, as in "Ship of Theseus," can be swapped out independently of the elements, though doing so tends to lead to confusion.<p>The example given of the sock with the hole in it: assume it's the only sock that the owner has with that hole. If the hole goes away, then it no longer has a unique identity, it's just another sock in his drawer. What gave it an identity in the first place was the fact that it was different.<p>With a ship, its identity appears to be tied to its designation. If you carried on replacing all the parts of the ship, it'd still be the Ship of Theseus, because that's what it's called. Back in the day when I owned a desktop computer, several times this would actually happen. Every component would got swapped out over a period of time. It carried on being my computer throughout all of it.<p>A computer's identity can be arguably split into two main elements, a computer and a system. If I replace the operating system and wipe all the data, using it feels completely different. Yet it's the same computer, just running different software. If you replaced the crew of a ship with a different crew, then the ship would operate differently, say, in battle, but it would still be the same ship.<p>You could restore the old system / crew and retrieve the original functionality, but if you replaced both the hardware and the 'software', yet kept the designation, you have two different things with the same name.<p>A person's body has all of its cells replaced after a period of years. But we don't go around emptying the prisons of long-serving inmates on the basis that the person that committed the crime isn't the same as the person currently in jail.<p>One can devise conceptions of identity with varying degrees of immutability. The conundrum makes the incorrect assumption that identity itself is an immutable concept. It's not.