[zookeeper]

WiPhi addresses the question and its significance for Khan Academy: https://www.youtube.com/watch?v=dYAoiLhOuao

I watched the first 4 minutes or so, and then stepped through the rest in a minute or two, and I didn't see any mention of significance.

On a more general note, questions like that can be useful in getting people interested in philosophy (because someone might very well have never thought about it before), but it can also be a big turn-off for those same people if they happen to realize how the question is actually nonsensical. For some mysterious reason, it seems that everyone who ever presents that kind of question pretends that it's something else than a linguistic or semantic dilemma: that it actually asks something about the world and not merely about how we talk about the world, whereas that's... obviously not true.

[Dragon]

There's also the proprietorial factor to consider, rather than a soul as such. Maybe as you replace memory, hard drives etc, it remains your computer because it is your computer, there are many computers in the world, there are many boats, but what makes them distinct in many ways is who owns them. It is mostly that, not wood and cloth, not hard-drives or memory that makes an item distinct.

Note, this is about who owned the item, not who currently owns it. The latter is easily resolved, because in most cases ownership can be easily determined (and we've got ways to figure it out when it isn't, though it comes with more lawyers than I'd like to involve in a philosophical discussion ). "There are many like this, but this one is mine" kind of distinction is very common. But we're talking about something else. If the Ship of Theseus isn't yours, what makes it different from any other trireme next to it? We're talking about things made special by something more than the current ownership.

[castor]

Is it still the same ship Theseus used? If not, when did it stop being Theseus's ship?

Since Theseus died, it's not been Theseus's ship. It's been the ship that used to be Theseus's ship.

[Flipside]

The problem with that is that artistic ownership is a weird thing, if Theseus designed the vessel then the 'ownership' is in the same format as, for example, a painting by a famous artist, it doesn't matter who is the warden of the item, even if they have paid for it and it is their property, the painting will always be Picasso's or Van Goch's, but not in the 'walk in and pick it up' sort of way (and it should be noted that even these paintings are, through restorations, going through a similar process).